Applied Metallurgy

Fabrizio D’Errico _______________________________

Lecture Notes in Applied Metallurgy for the course held at Politecnico di Milano for the Master

of Science (MS) Degree in Mechanical Engineering This booklet is based on bibliography of the course. Several parts of this booklet, as well as pic-tures and tables, have been freely taken from the original text books in the selected bibliography of the course. This booklet is provided by the teacher for internal use only to the students at-tending the course of “Applied Metallurgy”, course of the M.Sc. in Mech. Eng. at Politecnico di Milano. No other external uses and/or scopes that are out of preparation to final exam are therefore al-lowed. Any other different uses by the students shall be under their own responsibility.

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Table of Content Chapter 1 - Resuming basic principles of metallurgy ........................................ 8

Introduction ........................................................................................................... 8

Atomic Structure and Interatomic Bonding ....................................................... 8 Atomic arrangements of metals ....................................................................... 12

Vacancies, interstitial spaces and grain boundaries as drive-force for diffusion in metals ............................................................................................... 20

Elastic and plastic deformation in metal by micromechanical models ........... 31 Slip in polycrystalline crystal........................................................................... 41

Mechanisms of Strengthening in Metals ........................................................... 45 Strengthening by grain size reduction ............................................................. 45 Strain hardening .............................................................................................. 50 Phase boundaries as strengthening sources .................................................... 53

Grain Growth, Recovery and Recrystallization................................................ 57 Recovery .......................................................................................................... 58 Grain growth ................................................................................................... 59 Recrystallization .............................................................................................. 60

Mechanical behavior of metals by macroscopic approach .............................. 64 Tensile test ....................................................................................................... 64 Ductility ........................................................................................................... 67 Resilience ......................................................................................................... 67 Toughness ........................................................................................................ 68 Hardness .......................................................................................................... 70

Resuming the main contents, defining the main paradigm for mechanical response of metals ................................................................................................ 72

Microstructural features of fracture in metallic materials .............................. 77 Ductile Fracture .............................................................................................. 78 Brittle Fracture ................................................................................................ 81

Chapter 2 - Damage mechanisms and root cause failure analysis basics ....... 85 The contributing factor: the stress concentration ........................................... 92 The energy criterion for fast fracture .............................................................. 94

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Micromechanisms of fast fracture ................................................................... 97 Mechanisms of crack propagation by ductile tearing ...................................... 97 Mechanisms of crack propagation, 2: cleavage ............................................ 100 The three stages of fatigue failure ................................................................. 111 Theories on failure mechanisms involved in fatigue contact: the Hertzian theory of contact between elastic bodies ....................................................... 121 Traction and elasto-hydrodynamic lubrication (EHL) condition .................. 128 Subsurface crack initiated fatigue contact failure ......................................... 131

Friction and wear damage ................................................................................ 138 Actual surface contact between solids ........................................................... 138 Data for coefficients of friction ...................................................................... 141 Lubrication .................................................................................................... 143 Wear of materials .......................................................................................... 144 Adhesive wear ................................................................................................ 144 Abrasive wear ................................................................................................ 145

Corrosion ........................................................................................................... 147 Wet corrosion and electrochemical corrosion ............................................... 147 The corrosion morphology ............................................................................ 155 Uniform or generalized corrosion ................................................................. 155 Galvanic corrosion ........................................................................................ 156 Pitting corrosion ............................................................................................ 159 Crevice corrosion .......................................................................................... 161

Creep .................................................................................................................. 163 The Creep Curve ............................................................................................ 163 Creep Deformation Mechanisms ................................................................... 167 Creep Life Prediction .................................................................................... 169 Design Against Creep .................................................................................... 170

Chapter 3 – Special Steels ................................................................................. 172 Introduction ................................................................................................. 172 Designation of steels ...................................................................................... 172 Classification of steels ................................................................................... 175 Designation of steels ...................................................................................... 176 Classification of steels ................................................................................... 178 Microstructures and heat treatment in steels ................................................. 179 Strengthening of ferritic-perlitic structure ..................................................... 184 Quenching and tempering of steels. ............................................................... 191 Tempering martensite .................................................................................... 193 Prediction of hardenability ......................................................................... 195

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Review of phase transformations and mechanical properties for iron-carbon alloys................................................................................................. 200 Industrial quenching problems: distortions and quenching cracks ........ 202 Quenching and tempering steels ................................................................. 205 Basics of criteria selection ............................................................................. 215 The manufacturing cycle of quenching and tempering steels .................. 215 Reduction of microstructure and chemical composition inhomogeneity ....... 216 Control of quenching distortion ..................................................................... 220 Criteria for selection ...................................................................................... 226 Spring Steels ................................................................................................. 227 Heat treatments for steels and manufacturing cycle of springs ..................... 229 Patenting ........................................................................................................ 231 Pickling .......................................................................................................... 232 Shot peening................................................................................................... 232 Criteria selection ........................................................................................... 235 Surface hardening of mechanical components .......................................... 235 Surface Hardening by Localized Heat Treatment .......................................... 236 Manufacturing cycle for surface hardened product ....................................... 238 Criteria for steel selection for surface hardening .......................................... 239 Carburizing steels ........................................................................................ 240 Carburizing cycle description ........................................................................ 243 Design aspects of carburizing ........................................................................ 244 Nitriding steels ............................................................................................. 246 Design features of nitriding parts .................................................................. 249 Manufacturing cycle for nitriding parts......................................................... 250

Chapter 4 – Tool Steels ..................................................................................... 253 Classification of tool steels ............................................................................ 253 The AISI classification ................................................................................... 253 Important properties required for various applications ................................ 254 Secondary hardening of tool steels ................................................................ 255 Manufacturing cycle of tool steels ................................................................. 257 Criteria for selection of tool steels for specific applications ......................... 257

Steels for Special Applications – Specialty Alloyed Steels ............................. 260 High-Fracture-Toughness Steels ................................................................ 260 Mar-Aging Steels ......................................................................................... 262 High-Strength Low-Alloy Steels ................................................................. 264 Dual-Phase Steels ......................................................................................... 267 TRIP Steels ................................................................................................... 269

Chapter 5 – Stainless Steels .............................................................................. 270 Introduction.................................................................................................. 270

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Classification of stainless steels ................................................................... 271 Ferritic Stainless Steels ................................................................................ 273 Austenitic stainless steels ............................................................................. 279 Martensitic stainless steels .......................................................................... 284 Austenitic-Ferritic (Duplex) Stainless Steels ............................................. 288 Precipitation Hardening Stainless Steels ................................................... 290

Chapter 6 – High-Temperature Resistant Alloys: Steels for High Temperatures, Ni-Base Alloys and Ni-Superalloys ........................................ 292

Introduction ................................................................................................. 292 Chromium-molybdenum and chromium-molybdenum-vanadium steels294 Stainless steels for high temperatures ........................................................ 296

Chapter 7– Non-Ferrous Structural Alloys: Magnesium Alloys ................... 303 Introduction: the search for lightweighting in automotive ...................... 303 Magnesium Alloys for Structural Applications ......................................... 311 The ASTM designation of Mg alloys and most used Mg alloys ..................... 314 Casting Alloys ................................................................................................ 315 Wrought Magnesium Alloys ........................................................................... 317

Chapter 8–Titanium Alloys .............................................................................. 321 Titanium Metallurgy ................................................................................... 322 Titanium Alloys ............................................................................................ 324 Commercially Pure Titanium......................................................................... 325 Alpha and Near-Alpha Alloys ........................................................................ 325 Beta Alloys ..................................................................................................... 327 Basics of fabrication of titanium alloys ...................................................... 328

Chapter 9 – Steelmaking process: basics of primary fabrication and secondary operations ......................................................................................... 329

Introduction ................................................................................................. 329 Blast Furnace ................................................................................................ 332 Basic Oxygen Furnace ................................................................................... 334 Electric Arc Furnace ..................................................................................... 336 Ladle Furnace ................................................................................................ 337 From Ladle Furnace to Casting Process .................................................... 338 Ingot Casting ................................................................................................. 338 Continuous Casting ....................................................................................... 339 The cast product microstructure .................................................................... 341 Primary metalworking hot processes: the bulk deformation processes .. 345

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Chapter 1 - Resuming basic principles of metallurgy

Introduction

Some of the important properties of solid materials depend on geometrical atomic arrangements, and also the interactions that exist among constituent atoms or molecules. Several fundamental and important concepts— name-ly, atomic structure, electron configurations in atoms are here reviewed briefly (for more details you may refer to: William D. Callister, Materials Science and engineering: an introduction - 7. ed. - New York: John Wiley & sons, 2007; F.C. Campbell, Metallurgy and Engineering Alloys, ASM International, 2008). Atomic Structure and Interatomic Bonding

Bohr atomic model, in which electrons are assumed to revolve around the atomic nucleus in discrete orbitals, and the position of any particular elec-tron is more or less well defined in terms of its orbital. This model of the atom is represented in Figure 1.1a.

(a) (b)

Figure 1.1 – (a) A schematic representation of the Bohr atom; (b) covalent bond-ing requires that electrons be shared between atoms in such a way that each atom has its outer sp orbital filled. In silicon, with a valence of four, four covalent bonds must be formed. The electron configuration or structure of an atom represents the manner in which electron states—values of energy that are permitted for electrons

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states are occupied. Valence electrons are those ones that occupy the outermost shell: these electrons are extremely important for establishing the bonding between atoms. And bonding between atoms are necessary to form atomic and molecular aggregates. This implies many of the physical and chemical properties of solids are based on these valence electrons. The basics of atomic bonding are best illustrated by considering how two isolated atoms interact as they are brought close together from an infinite separation (Fig. 1.2). At large distances, attraction forces exerted between positive nucleus of one atom and the negative electrons of the other atom are negligible (mutual attraction): this depend on the fact the two atoms are too far apart to have an influence on each other. At small separation dis-tances, each atom can actually exerts forces on the other, but when dis-tance decrease too much, namely nuclei get close, repulsive forces be-tween positive nuclei surpass attraction force. These counteracting forces, attractive FA and repulsive FR, and the magnitude of each depends on the separation or interatomic distance r (refer to Figure 1.2). The entity of at-tractive force FA obviously shall depend on the particular type of bonding that exists between the two atoms, as discussed in brief above. In Fig. 1.2b the potential energy is shown (as integral of bonding force ʃ F∙dr ). Despite the above scheme deals with an ideal situation involving only two atoms, a similar yet more complex condition exists for solid materials. The magnitude of this bonding energy and the shape of the energy–versus in-teratomic separation curve (Fig.1.2b) that can vary from material to mate-rial influence physical properties of materials. For example, large bonding energies typically also have high melting temperatures; at room tempera-ture, solid substances are formed for large bonding energies, whereas for small energies the gaseous state is favored; liquids prevail when the ener-gies are of intermediate magnitude. How much a material expands upon heating or contracts upon cooling (that is, its linear coefficient of thermal expansion) is related to the shape of its E vs r curve (a deep and narrow “trough,” which typically occurs for materials having large bonding ener-gies, normally correlates with a low coefficient of thermal expansion and relatively small dimensional alterations for changes in temperature).

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Figure 1.2 - (a) The dependence of repulsive, attractive, and net forces on intera-tomic separation for two isolated atoms. (b) The dependence of repulsive, attrac-tive, and net potential energies on interatomic separation for two isolated atoms.

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Physical principles of elastic modulus Among various physical properties affected by energy or interatomic force versus relative distance r (see again Fig.1.2a) curve shape diagram, we fo-cus on the tangent to F versus r curve at its stable equilibrium (i.e. in r0 in the Fig.1.2). Look at the Fig.1.3 that shows the F-r curve around the equi-librium, r0 (equilibrium will vary at different temperature: increase if T in-creases, decrease while T decreases).

Figure 1.3 - The force-distance curve for two materials, showing the relationship between atomic bonding and the modulus of elasticity, a steep dF/da slope gives a high modulus. If we refer to general results obtained by a stress-strain curve (i.e. σ−ε curve, Fig. 1.4a), we observe most metals that are stressed in tension and at relatively low levels result in a proportional stress and strain correlation to each other, obeying to the relationship σ= Eε, also known as Hooke’s Law. We define deformation in which stress and strain are proportional as elas-tic deformation (a nonpermanent deformation) since each loading cycle performed in this stress-strain curve “region” is fully reversible (by un-loading, the piece returns to its original shape).

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(a) (b)

Figure 1.4 – (a) Typical engineering stress–strain behavior to fracture, point F; (b) a detail of the stress-strain curve in the proportionality regime. On an atomic scale, thus referring again to Fig.1.3, macroscopic elastic strain is manifested as small changes in the interatomic spacing and the stretching of interatomic bonds. As a consequence, the magnitude of the modulus of elasticity is a measure of the resistance to separation of adja-cent atoms, that is, the interatomic bonding forces. This modulus is propor-tional to the slope of the interatomic force–separation curve (Figure 1.3) at the equilibrium, and it is a physical properties of material class: it does mostly depend on atomic bonding force of crystal lattice of metals, over a very low influence of varying chemical analysis (steels exhibits atomic bonding force higher than aluminum, so its Young Modulus is higher; Young Modulus of any steels slightly varies in the range 200.000 – 220.000 MPa). Atomic arrangements of metals During cooling, and thus solidifying phase, the vibrational energy1 of at-oms tends to decrease. By opposite reasoning we can say that increasing vibration energy causes progressively equilibrium distance r0 to increase.

1 Atoms vibrates around their equilibrium r0 position at any temperature; at -273 K vibration ceases.

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The material, if it is solid, remains in this state till the equilibrium distance that is increased by increasing temperature (consider that heating up pro-vides energy for increase atom vibration) is lower than low-bonding ener-gy regime (see again Fig.1.2b: as interatomic atom distance increases, at-tractive force, i.e. bonding energy decreases). If atoms reaches high intera-interatomic distance, their mutual attractive force decreases and atoms separate each other. While this phenomenon happens in metal, it is observe a change in status of aggregation: it passes from solid to liquid state. Now, proceed again in back track: cool down temperature of metal that is provided in molten state. The vibration energy of atoms progressively de-creases, till some atoms can attract each others. These early movements make some atoms to link each others, and some nuclei of solidified materi-als appears in the melting phase (see Fig.1.5a) What distinguishes metals, some polymers and many ceramics is that when solid state is reached, atoms occupies regular ordering of atoms that ex-tends through the material (Fig.1.5b and c). Particularly here we refer to metals.

Figure 1.5 - Schematic diagrams of the various stages in the solidification of a polycrystalline material; the square grids depict unit cells. (a) Small crystallite nu-clei. (b) Growth of the crystallites; the obstruction of some grains that are adjacent to one another is also shown. (c) Upon completion of solidification, grains having irregular shapes have formed. (d) The grain structure as it would appear under the microscope; dark lines are the grain boundaries.

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For a metal, crystalline solid is built up during cooling down and solidifi-cation by way of a periodic and repeated arrangement of atoms that ex-tends throughout the entirety of the specimen. The basic cell that repeat in the space at is called the unit cell and its “geometry” varies for metals. In Fig. 1.6 are show various possibility of arrangement in metals and the highlighted ones are those we deal with in this course.

Figure 1.6 - The fourteen types of Bravais lattices grouped in seven crystal sys-tems. The highlighted structures are those of our interest.

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The representation in Fig.1.6 is just schematic; in reality, the lattice struc-ture is made up by atoms that get close each other, compacting and pack-ing in the unit cell above illustrated. In Fig.1.7 is shown the more real structure of a face centered cubic, or FCC, unit cell (Fig.1.7a) compared with the schematic representation (Fig.1.7b) of unit cell, and how the unit cells combine in the space to form solid material (namely, each single grain of Fig.1.5).

Fig.1.7 - For the face centered cubic crystal structure, (a) a “hard sphere” unit cell representation, (b) a reduced-sphere unit cell, and (c) an aggregate of many atoms. Now, imagine to start from the scheme in Fig.1.7b made of ping pong balls at the corner and in center of 6 faces of the cube, and pack as you can, try-ing to realize by outer uniform compression a compact cube. What hap-pens is that some spaces will remain in your compacted cube. These spaces we call interstitial spaces, or sites. In Fig.1.8, for example, are shown the

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interstitial spaces present in three type of unit cells. In Fig.1.9 the octahe-dral site inside the face centered cubic cell.

Figure 1.8 - The location of the interstitial sites in cubic unit cells. Only repre-sentative sites are shown. The name of the site (e.g. octahedral, tetrahedral, etc.) depends on its location in the

Figure 1.9 - The location of the octahedral site in a face centered cubic unit cell.

Imperfections in the Atomic and Ionic Arrangements Thus far it has been tacitly assumed that perfect order exists throughout crystalline materials on an atomic scale. However, such an idealized solid does not exist. Meanwhile cooled down, a metal solidifies by solid nuclei formation (see again Fig.5) and grain growth. It is worth of noticing that the simplified scheme of solidification in Fig.5 actually it is to be consid-ered as a low magnification representation; if you imagine to observe by an “atomic microscope” (we imagine we holds such a marvelous equip-

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ment) nuclei that are forming inside liquid phase as illustrated in Fig.5, ac-tually we have to consider they are building up meanwhile atoms by atoms occupy fixed position inside the specific unit cell. Each metal, we know, has its own specific atomic arrangement – it is just like the DNA code for organisms - that mainly depends on the base element, e.g. body cubic cen-tered, BCC, for Fe (at ambient temperature), face cubic centered, FCC, for aluminum, highly compact hexagonal for Mg, etc. Thus, when metal cools down and rapidly solidifies, it is impossible all atoms perfectly arrange to build up a perfect crystal lattice into perfect grain: in reality many atoms will occupy wrong positions. Point defects We call these wrong positions imperfections of crystal lattice, or more simply defects. Basic defects of a real crystal lattice consists in a punctual (single) wrong position occupied by an atom that is missing, thus we call it a vacancy, or it is inserted in an insufficient space, thus we can define a self-interstitial atom (see Fig. 1.10). We call this type of imperfections “point defects”, because of their effect onto lattice irregularity: they can be several, but they are punctual imperfections distributed in crystal planes.

Figure 1.10 - Two-dimensional representations of a vacancy and a self-interstitial. If you consider the most generalized case of non-pure metals, namely the solid solutions of two or more elements, we call metal alloys, like Fe-C al-loys, aluminum silicon added alloys, etc. exhibit same type of defects as vacancies, but additionally to the self-interstitial atoms, crystalline defects can refer also to irregular occupancy of an alloying element atom that would have a smaller or wider radius than base element. In Fig.1.11 it is

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shown a summary of possible point defect situations we can observe in metal alloys. Whichever is origin of point defect, all of these defects dis-rupt the perfect arrangement of the surrounding atoms.

Figure 1.11 - Point defects: (a) vacancy, (b) interstitial atom, (c) small substitu-tional atom, (d) large substitutional atom, Interfacial defects: grain boundary Grain boundary is represented schematically from an atomic perspective in Figure 1.14. Within the boundary region, which is probably just several at-om distances wide, there is some atomic mismatch in a transition from the crystalline orientation of one grain to that of an adjacent one. Various de-grees of crystallographic misalignment between adjacent grains are possi-ble (Figure 1.15).When this orientation mismatch is slight, on the order of a few degrees, then the term small- (or low-) angle grain boundary is used. These boundaries can be described in terms of dislocation arrays. One simple small-angle grain boundary is formed when edge dislocations are aligned in the manner of Figure 4.8. This type is called a tilt boundary; the angle of misorientation, �, is also indicated in the figure. When the angle of misorientation is parallel to the boundary, a twist boundary results, which can be described by an array of screw dislocations.

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Figure 1.14 – Schematic diagram showing small and high-angle grain boundaries and the adjacent atom positions.

Figure 1.15 – A tilt boundary having an angle of misorientation �, results from an alignment of edge dislocations.

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As special type of grain boundary twin boundary is worth of noticing: it exhibits a specific mirror lattice symmetry (it depends on crystal lattice). Thus atoms on one side of the boundary are located in mirror-image posi-tions of the atoms on the other side (Figure 1.16).

Figure 1.16 Schematic diagram showing a twin plane or boundary and the adjacent atom positions (colored circles).

Vacancies, interstitial spaces and grain boundaries as drive-force for diffusion in metals

Firstly we address the diffusion by the phenomenological point of view. Let us see the scheme in Fig. 1.16. The phenomenon of diffusion may be demonstrated with the use of a diffusion couple, which is formed by join-ing bars of two different metals together so that there is intimate contact between the two faces; this is illustrated for copper and nickel. which in-cludes schematic representations of atom positions and composition across the interface. This couple is heated for an extended period at an elevated temperature (but below the melting temperature of both metals) and cooled to room temperature. Chemical analysis will reveal a condition similar to that represented in Figure 1.15 —namely, pure copper and nickel at the two extremities of the couple, separated by an alloyed region. Concentra-tion of both metals vary with position as shown in Figure 1.15f. This result indicates that copper atoms have migrated or diffused into the nickel, and that nickel has diffused into copper. This process, whereby atoms of one metal diffuse into another, is termed inter-diffusion, or impurity diffusion. There is a net drift or transport of atoms from high- to low-concentration regions.

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Diffusion also occurs for pure metals, but all atoms exchanging positions are of the same type; this is termed self-diffusion. Of course, self-diffusion is not normally subject to observation by noting compositional changes. This was the experiment, to allow us to observe results of diffusion: but which are mechanisms that causes diffusion into metals?

Figure 1.16 – Start experiment time: (a) a copper–nickel diffusion couple before a high-temperature heat treatment; (b) schematic representations of Cu (red circles) and Ni (blue circles) atom locations within the diffusion couple; (c) concentrations of copper and nickel as a function of position across the couple; (d) the copper–nickel diffusion couple after a high-temperature heat treatment, showing the al-loyed diffusion zone; (e) schematic representations of Cu (red circles) and Ni (blue circles) atom locations within the couple; (f) Concentrations of copper and nickel as a function of position across the couple. Mechanisms of diffusion into metal From an atomic perspective, diffusion is just the stepwise migration of at-oms from lattice site to lattice site. In fact, the atoms in solid materials are in constant motion, rapidly changing positions. For an atom to make such a move, two conditions must be met: (1) there must be an empty adjacent site, and (2) the atom must have sufficient energy to break bonds with its

(a)

(b)

(c)

(d)

(e)

(f)

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neighbor atoms and then cause some lattice distortion during the displace-ment. As stated, this energy is vibrational in nature until cooling down metals to -273 K. At a specific temperature some small fraction of the total number of atoms is capable of diffusive motion, by virtue of the magni-tudes of their vibrational energies. This fraction increases with rising tem-perature. Several different models for this atomic motion have been proposed; of these possibilities, two dominate for metallic diffusion.

– Vacancy Diffusion: involves the interchange of an atom from a

normal lattice position to an adjacent vacant lattice site or vacancy, as represented schematically in Fig.1.17a. This process of course necessitates the presence of vacancies, and the extent to which va-cancy diffusion can occur is a function of the number of these de-fects that are present.

– Interstitial Diffusion: The second type of diffusion involves atoms that migrate from an interstitial position to a neighboring one that is empty; this mechanism is found for interdiffusion of impurities and very small-radius atoms (such as hydrogen, carbon, nitrogen, and oxygen) that are small enough to fit into the interstitial positions and move (Fig.1.17b). In most metal alloys, interstitial diffusion occurs much more rapidly than diffusion by the vacancy mode, because the interstitial atoms are smaller and thus more mobile. Furthermore, there are more empty interstitial positions than vacancies; hence, the probability of interstitial atomic movement is greater than for va-cancy diffusion.

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Figure 1.17 – Schematic representations of (a) vacancy diffusion and (b) intersti-tial diffusion.

Box - Modeling of diffusion into metals Diffusion is a time-dependent process—that is, in a macroscopic sense, the quantity of an element that is transported within another is a function of time. Often it is necessary to know how fast diffusion occurs, or the rate of mass transfer. This rate is frequently expressed as a diffusion flux (J), de-fined as the mass (or, equivalently, the number of atoms) M diffusing through and perpendicular to a unit cross-sectional area of solid per unit of time. In mathematical form, this may be represented as:

(𝑒𝑒𝑒𝑒. 1.1) 𝐽𝐽 = 𝑀𝑀𝐴𝐴 ∙ 𝑡𝑡

where A denotes the area across which diffusion is occurring and t is the elapsed diffusion time. In differential form, this expression becomes:

(𝑒𝑒𝑒𝑒. 1.2) 𝐽𝐽 = 1𝐴𝐴𝑑𝑑𝑀𝑀𝑑𝑑𝑡𝑡

The units for J are kilograms or atoms per meter squared per second (kg/m2. s or atoms/m2. s). If the diffusion flux does not change with time, a steady-state condition exists.

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Steady-state diffusion and Fick’s first law One common example of steady-state diffusion is the diffusion of atoms of a gas through a plate of metal for which the concentrations (or pressures) of the diffusing species on both surfaces of the plate are held constant. This is represented schematically in Figure 1.17a.

Figure 1.17 – (a) Steady-state diffusion across a thin plate. (b) A linear concentra-tion profile for the diffusion situation in (a). When concentration C is plotted versus position (or distance) within the solid x, the resulting curve is termed the concentration profile; the slope at a particular point on this curve is the concentration gradient:

(𝑒𝑒𝑒𝑒. 1.3) 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑒𝑒𝑐𝑐𝑡𝑡𝑐𝑐𝑐𝑐𝑡𝑡𝑐𝑐𝑐𝑐𝑐𝑐 𝑔𝑔𝑐𝑐𝑐𝑐𝑑𝑑𝑐𝑐𝑒𝑒𝑐𝑐𝑡𝑡 = 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

In the present experiment, the concentration profile is assumed to be line-ar, as depicted in Figure 1.17b, and:

(𝑒𝑒𝑒𝑒. 1.4) 𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑐𝑒𝑒𝑐𝑐𝑡𝑡𝑐𝑐𝑐𝑐𝑡𝑡𝑐𝑐𝑐𝑐𝑐𝑐 𝑔𝑔𝑐𝑐𝑐𝑐𝑑𝑑𝑐𝑐𝑒𝑒𝑐𝑐𝑡𝑡 = ∆𝑑𝑑∆𝑑𝑑 = 𝑑𝑑𝐴𝐴 − 𝑑𝑑𝐵𝐵

𝑑𝑑𝐴𝐴 − 𝑑𝑑𝐵𝐵

The mathematics of steady-state diffusion in a single (x) direction is rela-tively simple, in that the flux is proportional to the concentration gradient through the expression:

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(𝑒𝑒𝑒𝑒. 1.5) 𝐽𝐽 = −𝐷𝐷 𝑑𝑑𝑑𝑑𝑑𝑑𝑑𝑑

The constant of proportionality D is called the diffusion coefficient, which is expressed in square meters per second. The negative sign in this expres-sion indicates that the direction of diffusion is down the concentration gra-dient, from a high to a low concentration. Equation 1.5 is sometimes called Fick’s first law. When diffusion is according to Equation 5.3, the concen-tration gradient is the driving force.

Non-steady state diffusion and Fick’s second law The diffusion flux and the concentration gradient at some particular point in a solid vary with time, with a net accumulation or depletion of the dif-fusing species resulting. This is illustrated in Figure 1.18, which shows concentration profiles at three different diffusion times. In this case, in-stead the Fick’s first law, a partial differential equation is used to more precisely model the phenomenon: (𝑒𝑒𝑒𝑒. 1.6) 𝜕𝜕𝜕𝜕𝜕𝜕𝜕𝜕 = 𝜕𝜕

𝑥𝑥 (𝐷𝐷 𝜕𝜕𝜕𝜕𝜕𝜕𝑥𝑥)

The above equation is known as Fick’s second law. If the diffusion coeffi-cient is independent of composition (which should be verified for each particular diffusion situation), Equation 1.6 simplifies to:

(𝑒𝑒𝑒𝑒. 1.7) 𝜕𝜕𝑑𝑑𝜕𝜕𝑡𝑡 = 𝐷𝐷 𝜕𝜕2𝑑𝑑𝜕𝜕𝑑𝑑

Solutions to this expression (concentration in terms of both position and time) are possible when physically meaningful boundary conditions are specified.

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Figure 1.18 - Concentration profiles for nonsteady-state diffusion taken at three different times, t1, t2, and t3.

The use of Erf Function in modeling diffusion Frequently, the source of the diffusing species is a gas phase, the partial pressure of which is maintained at a constant value. Furthermore, the fol-lowing assumptions are made: 1. Before diffusion, any of the diffusing solute atoms in the solid are uni-

formly 2. distributed with concentration of C0. 3. The value of x at the surface is zero and increases with distance into the

solid. 4. The time is taken to be zero the instant before the diffusion process be-

gins.

These boundary conditions are simply stated as For t =0, C= C0 at 0 ≤ x ≤ ∞ For t > 0, C = Cs (the constant surface concentration) at x = 0 C= C0 at x = ∞ Application of these boundary conditions to Equation 1.7 yields the solu-tion:

(𝑒𝑒𝑒𝑒. 1.8) 𝑑𝑑𝑠𝑠 − 𝑑𝑑𝑥𝑥𝑑𝑑𝑠𝑠 − 𝑑𝑑0

= 𝑒𝑒𝑐𝑐𝑒𝑒 � 𝑑𝑑2√𝐷𝐷𝑡𝑡�

Where:

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o Cs is the surface concentration of gas diffusing into the surface, o Co is the initial concentration of the element in the solid, x is the

distance from the surface, o D is the diffusivity of the solute element in the solvent matrix,

and t is time; o erf (error function) is a mathematical function that can be found

in standard mathematical tables, also included in excel function; Case study - Carburization process modeling

9 Assume gas carburizing process conducted on 1020 steel, at 930 °C;

9 Assume that the steel has a nominal carbon content of 0.20%, and the carbon content at the surface is 0.90%.

9 The diffusion coefficient under these conditions is D930°C =1.28 ·10-11 m2/s

9 The time necessary to increase the carbon content to 0.40% at 0.50mm below the surface can be calculated in the following manner:

Figure 1.19 – Carbon concentration during carburizing.

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Internal factors that affect diffusion In the following are listed two main inner factors among various which af-fect diffusion kinetics. Diffusing species: The magnitude of the diffusion coefficient D is indica-tive of the rate at which atoms diffuse. The diffusing species as well as the host material influence the diffusion coefficient. For example, there is a significant difference in magnitude between self-diffusion and carbon in-terdiffusion in iron at 500°C, the D value being greater for the carbon in-terdiffusion (3.0 x 10-21 vs. 2.4 x 10-12 m2/s). This comparison also provides a contrast between rates of diffusion via vacancy and interstitial modes as discussed earlier. Self-diffusion occurs by a vacancy mechanism, whereas carbon diffusion in iron is interstitial. Temperature: Temperature has a most profound influence on the coeffi-cients and diffusion rates. For example, for the self-diffusion of Fe in �-Fe, the diffusion coefficient increases approximately six orders of magni-tude in rising temperature from 500°C to 900°C. The temperature depend-ence of the diffusion coefficients is: (eq.1.9) 𝐷𝐷 = 𝐷𝐷0 exp �−𝑄𝑄𝑑𝑑

𝑅𝑅𝑅𝑅� Where: D0 is a temperature-independent pre-exponential (m2/s) Qd is the activation energy for diffusion (J/mol) R is the gas constant, 8.31 J/mol·K T is the absolute temperature (K) The activation energy may be thought of as that energy required to pro-duce the diffusive motion of one mole of atoms. A large activation energy results in a relatively small diffusion coefficient.

29

Box - Determining D0 and Qd

Taking natural logarithms of Equation 1.9 yields:

(𝑒𝑒𝑒𝑒. 1.10) 𝐿𝐿𝑐𝑐𝑔𝑔 𝐷𝐷 = 𝐿𝐿𝑐𝑐𝑔𝑔 𝐷𝐷0 − Q𝑑𝑑2.3 𝑅𝑅 �1

𝑇𝑇�

Because D0, Qd, and R are all constants, Equation 1.10 takes on the form of an equation of a straight line: y = b+ mx. where y and x are analogous, respec-tively, to the variables log D and 1/T. Thus, if log D is plotted versus the re-ciprocal of the absolute temperature, a straight line should result, having slope and intercept of -Qd/2.3R and log D0, respectively. This is the manner in which the values of Qd and D0 are determined experimentally. From such a plot for several alloy systems (Figure 1.20), it may be noted that linear rela-tionships exist for all cases shown.

Figure 1.20 - Plot of the logarithm of the diffusion coefficient versus the re-ciprocal of absolute temperature for several metals.

30

Line defects: dislocations in metals Punctual defects are not the only type of wrong arrangement of atoms in-side crystal lattice. Several atoms can occupy wrong positions, at the same time. We therefore talk about the line or plane defect. Let us see what it does mean. Assume to consider a perfect ordered crystal lattice, as it is schematically represented by perfect cubes link together in a perfect spatial order, as the scheme in Fig.1.21a depicts.

Figure 1. 21 – Constructions of a line defect (dislocation): (a) a perfect crystal; (b) an extra half-plane of atoms is inserted; (c) the bottom edge of the extra plane is an edge dislocation. Now consider a half-plane is inserted in the perfect crystal, by operation on Fig.1.21b. The results is a locally deformed lattice (see Fig. 1.21c), be-cause of the presence of the added semi plane. We call this defect disloca-tion and it is a linear or one-dimensional defect around which some of the atoms are misaligned: the half-plane edge terminates within the crystal. This is termed also as edge dislocation and the final row of atoms that held to the dislocation plane is called the dislocation line, which, for the edge dislocation in Fig.1.21c is perpendicular to the plane of the page. A more detailed representation of an edge dislocation is provided in Fig.1.22.

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Figure 1.22 - The atom positions around an edge dislocation; extra half-plane of atoms shown in perspective. As the point defects above discussed disrupt the perfect arrangement of the surrounding atoms, irregularities induced by dislocations works in similar way: within the region around the dislocation line there is some localized lattice distortion. The atoms above the dislocation line in Figure 1.13 are squeezed together, and those below are pulled apart; this is reflected in the slight curvature for the vertical planes of atoms as they bend around this extra half-plane. Elastic and plastic deformation in metal by microme-chanical models

Let us consider the scheme in Figure 1.23, representing by micromechan-ics’ approach a perfect crystal lattice of metal: spheres represent atoms of same specie (thus we deal in this moment with pure metal), no defects, nei-ther vacancies, or dislocations are present. The link (electric bonding we discussed in previous paragraph) between atoms is represented by a spring that exhibits, if loaded in tension, an attractive force (this is in analogy with electric attraction between nuclei and opposite atom’s electrons). Fi-nally, we assume, for the sake of simplicity, that the box-shaped atoms grid that represents the 2D-dimension crystal lattice of our metal is actual-ly a single grain. This means that square perimeter of the grid in Fig.1.23a actually corresponds to the grain boundary. Now let us apply on this grid a tensile load, as it is illustrated by the arrows in Fig.1.23b. What does it happen to our grid in term of deformation?

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Figure 1.23 –(a) Tensile external load applied to perfect crystal lattice; (b) tensile stress leads to elastic deformation, and eventually to (c) a brittle rupture consisting in simultaneous breaking of atom bonds. Let us proceed reasoning about the assumptions we stated. Each “spring” in the micromechanical model that represents the atom bond obeys to a well-known mechanical relation F=K·x; this means, each spring has same behavior and same maximum strength. Applying tensile stress, the grid will extend as shown in Fig.1.23b. But, when the load is so high and springs extend too much that they exceed their own maximum re-sistance, springs finally break2. Moreover, if one single spring breaks, all the springs distributed in the row perpendicular to the force direction break at the same time (remember that they have same maximum strength, as they are similar). The result in this case is that all the atoms of the grid, from the left side to the right side, detach as Fig.1.23c shows. In other words, the grain (remember the square grid for us represent a single grain) rapidly fracture into two pieces. This is the failure scheme which is usual in brittle materials, like ceramics. Think to throw a ceramic piece onto floor: it breaks into two or more separate pieces, with no deformation. We know by experience that metals, usually, when they break exhibit also large deformed surface. The scheme in Fig.1.23 cannot therefore explain the plastic deformation in metals; on the other hand, it can well explain the elastic deformation, as in the next we can understand. Look again at

2 You can read this statement as follows: when atoms are separated by a distance that determine attractive force drastically reduces, see Fig. 1.2.

(a) (b) (c)

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Fig.1.4. We stated initial stage of the stress-strain curve in metal concerns on reversible, or elastic, deformation. Once the load is removed, the spec-imen recovers original dimension. This is well explained by the microme-chanical model shown in Fig.1.23a, since until tensile load we apply is suf-ficiently low (i.e. onto macro-mechanical model, this means keeping stress below the Yield Strength, YS), the springs in the “atomic grid” elas-tically extends. As soon as we remove the load, the grid recovers its origi-nal shape. Thus, which way should we modify the micromechanical model to well explain what we macroscopically observe when specimen surpasses the YS and enters in plastic deformation regime? We know in metals, as stress arises above the YS, the elastic regime stage is abandoned, thus metal starts to permanently deform. We now want to seek a micromechanical model that allows us to explain such a plastic regime. Let us consider the same “atomic grid” of Fig.1.13 but now we want to check what happens if we apply a shear stress scheme, instead of the tensile stress, accordingly with the scheme in Fig.1.24.

Figure 1.24 – (a) Shear stress applied to perfect crystal lattice; (b) on certain plane shear stresses can develop and induce atoms in two facing rows to slip. The final shape of the perimeter of the grid irreversibly changes, thus depicting plastic de-formation has occurred. By such a stress field, shear stresses develop onto the intermediate plane, as shown in the scheme of Fig.1.14b. Let us for the next that shear stress is higher enough (we’ll better comment how much high it should be), it is capable to make one crystal lattice plane to slip over the opposite one; the result of this movement is clearly shown in Fig.1.24b. The atoms of the upper part of the grid have moved of one step ahead, of the order of an in-teratomic space. If you imagine to remove the external load, the perimeter

τinternal

(a) (b)

Slip plane

34

of the grid cannot be restored at its original shape. The irreversible defor-mation has occurred, without implying brittle rupture of atomic bonds. Thus, the plastic deformation in metal can be effectively explained by this micromechanical scheme. But, there is still a but. If we refer to perfect crystal lattice shown in Fig.1.24, during the slip movement of one step order, 6 atomic bonds have been broken and 5 have been restored. It appears the net balance of energy concerns on 1 atomic bonds, but we need to consider the start of the movement has required in any case external load is sufficient to develop shear stresses capable to break out 6 atom bonds. You should take into ac-count that we’re enormously reducing the scale of a grain to a 36 atoms! But if we consider a grain in reality, the number of atoms from one border to the opposite border is of the order of millions! This means that to realize a very insignificant variation of perimeter of grain, shear stress along the grain should be capable to break millions of atomic bonds, simultaneously, thus recovering this huge quantity of energy as the atoms onto slip plane advance one step (see again the scheme in Fg.1. 24b). This cannot be ex-plainable in reality, since too much high would be the minimum shear stress to activate the slip that no machines on Earth would be adequate to plastically deform metals. From our knowledge of the metallic bond, it is possible to derive a theoretical value for the stress required to produce slip by the simultaneous movement of atoms along a plane in a metallic crystal. However, the strength actually obtained experimentally on single crystals is only about one-thousandth (1/1000) of the theoretical value, assuming simultaneous slip by all atoms on the plane. Obviously, slip does not occur by the simple simultaneous block movement of one layer of atoms sliding over another. The modern concept is that slip occurs by the step-by-step movement of dislocations through the crystal. But, how does it contribute in plastic deformation of metals? Dislocation and plastic deformation in metal Fortunately in metals there are millions of dislocations distributed into crystal lattice, as that one shown in the scheme of Fig.1.22. To compre-hend how dislocation positively works for plastic deformation, let us con-sider the scheme in Fig.1.25. When force is applied such that it shears the upper portion of the crystal to the right the plane of atoms above the dislocation can easily establish bonds with the lower plane of atoms to its right, with the result that the dis-location moves one lattice spacing at a time. Note that only single bonds are being broken at any one time, rather than the whole row. The atomic distribution is again similar to the initial configuration, and so, the slipping

35

of atom planes can be repeated. The movement is much like that of ad-vancing a carpet along a floor by using a wrinkle that is easily propagated down its length. This stress required to cause plastic deformation is orders of magnitude less when dislocations are present than in dislocation-free, perfect crystal-line structures.

Figure 1.25 - Line dislocation movement. If a large number of dislocations move in succession along the same slip plane, the accumulated deformation becomes visible, resulting in macro-scopic plastic deformation. This effect is represented by a simplified scheme in Fig.1.26 representing the macroscopic effect of grain boundary modification into polycrystalline metal. If a large number of dislocations move in succession along the same slip plane, the accumulated defor-mation becomes visible, resulting in macroscopic plastic deformation. Fig.1.26 also introduces further important key-point: dislocations do not move with the same degree of ease on all crystallographic planes nor in all crystallographic directions. Ordinarily, there are preferred planes, and in these planes, there are specific directions along which dislocation motion can occur. These planes are called slip planes, and the direction of move-ment is known as the slip direction. The combination of a slip plane and a slip direction forms a slip system

36

Figure 1.26 – Permanent deformation occurring at grain boundaries in polycrystal-line metals that reveal macroscopic deformation onto surface of specimen under tensile loading. Slip planes in metals For a particular crystal structure, the slip plane is that plane having the most dense atomic packing; that is, it has the greatest planar density. The slip direction corresponds to the direction, in this plane, that is most close-ly packed with atoms, that is, has the highest linear density. Consider, for example, the FCC crystal structure, a unit cell of which is shown in Figure 1.27a. There is a set of planes, the {111} family, all of which are closely packed. A (111)-type plane is indicated in the unit cell; in Figure 1.27b, this plane is positioned within the plane of the page, in which atoms are now represented as touching nearest neighbors.

No force applied, dislocationinside grain do not move

Force applied, maximum shear stress induces dislocations on 45°

slip planes to move to grainboundary

45°

σ

σ

37

Figure 1.27 – (a) A {111} slip system shown within an FCC unit cell. (b) The (111) plane from (a) and three slip directions (as indicated by arrows) within that plane constitute possible slip systems.

Slip occurs along -type directions within the {111} planes, as indicated by arrows in Figure 1.27. Hence, represents the slip plane and direction com-bination, or the slip system for FCC. Figure 1.27b demonstrates that a giv-en slip plane may contain more than a single slip direction. Thus, several slip systems may exist for a particular crystal structure; the number of in-dependent slip systems represents the different possible combinations of slip planes and directions. For example, for face-centered cubic, there are 12 slip systems: four unique {111} planes and, within each plane, three in-dependent directions. The possible slip systems for BCC and HCP crystal structures are listed in Table 1.1. For each of these structures, slip is possible on more than one family of planes (e.g., {110}, {211}, and {321} for BCC). For metals hav-ing these two crystal structures, some slip systems are often operable only at elevated temperatures.

Table 1.1. - Slip Systems for Face-Centered Cubic, Body-Centered Cubic, and Hexagonal Close-Packed Metals.

38

Face-centered cubic (fcc) metals have a large number of slip systems (12) and are therefore capable of moderate-to-extensive plastic deformation. Although body-centered cubic (bcc) systems often have up to 12 slip sys-tems, some of them, like steel, exhibit a ductile-to-brittle transition as the temperature is lowered due to the strong temperature sensitivity of their yield strength, which causes them to fracture prior to reaching their full po-tential of plastic deformation. In general, the number of slip systems avail-able for hexagonal close-packed (hcp) metals is less than that for either the fcc or bcc metals, and their plastic deformation is much more restricted. The hcp structure normally has only three to six slip systems, only one-fourth to one-half the available slip systems in fcc. Since plastic deformation takes place by slip, or sliding, on the close-packed planes, the greater the number of slip systems available, the greater the capacity for plastic deformation. Slip in single crystal: the Schmid’s law A further explanation of slip is simplified by treating the process in single crystals, then making the appropriate extension to polycrystalline materi-als. By mechanics in solid we know that, though an applied stress may be pure tensile (or compressive), shear components exist. Existence of shear stress is necessary to activate slip planes, so to move dislocation onto this plane along its slip direction. However the shear stress acting along this di-rection shall be sufficiently higher to promote dislocation movement. We need therefore to calculate the projected shear stress along the slip direc-tion of the external tensile force F applied (see again Fig.1.28a), thus com-pare the value of this shear stress to the minimum shear stress necessary for dislocation movement, or critical shear stress, τc. The former shear stress is called the resolved shear stress, τr and its magnitude depends not only on the applied stress, but also on the orientation of both the slip plane and direction within that plane. To best understand last statement, look at the scheme in Fig.1.28a. Assume the normal, n, of the slip plane lies at an angle, φ, to the tensile axis. The area A of the slip plane considered for all the specimen will be A0/cos φ. Similarly, if the slip plane lies at an angle, λ, to the tensile axis, the component of the axial force, F, acting on the slip direction will be F·cos λ. The resolved shear stress, τr, is then given by: (𝑒𝑒𝑒𝑒. 1.20) 𝜏𝜏𝑟𝑟 = 𝑃𝑃 cos𝜆𝜆

�𝐴𝐴 cos𝜙𝜙� �= 𝜎𝜎 cos𝜙𝜙 cos 𝜆𝜆

Where σ is the applied stress. If we consider the theoretical case of a single crystal (grain) specimen where the slip direction is orthogonal to tensile

39

stress we applied on specimen (see Fig.1.29), the shear stress τr for the Schmid law is 0: this means that also for high applied tensile stress, re-solved shear stress does not develop and any dislocations cannot move. Ul-timately, slip of planes cannot occur and plastic deformation cannot occur.

(a) (b)

Figure 1.28 – (a) Tensile test of single crystal and the Schmid’s Law components. (b) If dislocation is present perpendicular onto slip plane, it can be activated, and planes slip.

Figure 1.29 - If a slip plane is perpendicular to applied stress σ , the shear stress τr = 0. Also for high applied stress, no resolved shear stress develop and no disloca-tion can move. Slip cannot occur, deformation cannot occur. In general, φ + λ ≠ 0 because it need not be the case that the tensile axis, the slip plane normal, and the slip direction all lie in the same plane. A metal single crystal has a number of different slip systems that are capable of operating. The resolved shear stress normally differs for each one be-

40

cause the orientation of each relative to the stress axis (φ and λ angles) also differs. However, one slip system is generally oriented most favorably—that is, has the largest resolved shear stress, τr (max):

(𝑒𝑒𝑒𝑒. 1.21) 𝜏𝜏𝑟𝑟𝑟𝑟𝑟𝑟𝑥𝑥 = 𝜎𝜎𝑦𝑦(cos𝜙𝜙 cos 𝜆𝜆 )𝑟𝑟𝑟𝑟𝑥𝑥 In response to an applied tensile or compressive stress, slip in a single crystal commences on the most favorably oriented slip system when the resolved shear stress reaches a critical value, termed the critical resolved shear stress τcrss; it represents the minimum shear stress required to initi-ate slip and is a property of the material that determines when yielding oc-curs. The single crystal plastically deforms or yields when τr (max) = τcrss, and the magnitude of the applied stress required to initiate yielding (i.e., the yield strength σy) is:

(𝑒𝑒𝑒𝑒. 1.22) 𝜎𝜎𝑦𝑦 = 𝜏𝜏𝜕𝜕𝑟𝑟𝑠𝑠𝑠𝑠(cos𝜙𝜙 cos 𝜆𝜆)𝑚𝑚𝑐𝑐𝑑𝑑

The minimum stress necessary to introduce yielding occurs when a single crystal is oriented such that φ = λ = 45°; under these conditions:

(𝑒𝑒𝑒𝑒. 1.23) 𝜎𝜎𝑦𝑦 = 2𝜏𝜏𝜕𝜕𝑟𝑟𝑠𝑠𝑠𝑠 For example, if a single-crystal specimen is stressed in tension (see Fig.1.30), and their slip planes are favorably 45° oriented with tensile stress direction, slip occurs at minimum tensile stress value, accordingly with the Schmid’s law solved in eq.1.22 and calculated in eq.1.23.

41

(a) (b)

Fig.1.30 – Theoretical deformation occurring in a single crystal specimen. (a) A favorable slip direction in crystal lattice are favorable 45° around oriented; (b) in this particular case the tensile stress necessary for activating slip of planes is the minimum value, accordingly with the eq.1.22 and solve eq.1.23. Slip in polycrystalline crystal However, instead this very simplified and most theoretical case, most met-als used in industry are not single crystal. Under an applied axial load, the Schmid’s factor will be different for each grain3. Let us consider a 2D simplified scheme that can take into account existence of various slip sys-tem inside specimen loaded in tension. In the example, two grains are marked with bold arrows: the arrows represent the slip direction for each random oriented crystal lattices of various grains. These two grains have their slip directions 45° around oriented with the tensile stress direction. Thus, these two grains will result in the maximum Schmid’s factor, thus they will result in the minimum σ value in the eq.1.22, namely the mini-mum tensile stress for activating the movement of dislocations onto slip plane (necessary condition for grain plastic deformation).

3 For randomly oriented grains, the average value of the Schmid factor is ~1/3, which is referred to as the Taylor factor. It then follows that the yield strength should have a value of approximately 3τc.

42

Fig.1.31 – Scheme of polycrystalline plastic deformation initiation: in crystal lat-tice there are several grains with several slip systems. Because grains have random orientation, their slip planes have, too. Some grains therefore could result most fa-vorable oriented for activating dislocation movements if slip directions (represent-ed by arrows in the grains) are favorably ±45° angles oriented with the load axis. The ±45° orientations represents orientation of such planes where the shear stress produced by external tensile load reaches its maximum value. Dislocations start to move in these grains, thus plastic deformation initiates in these grains. However, with continued extension of specimen, σ in-creases and this causes other dislocation systems in other grains not 45° oriented will be activated (i.e. the Schmid’s factor is lower in other grains but the stress rises to values for satisfying the eq.1.22). Finally, you might consider that in real crystal lattice, 3D oriented, there are several slip systems, as Table 1.1 has shown. For FCC and BCC met-als, slip may eventually begin along a second slip system—the system that is next most favorably oriented with the tensile axis (see the Fig.1.32 and Fig.1.33).

σ

σ−45°+45°

τ

σσΙΙσΙ

τmax

τmax

43

Figure 1.32 - Slip lines on the surface of a polycrystalline specimen of copper that was polished and subsequently deformed.

Figure 1.33 - Alteration of the grain structure of a polycrystalline metal as a result of plastic deformation. (a) Before deformation the grains are equiaxed. (b) The de-formation has produced elongated grains.

44

Box - DEFORMATION BY TWINNING In addition to slip, plastic deformation in some metallic materials can occur by the formation of mechanical twins, or twinning. The concept of a twin concerns with a shear force that in some crystal lattices can produce atomic displace-ments such that on one side of a plane (the twin boundary), atoms are located in mirror-image positions of atoms on the other side. The manner in which this is accomplished is demonstrated in Figure 1.34. Here, open circles represent at-oms that did not move, and dashed and solid circles represent original and final positions, respectively, of atoms within the twinned region. As may be noted in this figure, the displacement magnitude within the twin region (indicated by ar-rows) is proportional to the distance from the twin plane.

Figure 1.34 - Schematic diagram showing how twinning results from an applied shear stress τ. In (b), open circles represent atoms that did not change position; dashed and sol-id circles represent original and final atom positions, respectively.

Slip and twinning deformations are compared in Figure 8.13 for a single crystal that is subjected to a shear stress τ.

Figure 1.35 - For a single crystal subjected to a shear stress τ, (a) deformation by slip, (b) defor-mation by twinning. Mechanical twinning occurs in metals that have BCC and HCP crystal struc-tures, at low temperatures, and at high rates of loading (shock loading), condi-tions under which the slip process is restricted; that is, there are few operable slip systems.

45

Mechanisms of Strengthening in Metals

Metallurgical and materials engineers are often called on to design alloys having high strengths yet some ductility and toughness; typically, ductility is sacrificed when an alloy is strengthened. Several hardening techniques are at the disposal of an engineer, and frequently alloy selection depends on the capacity of a material to be tailored with the mechanical characteris-tics required for a particular application. Important to the understanding of strengthening mechanisms is the relation between dislocation motion and mechanical behavior of metals. Because macroscopic plastic deformation corresponds to the motion of large numbers of dislocations, the ability of a metal to deform plastically depends on the ability of dislocations to move. Because hardness and strength (both yield and tensile) are related to the ease with which plastic deformation can be made to occur, by reducing the mobility of dislocations, the mechanical strength may be enhanced; that is, greater mechanical forces will be required to initiate plastic deformation. In contrast, the more unconstrained the dislocation motion, the greater is the facility with which a metal may deform, and the softer and weaker it becomes. Virtually all strengthening techniques rely on this simple princi-ple: Restricting or hindering dislocation motion renders a material harder and stronger. The present discussion is confined to strengthening mecha-nisms for single-phase metals by grain size reduction, solid-solution alloy-ing, and strain hardening. Deformation and strengthening of multiphase al-loys are more complicated, involving concepts beyond the scope of the present discussion; later chapters treat techniques that are used to strength-en multiphase alloys.

Strengthening by grain size reduction The size of the grains, or average grain diameter, in a polycrystalline metal influences the mechanical properties. Adjacent grains normally have dif-ferent crystallographic orientations and, of course, a common grain bound-ary, as indicated in Fig. 1.36. During plastic deformation, slip or disloca-tion motion must take place across this common boundary— say, from grain A to grain B in Fig.1.36.The grain boundary acts as a barrier to dis-location motion for two reasons:

1. Because the two grains are of different orientations, a dislocation passing into grain B will have to change its direction of motion; this becomes more difficult as the crystallographic misorientation increases.

46

2. The atomic disorder within a grain boundary region will result in a discontinuity of slip planes from one grain into the other.

It should be mentioned that, for high-angle grain boundaries, it may not be the case that dislocations traverse grain boundaries during deformation; ra-ther, dislocations tend to “pile up” (or back up) at grain boundaries. These pileups introduce stress concentrations ahead of their slip planes, which generate new dislocations in adjacent grains. A fine-grained material (one that has small grains) is harder and stronger than one that is coarse grained because the former has a greater total grain boundary area to impede dislo-cation motion. For many materials, the yield strength σy varies with grain size according to:

(𝑒𝑒𝑒𝑒. 1.24) 𝜎𝜎𝑦𝑦 = 𝜎𝜎0 + 𝐾𝐾𝑦𝑦 ∙ 𝑑𝑑−12

In this expression, termed the Hall–Petch equation, d is the average grain diameter, and σ0 and Ky are constants for a particular material. Note that Equation 1.24 is not valid for both very large (i.e. coarse) grain and ex-tremely fine grain polycrystalline materials. Fig.1.37 demonstrates the yield strength dependence on grain size for a brass alloy4.

Figure 1.36 - The motion of a dislocation as it encounters a grain boundary, illus-trating how the boundary acts as a barrier to continued slip. Slip planes are discon-tinuous and change directions across the boundary.

4 Grain size may be regulated by the rate of solidification from the liquid phase, and also by hot plastic deformation, as discussed in Chapter 9.

47

Figure 1.37 - The influence of grain size on the yield strength of a 70 Cu–30 Zn brass alloy. Note that the grain diameter increases from right to left and is not lin-ear.

It should also be mentioned that grain size reduction improves not only the strength, but also the toughness of many alloys; this fact can be explained as follows. Considering the scheme in Fig.1.31, if you imagine to reduce the grain size, many grains will “appear” in the same round window. This fact implies several further slip systems will add, because they are perti-nent to each single new grain you may consider. The result is the follow-ing. On one hand increasing of number of grain boundaries, that leads to increasing strength as above discussed; on the other hand, the increasing number of slip systems can contemporarily lead material to be prone dislo-cation movement inside the grain; this phenomenon results in higher ener-gy “absorption” during dislocation movement inside the grain, toward the grain boundaries where dislocation will pile up. Small-angle grain boundaries are not effective in interfering with the slip process because of the slight crystallographic misalignment across the boundary. On the other hand, twin boundaries will effectively block slip and increase the strength of the material. Boundaries between two different phases are also impediments to movements of dislocations; this is im-portant in the strengthening of more complex alloys.

48

Solid solution strengthening Another technique to strengthen and harden metals is alloying with impuri-ty atoms that go into either substitutional or interstitial solid solution. Ac-cordingly, this is called solid solution strengthening. High-purity metals are almost always softer and weaker than alloys composed of the same base metal. Increasing the concentration of the impurity results in an at-tendant increase in tensile and yield strengths, as indicated in Fig.1.38a and 1.38b, respectively, for nickel in copper; the dependence of ductility on nickel concentration is presented in Fig. 1.38c.

Figure 1.38 - Variation with nickel content of (a) tensile strength, (b) yield strength, and (c) ductility (%EL) for copper–nickel alloys, showing strengthening. Alloys are stronger than pure metals because impurity atoms that go into solid solution typically impose lattice strains on the surrounding host at-oms. Lattice strain field interactions between dislocations and these impu-rity atoms result, and, consequently, dislocation movement is restricted. For example, an impurity atom that is smaller than a host atom for which it substitutes exerts tensile strains on the surrounding crystal lattice, as illus-trated in Figure 1.39a.

49

Figure 1.39 - (a) Representation of tensile lattice strains imposed on host atoms by a smaller substitutional impurity atom. (b) Possible locations of smaller impurity atoms relative to an edge dislocation such that there is partial cancellation of im-purity–dislocation lattice strains.

Figure 1.40 - (a) Representation of compressive strains imposed on host atoms by a larger substitutional impurity atom. (b) Possible locations of larger impurity at-oms relative to an edge dislocation such that there is partial cancellation of impuri-ty–dislocation lattice strains. Conversely, a larger substitutional atom imposes compressive strains in its vicinity (Figure 1.40a).These solute atoms tend to diffuse to and segregate around dislocations in such a way as to reduce the overall strain energy—that is, to cancel some of the strain in the lattice surrounding a dislocation. To accomplish this, a smaller impurity atom is located where its tensile strain will partially nullify some of the dislocation’s compressive strain. For the edge dislocation in Figure 1.39b, this would be adjacent to the dis-location line and above the slip plane. A larger impurity atom would be situated as in Figure 1.40b. The resistance to slip is greater when impurity

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atoms are present because the overall lattice strain must increase if a dislo-cation is torn away from them. Furthermore, the same lattice strain interac-tions (Figures 1.39b and 1.40b) will exist between impurity atoms and dis-locations that are in motion during plastic deformation. Thus, a greater applied stress is necessary to first initiate and then continue plastic defor-mation for solid-solution alloys, as opposed to pure metals; this is evi-denced by the enhancement of strength and hardness. Strain hardening Strain hardening is the phenomenon by which a ductile metal becomes harder and stronger as it is plastically deformed. Sometimes it is also called work hardening or, because the temperature at which deformation takes place is “cold” relative to the absolute melting temperature of the metal, cold working. Most metals strain harden at room temperature. Fig. 1.41a and 1.41b demonstrate how steel, brass, and copper increase in yield and tensile strength with increasing cold work. The price for this en-hancement of hardness and strength is in a decrease in the ductility of the metal. This is shown in Fig.1.41c, in which the ductility, in percent elonga-tion, experiences a reduction with increasing percent cold work for the same three alloys.

Figure 1.41 - For 1040 steel, brass, and copper, (a) the increase in yield strength, (b) the increase in tensile strength, and (c) the decrease in ductility (%EL) with percent cold work The influence of cold work on the stress–strain behavior of a low-carbon steel is shown in Figure 8.20; here stress–strain curves are plotted at 0%CW, 4%CW, and 24%CW.

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Figure 1.42 - The influence of cold work on the stress–strain behavior of a low-carbon steel; curves are shown for 0% cold worked, 4% cold worked, and 24% cold worked. Strain hardening is demonstrated in a stress–strain diagram presented in Fig.1.43. Initially, the metal with yield strength σy0 is plastically deformed to point D. The stress is released, then reapplied with a resultant new yield strength, σyi. The metal has thus become stronger during the process be-cause is greater than σy0.

Figure 1.43 – Schematic tensile stress–strain diagram showing the phenomena of elastic strain recovery and strain hardening.

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The strain-hardening phenomenon is explained on the basis of dislocation– dislocation strain field interactions similar to those discussed for the solid solution strengthening, but more effective. The dislocation density in a metal increases with deformation or cold work because of dislocation mul-tiplication or the formation of new dislocations, as noted previously. Con-sequently, the average distance of separation between dislocations de-creases—the dislocations are positioned closer together. On the average, dislocation–dislocation strain interactions are repulsive. The net result is that the motion of a dislocation is hindered by the presence of other dislo-cations. As the dislocation density increases, this resistance to dislocation motion by other dislocations becomes more pronounced. As a metal is plastically deformed, new dislocations are thus created, so that the dislocation density becomes higher and higher. In addition to mul-tiplying, the dislocations become entangled and impede each others’ mo-tion. Dislocations, in fact, are influenced by the presence of other disloca-tions and interact with each other, as shown for a number of different interactions in Fig. 1.44.

Figure 1.44 – Examples of dislocation interactions. Dislocations of the same sign will repel each other, while dislocations of opposite signs will attract each other and, if they meet, annihilate each oth-er. If the two dislocations of opposite signs are not on the same slip plane,

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they will merge to form a row of vacancies. These types of interactions oc-cur because they reduce the internal energy of the system. The result, in any case, is increasing resistance to plastic deformation with increasing dislocation density. Work hardening thus results in a simultane-ous increase in strength and a decrease in ductility. Since the work hard-ened condition increases the stored energy in the metal and is thermody-namically unstable, the deformed metal will try to return to a state of lower energy. This generally cannot be accomplished at room temperature. Ele-vated temperatures, in the range of 1/2 to 3/4 of the absolute melting point, are necessary to allow mechanisms, such as diffusion, to restore the lower-energy state. The process of heating a work-hardened metal to restore its original strength and ductility is called annealing. Metals undergoing form-ing operations often require intermediate anneals to restore enough ductili-ty to continue the forming operation. Approximately 5% of the energy of deformation is retained internally as dislocations when a metal is plastical-ly deformed, while the rest is dissipated as heat. The imposed stress necessary to deform a metal increases with increasing cold work. In the mathematical expression relating true stress and strain shown by equation 1.25:

(𝑒𝑒𝑒𝑒. 1.25) 𝜎𝜎 = 𝐾𝐾 ∙ 𝜀𝜀𝑛𝑛 the parameter n is called the strain-hardening exponent, which is a meas-ure of the ability of a metal to strain harden; the larger its magnitude, the greater is the strain hardening for a given amount of plastic strain. Phase boundaries as strengthening sources While a grain boundary is an interface between grains of the same compo-sition and same crystalline structure (α/α interface) with different orienta-tions, a phase boundary is one between two different phases (α/β interface) that can have different crystalline structures and/or different compositions. In two-phase alloys, such as copper-zinc brass alloys containing more than 40% Zn, second phases, such as the one shown in Fig. 1.45, can form due to the limited solid solubility of zinc in copper.

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Figure 1.45 – Phase boundary in copper-zinc system. There are three different types of crystalline interfaces that can develop be-tween two phases (Fig. 1.46): coherent, semicoherent, and incoherent. A fully coherent phase boundary (Fig. 1.46a, b) occurs when there is perfect atomic matching and the two lattices are continuous across the interface. The interfacial plane will have the same atomic configuration in both planes. Since there is perfect matching at the interface, the interfacial ener-gy is low. When the distances between atoms at the interface are not iden-tical (Fig. 1.46c), coherency strains start to develop. However, since there is still perfect atomic matching, it is still a coherent phase boundary; only the interfacial energy will be higher than one with no distortion. When the mismatch becomes sufficiently large, dislocations form to accommodate the growing disregistry. The result is called a semicoherent interface (Fig. 1.46d) that has an medium-high interfacial energy. Finally, an incoherent interface (Fig. 1.46e, f) is an interphase boundary that results when the ma-trix and precipitate have very different crystal structures, and little or no atomic matching can occur across the interface. The interfacial energy is even greater. An incoherent boundary is essentially equivalent to a high-angle grain boundary.

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Figure 1.46 – Phase boundaries systems. In many instances, second phases have a tendency to form at the grain boundaries. This occurs because they reduce their interfacial energy by oc-cupying a grain boundary; that is, by occupying a grain boundary, part of the interfacial energy is eliminated, and the total energy of the system is reduced. Depending on the type of their phase boundaries, such fine particles can exhibit slight or very high obstruction to dislocation movement. These in fact are in any case an irregularity for the matrix crystal lattice constituting the grain where dislocation can move. These fine precipitate particles, in other words, act as barriers to the motion of dislocations and provide re-sistance to slip, thereby increasing the strength and hardness. Particles are usually classified as deformable or non-deformable, meaning that the dislocation is able to cut through it (deformable) or the particle is so strong that the dislocation cannot cut through (non-deformable). When a dislocation encounters a fine particle, it must either cut through the particle or bow (loop) around it, as shown schematically in Fig. 1.47.

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Figure 1.47 – Particle strengthening. For effective particle strengthening (Fig. 1.48), the matrix should be soft and ductile, while the particles should be hard and discontinuous. A ductile matrix is better in resisting catastrophic crack propagation. Smaller and more numerous particles are more effective at interfering with dislocation motion than larger and more widely spaced particles. Preferably, the parti-cles should be spherical rather than needlelike to prevent stress-concentration effects. Finally, larger amounts of particles increase strengthening.

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Figure 1.48 – Particle-hardening considerations. In summary we have discussed mechanisms that may be used to strengthen and harden single-phase metal alloys: strengthening by grain size reduc-tion, solid-solution strengthening, strain hardening and second phase-dispersed (or fine particles) hardening. Of course they may be used in con-junction with one another; for example, a solid-solution-strengthened alloy may also be strain hardened.

Grain Growth, Recovery and Recrystallization Plastically deforming a polycrystalline metal specimen at temperatures that are low relative to its absolute melting temperature produces microstruc-tural and property changes that include (1) a change in grain shape, (2) strain hardening, and (3) an increase in dislocation density. Some fraction of the energy expended in deformation is stored in the metal as strain ener-gy, which is associated with tensile, compressive, and shear zones around the newly created dislocations. These properties and structures may revert back to the pre–cold-worked states by appropriate heat treatment, sometimes termed an annealing treatment. Such restoration results from two different processes that occur at elevated temperatures: recovery and recrystallization, which may be fol-lowed by grain growth.

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Recovery Recovery is the initial stage of the annealing cycle before recrystallization occurs. During recovery, some of the stored internal strain energy is re-lieved by virtue of dislocation motion (in the absence of an externally ap-plied stress), as a result of enhanced atomic diffusion at the elevated tem-perature. There is some reduction in the number of dislocations, and dislocation configurations are produced having low strain energies. During recovery, basic types of processes that occur are:

(1) the annihilation of excess point defects, particularly vacancies; the vacancies that were generated during cold working are annealed out by migrating to dislocations, grain boundaries, or surfaces;

(2) the rearrangement of dislocations into lower energy configura-tions, which also annihilates many of them; At slightly higher temperatures, the rearrangement of dislocations occurs, and, in the process, the annihilation of dislocations of opposite signs takes place. The rearrangement of dislocations is assisted by thermal en-ergy, which aids in both climb and slip mechanisms.

(3) the formation of subgrains that grow and interlock into sub-boundaries (Fig.1.49).

Figure 1.49 - the coalescence mechanism of two grains by mutual accommodation (rotation) and coalescence.

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Grain growth It should also be noted that the strengthening effects due to grain size re-duction and strain hardening can be eliminated or at least reduced by an el-evated-temperature heat treatment. Regarding with the enlarging of grain size, heating up metals produces diffusivity to increase. The higher is the diffusivity (refer to eq. 1.9), the higher is the diffusion of species in matrix. This is true also for the self-diffusion of element. When atoms move from one position to another obeying to diffusion mechanisms (refer to par.” Vacancies, interstitial spaces and grain boundaries as drive-force for dif-fusion in metals”), they also can move from one grain boundary to anoth-er: what could happen is schematically shown in Fig.1.50a. Basing on the grain boundary “migration”, in the Fig. 1.50b is shown the mechanisms that provokes grain growth by small grains disappearing. Ultimately, grain growth occurs because of metal with its original microstructure is heated up to certain temperature (Fig.1.51).

(a)

(b)

Figure 1.50 – (a) Schematic representation of grain growth via atomic diffusion; (b) disappearing of small grains.

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Empirically, it has been shown that grain growth occurs according to: (𝑒𝑒𝑒𝑒. 1.26) 𝐷𝐷 = 𝐾𝐾 ∙ 𝑡𝑡𝑛𝑛 Where: D is the average grain diameter, t is time, n is a constant,

𝐾𝐾 = 𝐾𝐾0 ∙ 𝑒𝑒−𝑄𝑄2𝑅𝑅𝑅𝑅

The constant n increases with temperature and approaches a theoretical value of 0.5. It should also be noted that the activation energy, Q, also var-ies with temperature.

Figure 1.51 – Schematic representation of grain size versus treatment temperature relationship. Recrystallization Even after recovery is complete, the grains are still in a relatively high strain energy state. Recrystallization is the formation of a new set of strain-free and equiaxed grains (i.e., having approximately equal dimensions in all directions) that have low dislocation densities and are characteristic of the pre–cold-worked condition. The driving force to produce this new grain structure is the difference in internal energy between the strained and unstrained material. The new grains form as very small nuclei and grow until they completely consume the parent material, processes that involve short range diffusion. Two stages in the recrystallization process are repre-sented in Fig.1.52a, 1.52b and 1.52c. In these photomicrographs, the small, speckled grains are those that have recrystallized.

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Recrystallization of cold-worked metals may be used to refine the grain structure. Also, during recrystallization, the mechanical properties that were changed as a result of cold working are restored to their pre–cold-worked values; that is, the metal becomes softer and weaker, yet more duc-tile (the extent of recrystallization depends on both time and temperature), as shown in Fig.1.53. The influence of temperature is demonstrated in Figure 1.54, which plots tensile strength and ductility (at room temperature) of a brass alloy as a function of the temperature and for a constant heat treatment time of 1 h. The grain structures found at the various stages of the process are also pre-sented schematically. Recrystallization is considered complete when the mechanical properties of the recrystallized metal approach those of the metal before it was cold worked; on the other hand, recrystallization and the resulting mechanical softening completely cancel the effects of cold working.

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Figure 1.52 – Recrystallization progression in low-carbon steel. (a) Recrystallized 10%. (b) Recrystallized 40%. (c) Recrystallized 80%.

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Figure 1.53 – The influence of annealing temperature (for an annealing time of 1 h) on the tensile strength and ductility of a brass alloy. Grain size as a function of annealing temperature is indicated. Grain structures during recovery, recrystalliza-tion, and grain growth stages are shown schematically.

Figure 1.54 – The variation of recrystallization temperature with percent cold work for iron. For deformations less than the critical (about 5% cold work, CW), recrystallization will not occur.

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Plastic deformation operations are often carried out at temperatures above the recrystallization temperature in a process termed hot working (Fig.1.55), described in last paragraph of Chapter 9. The material remains relatively soft and ductile during deformation because it does not strain harden, and thus large deformations are possible.

Figure 1.55 – Recrystallization during hot rolling.

Mechanical behavior of metals by macroscopic approach

The mechanical behavior of a material is its response to an applied load or force. Important mechanical properties are strength, hardness, stiffness, and ductility. There are three principal ways in which a load may be ap-plied: tension, compression, and shear. Large number of mechanical prop-erty tests have been developed to determine a material response to applied loads or forces. Tensile test The tensile test is the most commonly used mechanical property test. Its chief use is to determine the properties related to the elastic design of structures. In addition, the tensile test gives information on the plasticity and fracture of a material. A typical stress-strain curve for a metal is shown in Fig. 1.55. The parameters used to describe the stress-strain curve of a metal are the tensile strength, yield strength or yield point, percent elongation, and reduction in area. The first two are strength parameters, and the last two are indications of ductility. As long as the specimen is loaded within the elastic region, the strain is totally recoverable. However, when the load exceeds a value to the yield stress, the specimen undergoes plastic deformation and is permanently deformed when the load is re-moved. The stress to produce continued plastic deformation increases with increasing strain, thus obeying to work hardening phenomenon, discussed

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above as one of strengthening mechanism active in metals. To a good en-gineering approximation, the volume remains constant during plastic de-formation (Al=A0l0), and as the specimen elongates, it decreases uniformly in cross-sectional area along its gage length. Initially, strain hardening more than compensates for this decrease in area, and the engineering stress continues to rise with increasing strain. However, even-tually, a point is reached where the decrease in area is greater than the in-crease in deformation load from strain hardening. This condition will be reached first at some point in the specimen that is slightly weaker than the rest. All further plastic deformation is then concentrated in this region, and the specimen begins to neck or thin locally. Because the cross-sectional ar-ea is now decreasing far more rapidly than the deformation load is being increased by strain hardening, the engineering stress continues to decrease until fracture occurs.

Figure 1.55 – Typical stress-strain curve.

Figure 1.56 – Different stress-strain responses.

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With most metals, there is a gradual transition from elastic to plastic be-havior, and the point at which plastic deformation actually begins is diffi-cult to define with precision. The transition from elastic to plastic defor-mation is illustrated in Fig. 1.57.

Figure 1.57 – Elastic and plastic behavior during tensile loading. Metals that yield discontinuously have a stress-strain curve similar to that shown in Fig. 1.58a, instead of a continuous gradual yield point as in Fig. 1.58b. While in the former case the yield point is univocally identified as lower and higher yield point (see Fig.1.58a), for the metals with indefinite yield point, yield strength is determined by drawing a straight line parallel to the initial straight line portion of the stress-strain curve. The line is nor-mally offset by a strain of 0.2% (0.002).

(a) (b)

Figure 1.58– (a) Transition from elastic to plastic behavior; (b) Discontinuous yielding in plain carbon steels.

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Ductility Measures of ductility that are obtained from the tension test are the engi-neering strain at fracture (εf) and the reduction of area at fracture. Both are usually expressed as percentages, with the engineering strain at failure of-ten reported as the percent elongation. Both of these properties are ob-tained after fracture by putting the specimen back together and taking measurements of the final length, lf, and final specimen cross section at fracture, Af. Percent elongation can be determined by:

where l0 is the original gage length, and lf is the final length of the gage section. Likewise, reduction in area can be determined by:

where A0 is the original area of the gage section, and Af is the final area of the gage section at fracture. Resilience Resilience is the capacity of a material to absorb energy when it is de-formed elastically and then, upon unloading, to have this energy recovered. The associated property is the modulus of resilience, Ur , which is the strain energy per unit volume required to stress a material from an unload-ed state up to the point of yielding. The modulus of resilience for a speci-men subjected to a uniaxial tension test is just the area under the engineer-ing stress–strain curve taken to yielding:

(𝑒𝑒𝑒𝑒. 1.27) 𝑈𝑈𝑐𝑐 = � 𝜎𝜎𝑑𝑑𝜀𝜀𝜀𝜀𝑦𝑦

0

Assuming a linear elastic region, we have:

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(𝑒𝑒𝑒𝑒. 1.28) 𝑈𝑈𝑐𝑐 = 12𝜎𝜎𝑦𝑦𝜀𝜀𝑦𝑦 = [𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑠𝑡𝑡𝑐𝑐𝑡𝑡𝑠𝑠𝑡𝑡𝑐𝑐𝑐𝑐𝑔𝑔 𝑡𝑡ℎ𝑒𝑒 𝐻𝐻𝑐𝑐𝑐𝑐𝐻𝐻 𝐿𝐿𝑐𝑐𝐿𝐿 ]

= 12𝜎𝜎𝑦𝑦2𝐸𝐸

in which εy is the strain at yielding (see scheme in Fig.1.59). The units of resilience are the product of the units from each of the two axes of the stress–strain plot. For SI units, this is joules per cubic meter (J/m3, equiva-lent to Pa).

Figure 1.59– Schematic representation showing how modulus of resilience (corre-sponding to the shaded area) is determined from the tensile stress–strain behavior of a material. Toughness Although there are a number of approaches to defining toughness, one of the oldest is to consider it as the total area under the stress-strain curve. This area is an indication of the amount of work per unit volume that can be done on a material without causing it to fail. As shown in Fig. 1.60, this definition of toughness implies that toughness is a function of both strength and ductility. Another way of defining toughness is as the ability of a material to absorb energy and plastically deform before fracturing. For dynamic (high strain rate) loading conditions and when a notch (or point of stress concentration) is present, notch toughness is assessed by using an impact test (Fig.1.61).

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Figure 1.60 – Area under stress-strain curve as a measure of toughness.

Figure 1.61 – Impact test machine (Charpy test) conducted onto notched speci-men.

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Box – Stress concentration Geometrical features, such as holes, fillets, and radii, produce higher local stresses than encountered in the body of the material. For example, the tensile stresses at the top and bottom of the hole shown in Fig. 1.62 are three times greater than they are in the body of the material. These higher stresses are a re-sult of the inability of the stresses to pass through the hole.

Figure 1.62 – Stress-concentration effect around a hole. Such stress increases are described by the stress-concentration factor, K: K = Maximum actual stress/ Nominal stress While the stress-concentration factor K for a round hole is 3, much higher stress concentration factors occur when there is a sharp notch in the material. Values for a wide range of geometries can be found in handbooks dealing with stress analysis.

Hardness Hardness is the resistance to penetration, and the majority of hardness test-ers force a small sphere, pyramid, or cone into a specimen by means of an applied load. A number is obtained, and the hardness can often be correlat-ed to the tensile strength of the metal. This proportional relationship de-pends on the fact both tensile strength and hardness are indicators of a metal’s resistance to plastic deformation, that occurs on same micro-mechanical mechanisms of dislocation movement. Consequently, they are roughly proportional, as shown in Figure 1.63 for tensile strength as a

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function of the HB for cast iron, steel, and brass. As a rule of thumb, for most steels, the HB and the tensile strength are related according to:

UTS (MPa) = 3.34 x HB (or HV for hardness higher than 500 HB) In any case, the same proportionality relationship does not hold for all metals, as Figure 1.63 indicates. This depend, in fact, by micro-mechanisms of dislocation movement in different matrix of different met-als.

Figure 1.63 – Relationships among hardness and tensile strength for steel, brass, and cast iron.

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Box – Hardness test, the basics.

Resuming the main contents, defining the main paradigm for mechan-ical response of metals

On an atomic scale level, plastic deformation corresponds to the motion of dislocations in response to an externally applied shear stress. For example, an edge dislocation moves by the successive and repeated breaking of atomic bonds and shifting by interatomic distances of half planes of atoms. For dislocation edge, in particular, dislocation line motion and direction of the applied shear stress are thus parallel. We call slip the motion of dislo-cations in response to an externally applied shear stress. It occurs on spe-cific crystallographic planes and within these planes only in certain direc-tions, depending on crystal structure of the metal. The combination of slip planes and slip direction, expressed by the Schmid’s Law, is defined slip system. The slip plane is that plane that has the densest atomic packing, and the slip direction is the direction within this plane that is most closely packed with atoms. Operable slip systems, namely the planes where dislo-cation are active, depend on the crystal structure of the material.

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A resolved shear stress is the shear stress resulting from an applied tensile stress that is resolved onto a plane that is neither parallel nor perpendicular to the stress direction. For polycrystalline materials, slip occurs within each grain along those slip systems that are most favorably oriented with the applied stress. As favorable oriented we mean that in such grains the resolved shear stress is highest and it can achieve the critical shear stress, namely the shear stress necessary to activate dislocation slip along slip plane and in the slip direction. During deformation, grains change shape and extend in those di-rections wherein there is gross plastic deformation. The basic concept is that the ease with which a material is capable of plas-tic deformation is a function of dislocation mobility—that is, restricting dislocation motion leads to increases hardness and strength. Various modes are practicable to inhibit dislocation mobility. We call these modes strengthening mechanisms:

- Grain Size Reduction: as grain boundaries are barriers to disloca-tion motion for two reasons: a) when crossing a grain boundary, a dislocation’s direction of motion must change; b) there is a discon-tinuity of slip planes within the vicinity of a grain boundary. A metal that has small grains will be stronger than one with large grains because the former has more grain boundary area, and, thus, more barriers to dislocation motion. For most metals, yield strength depends on average grain diameter according to the Hall–Petch equation.

- Solid-Solution Strengthening: the strength and hardness of a metal increase with increase of concentration of impurity atoms that go into solid solution (both substitutional and intersti-tial).Solid-solution strengthening results from lattice strain interac-tions between impurity atoms and dislocations; these interactions produce a diminishment in dislocation mobility.

- Strain Hardening: strain hardening is just the enhancement in strength (and decrease of ductility)of a metal as it is plastically de-formed. Degree of plastic deformation may be expressed as per-cent cold work, which depends on original and deformed cross-sectional areas. Yield strength, tensile strength, and hardness of a metal increase with increasing percent cold work; ductility dimin-ishes. During plastic deformation dislocation density increases, the average distance between adjacent dislocations decreases, and—because dislocation–dislocation strain field interactions, are, on average, repulsive—dislocation mobility becomes more restricted; thus, the metal becomes harder and stronger.

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On the opposite, mechanisms that tend to recover the dislocation mobility, driven by heating up structure, are:

- Recovery: There is some relief of internal strain energy by dislo-cation motion. Dislocation density decreases, and dislocations as-sume low-energy configurations. Some material properties revert back to their precold-worked values.

- Recrystallization: During recrystallization, a new set of strain-free and equiaxed grains form that have relatively low dislocation densities. The metal becomes softer, weaker, and more ductile. The driving force for recrystallization is the difference in internal energy between strained and recrystallized material. For a cold-worked metal that experiences recrystallization, as temperature in-creases (at constant heat-treating time), tensile strength decreases and ductility. The recrystallization temperature of a metal alloy is that temperature at which recrystallization reaches completion in one hour. Two factors that influence the recrystallization tempera-ture are percent cold work and impurity content. Furthermore, re-crystallization temperature diminishes with increasing percent cold work.

- Grain growth is the increase in average grain size of polycrystal-line materials, which proceeds by grain boundary motion. The driving force for grain growth is the reduction in total grain boundary energy.

The most important conclusion we point out is the full understanding the strengthening mechanisms for metals and the resulting high or low me-chanical properties on the microscopic scale is “easily” explained by a high or low dislocation motion resources. The higher is dislocation mobili-ty, the lower is the onset to which plastic deformation occurs, namely the yield strength (YS) and the higher is the plastic deformation capacity under static or impacting loads that we expressed respectively by: a) the elonga-tion percentage at break E% (alternatively or adding to % reduction of area at break) and b) the energy stored (i.e. the Joule absorbed) by breaking a standard notched sample by an impact test machine. Summarizing, we can quickly measure by tensile test and impact test some macroscopic mechanical parameters by which we can state whether metal-lic materials behave either by ductile and tough safe mode or brittle unsafe mode. To understand why we can correlate the ductile and tough behavior to a safe operating mode of a metal for structural application, consider whether you would be happy to know the axle of your car is so low ductile and tough that its mechanical behavior is like a ceramic material.

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Basing on the 3 basic mechanical tests we have discussed so far, tensile test, hardness test and impact test, we therefore can group the main me-chanical features we obtain by 3 type of tests, distinguishing in mechanical resistance properties and ductile properties, as shown in following Fig.1.65. Fig.1.65 – Basic mechanical properties from tensile test, hardness test and impact test grouped into: a) resistance capability (left side); b) ductility capability ( right side). As we already learned, the left side and right side properties for metal are strictly correlated, because of the following causal relationship:

i) Dislocations move and reach grain boundary Æ grain boundary perimeter modifies Æ macroscopic plastic deformation occurs(1) Note 1: For example macroscopic deformation is observed in surpassing the onset yield strength, necking occurs in tensile tests; indenting of test material by penetrator in the hardness test; highly plastically deformed regions in the notched section area of Charpy test specimen broken.

And its own counteracting relationship :

ii) Dislocations are temporarily locked Æ dislocation motion is inhibited Æ critical resolved shear stress �crss increases Æ in-crease magnitude of external load to unlock dislocation(2) Æ dislo-cation move and reach grain boundary…

Note 2: Refer to eq.1.22.

What happens in metals is that, as well as dislocations are inhibited in their movement (independently of reasons, namely whichever strengthening mechanism is established), the yield strength increases, the ultimate tensile strength increases, the hardness increases, as we expect because of the in-

Hardness (hardness test) YS; UTS (tensile test)

E%, A% (tensile test) KV (Impact test, e.g. Charpy)

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crease of such magnitude of external load capable to unlock dislocation; but at the same time, in strengthened matrix, mobility of dislocations de-creases, thus resulting in decrease of ductile properties. The basic framework of such mutual relationships of a metal is shown in Fig.1.64. For example, a high hardness and consequently lack of ductility of one phase found in steel, the martensite, is explained by a solid-solution strengthening effect, that leads to an increase of resolved critical shear stress and consequently external load necessary to unlock dislocations. But, in addition, the martensite structure has very few slip systems. These double conditions leads on one hand to a very high critical resolved shear stress, responsible of high hardness and the high strength of martensite; on the other hand very few possibilities offered to dislocation to move (few slip planes) causes few plastic deformation capability, that lead macro-scopically to very low ductility and toughness.

Fig. 1.65 - Understanding basic material properties and their mutual correlations. For example, a high stiffness material (scheme on the left side) is a material with high slope – measured in the origin - of the σ (stress) and ε (deformation) curve obtained by a tensile test on the material. This slope is called the elastic modulus of the material. Such a high stiffness material usually exhibits further high me-chanical strength (i.e. Ultimate Tensile Strength, UTS), low ductility (i.e. defor-mation at break, εr) and low toughness (i.e. energy stored to break, proportional to area below the σ−ε tensile test diagram).

σ

Strong, stiff and brittlematerial

High-tough and ductilematerial

Strong and low-toughmaterial

High toughness

High strength

Low strength

Low stiffness

High stiffness

Low toughness

ε

Low ductility high ductility

εr

UTSUTS

UTS

εr εr

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Microstructural features of fracture in metallic materials

The dislocation motion or their inhibition to movement plays a determi-nant role in the metal fracture. We mean as fracture in metals the same for any layman persons, not a metallurgist (actually you will be surprised in the following how much intuitive is the vocabulary of a metallurgist!). Thus, fracture is simply the separation of a solid body made of metal into two or more pieces, under the action of external load. For metals, fracture can be classified into two broad categories: a) ductile fracture and b) brittle fracture. The ductile or brittle mode depends pri-marily on the macroscopic appearance of the fractured material. More pre-cisely, the Fig. 13.1 shows a schematic comparison between two ductile fractures - on the right side – that are both characterized by extensive plas-tic deformation, prior to and during crack propagation.

Fig. 1.66 - Comparison of brittle and ductile fracture modes.

On the opposite, a brittle fracture occurs with little or no gross plastic de-formation and usually occur suddenly, without warning (thus in unsafe mode - remind the ceramic vehicle axle!). The tendency for brittle fracture increases as well as any external or inter-nal conditions work for: a) locking dislocations and/or b) reduce slip planes. Thus, the tendency for a material that has sufficient slip planes (this is not the case of the Hexagonal Close Packing crystal structure) to brittle behavior increases as well as its own dislocation population is inhib-ited in motion. This can happen, for example:

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– with decreasing temperature; as temperature decreases, the atomic

vibration reduces and thus atomic planes tend to compact; this fact results unfavorable for dislocation slip;

– increasing strain rate, namely under strain-hardening mechanisms for dislocation locking;

– under triaxial stress conditions; remember that in the Mohr’s dia-gram a triaxial tensile state of stress is represented by a point, not circles; in this special case, shear stresses are zero; no shear stress causes no dislocation slip can occur (refer to scheme in Fig.1.24);

In the following we go in depth in two modes as they appear to microscop-ic observations. Ductile Fracture Ductile fracture normally occurs in a transgranular manner (through the grains) in metals that have good ductility and toughness. Often, a consider-able amount of deformation—including necking—is observed in the failed component. The deformation occurs before the final fracture. Ductile fractures are usu-ally caused by simple overloads, or by applying too high a stress to the ma-terial. In a simple tensile test, ductile fracture begins with the nucleation, growth, and coalescence of microvoids near the center of the test bar (Fig-ure 1.67). Microvoids form when a high stress causes separation of the metal at grain boundaries or interfaces between the metal and small impu-rity particles (inclusions). As the local stress increases, the microvoids grow and coalesce into larger cavities. Eventually, the metal-to-metal con-tact area is too small to support the load and fracture occurs.

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Fig. 1.67 - When a ductile material is pulled in a tensile test, necking begins and voids form—starting near the center of the bar—by nucleation at grain boundaries or inclusions. As deformation continues, a 45° shear lip may form, producing a fi-nal cup and cone fracture. Deformation by slip also contributes to the ductile fracture of a metal. We know that slip occurs when the resolved shear stress reaches the critical re-solved shear stress and that the resolved shear stresses are highest at a 45° angle to the applied tensile stress (ref. to Schmid’s Law). These two as-pects of ductile fracture give the failed surface characteristic features. In thick metal sections, we expect to find evidence of necking, with a sig-nificant portion of the fracture surface having a flat face where microvoids first nucleated and coalesced, and a small shear lip, where the fracture sur-face is at a 45° angle to the applied stress. The shear lip, indicating that slip occurred, gives the fracture a cup and cone appearance (Figure 1.68).

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Fig. 1.68 – Dimples form during ductile fracture. Equiaxed dimples form in the center, where microvoids grow. Elongated dimples, pointing toward the origin of failure, form on the shear slip. Simple macroscopic observation of this fracture may be sufficient to iden-tify the ductile fracture mode. Examination of the fracture surface at a high magnification—perhaps using a scanning electron microscope—reveals a dimpled surface (Figure 1.69). The dimples are traces of the microvoids produced during fracture. Normally, these microvoids are round, or equi-axed, when a normal tensile stress produces the failure (see Figure 1.69a); however, on the shear lip, the dimples are oval-shaped, or elongated, with the ovals pointing toward the origin of the fracture (see Figure 1.69b).

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Fig. 1.69 – Scanning electron micrographs of an annealed 1018 steel exhibiting ductile fracture in a tensile test. (a) Equiaxed dimples at the flat center of the cup and cone, and (b) elongated dimples at the shear lip. Brittle Fracture Brittle fracture occurs in high-strength metals and alloys or metals and al-loys with poor ductility and toughness. Furthermore, even metals that are normally ductile may fail in a brittle manner at low temperatures, in thick sections, at high strain rates (such as impact), or when flaws play an im-portant role. Brittle fractures are frequently observed when impact, rather than overload, causes failure. In brittle fracture, little or no plastic defor-mation is required. Initiation of the crack normally occurs at small flaws, which cause a concentration of stress. The crack may move at a rate ap-proaching the velocity of sound in the metal. Normally, the crack propa-gates most easily along specific crystallographic planes by cleavage. Cleavage fractures are characterized by a planar crack that changes planes by the formation of discrete steps. River patterns are formed at grain boundaries (Fig. 1.70) where the cleavage plane in one grain is not parallel to the plane in the adjacent grain, the difference being accommodated by a series of steps. The river patterns eventually diminish as the crack propa-gates and adopts the cleavage plane of the new grain before being re-formed at the next grain boundary. Brittle fracture can be identified by observing the features on the failed surface.

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Normally, the fracture surface is flat and perpendicular to the applied stress in a tensile test. If failure occurs by cleavage, each fractured grain is flat and differently oriented, giving a crystalline or “rock candy” appear-ance to the fracture surface (Fig. 1.71).

Fig. 1.70 – Facetted brittle failure with river lines.

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Fig. 1.71 – Scanning electron micrograph of a brittle fracture surface of a quenched 1010 steel.

Another common fracture feature is the Chevron pattern (Figure 1.72), that appears at naked eye. They are produced by separate crack fronts propa-gating at different levels in the material. A radiating pattern of surface markings, or ridges, fans away from the origin of the crack (Figure 1.73). Since the Chevron pattern is visible with the naked eye or a magnifying glass and helps us identify both the brittle nature of the failure process as well as the origin of the failure. Actually we can say that the Chevron pat-tern are the naked eye result of the microscopic cleavage fractures, thus observed at grain scale.

Fig. 1.72 – The Chevron pattern in quenched 4340 steel. The steel failed in a brit-tle manner by an impact blow.

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Fig. 1.73 – The Chevron pattern forms as the crack propagates from the origin at different levels. The pattern points back to the origin. In some cases, however, the crack may take an intergranular (along the grain boundaries) path, when grain boundaries are abnormally weak (Fig.1.74).

Fig. 1.74 – The patter of: transgranular fracture (left side) and intergranular frac-ture (right side).

Transgranular fracture(NORMAL )

Intergranular fracture(ABNORMAL )

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Chapter 2 - Damage mechanisms and root cause failure analysis basics

Introduction

The failure of engineering materials is almost always an undesirable event for several reasons; these include putting human lives in jeopardy, causing economic losses, and interfering with the availability of products and ser-vices. Even though the causes of failure and the behavior of materials may be known, prevention of failures is difficult to guarantee. The usual causes are improper materials selection and processing and in-adequate design of the component or its misuse. Also, damage can occur to structural parts during service, and regular inspection and repair or re-placement are critical to safe design. It is the responsibility of the engineer to anticipate and plan for possible failure and, in the event that failure does occur, to assess its cause and then take appropriate preventive measures against future incidents. Various modes of failure are covered in the next, distinguishing in 6 failure modes (fast brittle fracture, fatigue, creep, wear, contact fatigue and corro-sion), thus excluding the overloading failure of component that brings to plastic ruptures. Fast fracture in metals Brittle failures are particularly dangerous as abnormal for mechanical components and structures made of metal alloys. It has been already ad-dressed how hazardous are brittle fractures in metal structures, since it oc-curs suddenly without any warnings. But similar behavior are also possible in non-brittle materials, when they are subjected to such conditions that lead to fast fracture failures. As brittle fracture, also fast fracture is sudden and it does not experience any external plastic deformation that can warn about imminent material collapse. Let us consider a simply example. All we may have experienced the aggravation of having to expend considera-ble effort to tear open a small plastic package that contains nuts, candy, or some other confection. And we have also noticed that when a small inci-sion (or cut) has been made into an edge, as appears in photograph (a), a minimal force is required to tear the package open. This phenomenon is re-lated to one of the basic tenets of fracture mechanics we will deal with in

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the next: an applied tensile stress is amplified at the tip of a small incision or notch. Instead this little home-made experience, take a look in the pho-tograph in Fig. 2.1a that shows an oil tanker that fractured in a brittle man-ner as a result of the propagation of a crack completely around its girth.

(a)

(b)

Fig.2.1 – Brittle fracture of: a) an US oil tanker ship during WWII; b) the ship-wreck of M V Kurdistan oil tanker ship in 1979.

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This crack started as some type of small notch or sharp flaw. The cata-strophic nature of brittle fracture was dramatically exemplified with fre-quent brittle failures of Liberty ships during World War II that broke in half while just sitting at dock. To produce ships quickly for the war effort, all-welded construction was used for the hulls instead of the traditional riveted design. Of the 2700 Liberty ships built, approximately 400 sus-tained fractures, 90 of which were considered serious. In 20 of these, the hull fractured in half. When the hatch covers were retrofitted with rounded reinforcements and riveted structures replaced some of the welded struc-tures, the incidence of fracture was greatly reduced. Even if a crack initiat-ed at a defective weld, it would be arrested at a rivet hole before it reached catastrophic dimensions. After the war, G.R. Irwin and his staff at the Na-val Research Laboratory laid the foundation for what is known today as fracture mechanics. Liberty ships are just one example of catastrophic brittle fracture. It has al-so been a recurring problem in aircraft, bridges, train wheels, and other heavy equipment. Although brittle fracture does not occur today with the frequency it once did, it can still be a problem if proper design and manu-facturing practices are not used. Two important failings of the require-ments for ships as First Year Ice Class vessels brought to shipwreck of the M V Kurdistan oil tanker ship in 1979 South of the Cabot Strait, off Nova Scotia (Fig.2.1b). Presence of defect in bilge keel welds combined with high thermal stresses was the cause of brittle fracture. Studying relationships between material properties, stress level, the presence of crack-producing flaws, and crack propagation mechanisms had led in past Century to development of the discipline named as fracture mechanics. By advancements in fracture me-chanics, design engineers are now better equipped to anticipate, and thus prevent, structural failures. Here in the following some of the fundamental principles of the mechanics of fracture are addressed.

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Box – Griffith experience and the theoretical critical stress for brittle materials In a first attempt to calculate the strength of such a crystalline material, one atomic plane perpendicular to the tensile load is considered. The bond-ing force f between two atoms in two neighboring planes depends on their distance r, as it is shown in Fig.2.2 (refer to the upper curve that decreases progressively and asymptotically to zero value for large r distance).

Fig. 2.2 - Atomic bond strength between atom in a lattice.

By first approximation, Griffith modelled the f=f(r) force with a sine func-tion, by using the equilibrium distance a0, the half wavelength λ and the maximum force fmax (refer to the embedded curve in the same Fig.2.2. that ends with zero value at r = 1/2λ distance). (eq.2.1) 𝑒𝑒(𝑑𝑑) = 𝑒𝑒𝑟𝑟𝑟𝑟𝑥𝑥 sin �2𝜋𝜋𝑥𝑥𝜆𝜆 � ; 𝑑𝑑 = 𝑐𝑐 − 𝑐𝑐0 With this approximation it is easy to calculate that interaction force is zero and the bond is broken, when: (eq.2.2) 𝑐𝑐 = 𝑐𝑐0 + 1

2 𝜆𝜆 Thus consider the Fig.2.3: it shows scheme of rupture of some atoms bonds in an area of S (namely, the formation of a S length crack) of the two lattice planes that are loaded in tension by applied force f.

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Fig. 2.3 – Schematic representation of braking of atoms bonds in the lattice and the formation of a S length crack as the a0+λ/2 distance is reached (re-fer to eq.2.2 and scheme in Fig.2.2). Since the stress σ is defined as the ratio of the total force f applied to an area S, it can be directly derived by the eq.2.1. by: (2.3) 𝜎𝜎(𝑑𝑑) = 𝜎𝜎𝑟𝑟𝑟𝑟𝑥𝑥 sin �2𝜋𝜋𝑥𝑥𝜆𝜆 � ; 𝑑𝑑 = 𝑐𝑐 − 𝑐𝑐0 Griffith focused on the calculation of the (theoretical) σmax stress, also named critical stress σc, for achieving debonding in brittle materials. He assumed that:

a) a brittle material exhibits until fracture a linear elastic relation-ship; thus, during crack formation it is valid also the Hook Law, σ = E· ε, or σ = E·(x/r0), if referred to diagram in Fig.2.2.;

b) in the diagram f(x) in Fig.2.2, the variation of distance x to achieve to rupture (i.e. maximum σmax value) are so small that the relationship 𝜎𝜎(𝑑𝑑) = 𝜎𝜎𝑟𝑟𝑟𝑟𝑥𝑥 sin �2𝜋𝜋𝑥𝑥𝜆𝜆 � can be approximated by the

𝜎𝜎(𝑑𝑑) = 𝜎𝜎𝑟𝑟𝑟𝑟𝑥𝑥 2𝜋𝜋𝑥𝑥𝜆𝜆 , thus exploiting the relationship for small an-gles: sin α ∼ α;

By the two a) and b) assumption, Griffith wrote the relationship between the stress s and deformation e (i.e. x/r0) for small distance variation in brit-tle materials as: (2.4) 𝐸𝐸 ∙ 𝑥𝑥𝑟𝑟0 = 𝜎𝜎𝑟𝑟𝑟𝑟𝑥𝑥 2𝜋𝜋𝑥𝑥𝜆𝜆 Or, rewriting it: (2.5) 2𝜋𝜋𝑥𝑥𝜆𝜆 = 𝐸𝐸

𝜎𝜎𝑚𝑚𝑚𝑚𝑚𝑚∙𝑟𝑟0

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Furthermore, by the eq.2.3 he therefore calculated the total (elastic) energy per surface unit (Nm-1) necessary to brake link between two atoms; it is approximated by the area under the curve representing the force f(x) be-tween atoms (refer again to eq.2.1):

(2.6) 𝑈𝑈 = ∫ 𝜎𝜎𝑟𝑟𝑟𝑟𝑥𝑥 sin �2𝜋𝜋𝑥𝑥𝜆𝜆 � 𝑑𝑑𝑑𝑑 = 𝜆𝜆 2�0

𝜎𝜎𝑚𝑚𝑚𝑚𝑚𝑚𝜆𝜆𝜋𝜋 [𝑁𝑁𝑚𝑚−1]

Actually to form a crack inside material, two surfaces are created: a factor of 2 is therefore necessary to exploit the result of eq.2.6 to account the to-tal energy per surface unit required for creating two opposite faces for-mation by atoms debonding: (2.7) U = 2·γ = 𝜎𝜎𝑚𝑚𝑚𝑚𝑚𝑚𝜆𝜆

𝜋𝜋 [𝑁𝑁𝑚𝑚−1] , or ·γ = 𝜎𝜎𝑚𝑚𝑚𝑚𝑚𝑚𝜆𝜆2𝜋𝜋 [𝑁𝑁𝑚𝑚−1]

Finally Griffith wrote the 2.7 eliminating the parameter λ/2π considering the eq.2.5:

(2.8) 𝜎𝜎𝜕𝜕 = 𝜎𝜎𝑟𝑟𝑟𝑟𝑥𝑥 = �𝐸𝐸𝐸𝐸𝑟𝑟0

That represents the Griffith theoretical critical stress value for the fracture of brittle material (i.e. atoms debonding). What it was observed experimentally, however, was a great discrepancy between the theoretical value above calculated and the experimental meas-ured values. For example, The surface energy γ does not differ much for various brittle solid materials and approximately equals 1 Jm−2 (diamond is an exception with γ = 5 Jm−2.) The equilibrium distance a0 between at-oms, is also almost the same for solids (about 10−10 m). The table below lists values of theoretical strength σth and experimental fracture stress σb for some materials. It is clear that there is a large discrepancy between the two values : the theoretical strength is much too high.

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The reason for this deviation has been discovered by Griffith in 1921. In 1921 Griffith determined experimentally the fracture stress σb of glass fi-bers as a function of their diameter. For d > 20 μm the bulk strength of 170 MPa was found. However, σb approached the theoretical strength of 14,000 MPa in the limit of zero thickness (namely zero defect, considering such a low thickness material do ot contain defects). Griffith was aware in 1913 of work of Inglis5 who calculated stress concentrations at circular holes in plates, being much higher than the nominal stress. He concluded that in his glass fibers such stress concentrations probably occurred around defects and caused the discrepancy between theoretical and experimental fracture stress. He reasoned that for glass fibers with smaller diameters, there was less volume and less chance for a defect to exist in the specimen. In the limit of zero volume there would be no defect and the theoretical strength would be found experimentally. However, the Inglis solution poses a mathematical difficulty: in the limit of a perfectly sharp crack, the stresses approach infinity at the crack tip. This is obviously nonphysical (actually the material generally undergoes some local yielding to blunt the cracktip), and using such a result would predict that materials would have near zero strength: even for very small applied loads, the stresses near crack tips would become infinite, and the bonds there would rupture. Rather than fo-cusing on the crack-tip stresses directly, Griffith employed an energy-balance approach that has become one of the most famous developments in materials science. Griffith published his work in 1921 and his paper can be seen as the birth of Fracture Mechanics. The ingenious insight that strength was highly influenced by defects has lead to the shift of attention to the behavior of cracks and the formulation of crack growth criteria.

5 Ref. Inglis, C.E. Stresses in a plate due to the presence of cracks and sharp corners. Transactions of the Institute of Naval Architects, Vol 55, 1913, pp 219-241

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The contributing factor: the stress concentration The measured fracture strengths for most brittle materials are significantly lower than those predicted by theoretical calculations based on atomic bonding energies (refer to box “Griffith experience and the theoretical crit-ical stress for brittle materials ”) . While the theoretical cohesive strength of a brittle elastic solid can be es-timated to be in the range of E/10, where E is the modulus of elasticity, the true fracture strengths of real materials are much lower, normally 10 to as much as 1000 times below their theoretical values. This discrepancy is ex-plained by the presence of microscopic flaws or cracks that always exist under normal conditions at the surface and within the interior of a body of material. These flaws are a detriment to the fracture strength because an applied stress may be amplified or concentrated at the tip, the magnitude of this amplification depending on crack orientation and geometry. This phe-nomenon is demonstrated in Figure 9.8—a stress profile across a cross sec-tion containing an internal crack. As indicated by this profile, the magni-tude of this localized stress decreases with distance away from the crack tip. At positions far removed, the stress is just the nominal stress σ0, or the applied load divided by the specimen cross-sectional area (perpendicular to this load). Because of their ability to amplify an applied stress in their lo-cale, these flaws are sometimes called stress raisers (see also Fig.1.62).

Fig.2.2 - (a) The geometry of surface and internal cracks. (b) Schematic stress pro-file along the line X–X’ in (a), demonstrating stress amplification at crack tip posi-tions.

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To model and simplify discussion, it is assumed that a crack is similar to an hole through a plate and is oriented perpendicular to the applied stress, the maximum stress, σm, occurs at the crack tip and may be approximated by:

(eq.2.9) 𝜎𝜎𝑟𝑟 = 𝜎𝜎0 �1 + 2 �𝑟𝑟𝜚𝜚𝑡𝑡�1/2�

where σ0 is the magnitude of the nominal applied tensile stress, ρt is the radius ρt=b2/a is the radius tangential at the tip (Figure 2.1a), and a repre-sents the length of a surface crack, or half of the length of an internal crack. Note that for a round hole (a=b), the quantity [1+2a/b] reduces to 3, which is the same stress-concentration factor that was introduced in Fig.1.62. For a relatively long microcrack that has a small tip radius of curvature, the factor (a/ρt)1/2 may be very large, and it brings to a simplification:

(eq.2.10) 𝜎𝜎𝑟𝑟 ≅ 2 𝜎𝜎0 �𝑟𝑟𝜚𝜚𝑡𝑡�1/2

This will yield a value of σm that is many times the value of σ0. If we want to represent how much higher is the actual σm than nominal stress σ0, we can calculate the ratio between the former and latter values accordingly with:

(eq.2.11) 𝐾𝐾𝜕𝜕 = 𝜎𝜎𝑚𝑚𝜎𝜎0

= 2 �𝑟𝑟𝜚𝜚𝑡𝑡�1/2

The quantity Kt is denoted by engineers as the stress concentration factor Kt. because it represent the increased magnitude of actual stress at crack tip over the nominal stress far . However, the above solution poses a math-ematical difficulty to define the analytical solution for defining material behavior in presence of small and sharp cracks, thus the conditions real-ized by Griffith experience. In the limit of a perfectly sharp crack, the stresses as defined by eq.2.9 alternatively by eq.2.10 for approach infinity at the crack tip. This is obviously nonphysical. Rather than focusing on the crack-tip stresses directly, Griffith employed an energy-balance approach that has become one of the most famous de-velopments in materials science.

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The energy criterion for fast fracture If you blow up a balloon, energy is stored in it. There is the energy of the compressed gas in the balloon, and there is the elastic energy stored in the rubber membrane itself. As you increase the pressure, the total amount of elastic energy in the system increases. If we then introduce a flaw into the system, by poking a pin into the inflated balloon, the balloon will explode, and all this energy will be released. The membrane fails by fast fracture, even though well below its yield strength. But if we introduce a flaw of the same dimensions into a system with less energy in it, as when we poke our pin into a partially inflated balloon, the flaw is stable and fast fracture does not occur. Finally, if we blow up the punctured balloon progressively, we eventually reach a pressure at which it suddenly bursts. In other words, we have arrived at a critical balloon pressure at which our pin-sized flaw is just unstable, and fast fracture just occurs. Why is this? To make the flaw grow, say by 1 mm, we have to tear the rubber to create 1 mm of new crack surface, and this consumes energy. We can increase the energy in the system by blowing the balloon up a bit more. The crack or flaw will remain stable until a critical pressure for fast fracture of a pressure vessel containing a crack or flaw of a given size. But how do we calculate this critical stress? We can write down an energy balance which must be met if the crack is to advance, and fast fracture is to occur. Suppose a crack of length a in a material of thickness t advances by da, then we require that: work done by loads is higher than change of elastic energy plus the energy absorbed at the crack tip, i.e.: (eq.2.12) 𝛿𝛿𝛿𝛿 ≥ 𝛿𝛿𝑈𝑈𝑒𝑒𝑒𝑒 + 𝐺𝐺𝜕𝜕 ∙ 𝑡𝑡 ∙ 𝛿𝛿𝑐𝑐 Where: 𝛿𝛿𝑈𝑈𝑒𝑒𝑒𝑒 = elastic energy 𝐺𝐺𝜕𝜕 = the energy absorbed per unit area of crack 𝑡𝑡𝛿𝛿𝑐𝑐 = the is the crack area formed. Now, consider a cracked plate of material loaded so that the displacements at the boundary of the plate are fixed. This is a common mode of loading a material - it occurs frequently in welds between large pieces of steel, for example - and is one which allows us to calculate 𝛿𝛿𝑈𝑈𝑒𝑒𝑒𝑒 quite easily.

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Fig.2.3 - Fast fracture in a fixed plate.

Since the ends of plate cannot move, the forces acting on them can do no work, and δW = 0. Accordingly, our energy formula in eq.2.12 gives, for the onset of fast fracture (i.e. sudden crack grow in plate): (eq.2.13) 𝛿𝛿𝑈𝑈𝑒𝑒𝑒𝑒 = − 𝐺𝐺𝜕𝜕 ∙ 𝑡𝑡 ∙ 𝛿𝛿𝑐𝑐 Now, as the crack grows into the plate, it allows the material of the plate near the crack to relax and loses elastic energy. We can estimate 𝛿𝛿𝑈𝑈𝑒𝑒𝑒𝑒 in the way shown in Fig. 2.4.

Fig.2.4 - The release of stored strain energy as a crack grows. The shaded area is the relaxed area once crack advances from a to a+δa. Each unit cube is has strain energy:

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(eq.2.13) Uel = ½σε = σ2/2E. If we now introduce a crack of length a, we can consider that the material in the dotted region relaxes (to zero stress) so as to lose all its strain ener-gy. The energy change for each surface (two are the surfaces formed) is:

(eq.2.14) 𝛿𝛿𝑈𝑈𝑒𝑒𝑒𝑒 = 𝑑𝑑𝑈𝑈𝑒𝑒𝑒𝑒𝑑𝑑𝑟𝑟 𝑑𝑑𝑐𝑐 = − 𝜎𝜎2

2𝐸𝐸 2𝜋𝜋𝑟𝑟𝜕𝜕2 𝛿𝛿𝑐𝑐

The critical condition of eq.2.13 therefore becomes: (eq.2.15) 𝐺𝐺𝜕𝜕 ∙ 𝑡𝑡 ∙ 𝛿𝛿𝑐𝑐 = 𝜎𝜎2 𝜋𝜋𝑟𝑟𝜕𝜕2𝐸𝐸 𝛿𝛿𝑐𝑐 ⟹ 𝐺𝐺𝜕𝜕 = 𝜎𝜎2 𝜋𝜋𝑟𝑟

2𝐸𝐸 And it represents the onset of fast fracture. Since two surfaces are formed, the onset value must be corrected by exact-ly a factor of 2. Thus, correctly, we have: (eq.2.16) 𝐺𝐺𝜕𝜕 = 𝜎𝜎2 𝜋𝜋𝑟𝑟𝐸𝐸 The eq.2.16 is also well known in the form: (eq.2.17) 𝜎𝜎√𝜋𝜋𝑐𝑐 = �𝐸𝐸𝐺𝐺𝜕𝜕 The left-hand side of our equation says that fast fracture will occur when, in a material subjected to a stress σ, a crack reaches some critical size a, or, alternatively, when material containing cracks of size a is subjected to some critical stress σ. The right-hand side of our result depends on material properties only; E is obviously a material constant, and Gc the energy required to generate unit area of crack, again must depend only on the basic properties of our mate-rial. Thus, the important point about the equation is that: the critical com-bination of stress and crack length at which fast fracture commences is a material constant. The term 𝜎𝜎√𝜋𝜋𝑐𝑐 is usually abbreviated to a single symbol, K, having units MPa √m; it is called, the stress intensity factor. Fast fracture therefore oc-curs when: (eq.2.18) 𝐾𝐾 = 𝐾𝐾𝜕𝜕

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Where 𝐾𝐾𝜕𝜕 = �𝐸𝐸𝐺𝐺𝜕𝜕 is the critical stress intensity factor, more usually called the fracture toughness6. Micromechanisms of fast fracture As stated above, if a material contains a crack, and is sufficiently stressed, the crack becomes unstable and grows - at up to the speed of sound in the material - to cause catastrophically rapid fracture, or fast fracture at a stress less than the yield stress. We are also aware now to quantify this phenom-enon and obtained a relationship for the onset of fast fracture by the eq.2.17 or equivalent 2.18. Some materials, like glass, have low G, and K, and can crack easily with very short cracks at low stress. Ductile metals have high G, and K, and are very resistant to fast-fracture, so that very long cracks are required to fast fracture. How can we explain these peculiarities? Mechanisms of crack propagation by ductile tearing Whenever a crack is present in a material, we already known the stress close to the crack is greater than the average stress applied to the piece of material, as it is shown by the eq.2.9 (here below reported for the sake of readability):

(eq.2.9bis) 𝜎𝜎𝑟𝑟 = 𝜎𝜎0 �1 + 2�𝑟𝑟𝜚𝜚𝑡𝑡

� The eq.2.9bis states that the stress at crack tip increase theoretically at in-finite value as the crack tip radius �t (see scheme in Fig.2.2) approximates zero value, as actually happens in case of sharp crack. Furthermore if we are interested to the mathematical relation of the local stress versus the distance r ahead of a sharp crack in an elastic material (see the scheme of Fig.2.5), we find that the closer one approaches to the tip of the crack, the higher the local stress becomes accordingly with the eq.2.19:

6 Strictly speaking, this result is valid only for a crack through the center of a wide plate of material. In practice, the problems we encounter seldom satisfy this geometry, and a numer-ical correction to 𝜎𝜎√𝜋𝜋𝑐𝑐 required to get the strain energy calculation right. In general we write: 𝐾𝐾 = 𝑌𝑌𝜎𝜎√𝜋𝜋𝑐𝑐 where Y is the numerical correction factor (Values of Y can be found from tables in standard reference books).

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(eq.2.19) 𝜎𝜎𝑒𝑒𝑙𝑙𝜕𝜕𝑟𝑟𝑒𝑒 = 𝜎𝜎 �1 + �𝑟𝑟2𝑟𝑟 �

Notice that the mathematical expression here above representing the local stress versus distance from crack tip is similar to the mathematical expres-sion of the stress at crack tip as function of the crack tip radius and crack length a (i.e. eq.2.9bis); on the other and they shall not be confused, be-cause the former may have non-infinite solutions as the crack tip radius approaches to a non zero value7, while the latter we read in eq.2.19 has always infinite values as we want to calculate the stress at crack tip. This fact means that the expression cannot represent what in reality happens in regions close to crack tip, namely r equal to zero. This discrepancy with reality is well solved whether we superimpose to stress curve in eq.2.19 the plastic behavior of ductile material. This implies that, as we consider a ductile material, until at some distance from the crack tip we call ry the theoretical stress calculated by the eq.2.19 cannot exceed the yield stress σy of the material: in fact in this area plastic flow occurs and stress here are fully relaxed, as it is shown in Fig.2.5a.

(a) (b)

Fig.2.5 - Crack propagation by ductile tearing: a) forming of plastic zone; b) ad-vancement of crack for ductile tearing occurring in plastic zone.

7 Notice we already verified that for crack tip radius equal to a in the scheme of Fig.2.2, the value is 3, namely the value typical for a circular hole in a large plate.

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This distance ry can be easily calculated by setting σlocal = σy in eq. 2.19, thus we obtain the following result:

(eq.2.20) 𝜎𝜎𝑦𝑦 = 𝜎𝜎 �1 + � 𝑟𝑟2𝑟𝑟𝑦𝑦

� Assuming ry to be small compared to the crack length, a, the result can be simplified by: (eq.2.21) 𝑐𝑐𝑦𝑦 = 𝜎𝜎2𝑟𝑟

2𝜎𝜎𝑦𝑦2

and by the following eq.2.22 where the fracture toughness K = σ√πa has been included: (eq.2.22) 𝑐𝑐𝑦𝑦 = 𝐾𝐾2

2𝜋𝜋𝜎𝜎𝑦𝑦2

The crack propagates by fast fracture mode when K is equal to Kc; the width of the plastic zone, ry, is then given by eq.2.22 with K replaced by Kc. And now, note that the zone of plasticity shrinks rapidly as σy increases: cracks in soft metals have a large plastic zone; cracks in hard ceramics have a small zone, or none at all. Coming back to ductile metals, most metals contain tiny inclusions (or particles). Within the plastic zone, plas-tic flow takes place around these inclusions, leading to elongated cavities (fracture by microdimple, see the scheme in Fig. 2.5b). As plastic flow progresses, these cavities link up, and the crack advances by means of this ductile tearing. The plastic flow at the crack tip naturally modifies original sharp crack (see Fig.2.5a) into a blunt crack (Fig.2.5b): the local stress at crack tip therefore decrease to values that are just sufficient to keep on plastically deforming the work-hardened material there, as the scheme in Fig.2.5b shows. Moreover, the important thing about crack growth by ductile tearing is that it consumes a lot of energy by plastic flow: the bigger the plastic zone, the more energy is absorbed. High energy absorption means that G, is high, and so is K,. This is why ductile metals are so tough.

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Mechanisms of crack propagation, 2: cleavage If you now examine the fracture surface of something like a ceramic, or a glass, you see a very different aspect. Instead of a very rough surface, you see a rather flat surface as produced by the cleaveage fracture mode (refer to Chapter 1) that indicates very little or usually no plastic deformation oc-curred. How do cracks in brittle materials spread? In case of brittle materials, the calculated local stress ahead of the crack tip as it is given by the eq.2.19 can clearly approach very high values close to the crack tip: this fact provides that blunting of a sharp crack tip does not occur. Due to very high yield strengths σy, very little plastic deformation takes place at crack tips in these materials, as it is easily demonstrated by applying the eq.2.21, here shown again for convenience: (eq.2.21) 𝑐𝑐𝑦𝑦 = 𝜎𝜎2𝑟𝑟

2𝜎𝜎𝑦𝑦2

The local stress at the crack tip is still in excess of the ideal strength and is thus large enough to literally break apart the interatomic bonds there; the crack then spreads between a pair of atomic planes giving rise to an atomi-cally flat surface by cleavage, as shown by the scheme in Fig.2.6. The en-ergy required simply to break the interatomic bonds at crack sharp tip is much less than that absorbed by ductile tearing in a tough material, and this is why materials like ceramics and glasses are so brittle. It is also why some steels become brittle and fail like glass, at low temperatures. At low temperatures in fact metals having b.c.c. and h.c.p. structures become brit-tle and fail by cleavage, even though they may be tough at or above room temperature. Only those metals with an f.c.c. structure (like copper, lead, aluminium, austenitic stainless steel) remain unaffected by temperature in this way. In metals not having an f.c.c. structure, the motion of dislocations is assisted by the thermal agitation of the atoms. At lower temperatures this thermal agitation is less, and the dislocations cannot move as easily as they can at room temperature in response to a stress. The result is that the yield strength rises, and the plastic zone at the crack tip shrinks until it be-comes so small that the fracture mechanism changes from ductile tearing to cleavage. This effect is called the ductile-to-brittle transition DBTT; for steels it can be as high as ∼0°C, depending mainly on the carbon content of the steel); steel structures like ships, bridges and oil rigs are much more likely to fail in winter than in summer.

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Ductile to Brittle Transition Temperature (DBTT) The ductile to brittle transition temperature is the temperature at which the failure mode of a material changes from ductile to brittle fracture. This temperature may be defined by the average energy between the ductile and brittle regions, at some specific absorbed energy, or by some characteristic fracture appearance. A material subjected to an impact blow during service should have a transition temperature below the temperature of the materi-al’s surroundings.

(a)

(b)

Fig.2.6 – a) Temperature dependence of the Charpy V-notch impact energy (curve A) and percent shear fracture (curve B) for an A283 steel; b) Photograph of frac-ture surfaces of Charpy V-notch specimens tested at indicated temperatures (in °C). Not all materials have a distinct transition temperature (Figure 2.7). BCC metals have transition temperatures that increases for steesl as the carbon content increases (see Fig.2.8) , but most FCC metals do not. FCC metals have high absorbed energies, with the energy decreasing gradually and,

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sometimes, even increasing as the temperature decreases. The effect of this transition in steel may have contributed to the failure of the Titanic as a re-cent discoveries in metallurgical analysis conducted onto steel constituting the rivets of the sunk ship (Fig.2.9).

Fig.2.7 – Schematic curves for the three general types of impact energy–versus–temperature behavior.

Fig.2.8 – Influence of carbon content on the Charpy V-notch energy–versus– Temperature behavior for steel.

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(a) (b)

Fig. 2.9 - a) The Titanic in the shipyard during her construction. Note the hull plates, fastened on all sides to the ship's main structure by thousands of rivets; b) a layout of the watertight compartments and the damage from the collision. The thick black lines below the waterline indicate the approximate locations of the damage to the hull.

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Fatigue failure Fatigue is a form of failure that occurs in structures subjected to dynamic and fluctuating stresses (e.g., bridges, aircraft, and machine components). Under these circumstances it is possible for failure to occur at a stress level considerably lower than the tensile or yield strength for a static load. The term fatigue is used because this type of failure normally occurs after a lengthy period of repeated stress or strain cycling. Fatigue is important in-asmuch as it is the single largest cause of failure in metals, estimated to comprise approximately 90% of all metallic failures. Furthermore, fatigue is catastrophic and insidious, occurring very suddenly and without warn-ing. Fatigue failure is brittlelike at naked eye observation even in normally ductile metals, in that there is very little, if any, gross plastic deformation associated with failure. The first known catastrophic fatigue failure, involving major loss of life, was the Versailles (France) railway accident in 1842 (Fig.2.10). The train was 17 carriages hauled by two steam engines. The front axle of the leading, four wheeled engine failed due to metal fatigue and the body of the leading engine fell to the ground. Fatigue testing of specially designed laboratory specimens started in the 1850s. It is generally accepted that the first fatigue tests on laboratory specimens were carried out by Wohler. In 1870 Wohler published a final report. This is cited in Schultz (1996) and contains the conclusions known as Wöhler’s8 laws:

• Materials can be induced to fail by many repetitions of stress, all of which are lower than the static strength;

• The stress amplitudes are decisive for the destruction of the cohe-sion of the material;

• The maximum stress is of influence only in so far as the higher it is, the lower are the stress amplitudes which lead to failure.

8 August Wöhler, chief superintendent of rolling stock on the Lower Silesia-Brandenberg Railroad, is known for his investigation on the causes of fracture in railroad axles that led to definition of bending rotating fatigue tests, the work that is basis of experimental tests today conducted onto materials for the definition of the S-N curve, also known as Wohler Diagram, in the next described.

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(a)

(b)

Fig.2.10 –a) Paint showing Versailles (France) railway accident in 1842; b) de-scription of rupture occurred on train axle.

Investigation on phenomena (early 1900s) led to understand fatigue fail-ures may because of the application of fluctuating stresses that are much lower than the stress required to cause failure during a single application of stress. A test apparatus was therefore designed to to duplicate as nearly as possible the service stress conditions, like stress level, time frequency,

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stress pattern, etc (Fig.2.11a). A schematic diagram of a rotating-bending test apparatus today frequently used is shown in Figure 2.11b (the com-pression and tensile stresses are imposed on the specimen as it is simulta-neously bent and rotated).

(a)

(b)

Fig.2.11 – a) Scheme of possible cyclic load for test specimens; from left to right and up to down: axial test, rotating bending with varying bending stress; rotating bending with constant bending stress; b) schematic diagram of fatigue-testing ap-paratus for making rotating-bending tests. A series of tests are commenced by subjecting a specimen to the stress cy-cling at a relatively large maximum stress amplitude (σmax) below the

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tensile strength and yield strength (see exemplifying scheme in Fig.2.12). The number of cycles to failure is therefore counted and this this procedure is repeated on other specimens at progressively decreasing maximum stress amplitudes. Data are plotted as stress S versus the logarithm of the number N of cycles to failure for each of the specimens. The values of S are normally taken as stress amplitudes σa (refer to scheme Fig.2.12); on occasion, σmax or σmin values may be used (refer to scheme Fig.2.12). Two distinct types of S–N behavior are observed, which are represented schematically in Fig. 2.13. As these plots indicate, the higher the magni-tude of the stress, the smaller the number of cycles the material is capable of sustaining before failure. For some ferrous (iron base) and titanium al-loys, the S–N curve (Fig.2.13a) becomes horizontal at higher N values; or there is a limiting stress level, called the fatigue limit (also sometimes the endurance limit), below which fatigue failure will not occur. This fatigue limit represents the largest value of fluctuating stress that will not cause failure for essentially an infinite number of cycles.

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Fig.2.12 – Variation of stress with time that accounts for fatigue failures. (a) Re-versed stress cycle, in which the stress alternates from a maximum tensile stress (σµαξ) to a maximum compressive stress (σmin) of equal magnitude. (b) Repeat-ed stress cycle, in which maximum and minimum stresses are asymmetrical rela-tive to the zerostress level; mean stress σm, range of stress σr, and stress ampli-tude σa are indicated. (c) Random stress cycle.

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Fig.2.13 – Stress amplitude (S) versus logarithm of the number of cycles to fa-tigue failure (N) for (a) a material that displays a fatigue limit and (b) a material that does not display a fatigue limit. For many steels, fatigue limits range between 35% and 60% of the tensile strength. Most nonferrous alloys (e.g., aluminum, copper, magnesium) do not have a fatigue limit, in that the S–N curve continues its downward trend at increasingly greater N values (Fig.2.13b).Thus, fatigue will ulti-mately occur regardless of the magnitude of the stress. For these materials,

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the fatigue response is specified as fatigue strength, which is defined as the stress level at which failure will occur for some specified number of cycles (e.g., 107 cycles). The determination of fatigue strength is also demonstrat-ed in Fig.2.13b. Another important parameter that characterizes a materi-al’s fatigue behavior is fatigue life Nf. It is the number of cycles to cause failure at a specified stress level, as taken from the S–N plot (Figure 2.13b). Unfortunately, there always exists considerable scatter in fatigue data—that is, a variation in the measured N value for a number of specimens test-ed at the same stress level. This variation may lead to significant design uncertainties when fatigue life and/or fatigue limit (or strength) are being considered. The scatter in results is a consequence of the fatigue sensitivity to a number of test and material parameters that are impossible to control precisely. These parameters include specimen fabrication and surface preparation, metallurgical variables, specimen alignment in the apparatus, mean stress, and test frequency. Fatigue S–N curves similar to those shown in Figure 2.14 represent “best fit” curves that have been drawn through av-erage-value data points. It is a little unsettling to realize that approximately one-half of the specimens tested actually failed at stress levels lying nearly 25% below the curve (as determined on the basis of statistical treatments).

Fig.2.14 – Fatigue S–N probability of failure curves for a 7075-T6 aluminum alloy; P denotes the probability of failure.

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The three stages of fatigue failure Fatigue failures typically occur in three stages, as illustrated by the simpli-fied scheme in Fig.2.15:

- STAGE I - Fatigue Crack Nucleation; - STAGE II - Fatigue Crack Growth; - STAGE III - Fast Fracture r catastrophic rupture.

Fig.2.15 - Schematic representation of a fatigue fracture surface in a steel shaft, showing the initiation region, the propagation of the fatigue crack (with beach markings), and catastrophic rupture when the crack length exceeds a critical value at the applied stress. Stage I – Fatigue crack nucleation First, a tiny crack initiates or nucleates often at a time well after loading begins. Normally, nucleation sites are located at or near the surface, where the stress is at a maximum, and include surface defects such as scratches or pits, sharp corners (see example in Fig.2.16) due to poor design or manu-facture, inclusions, grain boundaries, or dislocation concentrations that lead to high local stresses ahead the defects (refer to mechanism described in the previous section “Mechanisms of crack propagation by ductile tear-ing”). In the absence of a surface defect, crack initiation will eventually occur due to the formation of persistent slip bands (PSBs), as illustrated by the scheme in Fig.2.17b.

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Fig.2.16 - Fatigue crack nucleation at notched region in the sharp corners of com-ponent.

(a)

(b)

Fig.2.17 – a) Schematic view of early stage of crack initiation; b) development of initiation site onto defect-free surface by extrusions and intrusions phenomena.

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STAGE II - Fatigue Crack Growth. Next, the crack gradually propagates as the load continues to cycle. Final-ly, a sudden fracture of the material occurs when the remaining cross-section of the material is too small to support the applied load. The fracture surface—particularly near the origin—is typically smooth. The surface be-comes rougher as the original crack increases in size and may be fibrous during final crack propagation. Microscopic and macroscopic examina-tions reveal a fracture surface including a beach mark pattern and stria-tions, respectively observable by naked-eye macroscopic inspection (see Fig.2.18a and Fig.2.18; also represented in the scheme in Fig.2.19) and by microscopic fractographic analysis conducted at Scanning Electron Micro-scope (see Fig.2.18b).

Fig.2.18 - Fatigue fracture surface: (a) at low magnifications, the beach mark pat-tern indicates fatigue as the fracture mechanism. The arrows show the direction of growth of the crack front with the origin at the bottom of the photograph; b) at high magnification by Scanning Electron Microscope.

Fig.2.19- Fatigue crack growth in the origin of crack initiation in a high-strength steel: notice beach marks observable at the naked eye.

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Specifically, beach or clamshell marks as shown are normally formed when the load is changed during service or when the loading is intermit-tent, perhaps permitting time for oxidation inside the crack. Striations, which are on a much finer scale, show the position of the crack tip after each cycle as represented by the scheme of crack propagation in-side ductile metal in Fig.2.20. This is in accordance with the microme-chanics involving the crack opening and its propagation, as it has been de-scribed in the section “Mechanisms of crack propagation by ductile tearing”. Each marks always suggest a fatigue failure, but—unfortunately—the absence of beach marks does not rule out fatigue fail-ure.

(a)

(b)

Fig.2.20 – a) Schematic view of crack propagation stage; b) development of stria-tions due to mechanisms of ductile tearing driven by plastic radius formation at crack tip.

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Cracks grow from an initial size, a0, to a critical size, ac, corresponding to failure as a function of the number of load cycles (Fig. 2.21). The crack growth rate, da/dn, can be determined from the slope of the curve. Initial-ly, the crack growth rate is slow but increases with increasing crack length. Of course, the crack growth rate is also higher for higher applied stresses.

Fig.2.21 – Crack length as a function of cycles. In the fracture mechanics approach we have already learnt a crack can grow because of the role played by the stress-intensity parameter, K (refer to previous section ““Mechanisms of crack propagation by ductile tear-ing”) is determined by: (eq.2.22) 𝐾𝐾 = 𝑌𝑌𝜎𝜎√𝜋𝜋𝑐𝑐 Stated the above expression, we also know that specimens containing a sharp crack like that shown in Fig. 2.22 and subjected to cyclic loading at constant nominal stress σ, cycle by cycle increase the K value at crack tip, meanwhile the condition for plastic tearing are maintained (see Fig.2.23).

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Fig.2.22 – Fatigue-crack growth in pre-cracked components.

Fig.2.23 – Fatigue cracks grow mechanisms in tough materials.

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More specifically, we observe that during a cycle the K value will cyclical-ly vary, due to σ variation ranging from σmax to σmin (refer to Fig.2.22). Thus, over one cycle, the expression for intensity factor can be represented by: (eq.2.22) 𝐾𝐾𝑟𝑟𝑟𝑟𝑥𝑥 − 𝐾𝐾𝑟𝑟𝑚𝑚𝑛𝑛 = ∆𝐾𝐾 = ∆𝜎𝜎√𝜋𝜋𝑐𝑐 The cyclic stress intensity ∆K increases with time (at constant load) be-cause the crack grows in tension. It is found that the crack growth per cy-cle, da/dN, increases with ∆K in the way shown in Fig. 2.24.

Fig.2.24 – Fatigue crack-growth rates for pre-cracked material.

Particularly, in the regime for the crack growth, the crack grows at a con-stant rate, da/dn, accordingly with the mathematical expression: (eq.2.23) 𝑑𝑑𝑟𝑟𝑑𝑑𝑑𝑑 = 𝑑𝑑 ∙ Δ𝐾𝐾𝑟𝑟

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where C and m are material constants. The relationship in eq.2.23 is known as Paris Law or Paris equation and it is experimentally plotted for pre-cracked test specimen of various metals as illustrated in Fig.2.24. Obviously, if a0 (the initial crack length) is given, and the final crack length af at which the crack becomes unstable and runs rapidly is known or can be calculated, then the safe number of cycles can be estimated by inte-grating the equation: (eq.2.24) Substituting the ∆K with expression in eq.2.22, it is possible to write: (eq.2.25) That is valid for alternate stress (for average stress σm different from zero value, the Paris Law and the eq.2.25 should be corrected by further fac-tors). STAGE III - Fast Fracture A subcritical crack of a length a higher than non-propagating threshold (re-fer to Fig.2.24) will eventually grow to a length at which the metal imme-diately fails, that is (refer to previous section on fast fracture): (eq.2.18bis) 𝐾𝐾 = 𝐾𝐾𝜕𝜕 Or: (eq.2.22bis) 𝐾𝐾 = 𝑌𝑌𝜎𝜎𝑟𝑟𝑟𝑟𝑥𝑥√𝜋𝜋𝑐𝑐 → 𝐾𝐾𝜕𝜕 That is, solving for ac: (eq.2.26) 𝑐𝑐𝜕𝜕 = 𝐾𝐾𝑐𝑐2

𝜋𝜋𝑌𝑌2𝜎𝜎𝑚𝑚𝑚𝑚𝑚𝑚2

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Note that even if a component contains a detectable crack, it can remain in service, provided that it is periodically inspected. This philosophy forms the basis for what is known as the damage-tolerance design approach. Finally, in region III, the crack growth rate accelerates, since the fracture toughness of the material is approached, and there is a local tensile over-load failure. Contact fatigue9 Damaging phenomena developing in several mechanical component, such as cams, gears, and bearings, are related to surface contact. Substantial dif-ferences exist in various failure modes, the appearance of worn surface is different, and the type of contact interaction changes (as for pure rolling, rolling with sliding, linear sliding). In general, wear modes are basically classified into four categories, such as: fatigue wear, adhesive wear, abra-sion wear, and corrosion wear. Most commonly, fatigue wear is such fail-ure mode that occurs, for example, in a lubricated contact realized between two parts engaged in gearing. Since in many lubricated contacts surface adhesion is prevented and adhesive wear ideally avoided, a certain amount of wear is caused by surface asperities interaction, as discussed in the fol-lowing. In literature, contact fatigue failure (also called surface fatigue) is considered a subcategory of fatigue wear, and it includes all those fatigue surface damaging caused by a repeated rolling contact. In contact fatigue, cracks are promoted by reversal stress field generated below the contact area formed when two elastic bodies are pressed together and they roll. Depending on various operative conditions, either pure rolling or slid-ing rolling can be realized. In any case, contact fatigue damage consists in craters forming (namely, pits) on surface. In literature, it is common to distinguish in shallow (less than 10 µm) or deeper craters (from 10 µ,m to 200 µm); in the first case, this type of surface damage is called pitting, in the second case spalling. According to these definitions, it must be highlighted that pitting and spalling should be distinguished only in terms of the average dimensions of the craters, that is, they should be dis-tinguished on the basis of the surface damage appearance. Since it is not easy to clearly distinguish whether surface ruptures result from either in-creasing damage level (of a single rupture mode) or pitting changing into spalling, these two terms are frequently used indiscriminately. With re-

9 Main reference: G.Stachowiak and A.W. Batchelor, Engineering Tribology, Third Edition, Elsevier, 2005

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gards to possible evolving of a failure mode, small surface cavities often may enlarge because cracks branch and they evolve more deeply beneath the surface. The result is the formation of larger craters, i.e., a spall results from small pit degeneration. In this case, to distinguish whether spalling was induced by pitting degeneration, this failure mode is better called pro-gressive pitting (also called destructive pitting). On the other hand, many authors prefer to classify spalling and pitting ac-cording to Tallian, distinguishing them with regards to either the surface or the subsurface origin of rupture. According to this definition, spalling is better identified as damage caused by fatigue crack started in subsurface layers and then propagated. While the propagated cracks re-emerge, mate-rial portions detach inducing the spall formation; in a similar way, pitting is associated to most superficial damaging, which originates at the top sur-face.

Figure 2.25 –Voids created on top surface on gear tooth by cyclic loading (spall-ing rupture mechanisms).

Figure 2.26 –Subsurface crack propagation mechanism below hardened layer of a tooth gear: once subsurface crack emerges, entire pieces of top layer surface are broken away.

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Theories on failure mechanisms involved in fatigue contact: the Hertzian theory of contact between elastic bodies Uncertain identification of pitting or spalling is prevalently due to such in-sufficient assumptions to clarify damage mechanisms by the Hertzian scheme of contact on a macroscale. When two solid surfaces are loaded together there will always be some distortion of each of them. Deformations may be purely elastic or may involve some additional plas-tic, and so permanent, changes in shape. Such deflections and modifica-tions in the surface profiles of the components can be viewed at two differ-ent scales, either at macroscopic and microscopic scales. Hertzian stress status in no sliding static contact Consider two bodies in contact under a static load and with no movement relative to each other. Since there is no movement between the bodies, shearing does not occur at the interface and therefore the shear stress act-ing is equal to zero. According to the principles of solid mechanics, the planes on which the shear stress is zero are called the principal planes. Thus the interface between two bodies in a static contact is a principal plane on which a principal stress ‘σ1’ is the only stress acting. It is also known from solid mechanics that the maximum shear stress occurs at 45° to the principal plane, as shown in Fig. 2.27.

Figure 2.27 – Stress status in a static contact; σ1, σ 3 are the principal stresses, p is the hydrostatic pressure, k is the shear yield stress of the material.

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If the contact load is sufficiently high then the maximum shear stress will exceed the resolved shear stress in polycrystalline material, i.e. τmax > 1/3 σy10, and plastic deformation takes place. Material will then deform (slip) along the line of action of maximum shear stress. The maximum shear stress ‘τmax’, also referred to in the literature as ‘τ45°’ since it acts on planes inclined at 45° to the interface (in static contacts), is given by: (eq.2.27) 𝜏𝜏𝑟𝑟𝑟𝑟𝑥𝑥 = 𝜏𝜏45 = �𝜎𝜎1−𝜎𝜎32 � The stresses ‘σx’, ‘σz’ and ‘τ’ vary with depth below the interface. An ex-ample of the stress field beneath the surface of two parallel cylinders in static contact is shown in Fig. 2.28.

Figure 2.28 –Subsurface stress field for two cylinders in static contact; pmax is the maximum contact pressure, b is the half width of the contact rectangle.

10 Refer to Chapter 1, section “Slip in polycrystalline crystal”; in polycrystalline crystal e bcc and fcc materials, the Taylor factor (namely the factor that correlates yield strength to resolved shear strength) is about 3.06. Converting shear strength to an equivalent uniaxial yield strength, the Taylor factor of 3.06 is the most appropriate parameter. Note that values of 1.73 and 2.0 are frequently used, but they are result of a misunderstanding about the proper application of the von Mises and Tresca yield criteria.

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Hertzian stress status in sliding contact The most critical influence on subsurface stress fields, however, is exerted by sliding. To illustrate the effect of sliding on the stress distribution, con-sider two bodies in contact with some sliding occurring between them. Frictional forces are the inevitable result of sliding and cause a shear stress to act along the interface, as shown in Figure 2.29. The frictional stress acting at the interface is balanced by rotating the planes of principal stress-es through an angle φ from their original positions when frictional forces are absent (the magnitude of the angle φ depends on the frictional stress μq acting at the interface). The variation with depth below the interface of the principal shear stress ‘τmax’ for a cylinder and the plane on which it slides is shown in Figure 2.30. The contours show the principal shear stress due to the combined normal pressure and tangential stress for a coefficient of friction μ = 0.2. It can clearly be seen that as friction force increases, the maximum shear stress moves towards the interface. Thus there is a gradual increase in shear stress acting at the interface as the friction force increas-es. This phenomenon is very important in crack formation and the subse-quent surface failure and will be discussed later.

Figure 2.29 - Stresses in a contact with sliding; σ1, σ3 are the principal stresses, p is the hydrostatic pressure, k is the shear yield stress of the material, μ is the coef-ficient of friction, q is the stress normal to the interface or compressive stress due to load, φ is the angle by which the planes of principal stress are rotated from the corresponding zero friction positions to balance the frictional stress.

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Figure 2.30- Subsurface stress field for a cylinder sliding on a plane; pmax is the maximum contact pressure, b is the half width of the contact rectangle.

Box – Contact Between Two Parallel Cylinders The configuration of two elastic bodies with convex surfaces in contact was originally considered by Hertz in 1881 and is shown in Figure 2.31 and it is based on the following assumptions:

i. The surfaces are continuous, smooth, nonconforming and frictionless; ii. The size of the contact area is small compared to the size of the bod-

ies, i.e., the strains associated with the deformations are small; iii. Each solid can be considered to behave as an elastic half-space in the

vicinity of the contact zone; iv. The gap h between the undeformed surfaces can be approximated by

an expression of the form: h = Ax2+By2;

Figure 2.31 - Geometry of two Hertzian elastic bodies with convex surfaces in

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contact. The reduced radius of curvature for this case is defined by Hertzian theory as:

The contact area between two parallel cylinders is circumscribed by a narrow rectangle. The geometry of parallel cylinders in contact is shown in Figure 2.32 and the formulae for the main contact parameters are summarized in Ta-ble 2.1.

Figure 2.32 - Geometry of the contact between two parallel cylinders.

Table 2.1 - Formulae for contact parameters between two parallel cylinders.

Where:

– b is the half width of the contact rectangle [m]; – l is the half length of the contact rectangle [m]; – E' is the reduced Young's modulus is defined as:

– R' is the reduced radius of curvature for the two parallel cylinders in

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contact [m]. For the cylinders: Rax = RA, Ray = ∞, Rbx = RB, Rby = ∞ where ‘RA’ and ‘RB’ are the radii of the cylinders ‘A’ and ‘B’ re-spectively:

where:

The rest of the parameters are as defined for Table 2.1. EXAMPLE Find the contact parameters for two parallel steel rollers. The normal force is W = 5 [N], radii of the rollers are RA = 10 × 10-3 [m] and RB = 15 × 10-3 [m], Young's modulus for both rollers is E = 2.1 × 1011 [Pa] and the Poisson's ratio is ν = 0.3. The length of both rollers is 2l = 10 × 10-3 [m]. Reduced Radius of Curvature Since the radii of the cylinders are Rax = RA = 10 × 10-3 [m], Ray= ∞ and Rbx = RB = 15 × 10-3 [m], Rby= ∞ respectively, the reduced radii of curva-ture in the ‘x’ and ‘y’ directions are:

Since 1/Rx > 1/Ry condition is satisfied, the reduced radius of curvature is:

Reduced Young's Modulus:

Contact Area Dimensions:

Maximum and Average Contact Pressures:

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Maximum Deflection:

Maximum Shear Stress:

Depth at which Maximum Shear Stress Occurs:

Hertzian stress status in sliding and lubricated contacts by elasto-hydrodynamic film In a lubricated rolling contact, the contact stresses are affected by the lu-bricating film separating the opposing surfaces and the level of rolling and sliding. The hydrodynamic film (for more details, see the box “Basic principles of hydrodynamic lubrication” in the next) generated under these conditions and the relative movement of the surfaces cause significant changes to the original static stress distribution as shown in the scheme of Fig.2.33.

Figure 2.33 - Hydrodynamic pressure distribution in an elasto-hydrodynamic con-tact; hc is the central film thickness, h0 is the minimum film thickness.

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A subsequent modification of the Hertzian stress field in EHL lubricated conditions, is below described.

Traction and elasto-hydrodynamic lubrication (EHL) condition Traction is the application of frictional forces to allow the transmission of mechanical energy rather than its dissipation. The most common example of the distinction between traction and friction is the contact between a wheel and a road. When the wheel rolls without skidding, traction is ob-tained and the frictional forces available enable propulsion of a vehicle. When skidding occurs, the same frictional forces will now dissipate any mechanical energy applied to the wheel. Thus the difference between trac-tion and friction is in the way that the mechanical energy is processed, e.g. in the case of traction this energy is transmitted between the contacting bodies (i.e. one body is driving another) whereas with friction it is dissi-pated. Traction can also be applied to lubricated contacts in spite of the relatively low coefficients of friction involved. EHL contacts can provide sufficiently high traction to be used as interfaces for variable speed trans-missions. When traction is applied, there is a small but non-zero sliding speed between the contacting surfaces. This non-zero sliding speed is inevitable since all the tractional force in an EHL contact is the result of viscous shear. The envisaged simplified film geometry and velocity pro-files of the sheared lubricant are shown in Fig. 2.34.

Figure 2.34 - Simplified film geometry and generation of traction in an EHL con-tact.

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The traction force has the same effect of increasing the shear stress on top surface, as shown in the previous scheme of Fig.2.30 (refer to previous section “Hertzian stress status in sliding contact”). Particularly, it is important to note that this condition can occurs not only at macroscopic scale, namely considering opposite lubricated surfaces as homogeneous, but the EHL scheme is applicable to microscopic scale. Consider the effective roughness of a lubricated surface that is put, for ex-ample, into rolling contact (as it happens actually for lubricated gears). The effect of surface roughness on partial EHL is illustrated in Fig.2.35. It has been found that the ‘sharp peaks’, i.e. asperities with high slope or low ra-dius sustained a higher proportion of the contact load than ‘flat peaks’, i.e. asperities with a low slope or large radius. Improved surface finish enables a diminished fraction of contact load supported by the asperities and the likelihood of a perfect elasto-hydrodynamic film is enhanced11.

Figure 2.35 - Effect of roughness and asperity shape on survival of EHL films. At high levels of surface roughness (see Fg.2.35, left side), the EHL film sustains a reduction in minimum film thickness and rapid wear of the contact occurs that produces a corrective wearing of surface in early lifespan of contact system bod-ies. When asperities are sufficiently smooth, or smoothed after corrective surface wearing, they are prevented from contacting each other, due to the mechanism of ‘micro-elastohydrodynamic lubrication’ or ‘micro-EHL’, as schematically shown in Fig.2.36.

11 When surfaces are polished to an extreme smoothness, however, a contrary trend to lowered load capacity is probable. It has often been observed in engineering practice that if the surface is too smooth, e.g. with a surface roughness of 0.001 [μm] Ra, then there is a risk of sudden seizure. In this instance it is commonly believed that small asperities play a useful role as a reservoir for the lubricant by entrapment between asperities. Under ex-tremes of contact pressures the trapped lubricant can be expelled by asperity deformation to provide a final reserve of lubricating oil.

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Figure 2.36 - Mechanism of micro-elasto-hydrodynamic lubrication.

Box – Basic principles of hydrodynamic lubrication The principle of hydrodynamic pressure generation between moving non-parallel surfaces is schematically illustrated in Figure 2.33. It can be assumed that the bottom surface, sometimes called the ‘runner’, is covered with lubri-cant and moves with a certain velocity. The top surface is inclined at a certain angle to the bottom surface. As the bottom surface moves it drags the lubricant along it into the converging wedge. A pressure field is generated as otherwise there would be more lubricant entering the wedge than leaving it. Thus at the beginning of the wedge the increasing pressure restricts the entry flow and at the exit there is a decrease in pressure boosting the exit flow. The pressure gradient therefore causes the fluid velocity profile to bend inwards at the en-trance to the wedge and bend outwards at the exit, as shown in Figure 2.33. The generated pressure separates the two surfaces and is also able to support a certain load, as for example occurs in the Pivoted Pad Bearing (Fig.2.34).

Figure 2.33 - Principle of hydrodynamic pressure generation between non-parallel surfaces.

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Figure 2.34 - Schematic diagrams of the pivoted bearings: a) a offset line piv-ot, b) a button point pivot.

Subsurface crack initiated fatigue contact failure Due to the cyclic nature of the �45 shear stress, despite it is below the yield stress, it is capable to initiate a subsurface crack, accordingly with most of mechanisms discussed as valid for fatigue failure (refer to previous sec-tion “Fatigue failure”). Similarly to the S-N approach, it is possible to generalize the fatigue con-tact failure by the scheme in Fig.2.35:

– As the maximum shear stress exceeds the shear fatigue limit for ma-terial, the condition for crack initiation occurs;

– the crack initiates and, due to increasing of stress intensity factor, grows submerged;

– crack remerges toward surface, pieces of materials detached, thus micro-voids is created;

– on top surface micro-voids act as stress intensity factor for enhance failure mechanism.

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(a)

(b)

Figure 2.35 – (a) Subsurface shear stress produced during cycling of external load contact; (b) condition that leads to crack initiation (lifetime depends on loading condition, surface roughness, lubrication conditions, etc.) within the surface, pro-ducing subsurface propagation toward surface and void creation (pitting or spall-ing mechanisms).

Pmax

Time

tau

max

Depth below surface

Pmax

2a

W

τ1

τf (A)

τf (B)micropitting

(pitting/spalling)

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It is important to note that when materials contain inclusions (Fig.2.36a) and other imperfections which act as nuclei for void formation under plas-tic deformation (Fig.2.36b). These voids form a plentiful supply of initia-tors for crack growth.. The development of voids by plastic deformation is a result of dislocation pile up at hard inclusions. These voids enlarge with further deformation since they act as traps for dislocations. All these fac-tors favour the growth of a crack parallel to but beneath the surface. As stated, at some unspecified point the crack finally turns upwards to the sur-face and a long thin laminar particle is released.

(a)

(b) Figure 2.36 – (a) Material imperfection as the cause for contact fatigue; (b) illus-tration of a process of subsurface crack formation by growth and link up of voids. Surface crack initiated fatigue contact failure When some sliding is present, maximum shear stress could localize most probably at the surface; in this condition the crack is expected to initiate from surface, instead of subsurface regions. In severe sliding conditions (as it is in not lubricated contacts or in the presence of lubrication errors),

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with friction coefficient approximates unity, the material within the 0.1 mm of the surface is stretched along the sliding direction. In these regions, microstructure becomes hardly oriented, and this severe plastic defor-mation makes the dislocation density increase. Subsequent work hardening occurs in these high stretched layers, as they are schematically illustrated in Fig.2.37.

Figure 2.37 – Strain levels in a deformed surface.

The high strain induced by traction in EHL contact (or sliding in dry con-tact) eventually breaks down the original grain structure at the surface to form dislocation cells, as it occurs in severe work hardening processes. The example of such a work-hardened like deformed material is shown in the micrograph of Fig.2.38.

Figure 2.38 – Accumulation of material on the surface due to the passage of a blunt wedge and the resulting plastic deformation.

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The mechanism of surface crack initiated fatigue wear is illustrated sche-matically in Fig. 2.39. A primary crack originates at the surface at some weak point and propagates downward along weak planes such as slip planes or dislocation cell boundaries. A secondary crack can develop from the primary crack or alternatively the primary crack can connect with an existing subsurface crack. When the developing crack reaches the surface again a wear particle is released.

Figure 2.39 – Schematic illustration of the process of surface crack initiation and propagation. It is not infrequent that during unlubricated sliding, in particular reciprocal sliding, wear particles can form due to the growth of surface initiated cracks; planes of weakness in the material become orientated parallel to the surface by the already discussed deformation processes, and laminar wear particles are formed by a surface crack reaching a plane of weakness as illustrated in Fig.2.40.

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Figure 2.40 – Schematic illustration of mechanism of wear particles formation due to growth of surface initiated cracks and an example of fatigue wear particle for-mation on cast iron. To complete the preliminary analysis of cyclically loaded bodies in lubri-cated contact, typical of gears, the model in the Fig.2.35 is capable to ex-plain also the singular cases of case-crushing failure shown in Fig.2.26. As shown in Fig.2.41, the case-crushing condition occurs when the shear stress Herztian profile exceed somewhere at interface case-core interface the fatigue limit shear stress τf of the material.

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Figure 2.41 – Condition that leads to crack initiation in depth, at the interface be-tween the hardened layer, also named case, and the base material, also named core.

τ1

τf (A)τf (C)

Case-crushing

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Friction and wear damage

When two materials are placed in contact, any attempt to cause one of the materials to slide over the other is resisted by a friction force (Fig. 25.1). The force that will just cause sliding to start, Fs , is related to the force P acting normal to the contact surface by: (eq.2.28) F = µsP where µs is the coefficient of static friction. Once sliding starts, the limit-ing frictional force decreases slightly and we can write: (eq.2.29) F = µkP where µk (< µs), is the coefficient of kinetic friction (Fig. 25.1). The work done in sliding against kinetic friction appears as heat.

(static µs ) (dynamic µk )

Figure 2.42 – Static and kinetic coefficients of friction. How is it that the friction between two surfaces can depend only on the force P pressing them together and not on their area? In order to under-stand this behavior, we must first look at the geometry of a typical sur-face. Actual surface contact between solids Surface roughness limits the contact between solid bodies to a very small portion of the apparent contact area. The true contact over most of the ap-parent contact area is only found at extremely high contact stresses; con-tact between solid bodies at normal operating loads is limited to small are-as of true contact between the high spots of either surface. The random nature of roughness prevents any interlocking or meshing of surfaces. True

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contact area is therefore distributed between a number of microcontact ar-eas. If the load is raised, the number of contact areas rather than the ‘aver-age’ individual size of contact area is increased, i.e. an increase in load is balanced by newly formed small contact areas. A representation of contact between solids is shown schematically in Figure 10.12.

Fig. 2.43 - Real contact area of rough surfaces in contact; ar = Σai is the true area of contact. Even if the surface is polished for a long time using the finest type of metal polish, micro-asperities still survive. The load pressing the surfaces together is supported solely by the contact-ing asperities. The real area of contact, a, is very small and because of this the stress P/ a (load/ area) on each asperity is very large. Initially, at very low loads, the asperities deform elastically where they touch. However, for realistic loads, the high stress causes extensive plastic deformation at the tips of asperities. If each asperity yields, forming a junction with its part-ner, the total load transmitted across the surface (Fig. 25.3) is: (eq.2.30) P ≈ aσy where σy is the compressive yield stress. The real area of contact is there-fore given by: (eq.2.31) a∼ P/σy

ai

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Obviously, if we double P we double the real area of contact, a.

Fig. 2.44 - The real contact area between surfaces is less than it appears to be, be-cause the surfaces touch only where asperities meet. Let us now look at how this contact geometry influences friction. If you at-tempt to slide one of the surfaces over the other, a shear stress Fs / a ap-pears at the asperities. The intense plastic deformation in the regions of contact presses the asperity tips together so well that there is atom-to-atom contact across the junction. The junction, therefore, can withstand a shear stress as large as k approximately, where k is the shear-yield strength of the material. The asperities will give way, allowing sliding, when Fs/a ≥ k. The distinction between a static and a sliding contact is thought by modern theory as due to differences in structure and physical processes that occurs. It was found that while a static contact can be described in terms of a ran-dom distribution of point contacts as above described, this model is not applicable to a sliding contact. A basic feature of sliding contact is that it is distributed over a lesser number of larger contact areas rather than a large number of contact points. These areas do not have a fixed location inside the contact but instead move slowly across the surface as sliding progress-es. The frictional interaction appears to be controlled by mechanical inter-locking between ‘lumps’ on opposing surfaces as schematically illustrated in Figure 2.45.

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Fig. 2.45 - A comparison between static and dynamic contact.

Data for coefficients of friction If metal surfaces are thoroughly cleaned in vacuum it is almost impossible to slide them aver each other. Any shearing force causes further plasticity at the junctions, which quickly grow, leading to complete seizure (µ > 5). This is a problem in outer space, and in atmospheres (e.g. H2 ) which re-move any surface films from the metal. A little oxygen or H2O greatly re-duces µ by creating an oxide film which prevents these large metallic junc-tions forming. Experimentally, it is found that for some metals the junction between the oxide films formed at asperity tips is weaker in shear than the metal on which it grew (Fig. 2.46). In this case, sliding of the surfaces will take place in the thin oxide layer, at a stress less than in the metal itself, and lead to a corresponding reduction in µ to a value between 0.5 and 1.5.

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Fig. 2.47 - Oxide-coated junctions con often slide more easily than ones which are clean. Referring to data in Fig. 2.47, it can be generally observed that:

1. When soft metals slide over each other (e.g. lead on lead), the junctions are weak but their area is large so µ is large;

2. When ceramics slide on ceramics friction is lower: ceramics are very hard, stable in air and water so they have less tendency to bond and shear more easily.

3. Metals slide on bulk polymers, friction is still caused by adhesive junctions, transferring a film of polymer to the metal: any plastic flow tends to orient the polymer chains parallel to the sliding sur-face, and in this orientation they shear easily, so µ is low - 0.05 to 0.5.

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Fig. 2.47 - Bar chart showing the coefficient of static friction for various material considerations. Lubrication Friction absorbs a lot of work in machinery and as well as wasting power, this work is mainly converted to heat at the sliding surfaces, which can damage and even melt the bearing. In order to minimize frictional forces we need to make it as easy as possible for surfaces to slide over one anoth-er. The obvious way to try to do this is to contaminate the asperity tips with something that: (a) can stand the pressure at the bearing surface and so prevent atom-to-atom contact between asperities; (b) can itself shear easily. Polymers and soft metal, as we have said, can do this; but we would like a much larger reduction in µ than these can give, and then we must use lub-ricants. The standard lubricants are oils, greases and fatty materials such as soap and animal fats. These 'contaminate' the surfaces, preventing adhe-sion, and the thin layer of oil or grease shears easily, obviously lowering the coefficient of friction. What is not so obvious is why the very fluid oil is not squeezed out from between the asperities by the enormous pressures generated there. One end of each molecule reacts with the metal oxide sur-face and sticks to it, while the other attracts one another to form an orient-ed 'forest' of molecules (Fig. 2.48). These forests can resist very large forc-

3

1

2

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es normal to the surface (and hence separate the asperity tips very effec-tively) while the two layers of molecules can shear aver each other quite easily. This type of lubrication is termed partial or boundary lubrication, and is capable of reducing µ by a factor of 10 (Fig. 2.47). As described in the previous section “Contac fatigue”, hydrodynamic lubrication is even more effective, since it aims to separate surfaces.

Fig. 2.48 - Boundary lubrication. Wear of materials Even when solid surfaces are protected by oxide films and boundary lubri-cants, some solid-to-solid contact occurs at regions where the oxide film breaks down under mechanical loading, and adsorption of active boundary lubricants is poor. This intimate contact will generally lead to wear. Wear is normally divided into two main types: adhesive wear and abrasive wear. Adhesive wear Figure 2.49 shows that, if the adhesion between A atoms and B atoms is good enough, wear fragments will be removed from the softer material A. If materials A and B are the same, wear takes place from both surfaces - the wear bits fall off and are lost or get trapped between the surfaces and cause further trouble (see below). The size of the bits depends on how far away from the junction the shearing takes place: if work hardening extends well into the asperity, the tendency will be to produce large pieces.

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In order to minimize the rate of wear we obviously need to minimize the size of each piece removed. The obvious way to do this is to minimize the area of contact a. Since a = P/σy, reducing the loading on the surfaces will reduce the wear, as would seem intuitively obvious. The second way to reduce a is to in-crease σy, i.e. the hardness.

Fig. 2.49 - Adhesive wear. Abrasive wear Wear fragments produced by adhesive wear often become detached from their asperities during further sliding of the surfaces. Because oxygen is desirable in lubricants (to help maintain the oxide-film barrier between the sliding metals) these detached wear fragments can become oxidized to give hard oxide particles which abrade the surfaces in the way that sand-paper might. Figure 2.50 shows how a hard material can 'plough' wear fragments from a softer material, producing severe abrasive wear. Abra-sive wear is not, of course, confined to indigenous wear fragments, but can be caused by dirt particles (e.g. sand) making their way into the system, or - in an engine - by combustion products: that is why it is important to filter the oil. The wear rate W related to the wear path s is proportional to the normal load FN and the hardness of the worn surface HW and a factror k, accord-ingly with experimental Archard equation: (2.31)

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The rate of abrasive wear can be reduced by reducing the load - just as in a hardness test. The particle will dig less deeply into the metal, and plough a smaller. Increasing the hardness of the metal will have the same effect.

Fig. 2.50. Abrasive wear.

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Corrosion12 Corrosion is a form of degradation caused by chemical and electrochemi-cal reactions that take place at the interface between the surface of a mate-rial and the environment with which it is in contact: the result is a gradual decay of integrity of the metal surface occurring when the main constitu-ents of the alloy (Fe, C, Cr, Ni, etc.) combine with the aggressive agents present in the environment, thus forming corrosion products. The corrosion of metals can cause several problems. In the case of piping and tanks, the degradation can give rise to punctures that lead to leakage of the fluids contained within; in structural elements corrosion can cause the reduction of the resistant part with the consequent loss of the component’s load capacity. Other problems are also linked to the formation of corrosion products, which can lead to the alteration of the aesthetic features of the surfaces or the contamination of the processed substances (for example, in the case of foods, possible alteration to their organoleptic characteristics). The corrosion of metals can be divided into two basic forms:

– electrochemical corrosion – also called wet corrosion – in which the metal alloy undergoes an oxidation reaction in the presence of an electrolyte (usually water); the oxidation reaction is coupled with a reduction reaction of the substances present in the environment (usually oxygen): the combination of the two reactions, anodic (ox-idation) and cathodic (reduction), involve both chemical species (ions and molecules) and electrons;

– chemical corrosion (also called high temperature oxidation or dry corrosion) in which the metal alloy undergoes an oxidation reaction upon contact with a gaseous atmosphere (usually air); the phenome-non usually occurs at temperatures well above ambient temperature (>300°C) and the corrosion products are oxides and salts with low melting points.

Wet corrosion and electrochemical corrosion

12 Main references: – M. Boniardi, A. Casaroli, Stainless Steels, Lucefin Group, 2014 (free Eng-

lish version avaliable at: http://www.lucefin.com/wp-content/files_mf/stainlesssteels_low.pdf );

– M.F.Ashby and M.F.Jones, Engineering Materials 1, Engineering Materi-als 1, Second Edition. Butterworth Heineman, Oxford, 1996.

http://www.lucefin.com/wp-content/files_mf/stainlesssteels_low.pdf

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Wet corrosion of metals can be described using the electrochemical model: the mechanism that governs the phenomenon depends on the presence of a process as the result of the metal transforming in its ionic state. It is caused by a flow of electricity from one metal to another metal (Gal-vanic corrosion) or from one part of a metal surface to another part of the same surface (cathode-anode areas). For current to flow, a complete electrical circuit is required. In a corroding system, this circuit is made up of four components:

– The anode is the electrode where electrons flow away; – The electrolyte is an electrical conducting solution that contains

ions; water, especially saltwater, is an excellent electrolyte; in pure water, there are positively charged H+ and negatively charged OH- in equal amounts;

– The cathode is the electrode at which electrons flow toward; – The metallic path, thus an “external circuit” to complete the con-

nection between anode and cathode. To understand the problem further, refer to the diagram shown in figure 2.51, in which an iron plate is placed in contact with a copper plate and the drop of water is the electrolyte.

Figure 2.51 – Electrochemical diagram of the corrosive phenomenon of an iron plate in contact with a copper plate. As the copper is a nobler metal than iron (copper has a greater electro-chemical potential than iron), a potential difference is established be-tween copper and iron, i.e. an electromotive force that allows the circula-tion of current (see Box for more details). The analogy using the galvanic cell is clear: the iron behaves as an anode and the copper as a cathode and

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the potential difference between the two metals allows the circulation of current. The oxidation reaction occurs to the anode (iron) and the reduction reaction of oxygen occurs to the cathode (copper) at the same time.

Box – Voltage differences (electrochemical potential difference) as a driv-ing force for wet oxidation Wet oxidation in metals involves electron flow, as metals are electron conduc-tors. Thus, it is easier to measure the tendency of a metal to oxidise in a solu-tion by using a voltage scale, namely a measure of such a flow rate of elec-trons. Figure 2.52 shows the voltage differences that would just stop various metals oxidising in aerated water.

Figure 2.52 - Wet corrosion voltages (at 300 K).

What do these voltages mean? Suppose we could separate the cathodic and the

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anodic regions of a piece of iron, as shown in Fig. 2.53. Then at the cathode, oxygen is reduced to OH-, absorbing electrons, and the metal therefore be-comes positively charged. The reaction continues until the potential rises to +0.401 V. Then the coulombic attraction between the +ve charged metal and the -ve charged OH- ion becomes so large that the OH- is pulled back to the surface, and reconverted to H2O and O2; in other words, the reaction stops. At the anode, Fe++ forms, leaving electrons behind in the metal which acquires a negative charge. When its potential falls to -0.440V, that reaction, too, stops (for the same reason as before). If the anode and cathode are now connected, electrons flow from the one to the other, the potentials fall, and both reactions start up again. The difference in voltage of 0.841V is the driving potential for the oxidation reaction. The bigger it is, the bigger the tendency to oxidise.

Figure 2.53 - The voltages that drive wet corrosion. Obviously, it is not very easy to measure voltage variations inside a piece of iron, but we can artificially transport the 'oxygen-reduction reaction' away from the metal by using a piece of metal that does not normally undergo wet oxidation (e.g. platinum) and which serves merely as a cathode for the oxy-gen-reduction reaction. The corrosion voltages also tell us what will happen when two dissimilar metals are joined together and immersed in water. If cop-per is joined to zinc, for instance, the zinc has a larger corrosion voltage than the copper. The zinc therefore becomes the anode, and is attacked; the copper becomes the cathode, where the oxygen reaction takes place, and it is unat-tacked. Such couples of dissimilar metals can be dangerous: the attack at the anode is sometimes very rapid.

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The two reactions are:

(eq.2.32) Fe → Fe+2 + 2e- (anodic reaction of oxidation)

(eq.2.33) ½ O2 + H2O + 2e- → 2OH- (cathodic reaction of reduction) overall obtaining:

(eq.2.34) ½ O2 + H2O + Fe → Fe (OH)2 In summary: the iron gradually transforms into solution under the form of Fe+2 ions, corroding due to the effect of the presence of the copper cathode where the reduction of oxygen occurs. In the example shown previously, the anodic and cathodic zones are clearly distinct: the corrosive phenome-non occurs due to a galvanic coupling that creates a potential difference “E” because of the different nature of the two metals involved. However, it should not be believed that corrosion only occurs in these conditions: the case of degradation phenomena on metal alloys not in con-tact with dissimilar metals is much more common. To understand the problem better the experience of Evans should be con-sidered, as shown in Fig. 2.54: his experiment is especially significant as it explains the phenomenon of corrosion of homogenous metal materials.

Figure 2.54 – Experience of Evans; phenomenon of electrochemical corrosion in a homogenous metal material [Pedeferri, 2010].

By taking an iron plate on which a deaerated drop of water is placed as the electrolyte, after a short time corrosion phenomena are only observed near the central area of the drop: this can be explained by considering the pro-cess of oxygen diffusion in the water drop, also called differential aeration corrosion.

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Initially, the chemical composition of the drop is constant and the oxygen is totally absent: over time however, due to contact with air, diffusive phe-nomena will occur near to the external surfaces of the drop (which is the surface of exchange with the surrounding air) and a variation of the oxy-gen concentration will take place in the drop. The different concentration of O2 in the drop will create an anodic zone, i.e. the zone lacking in oxy-gen in the center of the drop, and a cathodic zone, i.e. the zone rich in ox-ygen on the outside of the drop. Therefore, a local anode-cathode micro bond is created which is able to trigger the corrosion process. The “E” po-tential existing between the anode and cathode is a kind of electromotive force that allows the corrosive process to take place: it is called “free cor-rosion potential”. The anodic reaction and the cathodic reaction are all the same as those ob-served previously for galvanic contact: (eq.2.35) Fe → Fe+2 + 2e- (anodic reaction of oxidation) (eq.2.36) ½ O2 + H2O + 2e- → 2OH- (cathodic reaction of reduction) overall obtaining: (eq.2.37) ½ O2 + H2O + Fe → Fe(OH)2

with the formation of corrosion products (iron oxides/hydroxides). If the oxidation reaction of iron occurs in an acid environment (such as when an iron plate is immersed in chloride acid), the cathodic process will be the reduction of the hydrogen ion to hydrogen gas (hydrogen evolu-tion), i.e.: (eq.2.38) Fe → Fe+2 + 2e- (anodic reaction of oxidation) (eq.2.39) 2H+ + 2e- → H2 (cathodic reaction of reduction) overall obtaining: (eq.2.40) 2H+ + Fe → Fe+2 + H2 For corrosion to occur, the two reactions, anodic and cathodic, must hap-pen at the same time: during the oxidation reaction of the iron, a certain number of electrons are generated on the anode which, following the re-duction reaction, are consumed by the cathode.

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The above reactions are very common in all metal materials subject to cor-rosion: the presence, for any reason, of an anodic-cathodic micro bond provides the electromotive force required to trigger and supply the degra-dation process. However, the phenomenon of differential aeration corrosion is not the on-ly type to give rise anodic-cathodic micro bonds able to trigger degrada-tion: often in the corrosive ‘material – environment’ combination there are already particular local conditions suitable for generating zones with dif-ferent electrical potential. The problem arises for various reasons: heterogeneity of chemical compo-sition of the metal mass, in homogenous phases of the microstructure of the matrix (inclusions, carbides, etc.), Tensile residual stress of high entity traction, local defects of the piece (micro cavities, blowholes, accentuated roughness etc.) All these areas act as the anode of the surrounding metal mass acting as a cathode, causing local micro bonds with preferential cor-rosion triggers. Similar situations also arise due to the variability of the electrochemical characteristics of the corrosive environment, such as that which occurs, for example, in solutions with various concentrations of noxious species, in electrolytes with greater or smaller stagnation zones or with non-uniform temperatures.

Box – Potentiodynamic curves During a corrosive process there is always a certain number of ions in solution in the electrolyte and a concomitant movement of electrons in the metal, i.e. a circulation of electrical current, as what occurs in a cell. The mechanism described is concatenated: the higher the quantity of iron ions, which will dissolve in the solution, the greater the number of electrons circulat-ing per surface unit exposed to the corrosive environment. This causes the in-crease of the surrounding current density “ic” and the corrosion rate “Vcorr” of this material will increase in that given environment, i.e.: corrosion rate: (Vcorr) ∝ ic = ianodic = icathodic It should be repeated that the corrosive phenomenon is a degradation process that occurs when there is an anodic zone and a cathodic zone: among these two zones a potential difference “E” is established (called free corrosion potential in the case of short circuits between anodes and cathodes) which ensures the circu-lation of a current density “i” proportional to the corrosion rate of the system. The correlation between potential “E” and current density “i” of the anode-cathode bond depends on both the electrochemical characteristics of the anodic

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process (i.e. “how quickly” the metal dissolves) and the electrochemical charac-teristics of the cathodic process (i.e. “how quickly” the oxygen or the hydrogen evolves). If the two contributions are separated, i.e. if the correlation “E – i” is studied separately for the anodic reaction and the cathodic reaction, it is possible to estimate what the trend of the surrounding current density “i” will be, in order to change the applied electromotive force “E”. This is exactly what Evans did experimentally and which is still possibly to recreate in the laboratory: to trace the curves that describe the anodic reaction and cathodic reaction with the varia-tion of the tension conditions “E” applied, or the reaction existing between the set tension “E” and the surrounding current density “i” both in the anodic area and in the cathodic area. The curves obtained experimentally are shown in fig.2.55: they are called poten-tiodynamic curves, or Evans diagrams, due to the anodic process (anodic char-acteristics, metal/alloy that is corroded) and the cathodic process (cathodic char-acteristics, oxygen reduction and hydrogen evolution). In the very simple case of common carbon steel in an aerated aqueous solution (the cathodic process is oxygen reduction), the two curves are as shown in fig.2.55a, whereas for a stainless steel, again in the same solution, the situation shown in fig.2.55b occurs.

Figure 2.55 - Indicative potentiodynamic curves (anodic characteristic A: mate-rial – cathodic characteristic B: environment) in aqueous solution 0.05 M of H2SO4: (a) for a material with active conduct and b) for a material with active-passive conduct. The intersection point of curves A and B shown in fig.2.55 represents the condi-tion of equivalence between the surrounding current densities (the rate of the two reactions, anodic and cathodic, is equal): it establishes the functioning point of the material-environment system and allows the determination of the free cor-

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rosion potential “Ec” and the surrounding current density “ic”, as well as esti-mating the corrosion rate of the material in that particular environment (Vcorr ∝ ic).In the case of carbon steels, for example, the anodic curve (curve A – fig.2.55a) increases monotonically: the current increases with the increasing ten-sion applied and with it, the corrosion rate increases. With regards to In the case of carbon steels, the anodic curve (curve A – fig.2.55a) increases monotonically: the current increases with the increasing tension applied and with it, the corro-sion rate increases. Concerning stainless steels the curve is that represented in fig.2.55b, and its different behaviors will be explained in Chapter 5 that is de-voted to stainless steels. For the moment, note the effect of the difference of the two potentio-dynamic behaviors represented in figure 2.55a and fig.2.55b that represent respectively a carbon steel and a stainless steel: because the surround-ing current “ic” of case “a” is much greater than the surrounding current “ic” of case “b”, the corrosion rate of a carbon steel, in that determined environment, will be a lot greater than that of a generic stainless steel.

The corrosion morphology Corrosive phenomena can also be classified based on the morphology with which the degradation occurs in the components, or rather in relation to the aspect of chemical aggression as it appears upon simple visual observation or using magnification microscopy. An initial distinction can be made between “generalized or uniform corro-sion” and “localized corrosion”:

– in the first case the whole surface of the material is subject to corro-sive attack (generalized), with penetration of the degradation quite consistent along the whole section of the component (uniform);

– in the second case the aggressive action is only expressed in some areas of the surfaces (localized), with penetrating attacks, craters or cracks.

Uniform or generalized corrosion A whole surface area of the metal material exposed to the aggressive envi-ronment is affected with very limited local variations of the degree of pen-etration of the damage along the thickness of the component. In the cases of generalised corrosion, the corrosion rate “Vcorr” can be suitably expressed in terms of mass loss (Δm) per surface unit (A) over time (t), or rather: (eq.2.41) Vcorr = Δm/A·t usually measured in mg per day in dm2 (namely, mdd).

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In industrial applications it is often more interesting to talk about penetra-tion or thinning rate “Vthin” of the corrosive phenomenon. To convert cor-rosion rate to the thinning rate simply add the material density (ρ), accord-ing to the formula: (eq.2.42) Vass = Vcorr/ρ = ∆m/ρ·A·t The formula is commonly used to predict the so-called “additional thick-ness for corrosion”, i.e. a thickness “in excess” on the component which, during operation, will be gradually removed due to the corrosive action of the environment. Galvanic corrosion An early form of localized corrosion is galvanic corrosion or corrosion due to galvanic coupling. It occurs when a metal and a metal alloy is connected (i.e. is in electrical contact) with another metal/metal alloy with greater or lower thermodynamic nobility: if there is a significant potential difference, a redox reaction may develop with consequent corrosion phenomena, even in the presence of just a mildly aggressive environment. The mechanism is very similar to that shown in Fig.2.51. Every metal or metal alloy has its own potential that depends on its nature, its chemical composition and on the environment in which it is placed (temperature, pH, agitation, presence of oxidants or other harmful species, etc.). If the difference between the various potentials exceeds a certain threshold, a significant passage of electrons is created between the “donor” (the an-ode, the less noble metal) and the “receiver” (the cathode, the nobler met-al). The intensity of this movement of electrons (actually an electric cur-rent) will be greater as the potential difference increases: as a consequence, the corrosion rate will be higher the further distance between the two mate-rials on the nobility scale. Another relevant aspect that governs the phe-nomenon of galvanic corrosion is the relationship between the areas of the two materials in contact: the rate of degradation increases with the increase of the ratio between the area of the cathodic zone (nobler) to that of the anodic zone (less noble) exposed to the environment. In order to assess whether the conditions of galvanic contact between the two metals/metal alloys can cause problems practically, it is better NOT to refer to the standard electrical potential scales: this is because there is a great variability in the behavior of the same material between one corro-sive environment and another (and at times also within the same environ-

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ment) and also because there are never conditions of equilibrium in the ac-tual environments and electrochemical system. Therefore the saltwater scale of nobility is used (figure 2.56), which is a scale of the potentials measured under conditions close to actual operation. A typical example of galvanic corrosion is when it occurs on carbon steel sheet metal (also gal-vanized) or on aluminum alloy sheet metal in contact with stainless steel fasteners, placed in marine environments, in aerate aqueous solutions or in mildly aggressive environments (see fig.2.57). The opposite situation would be much more serious, i.e. that of stainless steel sheets fastened with carbon steel or galvanized steel rivets: in this second case, in addition to the nobility difference between the two materi-als, the relationship between the areas would be very negative, in favor of stainless steel.

Figure 2.56 – Saltwater scale of nobility [from ASM-H.13 1992].

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Figure 2.57 – Galvanic corrosion of a carbon steel plate with stainless steel fasten-ers. The most correct solution to eliminate the corrosion phenomenon from galvanic contact is to avoid putting it into “electrical contact” (or direct contract with electronic continuity) with metal materials of different no-bility or, if impossible, providing for electrical insulation of the parts (see figure 2.58).

Figure 2.58 – Electric insulation with a non conductive material between two plates and the relative connection bolt. A particular type of galvanic corrosion is corrosion by superficial contam-ination.

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The degradation occurs when the surface of the stainless steel is “sullied” by foreign particles, such as dust from ferrous material that is often gener-ated during grinding operations and from common steel. The particles deposited on the surface can create conditions for localized corrosive attacks, even in not very aggressive environments. Marks appear on the surface (rust-colored in case of ferrous contamination, whitish in the case of contamination from aluminum or zinc) as a consequence of the rapid oxidation of the contaminant (steel, aluminum or zinc) and not, as wrongly believed, of the stainless steel. In the most extreme situation, the contaminant substance can also cause damage to stainless steel, as it can hinder the passivation phenomenon, as well as constitute a preferential trigger zone for other forms of corrosion. If surface contamination is suspected, the foreign particles must be re-moved through a chemical passivation operation, using nitric acid based dilute solutions. Pitting corrosion Pitting is the phenomenon of localized corrosion; it produces serious pene-trating damage and dangerous holes in the components during operation. Characteristic elements of pitting are the presence on the surface of the work piece of multiple small pits (hence the name of this corrosion); pit-ting usually leads to even deeper pits, i.e. grooves, ulcers, craters etc. The surface size of the holes is small, between 0.1 and 2 mm, as in the pitting phenomena the extent of the corrosion products is very limited. The greatest problem related to this form of corrosion is not the loss of mass affected by the degradation phenomenon, but rather the damage caused by penetrating through the resistant section of the component. For example, consider the case of a stainless steel tank affected by the pitting phenomenon: the pitting could lead to the creation of a hole in the recipi-ent, the subsequent spilling of the process fluid and the overall disruption of the system. Degradation due to pitting has various aspects; fig. 2.59 shows some mor-phologies typical in sections, as classified by the American standard ASTM G46.

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Figure 2.59 – Typical morphologies of degradation due to pitting [from ASTM G46].

Pitting occurs when discrete areas of a material undergo rapid attack while most of the adjacent surface remains virtually unaffected. Although the to-tal metal loss may be small, the part may be rendered useless due to perfo-ration. In addition to the localized loss of thickness, corrosion pits can also act as stress raisers, leading to fatigue or stress-corrosion cracking typical of austenitic stainless steels (refer to Chapter 5). Pitting occurs when the anodic or corroding area is small in relation to the cathodic or protected area. Pitting can occur in protected metals when there are small breaks in the continuity of the metal coating. Pitting can al-so occur on bare, clean metal surfaces as a result of irregularities in their physical or chemical structure. The rate of penetration into the metal by pitting can be 10 to 100 times that caused by general (uniform) corrosion. Pitting can cause structural failure from localized weakening while consid-erable sound metal still remains. Pitting usually requires a rather long initi-ation period before attack becomes visible. However, once a pit has start-ed, the attack continues at an accelerating rate. Pits tend to grow in a manner that undermines or undercuts the surface. Typically, a very small hole is seen on the surface. Poking at the hole with a sharp instrument may reveal a much larger hole under what had looked like solid metal. Pitting can cause visible pits, or they may be covered with a semipermeable mem-brane of corrosion products. Pitting corrosion may assume different shapes. Pitting normally occurs in a stagnant environment. Concentration cells can accelerate pitting. Concentration cells are areas on the metal surface where the oxygen or conductive salt concentrations in water differ. As a pit be-comes deeper, an oxygen concentration cell is started by depletion of oxy-gen in the pit. The rate of penetration of such pits is accelerated propor-

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tionately as the bottom of the pit becomes more anodic. Pitting attack in-creases with temperature. Variations in soil conditions can also trigger pit-ting.

Crevice corrosion Crevice corrosion is another form of localized aggression: it occurs in the presence of cracks, crevice, incrustations, deposits and geometrical discon-tinuities in which the electrolyte (generally water) is in stagnation with re-gards to the surrounding environment. A typical case of degradation due to crevice corrosion regards the seals of flanged piping or in the contact zones between bolted or riveted plates (fig. 2.60). Similar situations can occur in welded plates for points on cars, in arc welded seals where pene-tration is incomplete, between the strands of metal cables, underneath lu-bricating films such as graphite or molybdenum graphite and on surfaces coated with Teflon or polyethylene.

Figure 2.60 – Schematic of a constructive solution which could cause crevice cor-rosion. The presence of the geometric discontinuities create a macro bond due to differential aeration between the interstitial area, i.e. the anodic zone where the diffusion of oxygen is limited, and the surrounding metal mass which represents the cathodic zone in which the oxygen saturation is ensured (figure 2.61). It should be noted that in the interstices, the same critical factors occur that are in a pit formed by corrosion, i.e. gradual consump-

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tion of oxygen, accumulation of positive metal ions, chloride ions attracted and acid hydrolysis with pH decrease.

Figure 2.61 – Schematic of crevice corrosion.

A particular form of crevice corrosion is corrosion under a deposit. The degradation occurs in the presence of lime scale accumulations and/or de-posits (such as in household pipes penetrated by water rich in limestone): in the vicinity of the deposit and below it “clogged cells” are established with the formation of anodic- cathodic macro bonds and degradation phe-nomena characterized by mechanisms similar to those of the interstitial corrosion (see figure 2.62).

Figure 2.62 – Schematic of corrosion phenomenon under deposit in a pipe.

Further important corrosion mechanisms are integranular corrosion and stress corrosion cracking corrosion, both wet corrosion mechanisms, and the hot temperature corrosion, a form of dry corrosion mechanisms.

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Creep13 At high temperatures, permanent deformation can occur over a period of time at stresses well below the yield strength. This time-dependent defor-mation is known as creep and occurs at temperatures greater than approx-imately 0.3 to 0.5 of the absolute melting point Tm. In creep, thermal acti-vation enables plastic deformation at stresses below those needed to deform the lattice without thermal activation. When a metal is placed un-der a constant load, it stretches elastically but also gradually extends plas-tically. Thus, a metal subjected to a constant tensile load at elevated tem-perature will creep and undergo a time-dependent increase in length. Since the mobility of atoms increases with increasing temperature, diffusion-controlled mechanisms become active. Dislocation mobility increases, slip becomes easier, new slip systems become available, and dislocation climb is aided by both increases in temperature and the presence of a greater number of vacancies. Creep occurs in any metal or alloy at a temperature where atoms become sufficiently mobile to allow the time-dependent rear-rangement of structure. Since the elevated-temperature strength of metals is closely related to their melting points, it is normal practice to specify the homologous temperature, which is the ratio of the exposure temperature to the melting point (T/Tm), on an absolute scale. Creep behavior of a poly-crystalline metal or alloy often is considered to begin at approximately 1/3 to 1/2 of its melting point (~0.3 to 0.5 Tm). The Creep Curve In a creep test, the time-dependent strain is measured under long-term ele-vated temperature. Engineering creep is measured by applying a constant load on a tensile specimen at a constant temperature and measuring the strain, or extension, of the specimen as a function of time. A schematic of a test setup for a creep test is shown in Fig. 2.63. Creep tests may be run for as short as several months to as long as 10 years. Creep tests are usual-ly conducted at constant load rather than constant stress, and, as the speci-men elongates, the cross-sectional area decreases, so the applied stress in-creases with time.

13 Main reference: Flake C. Campbell, Elements of Metallurgy and Engineering Alloys, ASM International, 2008.

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Figure 2.63 - Typical creep test fixture

Constant load creep curves typically consist of three distinct stages, as shown in Fig. 2.64. Primary Creep. During primary creep, the specimen undergoes an initial elongation, ε0, and then the creep rate ( 𝜀𝜀̇ = dε/dt ) rapidly decreases with time. Primary creep, also known as transient creep, represents a stage of adjustment in the metal during which rapid, thermally activated plastic strain occurs. The competing processes of strain hardening and recovery eventually lead to a somewhat stable dislocation configuration. Primary creep occurs in the first few moments after initial strain and decreases in rate as crystallographic imperfections within the metal undergo realign-ment. This realignment leads to secondary creep. Secondary Creep. Being nominally constant at a minimum rate, generally known as the minimum creep rate, secondary creep it is also known as steady-state creep. It occurs when there is a balance between the compet-ing processes of strain hardening and recovery.

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Figure 2.64 - Typical creep curve. Since creep is a thermally activated process, it is not surprising that steady-state creep obeys an Arrhenius-type rate equation. The steady-state creep rate, 𝜀𝜀�̇�𝑠, in this intermediate temperature range (0.4 Tm<T<0.6 Tm) can be expressed as a power law function: (eq.2.43) where Q is the activation energy for creep; A is the pre-exponential con-stant; n is a constant, usually between 3 and 10; R is the universal gas con-stant; and T is the absolute temperature. This equation describes the de-pendence of creep rate on the key variables, temperature and This equation describes the dependence of creep rate on the key variables, temperature and stress. A correlation of creep and diffusion data for pure metals shows that the activation energy for creep, Q, is equal to the activation energy for

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self-diffusion, as shown in Fig.2.65.

Figure 2.65 - Correlation between diffusion and creep activation energies.

The minimum creep rate during steady-state creep is usually the most im-portant design parameter obtained during a creep test. Two criteria are common: (1) the stress to produce 1% creep in 10,000 h, or (2) the stress to produce 1% creep in 100,000 h. The first criterion is often used for jet en-gine components and the second for steam turbines. Tertiary creep. It is a region of drastically increasing strain rate with rapid extension to fracture. Tertiary creep is dominated by a number of weaken-ing metallurgical instabilities, such as localized necking, corrosion, inter-crystalline fracture, microvoid formation, precipitation of brittle second-phase particles, and dissolution of second phases that originally contribut-ed to strengthening of the alloy. When designing components for service at elevated temperatures, the steady-state creep rate is usually the significant design parameter. However, the duration of tertiary creep is also important, because it constitutes a safety factor that may allow detection of a failing component before catastrophic fracture.

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Creep Deformation Mechanisms The major classes of creep mechanisms are those that are governed by dis-location motion and those that are diffusion controlled. The dominating mechanism is determined by both the stress and temperature; however, several mechanisms may be active at the same time. In general, the ones governed by dislocation motion are more prevalent at lower temperatures and higher stresses, while those controlled by diffusion occur at higher temperatures and lower stresses. Dislocation motion induced creep is the result of dislocations, in combina-tion with vacancies and thermal activation, climbing over obstacles that would normally impede their motion at lower temperatures. The relevant dislocation mechanisms are dislocation glide and climb. As the temperature is increased, slip systems that were not available at room temperature become active, promoting dislocation glide. When disloca-tions encounter an obstacle, they are blocked and tend to pile up against the obstacle. At low stress levels, the applied stress is insufficient to enable the disloca-tions to bow around or cut through the obstacle. However, at elevated tem-perature, a dislocation may climb by diffusion to a parallel slip plane (Fig.2.66 and Fig.2.67). Having climbed, the dislocation proceeds along the new slip plane until it encounters another resistant obstacle, whereupon it climbs (or descends) to another parallel plane and the process repeats. Since dislocation motion depends on both dislocation glide and climb, the term climb-glide creep is used to describe this form of creep. Climb-glide creep depends more strongly on stress than does diffusion creep.

Figure 2.66 - Thermally activated dislocation climb.

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Figure 2.67 - Dislocations can climb (a) when atoms leave the dislocation line to create interstitials or to fill vacancies or (b) when atoms are attached to the dislo-cation line by creating vacancies or eliminating interstitials. Diffusion creep is often the dominating mechanism at high temperatures and low stresses. Under the driving force of an applied stress, atoms dif-fuse from the sides of the grains to the tops and bottoms in the manner shown in Fig. 2.68. The grain becomes longer as the applied stress does work, and the process will be faster at high temperatures because there are more vacancies. It should be noted that atomic diffusion in one direction is the same as vacancy diffusion in the opposite direction.

Figure 2.68 - Diffusion creep mechanisms.

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Grain size plays a role in creep of metals. The finer the grain size, the more rapid the mass transport, causing permanent deformation. Thus, under conditions where creep is solely due to diffusion, the creep resistance is improved by increasing the grain size. Note that this is different from low-temperature behavior, where a fine grain size is almost always beneficial to strength and ductility. Creep Life Prediction A frequent problem encountered in materials selection for component de-sign is that it may be desirable to use a new alloy in a high temperature structure; however, the alloy is so new that there are not sufficient data to substantiate its long-term creep resistance. Therefore, it is necessary to ex-trapolate higher temperature. In order to extrapolate the data to the re-quired times, a considerable amount of effort has been expended in devel-oping empirical prediction methods. One of the most widely used is the Larson-Miller parameter, P: (eq.2.44) where T is the absolute temperature, t is the time to rupture in hours, Q is the activation energy for creep, R is the universal gas constant, and C is the Larson-Miller constant, which typically has a value in the range of 30 to 65. If P is evaluated for pairs of t and T for a number of different stress levels, a single master curve can be plotted for the material. An actual set of stress-rupture data is shown for the nickel-base alloy In-conel 718 as log stress versus log time to rupture in Fig. 2.69a. The data are then replotted as constant-time curves on coordinates of stress versus temperature in Fig. 2.69b. Dashed horizontal lines have been added at stress levels of 550, 620, 760, and 830 MPa (80, 90, 110, and 120 ksi). Values for T at the intercepts of these dashed lines and the constant-time curves are then determined and plotted in Fig. 2.69c on coordinates of log t versus 104/TA. By extending the data in Fig. 2.69c, a set of converging isostress lines meeting on the ordinate at a value of log t = -25 can be ob-tained. The Larson-Miller equation for this set of data is: (eq.2.45)

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where absolute temperature, TA, is in units of the Kelvin temperature scales. The final master Larson-Miller curve is shown in Fig. 2.69d.

Figure 2.69 - Larson-Miller curve generation for Inconel 718. One of the dangers of any of the extrapolation methods is an unanticipated structural instability in the material that may go undetected. Since the in-stabilities usually occur at higher temperatures, several tests should be conducted at substantially higher temperatures than the actual part will see in service. Design Against Creep Design against creep can take several approaches. First, it makes sense to use a material with a high melting temperature in high-temperature appli-cations since, to a good approximation, diffusion coefficients on which the creep rate depends are proportional to the homologous temperature (T/Tm). Face-centered cubic (fcc) metals generally have superior creep re-sistance to body-centered cubic (bcc) metals at equivalent homologous

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temperatures, because the slightly more open bcc structure results in great-er diffusivities. Design against creep may also involve first determining the dominant creep mechanism. If diffusion creep dominates, then increasing the grain size is a beneficial microstructural alteration. Further, for diffusion creep, improved creep resistance can sometimes be obtained by placing inert par-ticles, such as carbides, on grain boundaries. This helps to pin the grain boundaries, enhancing creep resistance. As it will better discussed in Chapter 6, creep-resistant alloys include car-bon steels, chromium-molybdenum steels, chromium molybdenum-vanadium steels, stainless steels, nickel and cobalt alloys, and superalloys (a comparison of the stress-rupture properties for a number of different metallic alloy families is shown in Fig. 2.70).

Figure 2.70 - rupture comparison for several classes of alloys.

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Chapter 3 – Special Steels

Introduction Ferrous alloys, which are based on iron-carbon alloys, include plain carbon steels, alloy and tool steels, stainless steels, and cast irons. These are the most widely used materials in the world. In the history of civilization, these materials made their mark by defining the Iron Age. Steels typically are produced in two ways: by refining iron ore or by recycling scrap steel. In the Chapter 9 it is discussed in depth steelmaking processes for produc-ing primary steel either from iron ore (early pig iron is produced from iron ore, secondarily it is converted into steel by removing the excess of car-bon) or from steel scraps that are melted in an electric arc furnace, while in the last section of Chapter 9 some examples of metalworking operations employed in industry to produce semifinished products. In this section it is discussed the property of special steels, namely such steels that are available on market - produced into finished or semifinished shape – to be employed by designer for special machine construction pur-poses. Firstly we will necessarily build confidence in classification and designation of special construction steels (hereinafter, special steels), ac-cordingly two main classifications systems:

– the SAE/AISI classification originally developed by the SAE, Soci-ety of Automotive Engineers (SAE) and later refined in conjunction with the American Iron and Steel Institute (AISI); hereinafter, for the sake of brevity, we refer to AISI classification;

– the European Standard EN 10027-1, hereinafter EN classification.

Since we could indifferently refer to steels classified in the AISI or EN classifications, it is useful to learn the basics of these two classification systems. The European Standard classification and designation for steels The EN 10027-1 standard defines the classification and designation sys-tem. Firstly it is necessary to distinguish the classification system from the designation, as below described. Designation of steels

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The EN 10027-1 standard defines how to designate a steel that is included in any of the above classes. Designating a steel means writes its own code by which a steel is univocally identified. We can talk about designation system as the way to give a name to steels accordingly to specific code. Below the four possibilities to designate a steel by the European Standard EN 10027-1. i) Plain carbon steel for general purpose are designated by the generalized code:

X nnn that can be completed by optional further digits. The designation is therefore com-posed by: a) a single letter X that designates the application (see the list of letter in Table 3.1), b) then a three digit number nnn signifying the me-chanical property (often yield strength) dictated in the standard for that ap-plication designation (see again Table 3.1). Example: the S355 steel refers to structural application with minimum guaranteed yield strength of 355 MPa.

Application sym-bol Meaning Mechanical Property

S Structural steel Minimum Yield Strength

P Steel for pressure lines and vessels Minimum Yield Strength

L Steel for pipe and tube Minimum Yield Strength

E Engineering steels Minimum Yield Strength

B Steel for reinforced concrete Characteristic Yield Case

R Steel for rail use Minimum Yield Case

H High Strength Cold Rolled Minimum Yield Case

D Flat Products for Cold Forming T Tinmill Products Nominal Yield Case

M Electrical Steel

Table 3.1 – Common application code and mechanical properties contemplated by three digit numbers.

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The heat-treated steels, namely all such steels of any classes other than general purpose steels type, can be designated by three different codes, depending on the chemical composition, as below described: ii) Carbon steel, namely steels where no alloying elements are added in chemical composition:

C nn where nn is the approximate carbon content multiplied by 100. For example, C40, means 0.4% of carbon content. iii) Alloying steel where more alloying elements have been added to chem-ical composition, but with all the alloying elements less than 5% weight:

nn A B C a b c

where:

- nn is the approximate carbon content multiplied by 100; - A, B, C, etc. represent the alloying elements; elements are ordered

from left to right as they are sorted by higher to lower content; - a, b, c (but often only at least two digit number is present) whole

numbers that represent by a multiplying factor the percentage of the A, B and C elements respectively. Factor is:

o 4 referring to Cr, Co, Mn, Si, W, Ni; o 10 referring to Al, Be, Cu, Mo, Ti, Pb, V, etc.; o 100 referring to N, P, S, Ce; o 1000 referring to B.

For example, a UNI EN 40CrMnNiMo8-6-4 is a low-alloyed steel with 0.40 %C, 2%Cr (=8/4), 1.5% Mn (=6/4), 1% Ni (=4/4) and some percent-age of Mo lower than 1%.

iv) High alloying steel with at least one of alloying element more than 5%:

X nn A B C a.b.c

where:

– nn is carbon content multiplied by 100; – A, B, C, etc. represent the alloying elements; elements are ordered

from left to right as they are sorted by higher to lower content;

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– a, b, c (but often only at least two digit number is present) whole

numbers that represent the actual percentage of the A, B, C ele-ments respectively approximate to whole number.

For example, an UNI EN X4CrNiMo17.12.2 is a high alloyed steel with 0.04 %C, 17%Cr, 12% Ni, 2% Mo steel. Classification of steels When we talk about classification, we intend to refer to how steels are classified into families or groups accordingly with their specific purposes. The EN 10027-1 groups steels by their functional uses for specific engi-neering purposes, as below illustrated.

• General purpose steels (non-heat treated steels); they are low-cost steels that are used for construction purposes, not alloyed and non-heat treat-ed. The chemical composition is thus not the distinguishing factor for their own designation. They are classified into three main types:

o Low strength, plain low carbon steel; o Medium strength, with Si between 0.15-0.35% and

1%Mn; o High strength, with higher Mn content up to 1.65%;

• Special steels, that are heat-treated steels, classified into 5 sub-

categories:

– Quenched and tempered steels – Carburizing steels – Nitriding steels – Spring steels – Self-quenching steels

• Steel for special applications, that are also heat-treated steels that are distinguished for specific applications. Several families are grouped un-der such larger class (e.g. high fracture toughness steels, tool steels, low temperature steels, high temperature steels, etc.);

• The Stainless Steels grade, classified into 4 types:

– Austenitic stainless steels; – Ferritic stainless steels; – Martensitic stainless steels;

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– Duplex stainless steels; – Precipitation hardening stainless steels.

The SAE-AISI classification and designation for steels In the following, the basics of SAE-AISI classification and designation of steels is described. Designation of steels The combined SAE/AISI numbering system uses a numerical code. It dis-tinguish: i) Plain carbon steels:

– either 10xx or 10xxx for plain carbon steels; the prefix 10 indicates that the steel is a plain carbon steel, while the subsequent xxx’s specify the nominal carbon content in points of carbon (1 point=0.01% C). For example, 1045 steel would nominally contain 0.45% C (which actually varies between 0.43 and 0.50%). Typical-ly, compositions run from 1005 to 1095, but the designation 10125 would indicate a plain carbon steel containing 1.25% C (see exam-ples in Table 3.2).

– 12xxseries, are rephosphorized and resulfurized steels (steels with an increased machinability, S addition, and increased ferrite strength because of P addition; small quantity of P strengthens fer-rite crystal lattice by solid solution)14;

– 13xxseries, are carbon steels that contain more than 1wt% Mn and also have a minimum Si of 0.15 to 0.35 wt% (Si and Mn increase ferrite lattice strength by solid solution mechanisms) 14; 15xx series, are high Mn content carbon steels contain higher Mn levels (up to 1.65 wt%) than the 10xx series of carbon steels. Notice that Mn lowers the A3 temperature thus refining the resulting fer-rite-pearlite structures; Mn also contribute some solution-hardening of the ferrite, but it is limited compared to that of C, N and Si14.

ii) Alloy steels: – 40xx series, are Molybdenum steels14; Molybdenum is added in

small amounts, increases both the strength and hardenability of

14 The subsequent xxx’s specify the nominal carbon content in points of carbon (1 point=0.01% C).

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steels. Steels containing molybdenum are less susceptible to temper brittleness (i.e. Krupp brittleness).

– 41xx series, are Chromium-Molybdenum steels14; Chromium is added to increase hardenability and strength; however, the addition of chromium can also make this series susceptible to temper embrit-tlement;

– 43xx, 47xx, 81xx, 86xx, 87xx and 94xx designates the Nickel-Chromium-Molybdenum Steels series (refer to Table 3.2 for de-tails).

Table 3.2 – Summary of AISI/SAE designations for carbon and low-alloy steels.

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Classification of steels The AISI standard groups steels into following main classes:

– Plain carbon steels (10xxx series) A plain carbon steel is essentially an alloy of Fe-C that also contains manganese and a variety of re-sidual elements, in particular S, P (impurities) and Si (Si is added during the production process for deoxydation stage, refer to steelmaking section). AISI defines plain carbon steels as Fe-C with:

o 1.65 wt% maximum Mn, o < 0.6 wt% Si, o < 0.6 wt% Cu o no other deliberately added alloying element.

The carbon steels are classified as follows: o Nonresulfurized carbon steels (10xx or 10xxx series

steels); low, medium and high carbon content steels; o Resulfurized steels (11xx series); o Rephosphorized and resulfurized steels (12xx series); o High manganese carbon steels (15xx series);

– Alloy steels, namely Fe-C alloys with the addition of one or more of the following elements15: Mn, Cr, Ni, Mo, Ti, Co, W, V, Si, Al, B. Despite plain carbon steels are widely used, they are not adequate for all engineering applications because of the following limitations:

o They cannot be strengthened beyond approximately 700 MPa without a significant loss in toughness and ductility;

o They are not hardenable to great depths, thus limiting the maximum cross section that can be through hardened;

o Severe quench media (i.e. water) is required greatly in-creasing the susceptibility to distortion and cracking;

o They have poor corrosion resistance and readily oxidize at elevated temperatures.

– Stainless steels (Austenitic, Ferritic, Martensitic, Duplex and Precipitation Hardening Steels) in order to prevent corrosion.

– Tool steels, to prevent wear phenomena.

15 As better described in the next section, metallurgical basic effects of alloying elements are: a) lowering A3 and A1, thus shifting CCT curves (e.g. increase har-denability); b) stabilize interstitial carbides (e.g. CrxCy, TiC, etc.) formed during tempering (e.g. increase tempering temperature to increase toughness not decaying strength).

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Fig.3.1 - Classification of ferrous alloys. Relationship between microstructure and properties of steels Firstly it is worth of notice that strengthening mechanisms we discussed in the Chapter 1 are here fundamental to comprehend the relationship be-tween mechanical properties and microstructures - namely how micro-structures can exert control on dislocation mobility – which are the result of specific heat treatments specifically designed for the chemical composi-tion of special steel chosen for realize the part component for its specific engineering purpose.

Microstructures and heat treatment in steels Almost all of the heat treatments of steel are directed toward producing the mixture of ferrite and cementite that gives the proper combination of properties. Figure 3.2 shows the three important microconstituents, or ar-rangements of ferrite and cementite, that are usually sought. Pearlite is a microconstituent consisting of a lamellar mixture of ferrite and cementite.

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In bainite, which is obtained by transformation of austenite at a large un-dercooling, the cementite is more rounded than in pearlite. Tempered martensite, a mixture of very fine and nearly round cementite in ferrite, forms when martensite is reheated following its formation.

Fig.3.2 - Micrographs of (a) pearlite, (b) bainite, and (c) tempered martensite, il-lustrating the differences in cementite size and shape among the three microcos-tituents. The microstructures mentioned above in steels are produced by the trans-formation of the austenite microstructure (obtained by heating up structure over A1 and A3 temperatures) throughout: a) isothermal transformation that occurs below A1 temperature; b) continuous cooling from austeinitiz-ing temperature to ambient temperature.

Box - Isothermal transformation treatments for bainite or fine perlite for-mation The isothermal transformation heat treatment used to produce bainite, called austempering, simply involves austenitizing the steel, quenching to some tem-perature below the nose of the TTT curve, and holding, at that temperature until all of the austenite transforms to bainite (Fig.3.3). Very fine pearlite can be also formed by an isothermal anneal (Figure 3.3), with more uniform properties, since the cooling rates and microstructure obtained during continuous cooling can vary across the cross-section of the steel.

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Fig.3.2 - The austempering and isothermal anneal heat treatments in a 1080 steel.

Continuous cooling transformation treatments Four simple heat treatments — process annealing, annealing, normalizing, and spheroidizing — are commonly used for steels to produce mixture of ferrite and perlite structure (Figure 3.3). These heat treatments are used therefore to accomplish one of three purposes: (1) eliminating the effects of cold work, (2) controlling dispersion strengthening, or (3) improving machinability.

- Process Annealing—Eliminating Cold Work The recrystallization heat treatment used to eliminate the effect of cold working in steels with less than about 0.25% C is called a process anneal. The process anneal is done 80°C to 170°C below the A1 temperature. The intent of the process anneal treatment for steels is similar to the annealing of inorganic glasses in that the main idea is to signif-icantly reduce or eliminate residual stresses.

- Annealing and Normalizing—Dispersion Strengthening Steels can be dispersion-strengthened by controlling the fineness of pearlite. The steel is initially heated to produce homogeneous austenite (FCC α-phase), a step called austenitizing.

- Annealing, or a full anneal, allows the steel to cool slowly in a furnace, producing coarse pearlite. Normalizing allows the steel to cool more rapidly, in air, producing fine pearlite. Figure 3.4 shows

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the typical properties obtained by annealing and normalizing plain carbon steels16.

Fig. 3.3 - Schematic summary of the simple heat treatments for (a) hypoeutectoid steels and (b) hypereutectoid steels.

16 For annealing, austenitizing of hypoeutectoid steels is conducted about 30°C above the A3, producing 100% γ ; however, austenitizing of a hypereutectoid steel is done at about - 30°C above the A1, producing austenite and Fe3C. This process prevents the formation of a brittle, continuous film of Fe3C at the grain boundaries that occurs on slow cooling from the 100% region. In both cases, the slow furnace cool and coarse pearlite provide relatively low strength and good ductility. For normalizing, austenitizing is done at about 55°C above the A3 or Acm; the steel is then removed from the furnace and cooled in air. The faster cooling gives fine pearlite and provides higher strength.

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Fig. 3.4- The effect of carbon and heat treatment on the properties of plain carbon steels.

- Spheroidizing—Improving Machinability. Steels that contain a large concentration of Fe3C have poor machining characteristics. It is possible to transform the morphology of Fe3C using spheroi-dizing. The microstructure, known as spheroidite, has a continuous matrix of soft, machinable ferrite due to the presence of round small Fe3C carbides (Fig.3.12).

Fig. 3.12 - The microstructure of spheroidite with Fe3C particles dispersed in a ferrite matrix.

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Strengthening of ferritic-perlitic structure

Fe3C phase is much harder but more brittle than ferrite. Thus, increasing the fraction of Fe3C in a steel alloy while holding other microstructural el-ements constant will result in a harder and stronger material. This is demonstrated in Figure 3.13a, in which the tensile and yield strengths and the Brinell hardness number are plotted as a function of the weight percent carbon (or equivalently as the percentage of Fe3C) for steels that are com-posed of fine pearlite. All three parameters increase with increasing carbon concentration. Inasmuch as cementite is more brittle, increasing its content will result in a decrease in both ductility and toughness (or impact energy). These effects are shown in Figure 3.13b for the same fine pearlitic steels. The layer thickness of each of the ferrite and cementite phases in the mi-crostructure also influences the mechanical behavior of the material.

Figure 3.13 - (a) Yield strength, tensile strength, and Brinell hardness versus car-bon concentration for plain carbon steels having microstructures consisting of fine pearlite. (b) Ductility (%EL and %RA) and Izod impact energy versus carbon concentration for plain carbon steels having microstructures consisting of fine pearlite. Fine pearlite is harder and stronger than coarse pearlite, as demonstrated by the upper two curves of Figure 3.14a, which plots hardness versus the carbon concentration. The reasons for this behavior relate to phenomena

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that occur at the α–Fe3C phase boundaries. First, there is a large degree of adherence between the two phases across a boundary. Therefore, the strong and rigid cementite phase severely restricts deformation of the soft-er ferrite phase in the regions adjacent to the boundary; thus the cementite may be said to reinforce the ferrite. The degree of this reinforcement is substantially higher in fine pearlite because of the greater phase boundary area per unit volume of material. In addition, phase boundaries serve as barriers to dislocation motion in much the same way as grain boundaries (see Chapter 1). For fine pearlite there are more boundaries through which a dislocation must pass during plastic deformation. Thus, the greater rein-forcement and restriction of dislocation motion in fine pearlite account for its greater hardness and strength. Coarse pearlite is more ductile than fine pearlite, as illustrated in Figure 3.14b. This behavior results from the greater restriction to plastic deformation of the fine pearlite.

Figure 3.14 (a) Brinell and Rockwell hardness as a function of carbon concentra-tion for plain carbon steels having fine and coarse pearlite as well as spheroidite microstructures. (b) Ductility (%RA) as a function of carbon concentration for plain carbon steels having fine and coarse pearlite as well as spheroidite micro-structures.

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Box –The Continuous Cooling Transformation (CCT) Diagrams for steels and effect of alloying elements. We can develop a continuous cooling transformation (CCT) diagram by deter-mining the microstructures produced in the steel at various rates of cooling. Let us consider the CCT diagram of Fig.3.15. If we cool a 1080 steel at 5°C/s, the CCT diagram tells us that we obtain coarse pearlite; we have annealed the steel. Cooling at 35°C/s gives fine pearlite and is a normalizing heat treatment. Cool-ing at 100°C/s permits pearlite to start forming, but the reaction is incomplete and the remaining austenite changes to martensite. We obtain 100% martensite and thus are able to perform a quench and temper heat treatment, only if we cool faster than 140°C/s. Other steels, such as the low-carbon steel in Fig.3.16 have more complicated CCT diagrams (in various handbooks, you can find a compilation of TTT and CCT diagrams for different grades of steels).

Figure 3.15 – The CCT diagram (solid lines) for a 1080 steel (the dashed lines represent the compared line transformation for the TTT diagram). Referring to heat treatment and CCT diagrams, main effect of alloying elements that are added to steels: (a) provide solid-solution strengthening of ferrite, (b) cause the precipitation of alloy carbides rather than that of Fe3C, and (c) im-prove hardenability. The term hardenability describes the ease with which steels can form martensite. Plain carbon steels have low hardenability; only very high cooling rates produce all martensite, despite medium carbon and alloy steels, which have high hardenability (even cooling in air may produce marten-site). This is visible if the CCT curves of low carbon and alloyed steels are compared (Fig.3.17). The effect of alloying elements, including carbon, is to shift CCT curves to the right and down in the temperature versus log time dia-gram.

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Figure 3.16 – The CCT diagram for a low-alloy, 0.2% C steel.

Figure 3.17 – CCT diagrams for: (a) red lines, a low-carbon steel; (b) a medium carbon steel. It is worth to notice hardenability does not refer to the hardness of the steel. A low-carbon, high-alloy steel may easily form martensite but, because of the low-carbon content, the martensite is not hard (Fig.3.18).

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Figure 3.18 – Relationship between hardness of quenched martensite and car-bon content; the effect of presence of retained austenite and self-tempering is al-so considered. Furthermore, in practical cases, the final hardness developed onto piece is relat-ed to how easily we can form martensite in a thick section of steel that is quenched. While with a more hardenable steel we can “get away” with a rela-tively slow cooling rate and still form martensite, in case of low hardenability steel it is possible that thicker sections cannot be transformed to martensite. This is caused by the shifting of the cooling curves on thicker sections, as shown by two different round sections illustrated in Fig.3.19.

Figure 3.19 – Shifting of cooling curves for small and large diameters round bar quenched from austenitizing temperature. The problem of quenching thicker sections of low hardenability steel is there-fore illustrated in Fig.3.20. As it is shown, the smaller radius section piece is transformed into martensite and bainite structure, across the cross section. How-ever, increasing the section radius causes shift of cooling curves - accordingly with the Fig.3.19 - thus provoking the formation across the round section of

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mixture of soft structure, as perlite and ferrite, together with hard martensite and bainite.

Figure 3.20 – Shifting of cooling curves for small and large diameters round bar quenched causes development of soft structure (perlite and ferrite) mixed with hard structure (martensite and bainite). Residual Stresses and Cracking Further complication we have in the practical case of Fig.3.20. When the aus-tenite in the center later transforms, the hard surface is placed in tension, while the center is compressed. If the residual stresses exceed the yield strength, quench cracks form at the surface (Figure 3.21). To avoid this, we can first cool to just above the Ms and hold until the temperature equalizes in the steel; subse-quent quenching permits all of the steel to transform to martensite at about the same time. This heat treatment is called marquenching or martempering (Figure 3.22). Note that as discussed presently, strictly speaking, the CCT diagrams should be used to examine non-isothermal heat treatments.

Figure 3.21 – Formation of quench cracks caused by residual stresses produced during quenching. The figure illustrates the development of stresses as the aus-tenite transforms to martensite during cooling.

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Figure 3.22 – The marquenching (or martempering) heat treatment, designed to reduce residual stresses and quench cracking. Evaluation of steel hardenability: the standard quench-end Jominy test In order to separate the effect of thickness dimension of a quenching piece from the right-shifting of CCT curves obtained by alloying elements, a standard Jominy test is used to compare hardenabilities of steels. A steel bar 4 in. long and 1 in. in diameter is austenitized, placed into a fixture, and sprayed at one end with water (Fig.3.23a). This procedure produces a range of cooling rates—very fast at the quenched end, almost air cooling at the opposite end. After the test, hardness measurements are made along the test specimen (Fig.3.23b) and plotted to produce a hardenability curve (Fig.3.23c). The distance from the quenched end is the Jominy distance and is related to the cooling rate (Fig.3.24).

Fig.3.23 - Schematic diagram of Jominy end-quench specimen (a) mounted dur-ing quenching and (b) after hardness testing from the quenched end along a ground flat; (c) the hardenability curve.

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Fig.3.24 - Correlation of hardenability and continuous-cooling information for an iron–carbon alloy of eutectoid composition.

Quenching and tempering of steels.

Further continuous cooling transformation treatment is conducted for the opposite purposes, that is to produce a high strength but tough microstruc-ture. It is a double step treatment: a) cooling from austetizing temperature a steel to transform austenite into martensite, a tetragonal structure pro-duced because of lack of carbon atoms diffusion (Fig.3.25); b) tempering, namely heating up quenched martensite below A1 temperature, to allow carbon atom diffuse and tetragonal lattice transform into BCC. Of the various microstructures that may be produced for a given steel al-loy, martensite is the hardest and strongest and, in addition, the most brit-tle; it has, in fact, negligible ductility. Its hardness is dependent on the car-bon content, up to about 0.6 wt% as demonstrated in Figure 3.26, which plots the hardness of martensite and fine pearlite as a function of weight percent carbon (top and bottom curves). In contrast to pearlitic steels, the strength and hardness of martensite are not thought to be related to micro-structure. Rather, these properties are attributed to the effectiveness of the interstitial carbon atoms in hindering dislocation motion and to the rela-tively few slip systems (along which dislocations move) for the BCT struc-ture.

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(a) (b)

Fig. 3.25 – (a) simple model for non-diffusional transformation from the FCC γ- phase to the Body-Centered Tetragonal (BCT) structure of martensite (diagonal centered rotated structure) –the white atoms are Fe, distinguished from black spheres representing carbon interstitial position; (b) Photomicrograph showing the martensitic microstructure.

Fig. 3.26 - Hardness (at room temperature) as a function of carbon concentration for plain carbon martensitic, tempered martensitic (tempered at 371°C), and pearlitic steels.

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Tempering martensite In the as-quenched state, martensite, in addition to being very hard, is so brittle that it cannot be used for most applications; also, any internal stress-es that may have been introduced during quenching have a weakening ef-fect. The ductility and toughness of martensite may be enhanced and these internal stresses relieved by a heat treatment known as tempering. Temper-ing is accomplished by heating a martensitic steel to a temperature below the eutectoid for a specified time period. Normally, tempering is carried out at temperatures between 250°C and 650°C; internal stresses, however, may be relieved at temperatures as low as 200°C. This tempering heat treatment allows, by diffusional processes, the formation of tempered mar-tensite, according to the reaction: Martensite (BCT, single phase) Æ tempered martensite (α−Fe + fine car-bides) where the single-phase BCT martensite, which is supersaturated with car-bon, transforms into the tempered martensite, composed of the stable fer-rite, cementite phases and carbides (in presence of alloying elements with great affinity with carbon). The microstructure of tempered martensite consists of extremely small and uniformly dispersed particles embedded within a continuous ferrite matrix. The fine and hard particles reinforce the ferrite matrix being barriers to dislocation motion during plastic defor-mation. On the other hand, a continuous ferrite phase guarantee adequate toughness; the double phenomena, hard particles dispersing and α−Fe ma-trix formation accounts for the improvement of both two counteracting properties, hardness and toughness, for an optimal balance. The size of the precipitates influences the mechanical behavior of tempered martensite; increasing the particle size decreases the ferrite–cementite phase boundary area and, consequently, results in a softer and weaker material, yet one that is tougher and more ductile. Furthermore, the tempering heat treatment de-termines the size of the cementite particles. Because carbon diffusion is involved in the martensite–tempered martensite transformation, increasing the temperature will accelerate diffusion, the rate of cementite particle growth, and, subsequently, the rate of softening. The dependence of tensile and yield strength and ductility on tempering temperature for an alloy steel is shown in Figure 3.27.

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Fig. 3.27 - Tensile and yield strengths and ductility (%RA) (at room temperature) versus tempering temperature for an oil-quenched alloy steel (type 4340).

Box – Temper Embrittlement The tempering of some steels may result in a reduction of toughness as meas-ured by impact tests; this is termed temper embrittlement. The phenomenon oc-curs when the steel is tempered at a temperature above about 575°C followed by slow cooling to room temperature, or when tempering is carried out at between approximately 375°C and 575°C. Steel alloyed with Cr are more susceptible to temper embrittlement have been found to contain appreciable concentrations of the alloying elements manganese, nickel, or chromium and, in addition, one or more of antimony, phosphorus, arsenic, and tin as impurities in relatively low concentrations. The presence of these alloying elements and impurities shifts the ductile-to-brittle transition to significantly higher temperatures; the ambient temperature thus lies below this transition in the brittle regime. It has been ob-served that crack propagation of these embrittled materials is intergranular; that is, the fracture path is along the grain boundaries of the precursor austenite phase. Furthermore, alloy and impurity elements have been found to segregate preferentially in these regions. Temper embrittlement may be avoided by (1) Molybdenum addition and/or (2) tempering above 575°C or below 375°C, fol-lowed by quenching to room temperature. Furthermore, the toughness of steels

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that have been embrittled may be improved significantly by heating to about 600°C and then rapidly cooling to below 300°C.

Prediction of hardenability There are large quantities of Jominy hardenability curves available in the literature, such as the ones shown in Fig. 3.28. The hardenability of a steel can also be predicted from its composition and grain size. The ideal diameter (DI) is defined as the diameter of a steel bar that will harden to 50 vol% martensite when quenched in an ideal quench medium. The significance of this value is that a bar with a diameter larger than DI cannot be hardened all the way through its cross section, even in an infinitely rapid quench. Grossman originally developed a method for calculating hardenability. The DI calculation starts from the calculation of the DB, the base diameter. DB is influenced only by the carbon content and the grain size17, and it can be read from plot in Fig. 3.29. The DB takes into accounts only two contributing factors for hardenability of steel, car-bon content and grain size, while it considers steel quenched in an ideal quenching mean.

Fig. 3.28 - Typical Jominy hardenability curves for medium-carbon steels austen-itized at 845 °C from initial normalized condition.

17 The hardenability increases with larger austenite grain sizes, because larger grain siz-es means there are fewer nucleation sites for diffusion-controlled phase transformations (that is, pearlite, ferrite, or bainite). When the danger of quench cracking is remote (i.e., no abrupt changes in section thickness) and engineering considerations permit, it may some-times appear to be more practical to use a coarse-grained steel than a fine-grained steel to obtain hardenability. However, this is not recommended, because the use of coarser-grained steels usually involves a serious sacrifice in notch toughness.

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Fig. 3.29 - Plot of base diameter, DB, used for calculating ideal diameter.

However, each of the alloying elements in the steel contributes by a multi-plying factor that increases the depth of hardening. Such multiplying fac-tors are given in Table 3.3.

Table 3.3 - Multiplying factors for alloying elements.

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Now, let us consider a steel containing 0.45 wt% C with an ASTM grain size of 6 and an alloy content of 0.5 wt% Mn, 0.2 wt% Si, and 0.35 wt% Cr. By the use of the plot in Fig. 3.29, firstly we can calculate the base di-ameter (DB) of a steel with only 0.45 wt% C and a grain size of 6 ASTM, obtaining DB= 6.5 mm. Secondly, we can estimate the multiplying factors mf(element) from the Table 3.3, as it follows:

0.5 wt% Mn= 2.667 = mf(Mn) 0.2 wt% Si= 1.140 = mf(Si) 0.35 wt% Cr= 1.756 = mf(Cr)

By the following relationship, since we already know the DB and the mul-tiplying factors, we can calculate the ideal diameter (DI) for the alloyed steel: DI=DB · mf(Mn) · mf(Si) · mf(Cr) = = (6.5mm) (2.667) (1.140) (1.756) = 34 mm

However, we know that the critical diameter DC depends on the quench severity. The relationship between ideal diameter (DI) and critical diame-ter (DC) for various quench severities is given by empirical diagram as it is shown in Fig.3.30. To use the plot, we need to know the H factor. This is possible by the use of the Table 3.4: for example, if the steel were quenched in moderately agitated oil, an H=0.37 can be determined from Table 3.4.

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Fig. 3.30 - Relationship between ideal diameter and critical diameter.

Table 3.4 - Quench values for several quenching media.

For the sake of simplicity, in Fig. 3.31 is reproduced the same diagram of Fig. 3.30, with all the curves removed except for the one we need for our final calculation.

Dc = critical diameter DI = ideal diameter

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Fig. 3.31 – Simplified plot of Fig.3.30 for determination of critical diameter (DC). As shown, with the calculated DI, the plot in Fig.3.31 allows us to calcu-late the critical diameter DC for the specific quench severity factor H=0.37: the DC is determined to be 7.5 mm. As last analysis, the section size of bars with square cross sections and plates can be compared with round bars, by the plot diagram in Fig. 3.32. There is also an empirical relationship between the diameter of steel and the Jominy distance at which there will be 50% martensite at the center, as shown in Fig. 3.32.

(a) (b)

Fig. 3.32 – (a) Comparison of different geometries with the same cooling rate at the center; (b) Relationship between ideal diameter and Jominy position.

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Review of phase transformations and mechanical properties for iron-carbon alloys In previous sections we have discussed several different microstructures that may be produced in iron–carbon alloys, depending on heat treatment. Figure 3.33 summarizes the transformation paths that produce these vari-ous microstructures. Here, it is assumed that pearlite, bainite, and marten-site result from continuous-cooling treatments. Microstructural characteris-tics and mechanical properties of the several microconstituents for iron–carbon alloys are summarized in Table 3.5.

Fig. 3.37 - Possible transformations involving the decomposition of austenite. Sol-id arrows, transformations involving diffusion; dashed arrow, diffusionless trans-formation.

Table 3.5 - Microstructures and Mechanical Properties for Iron–Carbon Alloys.

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The creation of hard instead of soft structure in a thick section of steel piece is dependent on steel hardenability. Such properties depends mainly from chemical composition and austenite grain size achieved by structure during austenitization temperature. Both these two factors have in fact di-rect influence in retarding austenite transformation, delaying start of diffu-sion-driven (i.e. ferrite, perlite and bainite) and diffusionless (i.e. marten-site) austenite transformations. As a simplified and powerful method to evaluate different hardenability of steels, the Jominy end-quench test, gives immediate representation of the effect of alloying elements. A steel of medium hardenability gives a hardness profile measured along the dis-tance from the quenched-end - i.e. the hardenability curve – as shown in Fig. 3.38a; the hardness drops rapidly because the cooling curves intercept the curves that represent the start of transformation of austenite into struc-tures (bainite, perlite and ferrite) which are softer than martensite. On the opposite, hardenability increases as amount of alloying elements increases and this leads to formation of martensite at higher distances from the quench-end, namely the end of Jominy sample directly cooled by water jet.

(a) (b)

Fig. 3.38 - Jominy test on a steel of: (a) low hardenability; (b) high hardenability.

Secondarily, it is important to notice that tempering treatment is often re-quired to recover toughness. This is due to change of the high-strength and high-brittle medium and high carbon BCT lattice into a tougher BCC ma-

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trix with fine carbide particles here dispersed. Because of presence of such particles, the α-Fe BCC matrix is strengthened meanwhile it recovers tough behavior (i.e. dislocations can move again, but small particles op-pose to such movement, instead the previous situation of BCT lattice where dislocations are unmovable). Industrial quenching problems: distortions and quenching cracks Quenching is generally considered as the most critical step of heat treat-ment processes conducted onto steel parts. It may lead to failures that are generally distortions and, in most severe cases, cracks. Both distortion and cracks are due to high stresses which develop in the part during quenching. This occurs because massive parts are subjected to rapid cooling, and this determine mismatching among the temperatures on top surface and subsur-face layers, cross the part sections. We have already discussed about the variation of cooling curves diagram- we call the “cooling islands” when two different diameters round bars made of same steel are quenched in the same quenching mean. For the reader convenience, here below is shown again the figure 3.20 with the original caption.

Figure 3.20bis – Shifting of cooling curves for small and large diameters round bar quenched causes development of soft structure (perlite and ferrite) mixed with hard structure (martensite and bainite).

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The above figure illustrates one main problem due to limited hardenability of steels. Hardenability, we remember, is the ability of steels to penetrate martensite in depth, which depends on the fact cooling curves occurring inside the part section can intercept the Ms transformation, instead of crossing other curves representing the transformations of austenite in something other structures softer than martensite. Actually, for the sake of precision, also the case illustrated in the Fig.3.20bis is not the ideal case of fully quenched section; quenching the two steel bars reported in the figure actually produce martensite mixed to bainite (for 28mm diameter bar) and small fraction of martensite mixed with very varying structures that range from ferrite to perlite and bainite (for the 95mm diameter bar). As discussed, to increase hardenability, we need to increase the alloying elements in the chemical composition of steel. Alloying elements produces the lowering of all the critical temperatures and a delay in austenite trans-formation is produced as a benefit for quenching. Shifting the CCT curves toward the right, martensite can be obtained onto larger sections by quenching. This is the basics of quenching operations. However, one further beneficial effect obtained by alloying steel to in-crease the hardenability must be highlighted. Let us consider the simplified scheme in figure 3.39.

Figure 3.39 - Comparison of two possible quenching operations for a high harden-ability steels. Both the water and oil quenching is possible, in terms of martensite production in part section. The faster is the quenching operation, the larger is the instantaneous differences between surface and inner section temperatures.

Log t

Ms

T

Mf

A3

A1

∆1 ∆2

Water quenched

Oil quenched

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The CCT curves in the fig.3.39 show the steel may be quenched either in water or in oil. Even with water quenching is less expensive, it is not in-dustrially suitable for such a steel; this fact is due observing the instanta-neous temperatures achieved in the part sections. In case of water quench-ing, the temperatures achieved at same time at surface and in the center of a round section, for example, are very high if compared to the same bar section when it is quenched in oil. The higher is instantaneous temperature difference in part section, the higher is the differential volumetric expan-sion of steel. The volumetric expansion actually accounts for two concur-rent contributes (depending on temperatures investigated): a) thermal ex-pansion that is only function of the temperature and the coefficient of thermal expansion; b) the volumetric expansion due to transformation of FCC γ-phase into body-centered tetragonal (BCT) martensite. In any case, the results is the same: as the sections of a part are interested by too much temperature variations, for reason a) or b) or both, they are subjected to differential expansion. If the differential expansion remains in the elastic regime, the only result is temporary thermal induced stresses. However this case is very rare, while more frequent is the case that plastic deformations occur inside the part due to mismatching volumetric expan-sion. If the plastic deformation caused a beneficial drop of thermally-induced stresses (the stresses induced by differential thermal expansion fi-nally relax), such local plastic deformations are irreversible local volume changes, that at least cause macroscopic part distortions (e.g. torsion, bending, profile and hole ovalization, hole misalignments. It is worth of noticing that such problems can occur also in heating phase, especially for large parts; for high speed heating-up process, especially large parts can suffer of temperature mismatching that can cause distor-tions. For this reason the temperature ramp-up rate shall be controlled and equalization stages (Fig.3.40).

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(a)

(b)

Figure 3.40 - Schematic representation of heating during an austenitizing treat-ment: a) with final temperatures equalization stage; b) with final and intermediate equalization. Quenching and tempering steels They are steels with the carbon percentage ranging 0.20-0.60% with even-tually some elements added to increase hardenability. They are required when an optimum balance between toughness and strength is required. Toughness is a very important mechanical property, especially for components that must be able to withstand dynamic loading or impact. Despite ductility, toughness of a material, is a “two-dimensional” property because it is an integral (or product) of strength and ductility, as schematically shown in Figure 3.41. Steels of the same ductili-ty but different strength levels can differ in toughness. As Figure 3.41 shows, a normalized steel (N) having the same ductility as a hardened and

Surface

Core

Soaking

Time

Austenitizing or quenching temperature

Tem

pera

ture

Equalization

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tempered steel (V) will have lower toughness because of its lower strength level. Toughness is measured in separate tests as impact toughness (e.g. KV, J/cm2) or as fracture toughness ( KIC, MPa√m ). The lower the ductili-ty of a material, the more brittle it is. Total brittleness accordingly denotes zero ductility of the material.

Figure 3.41 - Schematic presentation of ductility, toughness, and brittleness.

The aim of quenching (also called hardening) and tempering steels is to achieve maximum toughness at a specified strength level. The metallurgical mechanisms of tempering process is below described. As the as-quenched martensite, a body-centered tetragonal (BCT) struc-ture, is heated up, the prolonging staying at temperatures allow carbon at-om diffusion. This leads carbon to abandon the BCT position allowing the tetragonal lattice - a body centered structure - to shrink by transforming in-to a body-centered cubic (BCC), namely a α-Fe phase structure. The dif-fusing carbon thus migrates into α-Fe matrix capturing any alloying ele-ments that are added in solid solution, particularly those elements that have greater affinity to carbon than the affinity with Fe. Diffusion of carbon at-oms therefore allow carbon itself to be available to form with high carbon-affinity alloying elements so fine carbides (fine particles) which widely disperse into the α-Fe matrix. These carbides are capable to inhibit the movement of dislocations (accordingly to precipitation hardening strength-ening mechanism). The diffusion of carbon therefore have two concurring effects: a) carbon atoms abandon positions that determined in the as-

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quenched BCT structure the high-strength but brittle behavior (remind that dislocations cannot move in a BCT structure); b) in presence of alloying elements carbon can form fine and more dispersed carbides, namely fine particles that are “visible” to dislocations and that can inhibit them in their own movement. Due to such temperature-time driven metallurgical mechanisms, tempering of martensite would be preferentially conducted at high temperatures, to speed up the treatment; o the other hand, tempering temperature for quenching and tempering steels shall be conducted at temperature lower than 680-700°C. In fact, if tempering temperatures are too much close to A1 temperature of the steel, they would vanish any quenching effects: at temperature higher than optimized, carbides formed (especially for carbon steels) would grow and finally coarse instead of fine carbides will be dis-tributed in α-matrix. The bigger are carbides, the lower is their capability to counteract dislocation movement. At least, we could also fail the tem-pering object by accidentally overpassing the A1 temperature, so that the microstructure will be turned into martensite mixed to soft structures18. This leads to tempering temperature for quenching and tempering steels range from 600 to 680°C to achieve the good balance of strength and toughness. The aim of the quenching and tempering process can also be explained by means of the stress–strain diagram schematically shown in Fig. 3.41. As hardened, a steel has high yield strength but low ductility, and a small area below the stress–strain curve (curve 2) indicates low toughness. As-hardened and tempered (curve 3) steel has higher yield strength than in its normalized condition but also much higher ductility than in its hardened condition. The greatest area below the stress–strain curve indicates a sub-stantial increase in toughness compared to either normalized or hardened conditions. For a certain steel grade, the relation between mechanical properties and the tempering temperature can be read off from a diagram as shown in Figure 3.42 for the steel DIN EN 20CrNiMo2 (0.15% C, 0.20% Si, 0.88% Mn, 0.53% Cr, 0.50% Mo, 0.86% Ni).

18 Some percentage of austenite may be produced by overpassing the A1; by slow cooling after tempering, such an austenite fraction produced in such a wrong tempering treatment will be therefore transformed into small quantities of ferrite and perlite grains, namely softer microstructure than tempered martensite.

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Figure 3.41 - Stress–strain diagram of a steel after different heat treatments. 1, Normalized; 2, hardened; 3, hardened and tempered.

Figure 3.42 - Hardening and tempering diagram of DIN 20CrNiMo2 steel.

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It can be clearly seen from the lower part of the diagram in Fig.3.42 how the impact toughness increases when the steel is tempered to a temperature above 550°C. Such diagrams enable precise optimization of the strength level and toughness by selection of the proper tempering temperature. Maximum toughness values are obtained when tempering a structure that, after quenching, consists of fine-grained martensite. How different micro-structures after different heat treatment processes influence the impact toughness of 3.5% Ni steel at low temperatures is shown in Figure 3.43. When testing the impact toughness at low temperatures, the so-called tran-sition temperature (the temperature at which a substantial drop in impact toughness begins) is of special interest. The lower is the transition temper-ature, the higher is the toughness.

Figure 3.43 - Influence of different microstructure and respective heat treatments on the impact toughness at low temperatures (ISO notch specimens) of a 3.5% Ni alloyed steel. a, Hardened by quenching in water and tempered; b, normalized and tempered; c, normalized only; d, hardened by quenching in water only. Certainly, when quenching workpieces of big cross section, not only mar-tensite is obtained, but also other constituents such as bainite, pearlite, and even pre-eutectoid ferrite, depending on the decrease in cooling rate at quenching, below the surface toward the core of the workpiece. So after tempering, besides tempered martensite, other structural constituents hav-ing lower toughness are present. From a series of tests with hardened and tempered steels with about 0.4% C, Figure 3.44 shows a general relation between the structural constituents and the properties characterizing ductil-

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ity (elongation and reduction of area) and impact toughness, respectively, for different levels of yield strength. It is clear that tempered martensite always gives the best ductility and toughness. If compared the tempered martensite with other structural constituents, it is worth mentioning that especially for high strength values the superiority of fine-grained martensite structure with respect to toughness is evident.

Figure 3.44 - Elongation; (b) reduction of area; and (c) impact toughness of hard-ened and tempered steels having about 0.4% C, as a function of structure constitu-ents and yield strength. F, Ferrite; P, pearlite; B, bainite; M, martensite. Grain size: ASTM 6–7.

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When comparing the impact toughness of tempered martensite at different strength levels (different hardness levels), one can perceive the influence of carbon content. As shown in Figure 3.44, of steels for hardening and tempering, those with 0.2–0.3% C have the best impact toughness19.

Figure 3.44 - Impact toughness as a function of tensile strength and carbon content for the structure of tempered martensite. Grain size: ASTM 6–7. The great influence of the microstructure achieved after hardening and be-fore tempering on the impact toughness of a steel is evident from Fig. 3.45. Appearance of pre-eutectoid ferrite or ferrite and pearlite in the structure results in a substantial decrease in the impact toughness. When selecting a structural steel for hardening and tempering, the ex-pected microstructure must be considered. Unalloyed steels for hardening and tempering, because of their low har-denability, exhibit a high degree of section sensitivity with respect to hard-ness distribution after hardening as shown in Figure 3.46.

19 When testing the impact toughness of a steel, one should be aware that toughness is usually higher in the longitudinal direction (rolling direction) than in the transverse direction. That is because some phases or nonmetallic inclusions that are present in every steel (carbides, oxides, and sulfides) are stretched during rolling in the longitudinal direction. In this way a textured structure originates that has lower impact toughness in the transverse direction than in the longitudinal di-rection. As a measure of this effect, the factor of isotropy (the ratio of transverse impact toughness to longitudinal impact toughness) is sometimes used.

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Figure 3.45 - Influence of the microstructure after hardening (before tempering) on the impact toughness of EN DIN 20CrMo4 steel. After quenching a bar specimen of 30-mm diameter of the steel in question in conventional quenching oil, a hardness of only 40 HRC was achieved at the surface. When specimens of the same diameter were quenched in fast quenching oil, the hardness was 45 HRC; when quenched in 10% aqua-quench solution the hardness was 56 HRC; and when quenched in water containing 5% Na2CO3, it was 58 HRC as shown in Fig. 3.47. This exam-ple leads to two important conclusions: 1. By using different quenchants and quenching conditions, different hard-ness distributions can be obtained with the same steel grade and same cross-sectional size. 2. With an unalloyed steel, even when the most severe quenchant is used, for large cross-sectional sizes, the depth of hardening will be small and the core will remain unhardened. Because of the second conclusion, when selecting a structural steel grade for hardening and tempering, its hardenability must always be adapted to the workpiece’s cross-sectional size and the required strength level. Fig. 3.48 shows the preferred fields for the application of some common steel grades for quenching and tempering according to the actual bar diam-eter and the strength level required. This recommendation is based on the

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assumption that a minimum impact toughness of about 50 J/cm2 at room temperature will be achieved. As can be seen from Figure 3.48, for bigger cross-sectional sizes (bigger diameters) and higher strength levels, steels of higher hardenability (i.e., with more alloying elements) are required.

Figure 3.46 - Hardness distribution (measured) on the cross section of bars of dif-ferent diameters made of unalloyed steel (0.52% C, 0.24% Si, 0.90% Mn, 0.06% Cr) quenched in conventional hardening oil from 860°C.

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Figure 3.47 – Hardness distribution (measured) on the cross section of bars of 10–50-mm diameters made of unalloyed steel (0.52% C, 0.24% Si, 0.90% Mn, 0.06% Cr) quenched from 860°C in water containing 5% Na2CO3.

Figure 3.48 – Applicability of steel grades for hardening and tempering according to required strength level and bar diameter. Steel designations according to EN 10083.

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Basics of criteria selection Form a metallurgical point of view, quenching and tempering steel selec-tion should be driven by hardenability and hardness to be achieved, fur-thermore considering importance of other features as weldability or possi-bility to realize surface quenching. Low carbon increases toughness and weldability, but with low mechanical strength (e.g. C25; C30; C35). Generally, increasing carbon content (e.g. C50, C55, C60) determine higher mechanical strength, but it lowers toughness. The decrease of toughness however is counteracted increasing alloying elements, especially those ones with great affinity to carbon (e.g. Cr, Mo) that allow to keep carbon content at lower values than the range 0.45-0.50% to achieve high mechanical strength (e.g. 38Cr2; 35CrMo4; 42CrMo4). If high hardness is required, the carbon content shall be in-creased (typically at 0.50% or higher), but obviously it causes the tough-ness. Percentage of alloying elements determine raw material price of quenching and tempering steels. Among typical elements added, Ni is one of most expensive: it is added to decrease the ductile-to-brittle transition tempera-ture. The alloying elements, as known, affect positively hardenability and the hardenability influence the critical diameter Dc. This means that as the homogenized tempered martensite structure is targeted in a large part sec-tion (remember that mechanical properties, the toughness too, drop when highly mixed and inhomogeneous microstructure is produced, as shown in Fig.3.45), high-alloyed steels (e.g. 39NicrMo3, 30CrNiMo8, 40NiCrMo7) shall be preferred. The manufacturing cycle of quenching and tempering steels The quench and temper step is the major step in the manufacturing cycle of mechanical part made of quenching and tempering steels. However, the whole manufacturing cycle for quenched and tempered parts requires further upstream and downstream steps, as shown in Fig.3.49. The additional steps are to allow:

- The correct homogenization of chemical composition and micro-structure in preliminary phases, before shaping;

- The control of undesired geometrical distortions that may occur in the quenching step, to respect the dimensional accuracy of parts.

The two main issues above are discussed below.

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Figure 3.49 – Manufacturing cycle for quenching and tempering steel part.

Reduction of microstructure and chemical composition inhomogeneity Preliminary heat treatment (Fig.3.49) is necessary to achieve as possible homogeneous local chemical composition in raw material which enters in the manufacturing cycle. It is not possible in practice to obtain by steelmaking process and/or secondary semifinished operations (to produce for example, billets, see Fig.3.50) a highly homogeneous structure as de-sired. For example, at the end of semifinished hot operations (Fig.3.50, right side) the microstructure of rolled bars made of medium carbon steel is typically an inhomogeneous structure of mixed ferrite and perlite grains. Furthermore, despite to theoretic Fe-C binary phase diagram, in the semi-finished steelmaking process products (i.e. billets, blooms, slabs), high variation of local chemical composition is usual. For a deeper discussion on the morphology of microstructure obtained in solidification of steel, reader may refer to Chapter 9 that specifically deals with the steelmaking process, the upstream steps shown in the Fig. 3.50 and steel microstructure evolution in solidification. Here we aim just to introduce the problem of local inhomogeneous chemical composition as residual into hot worked products. It is known that the Fe-C diagram allow to predict for an euctectoidic steel a ferritic-perlitic structure, as well as formation of ferrite and perlite grains

Machining operations(e.g hot forging)

Quench

Temper (∼600°C)

Finishing operations(e.g. surface finisihing,

hole drilling)

Full annealing (eventuallyNormalizing + soft annealing)Pre-heat treatments

Machining operations

Heat treatments

Finishing operations


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from austenitic grains occur in conditions where atoms can diffuse (Fe and C predominantly). However, industrial solidification produces macroscop-ic and microscopic partitioning of chemical elements between parent liq-uid and the growing solid crystals. A generic scheme of such a problem is shown in the Fig.3.54. As the grains of such segregated structures recrys-tallize during secondary hot forming processes (e.g. forging, rolling, etc.; see Fig.3.50), micro-segregations align with material flowing imposed by hot working; for example, they align with rolling direction or forging ma-terial flowing into dies, leading to appearance of fibers as shown in Fig.3.55. Particularly, such fibers are macroscopically observable and they are the result of aligned “bands”. They are the product of oriented micro-segregations that are developed parallel to the main hot working material flowing. Such bands are observed at microscopic scale by metallographic analysis (conducted onto polished and acid pickled metallographic sam-ples), as shown in Fig. 3.57. Full annealing treatment - which means high temperature and prolonged heating - usually is preferred when micro-segregations, responsible for banding structures, are willing to be eliminated. Full annealing in fact, in-stead of normalizing, may produce C and Mn (see box below) re-diffusion in order to reduce micro-segregation phenomena.

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Figure 3.50 – Scheme of steel making process, upstream and downstream process steps. The right side of figure shows the semifin-ished steel made products of larger size (billets, blooms, slabs) and lower size (bars, tubes, sheets, etc.).

Figure 3.55 – Forging fibers produced in hot forged connecting rod.

Figure 3.56 – Forging fibers produced in hot forged crankshaft, compared to lon-gitudinal fibers cut by fully-machined part from round bar.

Fig. 3.57 - Banding in a UNI EN 18CrNiMo7-6 (normalized condition): a) ac-ceptable banding for post heat-treatments; b) non acceptable banding phenomena after normalizing, due to too much high segregation occurred in solidification pro-cess.

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Control of quenching distortion As above discussed, residual stresses and associated distortions might re-sult in an unacceptable as-quenched shape of the part which could not re-spect geometry and final dimensions. For this reason the quenching and tempering step is interposed between the gross shaping (i.e. hot working coupled with the following gross machining operations) and the final ma-chining operations for the net-shaping. Additional material is therefore left in order to ensure a positive material envelope to take into account the dis-tortion and allow finishing operations to realize the final shape, as draw specifications require for the final assembling.

Fig.3.58 – Control of quench distortions by additional material left be-fore the quenching.

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Box – Equilibrium solidification of solid-solution alloy and non-equilibrium solidification with segregation phenomena In Fig.3.53 is shown a binary diagram of a Cu-Ni alloy. The Cu-40% Ni is melted and cooled, and as known solidification requires both nucleation and growth. If the freezing is conducted throughout equilibrium steps (i.e. atomic diffusion is fully allowed as it is time-temperature driven), the nucleation and growing of α-phase grains proceed until the solidus temperature: all of the solid grain will contain a uniform concentration of 40% Ni, as the melting phase orig-inally contained. This is typical for a fully miscible solid solution.

Figure 3.53–The change in structure of a Cu-40% Ni alloy during equilibrium solidifica-tion. The nickel and copper atoms must diffuse during cooling in order to satisfy the phase diagram and produce a uniform equilibrium structure. On the opposite, if we consider the same simple system but we cool it too rapid-ly, atoms cannot fully diffuse and produce equilibrium conditions: non-equilibrium structures are therefore produced in the casting. Let’s see what hap-pens to our Cu-40% Ni alloy on rapid cooling and refer to Fig.3.54.

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Figure 3.54 – The change in structure of a Cu-40% Ni alloy during non-equilibrium so-lidification. Insufficient time for diffusion in the solid produces a segregated structure. Notice the non-equilibrium solidus curve. The first solid, containing 52% Ni, forms on reaching the liquidus temperature. On cooling to 1260°C, the tie line tells us that the liquid contains 34% Ni and the solid that forms at that temperature contains 46% Ni. Since diffusion occurs rapidly in liquids, we expect the tie line to predict the liquid composition accu-rately; however, diffusion in solids is comparatively slow. The first solid that forms still has about 52% Ni, but the new solid contains only 46% Ni. We might find that the average composition of the solid is 51% Ni. This gives a dif-ferent nonequilibrium solidus than that given by the phase diagram. As solidifi-cation continues, the nonequilibrium solidus line continues to separate from the equilibrium solidus. When the temperature reaches 1240°C (the equilibrium sol-idus), a significant amount of liquid remains. The liquid will not completely so-lidify until we cool to 1180°C, where the nonequilibrium solidus intersects the original composition of 40% Ni. At that temperature, liquid containing 17% Ni solidifies, giving solid containing 25% Ni. The last liquid to freeze therefore contains 17% Ni, and the last solid to form contains 25% Ni. The average com-position of the solid is 40% Ni, but the composition is not uniform. The actual location of the nonequilibrium solidus line and the final nonequilibrium solidus temperature depend on the cooling rate. Faster cooling rates cause greater de-partures from equilibrium.

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Box - Origin of banded structures In hypoeutectoidic steels, the ferrite-perlite banding is explained often by the ef-fect of manganese and phosphorous, mostly manganese. During solidification, segregation of these two elements can occur. The secondary hot working pro-cess tend to align and distribute such elements along material flow. The Mn acts directly on A3, stabilizing austenite by lowering A3. This causes that, during cooling from austenitizing temperature, full ferrite structure is stim-ulated to form in low-content Mn zones in austenite grains. As ferrite grains preferentially form in such areas, progressively carbon is rejected to adjacent areas. Thus, conversely, the perlite grain forms in such new zones where high carbon content has been reached. During secondary heat treatment the austenitic grain size can play an important role in the appearance of bands, accordingly with the scheme shown in Fig.3.58:

– as the austenitic grain size is smaller than the microsegregation inter-spacing, ferrite grains nucleate firstly on austenite grain boundaries (and triple points) in Mn-poor regions (with high A3 temperatures); these grains grow in alignment with those low-Mn content (i.e. the rolling di-rection), and then proceed. – Conversely, as austenitic grain size is greater than the interspacing o segregation, it could result in the disappearance of banding.

Fig.3.58 – Scheme of potential disappearing of bands from macrosegregation phenomena.

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Self-quenching (Air-quenching) steels The UNI EN 36NiCrMo16 is a special steel of the category quenching and tempering type series. Despite it is classified in UNI EN 10083 as quench-ing and tempering steel, historically it has been referred as an air-quenching steel. As the name states, such a steel has capability to be quenched in air. This is clearly visible by the Jominy quench-end test of this steel, which is shown in Table 3.6.

Table 3.6 - Jominy test results and main mechanical properties for UNI EN 36NiCrMO16 round bars, various diameters. As shown by Jominy curve, the hardness is kept at high value also at far-end of Jominy test specimen, where normally quenching and tempering steels exhibit a drop in hardness (at high distances from the quenched end, the cooling curves cross the austenite-ferrite and austenite- perlite trans-formations areas on the CCT). In such a particular case, the high percentage of alloying elements, particu-larly Ni, Cr and Mo (Ni ranges 3.63-4.27%; Cr ranges 1.55-2.05%; Mo 0.26-0.64) shifts the CCT curves to the right so that air-cooling curve cross only the Ms and Mf.

YS min. UTS

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It is worth noticing that the chemical composition of such a steel is identi-fied in a specific range. Particularly, the sum of percentage of C, Ni and Cr shall be limited in the range 5≤ (%C+%Cr+%Ni) ≤7. The lower limit is necessary to allow chemical elements to reach minimum content to shift CCT to the right in order to allow air-quenching. The upper limit is due to not exceed the alloying elements to such values that would cause marten-site transformation also by furnace cooling. In this latter case, in fact, it would be not possible for such a steel to be heat treated in order to produce ferrite and perlite, namely the machinable structures. Comparing the manufacturing cycle for an air-quenched part with the cy-cle typically employed for a quenching and tempering steel part, only two are the differences, but so relevant:

- Full annealing is the only one allowed preliminary heat treatment to realize ferrite and perlite, the machinable structure; normalizing is not possible since it is an air cooling treatment, that represents quenching for such a steel;

- The tempering temperature is low, around 200°C; this is possible because as-quenched martensite structure is not brittle as for me-dium carbon quenching and tempering steel. This fact depends on: a) a high percentage of Ni added in solid solution to this steel (high percentage of Ni decrease the ductile-to-brittle temperature); b) air-quenching determine slow cooling across the large sections, thus it results in good homogenization of the instantaneous tem-peratures across the whole part section (i.e. low thermal induced stresses). As direct consequence of b), the austenite to martensite transformation starts almost at same time, thus reducing the stress-es induced by differential expansion in the section.

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Figure 3.59 – Manufacturing cycle for an air-quenching UNI EN 36NICrMo16 part. Criteria for selection The high percentage of Ni determines for such a steel a very high price. On the other hand despite a raw material high cost, sometimes a pay-off is possible when the part to be constructed is of very high added value (e.g. it is specifically customized for the scope). For example, such a steel is safe-solution for a non-series product, with large sections and very complicated geometry that could be subjected to non accountable deformation or, worst case, quenching cracks. Due to its very low sensitivity to distortion (low residual stresses develops due to air-cooling), such a steel can prevent unforeseeable problems that would cause economic loss because of non-recoverable geometry by finishing operations. Another criteria for choosing the air-quenching steel is the request for very high strength coupled with very high toughness (e.g. torsional spring bars equipping of passenger car bogies of some high-speed trains). Furthermore the presence of Ni in high percentage allows this high-strength steel to be used at low temperature, avoiding brittle behavior.


Quench

Temper (∼200°C)


hole drilling)

Full annealingPre-heat treatments


Heat treatments



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Spring Steels Spring steel is a low-alloy, medium-carbon steel or high-carbon steel with a very high yield strength. This allows objects made of spring steel to re-turn to their original shape despite significant bending or twisting. To in-crease yield strength, these steels are characterized by high carbon concen-tration that ranges 0.60-1.00% (e.g. UNI EN C60, C70 and C100). Due to high carbon content they are non-weldable steels. To increase toughness, the carbon content is lowered and the yield strength increase is therefore pursued by including Si. Silicon has capability to strengthen the α-Fe lattice by solid solution strengthening mechanism, thus it can raise the elastic limit of the steel and improve the resistance to permanent set of springs. The Ni–Cr–Mo steel, Cr–Mo steel with excellent hardenability were de-veloped as steel for large-sized springs. Table 3.7 shows the chemical compositions of spring steels designated or recommended by several countries. Oil quenching and tempering can be normal heat-treatments, while water quenching can be suitable for low carbon steels whose the carbon content is limited to 0.5% (e.g. UNI EN C55), because of risks of quenching cracks. Cr–V steels have good hardenability with high toughness, and is used for higher hardness application. The Si–Cr steel is mostly used for oil tempered wire material of cold-formed springs. Cr–Mo steel with higher hardenability than the boron add-ed.

Table 3.7 - Chemical composition of some spring steels.

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Summarizing, a classification by Steel Grade is the following: • Carbon Steel • Low Alloy Steel

o Si–Mn Steel o Cr–V Steel o Si–Cr Steel o High-Carbon Si–Cr o Si–Cr–V Steel o Si–Cr–Ni–V Steel o Si–Cr–V–Mo Steel

Or a classification by cross-sectional profile: • Round Section • Non-circular Section

o Egg-shaped profiles and similar profiles o Trapezoid (mainly for press die) o Rectangle (mainly for press die)

Examples of cross-sectional profiles of non-circular wire are shown in Fig. 3.60.

Fig. 3.60 - Example of cross sectional profiles of egg-shaped spring wire

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Heat treatments for steels and manufacturing cycle of springs The manufacturing processes for steel springs can be divided into: a) cold coil spring (Fig.3.61), a cold work process where wire is fed through roll-ers and fulcrum pins and travels around a fixed mandrel to form a coil; b) hot worked springs (wound and leaf springs) where the rolling of the springs is performed as a hot process (Fig.3.62).

Fig. 3.61 – Cold coiling of cold wound spring.

Fig. 3.62 – Coiling of hot wound spring. The general manufacturing cycle of steel made heat treated parts (i.e. pre-heat treatments, machining operations, heat treatments, finishing opera-tions, refer to previous section “Quenching and tempering steels”) is ad-justed for cold and hot worked as illustrated in the fig.3.63.

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Fig. 3.63 – Manufacturing cycles of cold and hot wound spring. Manufacturing process of leaf springs (Fig.3.64) is similar to hot wound spring manufacturing cycle, where the hot coiling step is substituted by forging, and assembling of leafs has to be added after finishing operations.

Fig. 3.64 – Forging of a single leaf spring.

Cut to lenght

(Hot) Coil

Quench

Temper (∼450°C)

Preset (if required)

Shot peen

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if possible)Pre-heat treatments


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Specifically regarding with heat treatments performed, most typical pre-liminary heat treatment is spheroidizing annealing (sometimes, full anneal-ing and normalizing can be carried out). The spheroidizing annealing is keeping the materials around the A1 transformation temperature for a cer-tain time and cooling to the A1 transformation temperature by the cooling speed of 10–20◦C/hr. The purpose is to have the cementite precipitates changed from the lamellar or net shape to spherical shape. Since this heat-treatment can soften the material by a great extent, this can be applied when the formability of materials is required. As shown in the scheme of Fig.3.63, quenching and tempering treatment is conducted to improve the spring characteristics. During quenching, mate-rial is heated to the temperature about 30–50◦C higher than the A3 trans-formation temperature, and immersed into water or oil (sometimes air cooling in high alloy steel) and cooled rapidly, to have martensite struc-ture. Since the solution content of carbon is high, there are many lattice de-fects (dislocation) and the crystal structure is fine, the hardness of the mar-tensite of medium-high carbon steel is as high as 60–65 HRC. The spring steel has a high yield point; besides suitable high ductility is required, therefore, it is tempered at about 450◦C. As shown in the fig.3.63 the pre-heating and the quenching and tempering treatments for the spring steels are only two steps of a more articulated manufacturing process that requires some further steps, mostly patenting, pickling and drawing as they are shortly illustrated in the next.

Patenting Patenting is heat treatment process eventually conducted to restore ductili-ty resources of materials that could be highly work hardened during cold coiling steps (work hardening causes ductility decrease that could lead to cracks during cold coiling steps). Most frequently it is conducted on high-carbon steel wires. By patenting, they are continuously transformed to mi-crostructure of fine pearlite, either by isothermal cooling or continuous cooling. In practice, wire rod, traveling continuously, is first held above the A3 point, and subsequently cooled down below the A1 point to be transformed to pearlite. Figure 3.64 shows a schematic of TTT diagrams of this heat treatment. Several kinds of cooling media, used in the patenting for the transformation of wire.

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Fig. 3.50 - Schematic of patenting in TTT diagram. Pickling Pickling, either by hydrochloric acid or sulfuric acid solution, is generally provided on patented wire and hot-rolled rod to remove their surface scale (ferrous oxide film). Shot peening It is well known (refer to Chapter 2) that most fatigue failures initiate at the surface as a crack and propagate under cycling until failure occurs. For these cracks to initiate, the surface must be in tensile stress and they will not propagate through a compressively stressed surface. If a residual com-pressive stress is produced in the surface, the tensile stress created by the applied load must first overcome the residual compressive stress before the resultant surface stress becomes tensile. Shot peening is the most effective and inexpensive method to produce the desired residual compressive stress at the surface of components. This in-volves bombarding the surface with rounded particles propelled at high ve-locity (fig. 3.51a), 60 m/sec. Each shot particle, with controlled shape and of uniform size, acts as a peening hammer to cold work the surface and produce compressive stresses (fig.3.51b and fig.3.52).

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(a)

(b)

Fig. 3.51 – Shot peening: a) process; b) scheme of effect on peened surface. The commercial origins of the technique go back to the automobile indus-try of about 1930, and today almost all automobiles use shotpeened valve springs, and, in many cases, suspension springs. The peening process is relatively inexpensive and has proven capable of increasing operating life by five to 10 times or more when compared to unpeened springs (Fig.3.53).

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Fig. 3.52 – Compressive stress induced in the peened surface of a shotpeened beam (A) prevents tensile stresses from occurring after a bending moment is ap-plied to the part.

Fig. 3.53 –Shot peening applied to surfaces exposed to high bending loads, such as carburized and hardened gear teeth, increased the life considerably. For example, the life of teeth subjected to loading of 80,000 psi (about 500 MPa) increased from 270,000 cycles before shot peening to 3 million cycles after shot peening.

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Criteria selection As the increasing in alloying element content is key cost-driver, carbon steel are used when reduced section have to be realized and toughness is not crucial. Carbon steel with medium and high carbon content are particu-larly indicated for cold-worked springs. For hot worked large section size springs, Si and Si-Cr alloyed steel are used (increased YS and hardenability of steel). In case high toughness value are targeted, e.g. safe component for trans-portation, Ni- alloyed spring steels are used. Surface hardening of mechanical components

There are some applications where it is necessary to have a hard surface for certain depth below surface but a tough, shock-resistant inner core. This is the case, for example, of such components that can be subjected to contact fatigue (refer to Chapter 2) as for example, cams, gears, and shafts. Such components require hard layers on surfaces to resist but tough inner cores to resist shock. As known it is not possible to match two opposite requirements for metal, namely having high hardness and contemporarily high toughness. In fact, while a low-carbon steel containing 0.1 wt% C will have a very tough core, its surface hardness will be low also after quenching. On the other hand, a euctectoidic steel containing 0.8 wt% C will have a very high sur-face hardness after quenching, but the core will not be tough and shock re-sistant. Thus, to satisfy design requirements there are two approaches to this prob-lem. One is to use a medium-carbon steel and only quench harden the sur-face through local heat treatment. The other approach is to diffuse some elements, namely locally adding chemical elements onto surface of a base steel, so to strengthen the top layer surfaces acting on various metallurgy strengthening mechanisms we will discuss in depth in the next. Despite two approaches pursue same objective, namely increase hardness on surface but keeping tough subsurface, they distinguish since the first method, called surface hardening of steels, does not change the chemical composition of steels, while the second approach needs to change local chemical composition, in order to strengthen lattice. Changes in chemical analysis on top layers are produced by feeding elements like carbon C and nitrogen N to steel by a temperature-time process – i.e. thermochemical treatment - that allows to increase diffusion on steel surface. If carbon is

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added, thermochemical process is called carburizing; if nitrogen is added, we talk about nitriding process. Surface Hardening by Localized Heat Treatment It is conducted generally onto parts that have been hardened by conven-tional quenching and tempering process in order to produce the desired core hardness20. The surface is then reheated into the austenitization range and immediately quenched to produce fresh as-quenched martensite (i.e. non tempered martensite) at the surface. Additionally to the hard surface, the surface layer is usually in a state of compression, which improves fa-tigue cracking resistance. The objective of surface hardening is therefore to austenitize the steel at and near the surface and then rapidly quench by water to produce as-quenched martensite. Occasionally a low temperature tempering – not higher than 100°C - is allowed to relief residual stresses. Three techniques are usually employed to heat up and rapidly austenitize surface, to prepare it to water quenching:

– surface heating by a gas flame created by burning acetylene, pro-pane, or natural gas;

– induction hardening technique; – laser hardening.

Mostly the 3 techniques distinguish because of is the heating source used. Flame hardening. It is a simple method since an operator – or automated systems - uses a torch to heat up surfaces while a quench jet follows right behind the torch to rapidly quench surface. The relatively low thermal conductivity of steel enables the surface regions to be austenitized using high rates of energy input without the interior being significantly affected. Flame hardening is a very rapid and efficient method for producing cases as deep as 5-8 mm. However, unless the process is automated, it can be difficult to control the case depth, and prolonged heating can result in a case depth deeper than desired.

20 Most frequent in industry applications normalized parts instead of quenched and tempered, are surface hardened, to reduce process costs. However, such pro-cess is not suggested by metallurgical point of view since normalized structure are not sufficiently homogeneous and tough, two main factors that can counteract lo-cal distortions and surface cracks.

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Induction Hardening. In induction hardening, heat is supplied by surround-ing the part with an inductor coil carrying a high-frequency current in the range of 2 to 500 kHz. Higher frequencies result in a shallower depth of heating and are therefore used for smaller-diameter workpieces. The coil acts like the primary winding of a transformer. The oscillating field pro-duced by the induction coil induces magnetic field electrical eddy currents in the steel within a certain depth of the outer surface, called the skin depth (Fig.3.53), which decreases as the frequency is increased. The eddy cur-rents produce Joule resistance heating in the skin depth that rapidly raises the surface temperature. The amount of heat released is proportional to the square of the current such that Q∝I2·R·t also called the Joule heating (obeying to Joule’s first law of conductive mean heating).

Fig. 3.53 – Principle of induction heating.

As in the case of flame hardening, heating system is equipped with quenching water jet in order to rapidly provide quenching of austenitized surfaces (Fig.3.54). Induction hardening is generally used to produce rela-tively thin cases. Larger depths, such as 3 mm, can be attained by leaving the current in contact with the surface for a longer period of time and by operating at lower frequencies. The case depth can be controlled more ac-curately in induction hardening than flame hardening process, since the depth can be controlled by varying the frequency of the current and the amount of time the current is in contact with the part (the higher the fre-quency, the more the current tends to flow over the outer surface only).

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Fig. 3.54 – Induction hardening onto a shaft. Coil and water jet system are syn-chronized in their relative movement with the heated shaft. Laser hardening. Laser heat treating is a highly selective hardening tech-nique in which a spatially well-defined beam of laser light is absorbed near the surface, causing rapid heating (heating is limited to the illuminated ar-ea) and penetration into the bulk material is limited. Laser hardening al-lows for a highly defined zone of influence without affecting neighboring surfaces. High cooling rates make fine structures and high levels of hard-ness possible. Intricate contours are easily hardened using lasers due to the flexible beam guidance possibilities. The maximum thickness obtainable with the laser hardening is 3 mm for steels. In the case of objects of high precision, limiting the layer thickness to 0.2 mm positively result in con-trolling local distortions since they are kept so low as they do not require any post- processing treatment. Manufacturing cycle for surface hardened product In the following figure, Fig.3.55, it is shown the manufacturing cycle for a surface hardened product.

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Fig. 3.54 – Manufacturing steps for surface hardened parts.

Criteria for steel selection for surface hardening When high hardness on surface top layer is targeted, and this is the major objective, a high carbon content is necessary. Surface hardening processes in fact exploits strengthening mechanisms typical of an as-quenched mar-tensite, where the carbon content is key feature for increasing as-quenched martensite. However too much high carbon content would result in too much high body centered tetragonal (BCT) lattice distortions; high lattice distortions, coupled with its own brittle behavior, can however result in cracking of hardened surface layers. To mitigate this problem usually the highest carbon content is limited to about 0.60 wt.% (e.g. AISI 1055). On the opposite, if control of surface local distortions and deeper hardened layers are favored instead very high hardness onto surface, medium carbon content steel is preferred (ranging from 0.35 to 0.50 wt%, e.g. AISI 1035, AISI 1045) is therefore usually selected. Furthermore, when the hardness profile below surface, not only the hard-ness on top layers, is a key feature for designers, alloyed steel with higher hardenability are employed instead cheaper carbon steels. Alloyed steel


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which are mostly used are: UNI EN 45Cr2, UNI EN 38 Cr4, UNI EN 37 CrMn4, UNI EN 41CrMo4 and UNI EN 40NiCrMo3, listed by increasing their own hardenability and their cost. It is important to notice that, when rapid cooling is guaranteed after heating up the parts, so rapid as critical interval of temperatures for the tempering brittleness (450-550°C) are rap-idly passed, Mo can be eliminated from steels for surface quenching, in order to reduce costs. Carburizing steels Carburizing is conducted by heating a low-carbon steel into the single-phase austenitic field, generally around 900°C, where the steel has a high solubility for carbon. Carbon is then absorbed onto surface layers, which increase progressively carbon content and thus hardened during the follow-ing quenching phase, as shown in the scheme of generic carburizing cycle in Fig. 3.55.

Figure 3.55 – Scheme of carburizing temperature vs time plot diagram. After quenching, the part is extracted from oil chamber and moved to low temperature furnace where it is tempered at low temperature, around 180°C, in order to relieve stressed but avoiding carbon to diffuse out from martensite tetragonal lattice, thus vanishing the carburizing and quenching results in terms of high hardness. The final result of carburizing process is therefore hard high-carbon case on top of a tough low-carbon steel core.

∼920°C

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Steels used for carburizing usually have carbon contents of approximately 0.2 wt% (the lower is carbon content of base material, the higher is the carbon diffusion rates), with carburized cases containing up to 0.8 to 1.0 wt% C. As stated, and as it is usual for any process that involves chemical species diffusion, the carbon concentration gradient of carburized layers is a func-tion of the carburizing temperature, exposure time and carbon concentra-tion of outer atmosphere. From an analytical point of view, the result of carburizing process in terms of hardened layer can be approximated by a simplified formula developed by Einstein: (eq.3.1) Case Depth = √2Dt where D is the diffusion coefficient of carbon into iron. However, most precisely, the process is governed by diffusion laws, the two Ficks’ laws. The increasing concentration of carbon during carburizing is approximated by the equation:

(eq.3.2) Where:

– C(x,t) is the carbon concentration at certain depth x and fixed time t; – C0 is the initial condition, namely the carbon content before carbu-

rizing starts (i.e. the carbon content of base core material); – Cp is the carbon potential of atmosphere, namely the measure of the

concentration of carbon atoms in carburizing outer atmosphere21,

21 While carburizing can be done in a solid, liquid, or gaseous medium, gas car-burizing processes are mostly industrially used, since they can be highly automat-ed and controlled and for series production (here in the following we refer to this type of carburizing process). Gas carburizing uses either natural gas, propane, or butane as carrier gases to realize the carbon potential in atmosphere, accordingly with following relations:

2CH4 + O2 + 4N2 Æ 2CO + 4H2+ 4N2 CO + H2 ÆC + H2O Feγ + CH4 → Feγ (C) + 2H2 Feγ + CO + H2 → Feγ (C) + H2O

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expressed in percentage. The meaning of carbon potential Cp is the following: it is the carbon concentration, in weight %, which can be asymptotically obtained on top layer surface for prolonged exposure times - e.g. carbon potential 0.7% means that the outer atmosphere is capable to diffuse 0.7% of carbon in top layer of steel treated for prolonged time.

As shown by the scheme in Fig. 3.56, during the carburizing phase, carbon diffuses slowly into the bulk of the part, and a carbon concentration gradi-ent below the surface is established. Possible carbon profiles are shown as examples in Fig.3.57. As the 3 carbon profiles illustrates, within the steel part, the high-carbon surface has a higher carbon potential than the low-carbon interior, since carbon tends to diffuse from the surface toward the center22.

Figure 3.56 – A simplified scheme of carburizing diffusion phenomena from outer atmosphere into the steel part.

22 It is worth mentioning the carburizing atmosphere shall have a higher carbon potential than does the surface of the steel, to avoid carbon flowing out from the carburizing surface. Control of carbon potential is vital for correct carburizing of surface: if, during processing, the atmosphere carbon potential should fall below the carbon potential at the steel surface, then carbon will be removed from the steel (decarburization).

Fe-γ latticeC atoms

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(b)

Figure 3.57 – a) Scheme of carburizing process, where carbon atoms diffuses from high-carbon concentration atmosphere (i.e. high carbon potential mean) into aus-tenitic lattice; b) 3 different carbon profiles obtained by varying: carbon potential of external atmosphere (i.e. 0.50%, 0,75% and 1.10%), exposure times (i.e. 2h, 4h, 8h, 16h). Carburizing cycle description Looking at the cycle in Fig.3.55, four main stages are recognized:

1. The carburizing phase; it is conducted in potential carbon atmos-phere at high temperature, where carbon absorption onto steel sur-face and diffusion to deeper layers is realized. The temperature is set around 900°C, thus as higher as possible in austenite phase to facilitate the diffusion of carbon (i.e. the higher expansion of γ-Fe, the higher is diffusion of interstitial carbon atoms), but not exceed-ing that temperature to which grain coarsening might start (safely temperature should be kept lower than 1000°C);

2. Targeting the correct quenching temperature. The carburizing temperature is too high for quenching stage, thus the part shall be cooled to correct quenching temperature. Because of the surface and core have two different carbon content, the A3 temperatures are different. In this case it is set the correct temperature the lower A3 of the two ones. In other words, it is preferred to target the cor-rect quenching temperature of the high carbon content layers, as they are more critical for quenching stage. Despite temperature in this steady-state phase is lower than A3 for the core of parts, lim-ited times allow to prevent austeniteÆferrite transformation to start.

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3. Once a high carbon content - approximately the euctectoidic con-tent - is achieved on top layers, the part is oil-quenched. The quenching phase has the scope to produce high-carbon content and hard martensite on top layers (i.e. case hardened), while maintain-ing low-carbon content and tough martensite within the part (i.e. core) - at least, mixed martensite-bainite is produced at core, de-pending on hardenability of steel and the part size.

4. The final stage consists in reheating quenched parts for tempering treatment, which shall be conducted at low temperatures (usually around 150-180°C). Tempering is required to reduce residual stresses develop onto surface layers by quenching.

Design aspects of carburizing Typical case depths range from few millimeters (e.g. around 1-2 mm) to 3-4mm. in the latter case prolonged carburizing times are required. Since carbon content on top layers is targeted around 0.8-1.1 wt.%, and because of the low tempering temperature, surface hardness usually obtained is about 850-900 HV (about 64-63 HRC). Effective case depth (see Fig.3.57) is function of both carbon profile and hardenability of base steel.

Figure 3.57 – Typical hardness profile for carburized part and definition of effec-tive depth.

(mm)

HV

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550 HV

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Manufacturing cycle for carburizing steel parts The manufacturing cycle for carburizing steel parts is shown in Fig.3.58. Similarly to manufacturing cycle adopted for quenching and tempering steels – which can be considered our base reference – parts that are carbu-rized require additional materials to be left on parts, to mitigate distortion problems that may occur during the critical quenching step.

Figure 3.58 – Manufacturing cycle of carburizing steels. Criteria for carburizing steel selection Main criteria for orienting choice of carburizing steels are design factors like top surface hardness, effective case depth and case hardened tough-ness, raw material and process costs. Cheapest solutions in terms of raw material and reduced machining costs is represented by carburizing carbon steels, like UNI EN C10 or UNI EN C15 (AISI 1010 and AISI 1015). However such steels have a very low hardenability and they require to be water quenched. Despite the water quenching is benefit in terms of further reduced process cost, instead of oil quenching, this restrict part size to small dimensions and geometry to be as


Carburizing (∼900°C)

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hole drilling)



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simple as possible. As size and shape complexity increase, residual stress-es produced onto part by rapid cooling might increase the risks of non-restorable distortions and, at least, cracks (such risks are also increased be-cause of the low mechanical strength of low carbon austenite). A first conclusion is that, as the part size increases, oil quenching is re-quired, and alloyed steels are therefore used. Considering toughness as ma-jor feature together with cost reduction, the UNI EN 16MnCr5 is one pos-sible solution; because of low carbon content, such a steel is easy to hot-work and has good machinability (presence of higher content of Mn). Addition of Cr increases hardenability, is compared to carburizing carbon steel, but martensite is limited to low-medium thickness (not more than 20 mm). Since such a steel can suffer of temper embrittlement, this problem is solved by using the UNI EN 18CrMo 4, which has similar hardenability of UNI EN 16MnCr5. Comparable hardenability, but higher toughness, is achieved by the UNI EN 16NiCr4, due to presence of Ni. Costs in this case increases. For automotive applications most frequently are used steels with higher percentage of carbon, alloyed with Cr for increase hardenability (up to 60-70mm), and Ni for increasing toughness, like the UNI EN 20NiCrMo2. This steel has high carbon content (it targets 0.2% wt. limit for carburizing steels) that increases core and surface strength, while its moderate-high hardenability allow it is used for complicate shape. Finally, the UNI EN 18 NiCrMo 5 and UNI EN 18 NiCrMo 7 series are most used carburizing steel. Despite higher raw material costs, they are considered safe materials to oil-quench due to high toughness (i.e. high Ni content) and high hardenability with good machinability. It is important to highlight that the low-temperature tempering stage limits the service temperature below the tempering temperature. If higher, ser-vice temperature would cause decay in surface hardness due to carbon dif-fusion from BCT lattice, and its partial transformation into α-Fe, the duc-tile BCC lattice Nitriding steels Nitriding process has same scope of carburizing process: develop onto tough base materials hard surface layers, to certain depth. Similarly, nitrid-ing pursues such an objective by locally changing chemical composition of the base steel, as it is usual for thermochemical processes. In the specific case, the chemical specie which is absorbed onto surface is nitrogen N, a small interstitial atom, too, capable to diffuse in iron lattice. As the N is absorbed and it diffuses within the part, it combines with Fe to form small

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particles we call nitrides. Such particles are randomly dispersed into matrix and they are capable to intercept dislocation, providing a precipitation hardening strengthening effect. This is the strengthening mechanism by which nitriding process increase hardness, and mechanical strength, on surfaces. By this fact, we can immediately recognize great differences in terms of metallurgical strengthening phenomena existing between carburizing and nitriding. While carburizing process strengthens the carbon-enriched sur-face layers by exploiting lattice transformation, from austenite to marten-site BCT lattice, by quenching, nitriding process strengthens the pre-existing α-Fe (BCC lattice) by precipitates. To make reader clear such great difference, it is worth mentioning that nitriding is conducted at around 500°C, for one reason that will be explained soon in the next. By this fact, instead carburizing which requires that the steel be quenched and then tempered, nitriding is done at temperatures largely below the aus-tenitization temperature. Some direct benefits of this fact are: a) the distortion inherent in the martensitic transformation during harden-ing is completely removed; thus, nitriding allows excellent dimensional control; b) since the nitriding temperature is below the tempering temperature of quenched and tempered steels, nitriding can be conducted as final stage to increase hardness onto very optimized structures that are typical of the quenched and tempered steels. Similar to carburizing, nitriding can be done in several different media; here in the following we refer to industrial gas carburizing. In gas carburiz-ing, nitriding is conducted in atmospheres that decompose ammonia NH3 to provide nitrogen to the surface by catalytic reaction: (eq.3.2) NH3Æ N+3H The nitrogen is therefore absorbed and it diffuses into the steel. At top sur-face atomic nitrogen combines with the iron to form iron nitrides Fe2N and Fe4N types. These phases are clearly visible in the iron-nitrogen phase dia-gram shown in Fig.3.59. Firstly, by this diagram it is possible to explain why nitriding temperature must not exceed around 500°C. This limitation is required to nitride steel with safe margin to keep steel below the euctec-toidic temperature that is set at 590°C. If the euctectoidic temperature is overpassed, the structure turns into Fe-γ and the following cooling would proceed by the euctectoidic transformation from Fe- γ into lammellar

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euctectoidic structure, called braunite, that is too much brittle to be accept-ed onto mechanical parts.

Figure 3.59 – Iron-Nitrogen phase diagram. They are highlighted by circles the two high nitrogen content phases that form onto surface, the γ' (i.e. Fe4N) and the ε (Fe2N) phases. By diagram in fig.3.59 we can recognize:

– The α-Fe phase, namely nitrogen in solid solution of Fe BCC lat-tice;

– The γ’ phase, interstitial compound Fe4N, with nitrogen concentra-tion max 6% wt;

– The ε phase, interstitial compound Fe2N, with very high nitrogen concentration over 10%.

FexN compounds that form onto surface during nitrogen absorption and are also visible by metallographic analysis, as shown in Fig3.60.

Figure 3.60 – Nitrided layer structure: a) simplified scheme of surface structures; b) metallography at Scanning Electron Microscope of outer layers.

Phases:

� N(Fe-α): Nitrogen in solid solution of Iron

� γ’(Fe4N): lattice structure CFCnitrogen concentrdion max. 6%

� ε (Fe2N): lattice structure EC, high nitrogen concentration over 10%

DIFFUSION LAYER

POUROS ZONE

COMPACT ZONE

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The metallurgical phenomena involved during surface compounds for-mation are below summarized:

– Nitrogen absorbed onto surface form compound layers, nitride ε (Fe2N) and nitride γ’(Fe4N) with minor presence of complex ni-trides if alloying elements when alloying element with great affinity with nitrogen are present (mainly Ti, Al, V, Cr, Mo).

– The continuous decomposition of γ’(Fe4N) at interface with diffu-sion zone feed N for diffusion into solid solution Fe-α and for-mation of complex nitrides, when alloying element with great af-finity with nitrogen are present (mainly Ti, Al, V, Cr, Mo).

It is clear therefore that the presence of alloying elements with great affini-ty with nitrogen allow formation of complex and stable complex nitrides; these nitrides are major responsible for increasing strength and hardness on top surface layers interested by nitrogen diffusion.

Design features of nitriding parts Due to low treatment temperature, the diffusion of nitrogen is low. This fact limit in practice nitriding case depths, that are thin if compared to car-burizing. Usually case depth is less than 0.80mm, even though nitriding times can exceed 100 h. On the contrary, the surface hardness can achieve very high values, rang-ing from 900HV to 1200 HV, the latter when Al is added (aluminum forms very fine AlN precipitates). Molybdenum, in addition to its contribution as a nitride former. During single stage nitriding treatments, in which a single nitriding atmos-pheric composition is maintained, a white layer of iron nitride is formed (i.e. the porous layer shown in Fig.3.60). This iron nitride layer is hard but can crack and spall. When this is unac-ceptable, the layer is removed by surface grinding. Alternatively, a two-stage nitriding process can be used in which, after the first stage, the at-mospheric conditions are changed so that iron nitride no longer forms at the surface, and the existing layer is removed as the nitrogen dissolves into the steel (Fig.3.61).

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Figure 3.61 – Effect of one- and two-stage nitriding on white layer. (a) Single stage, gas nitrided for 24 h at 525°C. (b) Double stage, gas nitrided for 5 h at 525°C followed by second stage at 565°C for 24 h. Together with high hardness advantages (nitriding onto Al alloyed steel produces the hardest cases) other important features can be exploits by de-signers. No heat treatment is required after nitriding, which, along with the low temperatures employed, minimizes warpage and distortion. Nitrided parts have good elevated temperature resistance. Reheating parts to 540 to 595°C for short periods does not affect their hardness, while long-term exposures to 315 to 425°C will affect carburized but not nitrided parts. The disadvantages of nitriding are primarily the long cycle times and the inherent cost. A 0.75 mm case depth may take several days to produce, and ammonia gases are more expensive than the natural gases used for carbu-rizing. Other disadvantages include some size growth that occurs during nitriding, and the extreme hardness produced precludes machining after nitriding. However, this problem is well mitigated by skilled heat treaters, since the increase in volume during nitride formation is homogeneous and without distortion (it depends only by formation of nitrides inside lattice, and not because of structure transformation). Thus, heat treater is capable to ana-lyze by preliminary sampling how much will be expansion of surface lay-ers, so allowing designer to take into account this final volume expansion. Manufacturing cycle for nitriding parts In the following Fig.3.62 is shown the manufacturing cycle for nitride parts. As it is shown, due to absence of distortions and temperature below

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600°C, the nitriding process can be conducted as final stage, onto finished parts.

Figure 3.62 – Manufacturing cycle for nitride parts. Criteria for nitriding steel selection Nitriding steels are commonly high hardenability steels, since they have features that are typical of medium-carbon and alloyed quenching and tempering steel. The presence of elements like Al, Ti, V, Cr and Mo to avoid temper brittleness have double positive effect: they increase harden-ability by usual shifting to the right the CCT curves, and they form dis-persed and highly stable nitrides. Among nitriding steels, UNI EN 31CrMo12 has lower hardenability than the most used UNI EN 41CrAlMo7, and lower surface hardness. When higher toughness at core is required with high surface harness, the UNI EN 34CrAlMo7 is usually employed as substitute of the UNI EN 41 CrAlMo7 since it has less carbon that causes higher toughness in the BCT martensite.


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Regarding with the industrial practices, despite UNI EN 42CrMo4 is not a nitriding steels but a quenching and tempering steel, it is mostly used in ni-triding process of automotive parts because of satisfying surface hardness obtained. Despite 900 HV surface hardness is actually similar to what it is usually obtained by carburizing, one advantage is nitriding allows to avoid any distortions. This fact is relevant in case of high-reliable large series production. Furthermore, due to higher hardenability and higher carbon content of martensite at core, higher strength are achieved than typical car-burizing parts.

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Chapter 4 – Tool Steels

Tool steels are very special steels used to shape, cut, and form an extreme-ly wide variety of metals and other materials under demanding conditions. The earliest tool steels were based on plain carbon steel, but in the mid-19th century and early in the 20th century , highly alloyed tool steels were developed to meet very stringent requirements for specific applications.

Classification of tool steels Tool steels have been organized into groups that have evolved to perform specific functions, such as:

forging, cold working, die casting, high -speed machining,

in a variety of operating conditions. Within each group may be many grades that differ slightly from one another to accommodate somewhat dif-ferent processing requirements, operating conditions, or work materials. Various systems are used to classify tool steels. The most widely used sys-tems are the American Iron and Steel Institute (AISI) and in Europe the UNI EN standard for classifying alloying steels. The AISI classification AISI arranges tool steels into groups that are based on prominent charac-teristics such as alloying, application, or heat treatment. Table 4.1 lists nine main groups of tool steels and their identifying letter symbols.

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Table 4.1. Main Groups of Tool Steels and AISI Letter Symbols.

Important properties required for various applications As defined by their classification - accordingly to Table 4.1 - the field of application of tool steels includes machining, cutting, forming by stamp-ing, pressing or forging, forming of shapes from the molten state in glass, plastics, or metals, and die casting. Therefore, tool characteristics are provided by heat treatment, quenching and tempering. Final properties thus depends on tempered martensite mi-crostructure and a variety of fine carbides, due to chemical elements add-ed. Specifically, the important properties of tool steels are:

constant hardness at low and high temperatures, hardenability, retention of hardness (at operational temperature); high compression strength and pressure resistance, fatigue strength, toughness at operational temperatures, wear resistance at room and high temperatures, thermal fatigue resistance, corrosion resistance

Hardness is the most important characteristic of steels from which their po-tential application can be recognized. The wear resistance of tool steels in-creases with increasing hardness, and toughness is reduced with increasing hardness. Normal hardness values vary between about 200 HV for glass-mold steels at the lower level, and 900 HV for forming and machining tools at the upper level. Carbon content and elements with higher carbon affinity such as Mo, Cr, V and W are the dominant factor controlling the strength of tempered mar-tensite, as they can form fine dispersed carbides during tempering stage (refer to Chapter 3, as basics of quenching and tempering strengthening phenomena are described). However, while the hardness for steels usually rapidly decreases with increasing temperature, as Class 1in Fig.4.1 shows, tool steels exhibit various behavior (see Class 2 to 4).

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Figure 4.1 - Four major types of hardness versus tempering temperature in tool steels. Particularly we observe tht:

Class 1 is typical of carbon and low-alloy tool steels in which the hardness is decreasing progressively with increasing temperature due to the precipitation and coarsening of cementite, or of other low-alloy carbides (this is also typical of quenching and tempering steel);

Class 2 is characteristic of medium - to high-alloy cold-working die steels in which the alloying addition retards carbide precipita-tion and related softening. Curves between Class 1 and Class 2 could be obtained for low - to medium-alloy steels.

Class 3 is representative of highly alloyed high-speed steels in which secondary hardening occurs at high-tempering tempera-tures. The final hardness of these steels could exceed that in the untempered condition.

Class 4 is representative of the medium - to high-alloy hot –working tool steels that exhibit a secondary hardening, as is the case with Class 3. In Class 4, the as-quenched hardness is lower than that of Class 3 due to its lower carbon content.

Secondary hardening of tool steels

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Secondary hardening is a result of the transformation of retained austenite to martensite on coo ling from the tempering temperature, and of precipita-tion of an ultrafine dispersion of alloy carbides. Tungsten, vanadium , chromium, and molybdenum that are the strong carbide –forming elements are most commonly used to achieve secondary hardening. To take ad-vantage of their precipitation characteristics, they must be dissolved in aus-tenite during the austenitizing treatment in order to be incorporated into the martensite formed during quenching with sufficient supersaturation for secondary hardening during tempering. for secondary hardening during tempering. Figure 4.2 through Figure 4.3 show the effect of strong carbide -forming elements on the secondary hardening of 0.5% C tool steel. The tempering treatment should be performed as soon as possible after quenching, and heating to tempering temperatures should be slow to en-sure temperature homogenization within the tool steel and the prevention of cracking. Slow cooling in still air is also recommended to minimize the development of residual stresses.

Figure 4.2 - Secondary hardening caused by alloy carbide precipitation produced by V additions.

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Figure 4.3 - Secondary hardening caused by alloy carbide precipitation produced by chromium additions. Manufacturing cycle of tool steels The manufacturing cycle of tool steel requires heat treatments is similar to quenching and tempering steel cycle. Compared with the manufacturing cycle of a quenching and tempering steel, for such steels three aspects are of importance to tool steels. The first is homogenization (or reduction) of microstructure heterogeneity that is produced by segregation phenomenon during solidification; the sec-ond is dissolving large complex and stable carbides formed during the re-finement of grains, the third is the refinement of coarse grains that would appear as result of high temperature annealing and austenitizing tempera-tures. In fact, when no prolonged hot working operations with high reduc-tion are foreseen, a full annealing shall be conducted at high temperatures. But such a high temperature annealing is detrimental for grain size coars-ening; thus, a homogenizing treatment, normalizing usually followed as a grain refinement step. When required, to enhance hot ductility, spheroidization treatment can be conducted instead of or following the normalizing treatment for grain re-finement. Criteria for selection of tool steels for specific applications

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Tool steels that are included into the nine groups by Table 4.1, are in the following classified into 4 main categories of specific applications. Each application requires specific properties to be enhanced. 1. Steels for plastic molds. During the formation of plastics, dies are sub-jected to heat and pressure. The temperature of the dies is as high as 250°C and the strength of about 100 MPa. In this case, hardness retention and strength requirements are of minor importance, instead high machinability properties and a low degree of distortion in hardening of plastic molds are very important. The P20 steel (0.30% C, 1.70% Cr, 0.40% Mo, Table 4.1) is a good choice for molds due to its low degree of distortion and good machinability. In the case of abrasive plastics, the molds are made of steels oil-hardening cold working steel (see Table 4.1) as O1 (0.90% C, 1.0–1.4% Mn, 0.50% Cr, 0.50% Ni, 0.50% W) that can be hardened to about 57-61 HRC thanks to a low tempering (between 100°C and 350°C). The low tempering temperature defines the low temperature for such steels that are suitable for tools used to cut or form materials that are at low tempera-tures. 2. Steels for high-pressure die casting molds. In die casting, tools are heat-ed to about 500°C and are subjected to high mechanical forces and erosion. Most important property in this case is hardness retention at high tempera-ture. Steels that exhibit secondary hardening are required, low carbon and moderate to high alloy that provide good hot hardness and toughness and fair wear resistance due to a substantial amount of carbide (class 4 of fig.4.1). Dies used for light metal casting are therefore commonly made of H-type steels, as H11 (0.33% C; 4.75%Cr; 0.3% Ni; 1.10% Mo; 0.3% V). 3. Steels for cold-forming tools and machining. Cold-forming processes such as cold rolling, stamping, deep drawing, extrusion, and bending have the advantage of making parts with high-dimension accuracy and good surface quality that does not need machining. As well, tools for high speed machining, as turning, requires abrasive wear resistance and hardness at high temperature, for not prolonged time. In such processes, tools are sub-jected to high stresses (from pressure and friction) and possible localized high temperature, due abrasive forces. Tool steels with a high hardness are used in these applications. The M-type tool steels, namely the Molyb-denum high-speed tool steels, are used due to high strength and hardness also retained at temperatures up to or exceeding 760 °C. For example, the M2 high-speed steel with 0.85% C; 4.10% Cr; 5.00% Mo; 6.40% W;

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1.80% V achieves 61HRC by tempering at 650°C and it can withstand high temperature, around 700°C, for not prolonged time. 4. Steels for hot working. Forging hammers and hot extrusion dies are ex-amples of hot working process tools. The tool steels H11 and H13 of H-types, based on a chromium content of 5% and medium carbon (0,38% C) are suitable for the forging and extrusion of light metals. In the case of heavy metals, such as copper and steels, Ni-base super alloy steels are more suitable.

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Steels for Special Applications – Specialty Alloyed Steels23

High-Fracture-Toughness Steels

Main feature for such steels is their high toughness with high strength properties. This is achieved by limiting carbon content, that is kept at low-er value than reference quenching and tempering medium-carbon steel AISI 4340 (similar to UNI EN 40 Ni Cr Mo 7). As known, the lower car-bon content significantly contributes to their better ductilities and higher fracture toughness that is also increased by high nickel contents. Further addition of alloying elements, as Co and Cr, provide deep harden-ing and specifically cobalt helps to prevent retained austenite. For a further increase in toughness, all these steels are vacuum melted so to avoid hy-drogen, oxygen and residual inclusions highly detrimental for tough prop-erties of steels that usually contaminate steel in steelmaking refining pro-cess steps24. Three are the high-fracture-toughness steels, classified AISI:

HP-9-4-30, AF1410, AerMet 100,

The mechanical properties for HP-9-4-30, AF1410, and AerMet 100 are given in Table 4.2. These alloys are not corrosion resistant, and parts must be protected with a corrosion-resistant coating. Heat treatments, mechanical properties and applications All these steels are quenched and tempered, to achieve high strength and high toughness due to tempering martensite structure with fine carbides. The high toughness provided by high nickel content and relative lower carbon content allows to temper quenched martensite to lower tempera-tures than quenching and tempering steels. The HP-9-4-30 nominally contains 0.30 wt% C, 9 wt% Ni, and 4 wt% Co. It was developed as high-fracture-toughness steels capable of being heat

23 Main reference for this section, F.C.Campbell, Elements of Metallurgy and Engineering, ASM International, 2008, Chapter 20.

24 Vacuum degassing is used to remove hydrogen from liquid steel. Particular-ly, vacuum deoxidization is also being used to eliminate oxygen that yield cleaner steel with a lower inclusion content.

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treated to high strength levels in thick sections. Due to high hardenability provided by alloying elements, it is capable of being hardened in sections up to 15 cm thick to an ultimate tensile strength level of 1520 to 1655 MPa while maintaining a fracture toughness, KIc, of 110 MPa. Double temper-ing is normally employed to prevent retained austenite. The alloy AF1410 has nominal composition 14 wt% Co, 10 wt% Ni, 2 wt% Cr, 1 wt% Mo and 0.15 wt% C. Its lower carbon content than the HP-9-4-30 assures higher weldability. Furthermore the higher toughness at cryo-genic temperatures and has high strength and stability at temperatures up to 425°C. AerMet 100 is a nickel-cobalt high-strength steel containing 0.23 wt% C, 3.1 wt% Cr, 1.2 wt% Mo, 11.1 wt% Ni, 3.4 wt% Co. AerMet 100 is re-placing older steels such as 4340 in many applications due to its good combination of strength (ultimate tensile strength is 1965 MPa) and tough-ness (KIc is 110 MPa√m). Other advantages include good toughness at cryogenic temperatures, a critical flaw length of nearly 6.3 mm, and an op-erating temperature up to 400°C. Examples of applications for such steels include armor, fasteners, airplane landing gear, jet engine shafts, structural members, and drive shafts.

Table 4.2 - Typical properties of high-fracture-toughness steels.

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Mar-Aging Steels Maraging steels are a class of high-strength steels with very low carbon contents (0.030 wt% maximum) and additions of substitutional alloying elements that produce age hardening of iron-nickel martensites. The term maraging was derived from the combination of the words “martensite” and “age hardening.” Maraging steels have high hardenability and high strength combined with high toughness. The maraging steels have a nominal composition by weight of 18% Ni, 7 to 9% Co, 3 to 5% Mo, less than 1% Ti, and very low carbon contents. The commercial maraging steels, 18Ni(200), 18Ni(250), 18Ni(300), and 18Ni(350), have nominal yield strengths after heat treatment of 1380, 1725, 2070 and 2415 MPa (200, 250, 300, and 350 ksi), respectively. The name derives from the combination of nominal content of Ni and the average UTS in ksi. Typical properties of maraging steels are shown in Table 4.3

Table 4.3 – Typical properties of Mar-Aging steels.

Heat treatments, mechanical properties and applications Heat treatment consists of solution annealing, air cooling, and then aging. Solution annealing is usually conducted at 815°C for 1 h. Since the nickel content is so high, austenite transforms to martensite on cooling from the austenitic temperature. The martensite start temperature (Ms) is approximately 155 °C, and the martensite finish temperature (Mf) is approximately 100°C . The formation of martensite is not affected by cooling rate, and thick sec-tions can be air cooled and still be fully martensitic. Since the martensitic

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transformation involves only an austenite-to martensite transformation of iron-nickel and does not involve carbon25 to any considerable extent, the martensite formed is relatively soft (30 to 35 HRC), which can be easily machined or formed is relatively ductile. Before aging, maraging steels have yield strengths in the range of 655 to 830 MPa. They are then aged to high strength levels at 455 to 510 °C for times ranging from 3 to 9 h. The effect of aging temperature on 18Ni(250) is shown in Fig. 4.4. Since high stability of their low-carbon martensite structure at relatively high temperature, they can be used up to 450°C. The properties of high malleability and machinability in annealed state, the high stability at relative high temperatures and very high toughness with high strength make them suitable for engine components, such as crank-shafts and gears, and the firing pins of automatic weapons that cycle from hot to cool repeatedly while under substantial load.

Fig.4.4 - Effect of aging temperature on 18Ni(250) maraging steel.

25 In these Fe-alloys, carbon is considered an impurity and kept to as low a lev-el as possible to minimize the formation of titanium carbide (TiC), which can ad-versely affect ductility and toughness.

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High-Strength Low-Alloy Steels Conventional hot rolled mild steels have rather low strengths but are readi-ly weldable. As the carbon content is increased to increase strength, the amount of lamellar pearlite increases, reducing weldability and toughness and increasing the ductile-to-brittle transition temperature (DBTT). The development of high strength low-alloy (HSLA) steels in the early- 1980s provided an answer to this dilemma. High-strength low-alloy steels are a hybrid between plain carbon steels and alloy steels and are often considered to be a separate class of steel. They contain alloying elements; however, the alloy content is usually on the or-der of only 0.1 wt% and is referred to as microalloying. The HSLA steels are essentially low-carbon steels (0.03 to 0.1 wt% C) containing approximately 1.5 wt% Mn and less than 0.1 wt% of niobium, titanium, and/or vanadium, which have been hot rolled under controlled conditions to produce ultrafine ferrite grain sizes of less than 5 to 10 µm. Mechanical properties, heat treatments and applications They attain yield strengths of 275 to 550 MPa and tensile strengths of 415 to 690 MPa, with a DBTT of approximately 75 °C. They are hot rolled un-der controlled conditions to produce ultrafine ferrite grain sizes of less than 5 to 10 µm (Fig.4.5b). This is the result from the control of the austenite grain size at rolling temperature (i.e. austenitic grain pinning) by the for-mation of carbides, carbonitrides, and nitrides realized by presence of small addition of Nb, Ti, V.

Fig.4.5 - Fine grain size in; a) common plain carbon steel; b) high-strength low-alloy (HSLA) steel.

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These fine precipitates pin the austenite grain boundaries, hindering grain growth. At still lower rolling temperatures, they inhibit recrystallization of the severely deformed austenite grains. The elongated and pancaked grains can then rapidly transform to fine ferrite. These fine precipitates also pro-vide additional locations for ferrite nuclei to form during cooling, resulting in an even finer ferrite grain size. In addition, as shown in Fig. 4.6, nuclei locations are also formed within the austenite grains at locations of de-formed shear bands.

Fig.4.6 - Microstructure development in low-carbon steels. High-strength low-alloy steels are primarily hot rolled into the usual wrought product forms (sheet, strip, bar, plate, and structural sections) and are commonly furnished in the hot rolled condition. In addition to hot rolled products, HSLA steels are also furnished as cold rolled sheet and forgings. Since HSLA steels do not contain a large percentage of alloying elements, they can be competitively priced against plain carbon steels. The HSLA steels are extensively used as structural beams for bridge con-struction, off-shore oil and natural gas platforms, ship hull and deck plate, and electrical transmission towers and poles. In automobiles, HSLA steels are used for safety applications such as ultrahigh-strength impact door beams and energy-absorbing bumper assemblies and for increasing fuel economy through thinner and lighter-weight chassis sections (Fig.4.7).

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Fig.4.7 – Application of HSLA steel in automobiles . Recent developments about good nitridability of types of HSLA steels when nitride in the bainite condition resulted from air-cooling of forged parts would lead to use such steels to reduce manufacturing costs of con-ventional nitriding steels (or the mostly used quenching and tempering UNI EN 42CrMo 4 steel, finally nitrided) by reducing manufacturing cycle steps (Fig.4.8).

Fig.4.8 – Application of HSLA steel in alternative nitriding of automobile crank-shaft.

25MnCrSiVB6

42CrMo4

Forging

ForgingQuenching

and tempering

Nitriding

LMUmachining LMUfinishing

LMUmachining

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Dual-Phase Steels A dual-phase steel is one that consists of islands of hard martensite em-bedded in a tougher continuous ferrite matrix. This mixture of fine ferrite and austenite grains is produced by heating into the two-phase a+c field, followed by quenching to convert the austenite to martensite (Fig.4.9). The microstructural constituents that can be present in dual-phase steels after processing are therefore a fine grained ferrite matrix, some proeutectoid ferrite that formed from the austenite during cooling, and martensite or lower bainite, depending on the alloy content and the Ms temperature.

Fig.4.8 – Microstructure of dual-phase steel.

Mechanical properties, heat treatments and applications The unique characteristic of dual-phase steels is the continuous yielding behavior during deformation; that is, there is a lack of a yield point during deformation. This provides increased uniform elongation and work harden-ing so that parts produced from a dualphase steel actually gain strength during the forming operation. Dual-phase steels yield at relatively low stresses and then work harden rapidly. Any retained austenite usually transforms to martensite during deformation. The tensile strength varies approximately linearly with the amount of martensite or lower bainite. Typical values are 550 MPa for 10% by volume rising to 760 MPa at 30%. Elongations of approximately 20% are typical (Fig.4.9).

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Fig.4.9 – Stress-strain curves for plain carbon, high strength low-alloy (HSLA), and dual-phase steels. To be successful, the hat treatment of these steels requires suitable contin-uous cooling transformation characteristics and controlled cooling rates, as shown in the scheme of Fig.4.10.

Fig.4.10 – Scheme of heat treatment cycle for dual-phase steels.

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Dual-phase steels are used in applications such as automobile wheel rims and wheel disks. Because of their energy-absorbing characteristics, dual-phase steels are also used in critical locations of automobiles for safety to protect the occupants in the event of a crash.

TRIP Steels

The term TRIP is derived from the mechanism of transformation-induced plasticity. The nominal composition by weight of these steels is 0.25% C, 2% Mn, 2% Si, 10% Cr, 9% Ni, and 5% Mo. They contain a high percent-age of retained austenite (10 to 15%). The austenite transforms to marten-site during forming of the part, thus providing enhanced formability, or it transforms on impact, as in an automotive crash. Mechanical properties, heat treatments and applications Similar to dual-phase steels, TRIP steels are annealed in the intercritical region, but instead of direct cooling to room temperature to form marten-site, they are isothermally treated. The isothermal hold during heat treat-ment is specifically designed to produce large, dispersed volume fractions of retained austenite in the ferrite matrix after intercritical annealing. Thus products of transformation therefore include bainite and retained austenite. The scope of dispersed retained austenite is comprehensible when these steels are cold worked or plastically deformed. During cold plastic defor-mation, the unstable retained austenite transforms to martensite, hence the term transformation-induced plasticity. The strain induced martensitic transformation increases strain hardening; furthermore, it helps to delay necking instability during forming opera-tions. Due to dynamic increase of strength during impact, similarly to Dual-Phase steels they are suitable for safety components to absorb impact ener-gy in automotive crash.

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Chapter 5 – Stainless Steels26

Introduction Under favorable environmental conditions the iron in steels tends to return to its former state of iron oxide as it is available in nature by forming rust or scale. Since the corrosion product is not effective protection, once cor-rosion mechanism starts, the steel will continue to rust. In case of high temperature, oxidation can occur, the oxide scale spalls off, and oxidation will continue as long as the steel is hot. Other corrosion processes, such as dissolution in electrolyte as differential aerated water or dilute acids pro-ceeds with corrosion products formation, that similarly will progressively detach from surface. In the former case we talk about dry corrosion, in lat-ter case about humid corrosion. Whichever mechanisms of corrosion you consider, the addition of chromium in solid solution of iron dramatically improves the corrosion and oxidation resistance of steel. Chromium onto top surface layer immediately reacts with oxygen in environment to oxi-dize and forms a thin, tightly adherent layer of oxide (Cr2O3) on the sur-face. This layer is spontaneously created, transparent, adherent, self-healing when damaged and moreover is capable to prevent or minimizes further corrosion to proceed, by isolation of subsurface metal and external oxygen, key-factor necessary for corrosion mechanisms to advance. To achieve formation of such protective layer, namely for being stainless, steel must contain at least 11.5 wt% Cr – at least, 12 wt% Cr in aqueous solutions and even higher chromium content is necessary for corrosion re-sistance in nonaqueous solutions. Few stainless steels contain more than 30 wt% Cr or less than 50 wt% Fe. Other important alloying elements include nickel, molybdenum, copper, ti-tanium, aluminum, silicon, niobium, nitrogen. Stainless steels are used in a wide variety of applications. Most of the structural applications are in the chemical and power engineering indus-tries, which account for more than a third of the market for stainless steel products. These applications include an extremely diversified range of us-es, including nuclear reactor vessels, heat exchangers, oil industry tubes, components for chemical processing and pulp and paper industries, fur-nace parts, and boilers used in fossil-fuel-fired electric power plants.

26 Reference: M.Boniardi, A.Casaroli, “Stainless Steels”, Gruppo Lucefin Edi-tion, 2014 (free version available at: http://www.lucefin.com/wp-content/files_mf/stainlesssteels_low.pdf).



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Classification of stainless steels There are five types of stainless steels: austenitic, ferritic, duplex, marten-sitic, and precipitation-hardening steels. These five types of stainless steel have a somewhat simplified AISI classification system (mostly diffused in industry), that is also supplemented by the EN designation system for high alloyed steels (i.e. the code with X devoted to distinguish steels with at least one element with wt.% higher than 5%) as follows:

Austenitic stainless steels: 3xx series (AISI 2xx series for low nickel alloys) which are Cr-Ni high alloyed steels in EN designa-tion, such as X5CrNi18-10;

Ferritic stainless steels: 4xx series or Cr high alloyed steels in EN designation, such as X6Cr17;

Duplex stainless steel: Manufacturer’s designation is frequent or EN designation such as such as X2CrNiMoN22-5-3;

Martensitic stainless steels: 4xx series or Cr high alloyed steels in EN designation such as X30Cr13;

Precipitation-strengthening stainless steels: xx-x PH; this type is not defined by the metallurgical structure of the steel at ambient temperature but rather, as per tradition, by the heat treat-ment/strengthening mechanism used to produce it (precipitation hardening).

Before dealing in detail with the relevant metallurgical and mechanical characteristics, the main types of stainless steel available on the market can be summarized in a simple tree view (see figure 5.1).

Figure 5.1 - Schematic of the evolution of stainless steels starting from plain car-bon steels: the stainless steel tree structure.

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To begin with we consider a common heat-treatable plain steel, such as steel grade C30: to make this steel stainless it is sufficient to add a set con-tent of chromium (~13%) to obtain an initial possible version of stainless steel. This is grade X30Cr13. A steel with this type of chemical composi-tion can undergo heat treatment (in fact this is a heat-treatable steel) and, after tempering and quenching (hardening), it takes on a tempered marten-sitic structure at ambient temperature. It also offers the benefit of offering good resistance to corrosion, combined with good mechanical resistance. With the aim of further increasing corrosion resistance of stainless steel as proposed above, a larger quantity of chromium needs to be added, while the presence of carbon should be reduced. In this case the steel grade ob-tained will be X6Cr17, with a ferritic structure at ambient temperature, due to the significant presence of chromium, with notable ferrite forming prop-erties. The level of corrosion resistance of the new steel will be greater than that of the X30Cr13 steel; on the contrary the mechanical resistance of the X6Cr17 will be much more limited as no hardening heat treatment will be possible. To obtain a steel with even greater corrosion resistance than the two grades described above, the addition of nickel and molyb-denum will be necessary, and possibly a further increase in chromium con-tent. In this case, there are two alternative procedures:

starting with the X6Cr17, nickel could be added to obtain stainless steel grade X5CrNi18-10 or both nickel and molybdenum to obtain the grade X5CrNiMo17-12-2: this will thus obtain an austenitic structure at ambient temperature, due to the austenite stabilizing properties of nickel that predominate over the ferrite stabilizing effect of Cr (we talk about austenitic steels);

alternatively, again starting with X6Cr17, smaller quanti-ties of nickel can be added, along with greater quantities of chro-mium, with a set percentage of molybdenum, to obtain the stain-less steel grade X2CrNiMoN22-5-3: this solution obtains a mixed (or two-phase) structure of ferrite and austenite, and we talk about Duplex Stainless Steels.

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Ferritic Stainless Steels Ferritic stainless steels (the AISI 4xx series) are essentially iron-chromium alloys with body centered cubic (bcc) crystalline structures. Ferritic stain-less steels contain 11.5 to 30 wt% Cr, with most compositions containing 17 to 26 wt% Cr. The presence of high percentage of Cr modifies the iron-carbon diagram as depicted in Fig.5.1. chromium stabilizes ferrite and forms a gamma (γ) loop in which austenite is the stable phase. When the chromium content exceeds 12 wt%, it is possible for ferrite to exist at all temperatures27. The ferritising effect of the chromium is no longer com-pensated for by the austenitizing action of the carbon and the structure of the stainless steel will be ferritic at ambient temperatures: this is precisely what occurs on steel type X6Cr17 (similar to AISI 430), the progenitor of ferritic stainless steels.

Fig.5.2 - Iron-chromium phase diagram.

In table 5.1 some typical ferritic steels are The relative designation in ac-cordance with the standard EN 10088 refers to alloyed steel type, with X followed by carbon content in percentage and other alloying elements, e.g. Cr, with their own actual weight percentage. The last column provides the most appropriate AISI designation for such steels.

27 The phase diagram shows that for some compositions with Cr below 12%wt., solid solutions can be transformed into austenite by heating them into the gamma loop, and, when cooled, austenite transforms into ferrite. As shown in the following, this transfor-mation forms the basis for the heat treatable martensitic stainless steels.

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Table 5.1 - Chemical composition of some of the main types of ferritic stainless steels from EN 10088 and AISI designations. Figure 5.2 illustrates the “metallurgic” logic that led to the creation of the main types of ferritic stainless steels present on the market, starting from type X6Cr17. The first family, to which the X6Cr17 belongs, has a chro-mium content ranging from 15.5% to 18%: this family is the most numer-ous in terms of the quantity of alloy types present on the market. There are a further two families, one characterized by chromium content ranging from 11.5% to 14.5% (ferritic stainless steels with low chromium content) and the other with a chromium content of more than 18% (known also as “superferritic” stainless steels). In all three of the above families - with low, medium and high carbon chromium content - other alloy elements may also be present: these in-clude aluminum and silica, aimed at stabilizing the ferritic structure and improving resistance to oxidation under heat, molybdenum, necessary to improve corrosion resistance, titanium and niobium, to prevent precipita-tion of the harmful chromium carbides, as below described.

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Figure 5.2 - Schematic of the main types of ferritic stainless steels, starting from X6Cr17 (similar to AISI 430), progenitor of this family.

Box – The intergranular corrosion induced by carbide precipitations A metallurgical problem typical in stainless steels, including ferritic, is related to the precipitation of chromium carbides, type Cr23C6. This occurs due to the high level of affinity between the chromium and carbon. Chromium carbides usually deposit on the grain boundary and leading to a localized, i.e. within the boundary of the grain itself, depletion of chromium: a consequence of this pro-cess is that the chemical composition of the metal mass falls below the pas-sivation threshold (10.5% chromium) giving rise to intergranular corrosion, also in only slightly aggressive environments. The scheme of such a phenomenon is shown in Fig. 5.3. The entity of corrosion depends both on the quantity of car-bide precipitation and the lesser or greater ability of the chromium to spread in the steel lattice: in the crystalline structure of the steel, this causes short or long range depletion of the chromium with differing effects in terms of material dete-rioration. As the solubility of carbon in the body-centered cubic lattice is signif-icantly limited, the precipitation of chromium carbides in ferritic stainless steels is practically impossible to eliminate. On the other hand, due to the high diffu-sivity of chromium in the lattice of phase α, the chromium gradients in the vi-cinity of the ferritic grain boundary are much less pronounced with respect to what occurs in austenitic stainless steels (refer to Fig.5.3a): as a consequence the problems of intergranular corrosion in ferritic stainless steels, under the ef-

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fect of carbide precipitation on the grain boundary, are less marked with respect to the same phenomena in austenitic stainless steels.

Figure 5.3 - Trends in chromium concentrations at a grain boundary where chromium carbide precipitation occurs: a) in the case of ferritic stainless steel (high diffusivity of chromium); b) in the case of austenitic stainless steel (low diffusivity of chromium). With the exception of the case in which high mechanical properties are required (such as the case of martensitic stainless steels), this problem is avoided by min-imizing the carbon content or attempting to neutralize the effect of the latter, by combining it with other chemical elements, such as titanium and niobium. Also, as explained further in the section below, the semi-finished products should also undergo a complete annealing heat treatment before being used.

Heat treatments The only heat treatment possible for the family of ferritic stainless steels is complete annealing or simply annealing: its role is to optimize corrosion resistance of the steel, aiding a uniform distribution of the chromium in the crystalline structure of the semi-finished part. Great care is taken in select-ing the temperature and hold time, as this family of materials is particular-ly sensitive to the phenomena of crystalline grain enlargement. Annealing

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of ferritic stainless steels also has another important characteristic. If the material to be treated is in the hardened state, the heat treatment would al-so serve to re-crystallize the microstructure, i.e. to reform new crystalline grains, starting from the original grains that have extended under the effect of cold plastic deformation. In general, these newly formed grains are finer that the original hot formed grains in the semifinished part. This is normal-ly referred to as recrystallization annealing (Fig.5.4).

Figure 5.4 - Effect of recrystallization annealing on ferritic stainless steels.

Physical and mechanical properties The resistance properties of ferritic stainless steels are not particularly sig-nificant; in fact these steels are made up of uniform ferrite grains and are used in an annealed state. The unitary value of tensile strength Rm ranges between 450 MPa and 600 MPa, according to the chemical composition, with hardness values of 150-220 HB. As already mentioned, ferritic stain-less steels cannot be hardened by means of a quenching heat treatment: the only way to increase mechanical resistance is by means of cold plastic de-formation processes, such as cold drawing or rolling, which harden the steel: in this case the unitary value of tensile strength can reach up to 900-1000 MPa. In addition to the chromium content, as shown in Fig. 5.5a, the resistance to brittle fractures also depends on the combined effect of other metallur-gical parameters, thus it increases with the increase in contents of intersti-tial elements (carbon and nitrogen) and decreases under the effect of a re-duction in the average size of the crystalline grain; the thickness of the semi-finished part also has an interesting effect on the brittle fractures of the ferritic stainless steels (see Fig. 5.5b).

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(a)

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Figure 5.5 – a) Effect of chromium content on transition curves of iron-chromium alloys (the carbon content is ~ 0.01); b) Effect of thickness of semi-finished part on the transition temperature of two ferritic stainless steels. Main applications Steel grade X6Cr17 (similar to AISI 430) is used for machine parts in the industry for the production and transformation of nitric acid (tanks, con-densers, pipelines, coils, etc.); it is also widely used for cracking and re-forming plants in the oil sector, for the production of low cost cutlery, household applications, decorative elements and furnishing accessories for interiors, coverings for bar counters and tables, and kitchen extractor hoods. It is also used in a number of applications in the cheese/milk dairy sector and for manufacture of train carriages and buses. Ferritic stainless steel grade X6Cr17 is also used in components operating at temperatures up to 750°-800°C due to its optimal resistance to oxidation under heat. In more aggressive environments, the ferritic stainless steel X6CrMo17-1 (similar to AISI 434) can be used, in which the presence of molybdenum

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improves resistance to corrosion due to pitting; as well as for exhaust sys-tems in the automotive sector, these steels are also used for internal clad-ding of buildings, on escalators, lifts and conveyor belts, for drinking wa-ter pipelines or as supports for photovoltaic cells. Austenitic stainless steels If the chromium content is increased to at least 17-18% and at the same time nickel is added to a percentage of 8% to 9%, the steel will have an austenitic structure at ambient temperature. For better understating, you may refer to Fig. 5.6 that shows the simplified phase diagram of a steel with 18% chromium and 8% nickel on variation in carbon content, namely the grade X5CrNi18-10 (similar to AISI 304) progenitor of the family of austenitic chromium-nickel stainless steels. The significant austenitizing effect of the nickel predominates over the ferritizing action of the chromi-um. An significant aspect of the phase diagram of austenitic stainless steels is the absence of critical points, as no transformation temperature γ→α are visible. After initial solidification at very high temperatures in phase γ + δ, the stainless steel becomes completely austenitic (phase γ) and remains in this state through to ambient temperature, without the inevitable chromium carbides.

Fig.5.6 – Fe-C binary section of Fe-Cr-Ni-C quaternary diagram with Cr =18% and Ni = 8%; C1 are carbides type (Cr,Fe)23C6.

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To limit carbide formation and detrimental effect on intergranular corro-sion (refer to Box – The intergranular corrosion induced by carbide pre-cipitations) the carbon content is fixed to very low values, usually it ranges 0.02-0.06%. The combination of chromium and nickel in the alloy obtains a stainless steel with an austenitic structure, i.e. with a face-centered cubic lattice, highly resistant to atmospheric corrosion and water-based solu-tions28. In austenitic stainless steels, added corrosion resistance can be achieved by increasing the nickel content up to 11-12% or adding molybdenum to val-ues of 2-3%. The latter action leads to another widely used stainless steel, i.e. the X5CrNiMo17-12-2 (similar to AISI 316), progenitor of the second family of austenitic stainless steels, i.e. chromium-nickel molybdenum29. Finally, a further possibility to obtain an austenitic structure in a stainless steel consists in replacing the nickel part with manganese30, the element which otherwise would only act as a deoxidant in the alloy. This solution was developed in the 1950s, with the aim of limiting production costs; the progenitor of the family of austenitic stainless steels with chromium-manganese-nickel is the X12CrMnNiN17-7-5 (similar to AISI 201). Figure 5.6 illustrates the “metallurgical” logic, which led to the creation of two main types of austenitic stainless steels available on the market: one is chromium-nickel stainless steels such as X5CrNi18-10 and the other is the chromium-nickel-molybdenum such as X5CrNi17-12-2 and their respec-tive by-products.

28 In air and water-based solutions, even partially contaminated by chlorides (generally up to 500ppm of ions Cl-) the corrosion resistance of austenitic stainless steel X5CrNi18-10 is superior with respect to martensitic and ferritic types such as X30Cr13 and X6Cr17.

29 The austenitic chromium-nickel-molybdenum stainless steel X5CrNiMo17-12-2 (sim-ilar to AISI 316) is suitable for applications in contact with sea water (Cl- 20,000ppm = 2%) or with water-based solutions strongly contaminated by chlorides.

30 The alternative to manganese with respect to nickel is based on the austenitizing ef-fect that both elements show if added to Fe-C alloys: as the austenitizing effect of the man-ganese is equal to half that of nickel, around 2% of Mn needs to be added for each 1% of replaced Ni.

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Fig. 5.7 - Schematic of main types of austenitic chromium-nickel and chromium-nickel-molybdenum starting from X5CrNi18-10 and X5CrNiMo17-12-2. The sensitization of austenitic steels The phenomena of carbide precipitation, also known as “sensitization” for austenitic stainless steels occurs at temperatures between 450°C and 900°C and at highly variable exposure times: the most critical conditions are found at around 700°C for time intervals of just a few minutes. As already discussed (refer to Box – The intergranular corrosion induced by carbide precipitations), sensitization of austenitic stainless steels leads to a decline of chromium in the immediate vicinity of areas where the carbides form, i.e. on the boundaries of the crystalline grains: consequently, the chromium content of the grain boundaries is below the passivation limit of the steel, leading to local deterioration in corrosion resistance and the phenomena of inter-crystalline corrosion, even in only slightly aggressive environments (Fig.5.3b). A method of intervention, in many ways simpler than the first, consists in minimizing the carbon content of the steel down to values of around 0.02-0.03%. As a consequence the time required for incubation and the formation of chromium carbides changes from a few minutes to several hours, which practically renders sensitization of the material negligible, as shown by sensitization curves in Fig.5.7. the time required to sensitize the steel depends, as well as on the exposure temperature, on the carbon con-tent in the alloy: for example, if the carbon content is 0.08%, the time for carbide precipitation is around one minute, while this can extend to several hours if carbon is reduced to 0.02%.

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On the basis of the “C curves” austenitic steels with low carbon content have been developed, such as X2CrNi18-9 (similar to AISI 304L27) or X2CrNiMo17-12-2 (similar to AISI 316L) which are virtually insensitive to the phenomena of chromium carbide precipitation.

Fig.5.7 - Time-temperature diagram (“C curve”) showing precipitation of chromi-um carbides on variation of the carbon content, for austenitic stainless steels with 18% chromium and 9% nickel. Further but quite more expensive method to prevent sensitization consists in adding titanium or niobium, as for the ferritic stainless steels, too. Tita-nium and niobium leads the formation of very stable Ti- and Nb- base car-bides, thereby preventing carbon to engage chromium to form chromium-based carbides. The heat treatments Due to absence of critical phase-transformation temperature, the only fea-sible heat treatment is solubilization, also known as negative quenching or austenitic quenching: this treatment is normally performed on semi-finished products and finished products in austenitic stainless steel, down-line of the various manufacturing processes. The treatment is performed at high temperatures (approximately in the range 1000°C to 1100°C), for a sufficient time to ensure homogenization of the chemical composition of the steel. Scope of treatment is to cancel microstructural irregularities and moreover allowing full solubilization of chromium carbides to avoid to put into service a sensitized stainless steel. After solubilization, austenitic

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stainless steels must be cooled rapidly in water, moreover in case of thick parts. Particularly for steels subjected to sensitization, cooling rate must be rapid in the range 450°C-900°C to prevent carbide formation (remember that sensitization is temperature-time dependent phenomenon). In the case of thin parts, a high pressure flow of nitrogen can also be used, although cooling is preferable. On the other hand a special treatment is used on Ti and Nb added austenit-ic stainless steels, named stabilization. This consists in maintaining the steel at temperatures between 850°C and 950°C for times ranging from 1 to 4 hours depending on the dimensions of the semi-finished part. During treatment, precipitation of the titanium and niobium carbides occur and fixes carbon, thus preventing carbon to subtract Cr from matrix to form chromium carbides. The subsequent cooling is in air. Physical and mechanical properties The linear heat expansion of austenitic stainless steels, for example, is 50-60% greater than that of ferritic or martensitic stainless steels, as well as the thermal conductivity, which on the contrary is 40-50% lower. These particular properties must be taken into consideration in an industrial con-text: in the heating and cooling during thermal treatment, the dimensional variation of the stainless steel pieces will be much greater than in common steels, but heat exchange will be much more limited. Austenitic stainless steels have nonmagnetic behavior, this characteristic makes them well suited to some military applications (but, as a result of cold plastic deformation operations, the semi-finished products tend to be-come slightly ferromagnetic). The mechanical characteristics of austenitic stainless steels are rather lim-ited, due to the high deformability of the austenite matrix. In an annealed condition, these steels provide a tensile strength UTS of 550-650 MPa and a yield stress YS of 220-280 MPa. Conversely, the austenitic microstruc-ture has high ductility, with percentage values of elongation at break of 40-50% and hardness of 160-200 HB. The only way to increase the traction resistance of austenitic stainless steels is through work-hardening; by cold plastic deformation (rolling, drawing etc.) it is possible to obtain a tensile strength UTS 1500-1800 MPa and yield stress YS 1300-1600 MPa, much greater values than those that would be obtained using a low carbon common steel. Main applications The X5CrNi18-10 (similar to AISI 304) is widely used in various applica-tions: boilers, pressure tanks, vessels, heat exchangers, fluid transport

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pipes, plumbing, elevators and signs. It is also used in building and urban furnishings, in domestic utensils (cookware, cutlery, appliances), in sinks and cabinets, as well as in the chemical, petrochemical, nuclear and phar-maceutical industries as well as for the production of milk, beer, canned food, paper and pulp, colorants and explosives. Due to its high toughness at low temperatures, it is also widely used in the cryogenics sector for the storage and transport of liquefied gases. the types X6CrNiTi18-10 (similar to AISI 321) and X6CrNiNb18-10 (sim-ilar to AISI 347) are the stabilized versions with titanium and niobium. As these materials have a high resistance to corrosion comparable with that of X5CrNi18-10, they are used in the same applications, especially for the production of large sized and/or very thick items that are subjected to welding operations. X2CrNi18-9 (similar to AISI 304L) is actually the low carbon version of X5CrNi18-10: this composition is also used to solve issues of the precipi-tation of chromium carbides during welding and is a good alternative to the previously indicated stabilized types. The stainless steel X5CrNiMo17-12-2 has high resistance to corrosion in seawater, in contact with process waters contaminated with halides (Cl-, I-, F-), with acid condensates and with waste water; it has excellent behavior in the presence of organic acids or alkaline solutions, also showing a small resistance in dilute sulphuric, hydrochloric or phosphoric acid solutions.

Martensitic stainless steels The martensitic family of stainless steels is characterized by limited chro-mium content (normally between 11.5% and 18%) and carbon contents among the highest of the stainless steels most commonly used (generally between 0.1% and 1%). Chromium, a highly ferritising element, and carbon, an austenitising ele-ment, are balanced so that the steel has an austenitic structure at high tem-perature and a martensitic structure at ambient temperatures after temper-ing. It must be pointed out that the presence of a high content of carbon, re-quired to ensure a good level of hardness and mechanical resistance for the steel, also tends to aid the formation of chromium carbides. Consequently martensitic stainless steels are, among all types, the least resistant to corro-sion; their field of application in fact is limited to only slightly aggressive environments. Fig. 5.8 illustrates the “metallurgical” logic that has led to the creation of the main types of martensitic stainless steels, starting with

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X30Cr13 (similar to AISI 420B), the progenitor of this family, and still to-day widely used in the knife sector.

Fig. 5.8 - Schematic of the main types of martensitic stainless steels, start-ing from X30Cr13 (similar to AISI 420B), progenitor of this family. When such steels are heated to temperatures above the critical points, their original microstructure transforms completely into austenite plus carbides, to then become martensite plus carbides under the effect of cooling the steel in oil or in air. Given the existence of critical points, it is therefore possible to trace the isothermal transformation curves (TTT) and aniso-thermal curves (CCT) of the austenite: these curves are shown in fig. 5.9 for a martensitic stainless steel grade. Due to similarities of heat treatments conducted onto martensitic stainless steels and to hardened and tempered steels, their manufacturing cycle are very similar, too.

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Figure 5.9 - Isothermal transformation curves (TTT) and anisothermal transfor-mation curves (CCT) for martensitic stainless steel type X39Cr13 (similar to AISI 420C). Heat treatments If no substantial differences exist in heat treating martensitic stainless steels and common quenched and tempered steels, actually some peculiari-ties should be taken into account. In case of martensitic stainless steels, heating phase must be carefully conducted since stainless steels has very low conductivity. To avoid permanent deformation of parts, or crack for-mation, a worst case, the heating phase must be controlled with pre-heating

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between 550°C and 800°C, especially in the case of large size parts and/or parts with complex geometry. As regards the subsequent austenitization phase, a higher temperature must be envisaged with respect to common quenching and tempering steels, thus it should be as higher as possible to solubilize carbides. However, grain coarsening phenomena may occur at high temperatures, that leads to con-sequent reduction in resistance properties of the steel. For these conflicting objectives, the optimized austenitizing temperature shall be chosen, de-pending on specific steels, in the range 950° C – 1100° C. Martensitic stainless steels can be tempered either at low temperatures (be-low 400°C) or at high temperatures (over 640°C). However, temperature range of 450- 600°C must be avoided. This interval is considered critical as it reduces resistance to brittle fractures (a type of temper brittleness) and significantly reduces corrosion resistance. Physical and mechanical properties The physical properties of martensitic stainless steels are very similar to those of the common quenching and tempering steels, sharing the same martensitic tempered microstructure. In the hardened state most martensit-ic stainless steels have a unit resistance under traction Rm of between 700 MPa and 1700 MPa depending on the chemical composition and temper-ing conditions; the fatigue limit in air remains around the value 0.45∙Rm. The ductile to brittle transition behavior is similar to that of special heat-treatable steels used frequently in industrial applications. Main applications The martensitic stainless steels most commonly used in industrial sectors are X30Cr13 (similar to AISI420B) and X12Cr13 (similar to AISI 410): among the two, the first will guarantee hardness with a higher carbon con-tent, while the second features increased strength. These two steels are widely used where high mechanical resistance and wear resistance is required. Corrosion resistance is good, especially in ru-ral environments, fresh water not contaminated by chlorides, in contact with foodgrade substances, or with weak acids (such as organic acids), with petrol products (crude and intermediate) and with oxidating saline so-lutions (chromates, permanganates, etc.).These are frequently used for the production of table knives, industrial cutting knives, surgical instruments, rasors, scissors, calipers, machine gun barrels, brake disks for motor vehi-cles; they are also used in the sector of moulds for plastic materials and for springs.

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Type X17CrNi16-2 (similar to AISI 431) is must more resistant to corro-sion with respect to those described above, due to the increased chromium content in the alloy: it also offers increased strength due to the presence of nickel (not present in types X30Cr13 and X12Cr13). The steel type X17CrNi16-2 is used in particular for shafts on marine engines, propeller shafts, pump parts, hydraulic machinery shafts, valves, turbine blades and wear-resistant components in reforming oil plants. Austenitic-Ferritic (Duplex) Stainless Steels Austenitic-ferritic stainless steels (also called duplex or biphasic) owe their name to the presence of a mixed structure of austenite and ferrite at ambi-ent temperature. This is the result of the combination of chromium and nickel suitably balanced in the chemical composition of the alloy: typical-ly, duplex stainless steels have a chromium content between 22% and 25%, nickel content between 4% and 7%, with added molybdenum (3-4%) and nitrogen (0.1-0.25%) in many cases. The commercial name originally developed by Sandvik is most commonly used: it includes two pairs of numbers of which the first indicates the chromium content and the second the nickel content (for example 2205 in-dicates a biphasic stainless steel containing 22% chromium and 5% nick-el). Duplex stainless steels allow the combination of the specific properties of resistance to corrosion of the austenitic and ferritic stainless steels; however, they also share a number of specific problems, typical of both, such as the precipitation of chromium carbides and the presence of a harm-ful phase that forms at around 800°C as well as an embrittlement issue at 475°C. Heat treatments An annealing treatment before being put into operation is required in tem-perature interval of 1050-1150 °C; it is then rapidly cooled in water to op-timize the austenite ferrite ratio that should be close to unity. Physical and mechanical properties Most of the physical properties are all comparable with those of austenitic stainless steels (specific heat, conductivity, resistance and elastic modu-lus); the only exception is thermal expansion between austenitic and ferrit-ic stainless steels. When it is exposed to magnetic fields, the duplex com-ponent is ferromagnetic, similar to what happens for ferritic stainless steels. The peculiar biphasic microstructure of such steels allows high values to be obtained of both the yield stress (which is around double that of austen-

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itic stainless steels) and the tensile strength. Furthermore, they have an ex-cellent behavior in terms of DBTT, due to transition temperature set to around -80°C.

Figure 5.10 - Effect of the microstructure of the resilience of some families of stainless steels (γ = austenite; α+γ = ferrite and austenite; α = ferrite).

Main applications X2CrNiN23-4 (type 2304) was the first of the low alloy biphasic stainless steels: this steel was developed to economically compete with the most common austenitic stainless steels used in applications where mechanical resistance and resistance to corrosion in chloride environments are essen-tial. It is used in the production plants of nitric acid and for plants in con-tact with caustic substances (concentrations <30%), with organic acids or aqueous solutions rich in chlorides. The steel X2CrNiMoN22-5-3 (type 2205) is most used duplex stainless steel, thanks to its high mechanical resistance and excellent anti-corrosion characteristics. It is largely used in the petrochemical and chemical field, in environments contaminated by chlorides and in the presence of carbon dioxide CO2 or hydrogen sulphide H2S; it is widely used in desalinisation plants and plants where steel parts shall be in contact with dilute and con-centrate solutions of sulphuric, phosphoric, acetic and formic acids.

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Precipitation Hardening Stainless Steels Precipitation hardening (or PH) stainless steels were developed to improve mechanical properties of martensitic stainless steels, especially low frac-ture toughness and to increase the resistance to corrosion at the same time. They are classified based on the microstructure achieved through their heat treatment, thus they are divided into: martensitic, semi-austenitic and aus-tenitic. The hardening phase (after annealing) involves cooling the material through the finely dispersed precipitation of intermetallic compounds and interstitials in the crystalline matrix of the steel. For this purpose, alloy el-ements are added such as aluminum, copper, titanium and niobium which give rise to compounds of the type Ni3(Al, Ti), Ni3Ti and NiAl or Fe2(Mo, Nb) or even carbonitrides type M(C, N) with M = Nb, Ti, Cr. Nickel is always present in precipitation hardened stainless steels, both to improve resistance to corrosion and to make the metal mass tough; it usu-ally has very low carbon content (C≤0.1%) and molybdenum is often add-ed for anti-corrosion. Heat treatments, physical and mechanical properties After the annealing treatment, semi-finished products have good cold plas-tic deformability and good machinability; the work piece is then subjected to the aging treatment – namely, the precipitation hardening treatment - to obtain mechanical properties aimed to withstand operating stresses. Martensitic type precipitation hardening stainless steels, such as for exam-ple X5CrNiCuNb16-4 (also called 17-4 PH), are usually annealed at 1030°-1060°C and then cooled in air: a low carbon martensitic structure is obtained with low hardness and good deformability. At the end of the operations of forming and machining operations, the semi-finished product is subjected to aging treatment at temperatures be-tween 480°C and 630°C and for times ranging 1 to 4 hours. By this way it is possible to obtain a tensile strength that ranges 850-1400 MPa, with an elongation A% ranging 25% to 12% (see Fig. 5.11); resilience at ambient temperature ranges 40- 100J.

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Fig.5.11 - Steel X5CrNiCuNb16-4 (also called 17-4 PH) annealed at 1050°C in air, then aged according to various methods: curves σ – ε. Semi-austenitic precipitation hardening stainless steels, such as for exam-ple X7CrNiAl17-7 (also called 17-7 PH), have a predominantly austenitic structure after annealing at ambient temperature and cold-working opera-tions, such as cold rolling, can be more easily conducted. After annealing the austenitic structure is unstable so that either cold plastic deformation operations or post heat treatment transform microstructure into martensite. The aging heat treatment will be performed on the martensitic structure ob-tained in this way, similarly to what happens in normal martensitic PH stainless steels. Main applications Precipitation hardening stainless steels are generally commercialized onto market in form of long products, round or hexagonal section bars, plates and sheets. Thanks to high mechanical resistance and resistance to corro-sion, they are employed in many sectors to fabricate valves, shafts, bear-ings and turbine and compressor blades. They are also used in applications for load cells, sprockets, firearms, utensils, springs and surgical instru-ments.

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Chapter 6 – High-Temperature Resistant Alloys: Steels for High Temperatures, Ni-Base Alloys and Ni-Superalloys31

Introduction Main problems metals suffer at high temperatures are related usually to both creep phenomena (refer to Chapter 2) and progressive deterioration of surface oxidized layers that is typical of hot-corrosion damage mecha-nisms. In Chapter 2 we already discussed about the creep damage mecha-nisms, and the main approaches for design against creep phenomena, such as the selection of materials with a high melting temperatures32, the selec-tion of face-centered cubic (fcc) metals33 and the possibility to place inert particles, such as fine carbides, on either grain boundaries, so to helps to pin the grain boundaries sliding (in case diffusion creep dominates) or in-side grains, so to counteract dislocation movements (in case dislocation creep dominates). On the other side, hot corrosion is the second important damage phenome-non that may occurs in components that works at high temperatures. Main problems are in this case related to hot-oxidation or gaseous corrosion, namely all those damage mechanisms which basically refer to the reaction of metal surface with oxygen at high temperatures usually in the absence

31 Main reference: F.C. Campbell, Elements of Metallurgy and Engineering Alloys, ASM International, 2008 (Chapters 15, 29, 30).

32 Diffusion coefficients on which the creep rate depends are proportional to the homol-ogous temperature (T/Tm).

33 Face-centered cubic (fcc) structures generally have superior creep resistance to body-centered cubic (bcc) metals at equivalent homologous temperatures due to their slightly more open bcc structure (i.e. fcc, at same temperature, has higher compaction factor than bcc, namely 0.74 against 0.68) that results in greater diffusivity of solution atoms (e.g. Fe, in steels) in bcc than fcc. This fact implies that solution atoms can diffuse easily and thus creep diffusion mechanisms are favored compared to such crystal lattice with lower diffu-sivity of solution atoms. Finally, to avoid misunderstanding, it is necessary to distinguish the solution atom diffusivity from interstitial atom diffusivity; typical is the case of iron-alloys: it is known (refer to Chapter 1) that fcc structure has higher capability to host inter-stitial carbon atoms than bcc at same temperature; you may refer to Fe-C diagram for for quick check: at 800°C, for example, for a 0.30 C %wt. both Feα and Feγ exist; the percent-age of carbon dissolved in Feα is much lower than percentage of carbon hosted in Feγ. As consequence of higher compaction factor of fcc above discussed, the number of interstitial sites (namely, the available spaces for hosting carbon) are higher in fcc than bcc. This ex-plains the higher carbon diffusivity in fcc in iron alloys, notwithstanding the lower self-diffusivity (i.e. solution atom Fe diffusivity) of fcc than bcc.

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of moisture (for that, we also call it dry-corrosion). For example, one of the requirements of a high-temperature material in a turbine blade, or a su-per-heater tube, was that it should resist attack by gases at high tempera-tures and, in particular, that it should resist oxidation. Turbine blades do oxidize in service, and react with H2S, SO2 and other combustion products. In such environments, an oxidation film forms onto surface and its grow-ing rate and its solubility in dry and hot environments are two important factors to evaluate hot corrosion rate of metal alloys34. Some films are more protective than others; it is known that protective films are those with low diffusion coefficients, namely those ones with high melting points. That is one reason why A12O3 protects aluminum, Cr2O3 protects chromi-um and SiO, protects silicon so well, whereas Cu2O and even FeO (which have lower melting points) are less protective. Furthermore, as the oxide film thickens, due to an intrinsic brittleness, it may develop cracks and it either totally or partly lifts away from the material. Figure 6.1 shows how this can happen. Generalizing, if the volume of the oxide is much less than that of the material from which it is formed, it will crack to relieve the strain (oxide films are usually brittle); conversely, if the volume of the ox-ide is much greater, the oxide will tend to release the strain energy by breaking the adhesion between material and oxide, and springing away. By this way, the protective barrier offered by oxides to metal surface does not become any more effective as oxidation proceeds. For protection, then, we need an oxide skin which is neither too small and splits open (like the bark on a fir tree) nor one which is too big and wrinkles up (like the skin of a rhinoceros), but one which is just right.

34 When designing with oxidation-prone materials, it is obviously vital to know how fast the oxidation process is going to be. Intuitively one might expect that, the larger the energy released in the oxidation process, the faster the rate of oxidation. For example, aluminium oxidizes much more slowly than iron. If you heat a piece of bright iron in a gas flame, the oxygen in the air reacts with the iron at the surface of the metal where the oxygen and iron atoms can contact, creating a thin layer of iron oxide on the surface, and making the iron turn black. The layer grows in thickness, quickly at first, and then more slowly because iron atoms now have to diffuse through the film before they make contact and react with oxy-gen. If you plunge the piece of hot iron into a dish of water the shock of the quenching breaks off the iron oxide layer, and you can see the pieces of layer in the dish. The iron sur-face now appears bright again, showing that the shock of the quenching has completely stripped the metal of the oxide layer which formed during the heating; if it were reheated, it would oxidize at the old rate. Thus, the important thing about the oxide film is that it acts as a barrier which keeps the oxygen and iron atoms apart and cuts down the rate at which these atoms react to form more iron oxide. Aluminum, and most other materials, form ox-ide barrier layers in just the same sort of way - but the oxide layer on aluminum is a much more effective barrier than the oxide film on iron is.

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Fig. 6.1 – Breakdown of oxide films, leading to linear oxidation behavior.

Due to common main factor which contributes to both creep and hot corro-sion damage mechanisms, the high temperature, when we talk about high-temperature resistant alloys we have necessarily to talk about alloys that are capable to resist both to creep and hot oxidation phenomena. Generalizing, for metals, Cr2O3 is a good protective oxide, thus the level of oxidation resistance at temperatures below 980 °C for metal alloys is a function of the chromium content. High-temperature nickel alloys can con-tain 8 to 48% Cr. At temperatures above 980 °C, the aluminum content be-comes an important component in metals, as Al2O3 becomes the dominant oxide protector, especially when thermal cycling is involved. Furthermore chromium and aluminum can contribute in an interactive manner to provide oxidation protection to metals, namely the higher the chromium content, the less aluminum that may be required. Alloys that are designed as heat-resistant materials include:

among ferrous alloys: chromium-molybdenum, chromium-molybdenum-vanadium steels and stainless steels;

among non-ferrous alloys: nickel alloys and nickel superalloys. In the following a brief description of these main heat resistant alloys is provided. Chromium-molybdenum and chromium-molybdenum-vanadium steels The chromium content increases oxidation resistance, while molybdenum increases elevated temperature strength because it serves to prevent de-composition of iron carbides (such a phenomenon is also called iron-graphitization) up to 500°C. For this reason, creep resistance is adequate when steels are exposed for prolonged times just below this temperature,

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since molybdenum is effective for these steels against coarsening of car-bides in such temperature range. Among chromium-molybdenum structural steels, low alloyed CrMoNiMn are weldable ferritic steels. The 8CrMoNiNb9-10 (equivalent to ASTM A335 grade P24) series are the mostly used for seamless alloy-steel pipe for high-temperature service. The increase of chromium to above 7% in CrMo steels leads to a group of steels containing also martensite. This microstructure introduces a new el-ement of structural hardening, despite ferritic steels, due to its a fine lath structure with stabilized fine carbides dispersed in matrix. Thus, structural hardening by martensite is responsible for the large increase in strength of X11CrMo9-1, as compared to 8CrMoNiNb9-10, as shown by Fig.6.2. Further improvements, especially of the creep strength, have been achieved by alloying with vanadium, niobium, tungsten and boron, as also shown in Fig. 6.2b. The introduction of X20CrMoNiV11-1 at the begin-ning of the sixties allowed major increases in power plant efficiency. The transformation behavior and microstructure of this alloy are comparable to those of X11CrMo9-1. The higher creep-rupture strength of X20CrMoNiV11-1 results mainly from the larger volume of dispersed M23C6 carbides in the microstructure, a result of the alloy's higher carbon content. The best results in terms of elevated-temperature strength are ob-tained by quenching and tempering to produce a microstructure consisting of upper bainite. Both the chromium molybdenum and the chromium-molybdenum vanadi-um steels extend the operating range up to 540°C.

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(a)

(b)

Fig.6.2 - Creep-rupture strength of some Cr-Mo and Cr-Mo-V heat-resistant steels. Stainless steels for high temperatures Stainless steels are also used for elevated temperature applications. Mar-tensitic stainless steels are used at temperatures up to 540 to 650°C, but they must be tempered at approximately 55°C higher than the operating temperature so to prevent softening in service (due to coarsening of car-bides formed during previous tempering treatment). Due to their higher chromium contents, ferritic stainless steels have the best scaling resistance, but they are limited to service temperatures of ap-proximately 370°C to avoid the precipitation of the embrittling σ phase (refer to Chapter 5, Fig. 5.2). Austenitic stainless steels have the best creep resistance of the stainless steels and are used at temperatures up to 870°C. In austenitic stainless steels, strengthening mechanism for enhancing creep resistance is related

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to both the limited diffusivity of iron in austenitic matrix - which is smaller than in a ferritic matrix - and precipitation hardening by fine intermetallic phases or carbonitrides as they are capable to counteract dislocation creep mechanism. Particularly, small quantities of Nb and Ti that are added to stabilize austenitic stainless steels by subtracting carbon to chromium by forming fine Nb- and Ti-types carbides (refer to Chapter 5) are also bene-ficial in reducing creep rate, due their intrinsic high-temperature stability (they do not coarse for high temperature prolonged exposure, so they rep-resent an effective barrier to dislocation movements). However, a major problem with the austenitic grades is their high coefficients of thermal ex-pansion, which must be compensated for during design. For these reason, austenitic stainless steels are frequently used in the power generation in-dustry at temperatures greater than 650 °C in low-stress part (limited around 50 MPa or some higher) which are expected to remain in service for more than 100,000 h. Ni-base alloys Nickel and nickel alloys have an excellent combination of corrosion, oxi-dation, and heat resistance, combined with good mechanical properties. They are used extensively in aggressive environments, such as in the chemical processing, pollution control, power generation, electronic, and aerospace industries. Nickel is ductile and can be made by conventional processing methods into castings, powder metallurgy parts, and various hot- and cold-worked wrought products. Commercially pure nickel has a moderately high melt-ing temperature (1468°C), a density of 8.89 g/cm3, and low elastic modu-lus of 209 Pa. Nickel is used principally as an alloying element to increase the corrosion resistance of ferrous and copper alloys, with only approxi-mately 13% of the annual production used for nickel-base alloys. Approx-imately 60% is used in stainless steel production, with another 10% in al-loy steels and 2.5% in copper alloys. Basics of Nickel Metallurgy As a result of its face-centered cubic (fcc) crystal structure, nickel has ex-cellent ductility and toughness. Alloying is used to further improve corro-sion and heat resistance. Austenitic nickel matrix can be strengthened by solid-solution hardening, carbide precipitation, precipitation hardening, and/or work hardening. Solid-solution hardening is provided by cobalt, iron, chromium, molyb-denum, tungsten, vanadium, titanium, and aluminum. Iron, cobalt, titani-um, chromium, and vanadium are weaker solid-solution-hardening ele-

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ments. Although nickel itself is not a carbide former, the presence of car-bon as an alloying element leads to the formation of carbides. The carbides most frequently found in nickel alloys include MC, M6C, M7C3, and M23C6, where “M” is the carbide-forming element or elements, such as chromium, which forms Cr7C3. In general, carbides and fine particles im-prove the elevated-temperature strength if they are located on the grain boundaries as discrete particles. However, if they form continuous grain-boundary films, they can cause embrittlement. Nickel-Chromium-Iron Alloys. This family of alloys was developed for high-temperature oxidizing envi-ronments. They typically contain 50 to 80 wt% Ni, which permits the addi-tion of other alloying elements to improve strength and corrosion re-sistance while maintaining toughness. The Ni-Cr-Fe alloys contain chromium ranging from 14 to 30 wt% and they form a protective surface film of Cr2O3, they have excellent corrosion resistance in many severe en-vironments, including immunity to chloride ion stress corrosion cracking. They also have good oxidation and sulfidation resistance along with good strength at elevated temperatures. Among variety, the alloy 800 commercially known as INCOLOY is an Ni-Cr-Fe alloy austenitic, solid-solution alloy. Titanium nitrides, titanium car-bides, and chromium carbides normally appear in the alloy’s microstruc-ture. The nitrides are stable at all temperatures below the melting point and are therefore unaffected by heat treatment. At elevated temperatures it offers resistance to oxidation, carburization, and sulfidation along with rupture and creep strength. It is widely used ma-terial for construction of equipment requiring corrosion resistance, heat re-sistance, strength, and stability for service up to 816°C. For applications requiring greater resistance to stress rupture and creep, especially at tem-peratures above 816°C, INCOLOY alloys 800H and 800HT35 are used. INCOLOY is approved under the Boiler and Pressure Vessel Code of the American Society of Mechanical Engineers (ASME).

35 Incoloy 800, 800H and 800HT are identical except for the higher level of carbon in alloy 800H compared to 800 series and the addition of up to 1.20 per-cent aluminum and titanium in alloy 800HT, compared to 800 and 800H. Incoloy 800 was the first of these alloys and it was slightly modified into Incoloy 800H. This modification was to control carbon (0.05-0.10%) and grain size to optimize stress rupture properties. Incoloy 800HT has further modifications to the com-bined titanium and aluminum levels (.85-1.20%) to ensure optimum high tempera-ture properties.

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Ni-Superalloys Ni-superalloys are heat-resistant alloys of nickel, iron-nickel that are fre-quently used at temperatures exceeding 540°C. However, some superal-loys are capable of being used in load-bearing applications in excess of 85% of their incipient melting temperatures. They exhibit the best combi-nation of high strength, good fatigue and creep resistance, good corrosion resistance, and the ability to operate at elevated temperatures for extended periods of time (i.e., metallurgical stability). Their combination of elevated temperature strength and resistance to surface degradation is unmatched by other metallic materials. Superalloys have been used in aircraft, industrial, and marine gas turbines, nuclear reactors, aircraft skins, spacecraft struc-tures, petrochemical production, orthopedic and dental prostheses, and en-vironmental protection applications. Today’s modern, high-performance aircraft jet engine could not operate without the major advances made in superalloy development over the past 50 years. Thanks to superalloys, in-creases in engine operating temperatures over the last 50 years have been gradual but significant, from approximately 400°C to 1290°C, that result-ed increase in operating temperature translates into improved engine effi-ciency. Typical applications for superalloys in a jet engine are shown in Fig. 6.3.

Fig.6.3 - Typical materials selection for jet engine components.

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The main strengthening mechanisms for nickel and iron-nickel superalloys are solid solution hardening and precipitation hardening. In addition, grain-boundary carbides are important in providing high-temperature stability. The microstructure consists of fine γ’ carbides, the Ni3Al particles, dis-persed in a fcc nickel-rich solid solution; thus, this alloy is mainly strengthened by a combination of solid solution (addition of alloying ele-ments) and the precipitates dispersed as high-temperature stable γ’ carbides into γ matrix, to prevent dislocation creep phenomena, and formed at grain boundaries, to prevent diffusion creep phenomena (see Fig.6.4).

Fig.6.4 - Microstructure of a precipitation-strengthened nickel-base superalloy. Actually the precipitate morphology is determined by degree of lattice mismatch between the γ' precipitate and the γ matrix, ranges from spherical precipitates when lattice mismatches is in the order of 0 to 0.2%, cubical – as in the figure - for mismatches of 0.5 to 1%, and platelike at mismatches above approximately 1.25%. The high coherency between the precipitate and matrix is maintained to high temperatures, and the precipitate coarsens very slowly, so that the precipitate overages slowly, even at temperatures as high 0.7 Tm. Nickel-base superalloys have the best creep resistance of the superalloys and are used as turbine blades in engines operating at temperatures as high as 1290°C (T/Tm=0.9). Among commercial superalloys, we mention:

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Hastelloy series, solid-solution-strengthened nickel-base superal-loys primarily developed for low-temperature service, often in cor-rosive environments.

Inconel 718, a superalloy that contains niobium which is strength-ened primarily by γ’’ phase (i.e. Ni3Nb particles); it rapidly loses strength in the range of 650 to 815°C because of the instability of the γ’ precipitates. However a widespread use of Inconel 718 is due to its excellent combination of mechanical properties, moder-ate price, and ease of processing, including weldability. Inconel 718 may account for as much as 60 wt% of the total consumption of superalloys.

An example of application: Ni-superalloy made turbine blade Improved high-temperature material properties are largely responsible for the increase in the engine operating temperature. Some improved material performance has come about from minor alterations in alloy chemistry, and some has resulted from processing changes. For example, the major stress axis in a turbine blade is parallel to the blade axis. In a polycrystal-line blade, this stress is normal to some grain boundaries, and this causes voids, precursors to fracture, to initiate on the boundaries (Fig.6.5).

Fig. 6.5 – Creep cavitation mechanisms. Directional solidification (i.e., solidifying the material sequentially from the blade bottom to its top) results in columnar grains having boundaries aligned along the blade axis. This significantly reduces the cavitation prob-lem. Further improvements came with the casting of single crystal blades. Increasing the superalloy grain size from 100 mm to 10 mm (the order of the thickness of a turbine blade) reduces the creep rate by approximately 6

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orders of magnitude when Coble creep36 is the dominant creep mechanism, as it often is under typical blade operating conditions.

Fig.6.6 - Creep comparison of a nickel-base superalloy for different casting proce-dures. For further increase in creep resistance, the turbine blades made of superal-loys are coated with thermal barrier coating. To insulate blade of Ni-Superlloy, overlay protective coatings are generally deposited on deposited on top surface of base Ni-superalloy metal; MCrAl or MCrAlY, zirconia layers (0.3-0.4mm thick) coatings, are derived directly from the deposition process. They do not require diffusion for their formation. The constituent denoted “M” in these designations has, at various times, been iron, cobalt, nickel, or combinations of nickel and cobalt. Overlay coatings are usually applied by physical vapor deposition (PVD) in vacuum chambers. They al-so may be applied by plasma spray techniques.

Fig.6.5 - Thermal barrier coating for turbine blades.

36Coble creep is a diffusion creep mechanism that consists in diffusion of atoms in a ma-terial along the grain boundaries, which produces a net flow of material and a sliding of the grain boundaries.

Temperature °C

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Chapter 7– Non-Ferrous Structural Alloys: Magnesi-um Alloys37

Introduction: the search for lightweighting in automotive A 2013 KPMG’s study (KPMG’s Global Automotive Executive Survey 2013) conducted to automotive market and trend shows the automotive in-dustry is being shaped by various driving forces. Environmental pressures are leading to more efficient engines either via e-mobility or improvements to internal combustion engine (ICE) traditional technologies. With an in-creasing proportion of the world’s people, increasing BRIC’s economies, emerging markets demand are pushing for request of increased mobility for overcrowded cities. In old Europe many cities are limiting downtown pollutions and traffic congesting by closing large urban areas to pollutant vehicles. New, smaller, urban friendly vehicles are necessary while car-sharing and other mobility concepts are rapidly growing in popularity, as shown in Table 7.1.

Table 7.1 – The major driving forces for competing on today automotive market.

Recent changes to the Corporate Average Fuel Economy (CAFE) are driv-ing automakers to seek more aggressive methods for fuel consumption re-ductions. Lightweighting of vehicles will be a factor in meeting these re-

37 Main reference: F.C. Campbell, Elements of Metallurgy and Engineering Alloys, ASM International, 2008 (Chapters 27).

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quirements due to the inherent relationship between mass and fuel con-sumption. In addition, lightweighting may benefit other advanced fuel-saving but load constrained technologies, such as battery-powered vehi-cles. The ability to introduce new lightweight materials into vehicles is not a trivial matter. Many see a new concept, or limited production, vehicle in-troduced to the market with lightweight “space-aged” materials and feel that adoption by mass produced vehicles is a simple matter of “remove and replace.” However, this is not the case; factors such as existing infrastruc-ture, material cost, and high volume capacity become of great importance for mass production vehicles. In addition, many of the low production ve-hicles incorporate these lightweight materials as a method for gaining ex-perience on their performance. Without significant data to support durabil-ity, the risk-averse automotive culture will not adopt new materials. Therefore it often takes many years to implement lightweight technology in mainstream production vehicles. Today, there is a high emphasis on greenhouse gas reductions and improv-ing fuel efficiency in the transportation sector, all car manufacturers, sup-pliers, assemblers, and component producers are investing significantly in lightweight materials Research and Development and commercialization. All are moving towards the objective of increasing the use of lightweight materials and to obtain more market penetration by manufacturing compo-nents and vehicle structures made from lightweight materials. Because the single main obstacle in application of lightweight materials is their high cost, priority is given to activities to reduce costs through development of new materials, forming technologies, and manufacturing processes. Yet the weight reduction is still the most cost-effective means to reduce fuel con-sumption and greenhouse gases from the transportation sector. The reason-ing behind this is simple; it takes less work to accelerate and move a light-er object. It has been estimated that for every 10% of weight eliminated from a vehicle's total weight, fuel economy improves by 7%. This also means that for every kilogram of weight reduced in a vehicle, there is about 20 kg of carbon dioxide reduction. In terms of lifecycle manage-ment, the use cycle of the vehicle typically dominates the overall CO2 emissions generation of the vehicle (see Figure 4). Lighter weight materi-als have the advantage of providing sustained greenhouse gas emission re-ductions over the use cycle of the vehicle. Conventional steels have been a dominant force in the material selection of automotive parts. A combina-tion of high-strength, low cost and capacity to be produced in high vol-umes has made mild steel a very attractive material in automotive applica-tions. However, as technology changes and fuel economy increases in

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importance, other materials are gaining acceptance in the automotive in-dustry. Materials such as high-strength steel, aluminum, composites, and to date to a much lesser extent magnesium have increased their overall utili-zation over the past 30 years, while mild steels have seen a steady decline (see Fig.7.1). At the same time, regular steel and iron castings have also seen a steady decline.

Figure 7.1 – Vehicle Material Composition by Percent Mass.

Box –Requirements of the materials in automotive

Generally speaking, the materials used in automotive industry need to fulfil several criteria before being approved. Some of the criteria are the results of regul tion and legislation with the environmental and safety concerns and some are the requirements of the customers. In many occasions different factors are conflicting and therefore a successful design would only be pos-sible through an optimized and balanced solution. Below four main key-factors are addressed:

Lightweighting capability. To reduce part weight onboard, all car

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manufacturers, suppliers, assemblers, and component producers are investing significantly in lightweight. Actually it is better to refer to specific strength, strength limit (fatigue limit, for example, in fa-tigue design) versus density for selection of candidate weight-saving materials. On the other hand, often the industrial application of lightweight materials is the higher cost of part made of an un-conventional materials (for the specific purpose/components) than conventional one. The unitary cost of the lighter re-designed part usually increased since increased costs accounted for product de-velopment with new material, not fully optimized/mature forming and joining technologies that contribute to increase final manufac-turing process costs. At the present state, the replacement of steel is being pursued with aluminum, magnesium, carbon fiber composites and foams. Further key-issues related to the recycling and recovery of end-of-life vehicles have been addressing by automakers since recovery target of 85% of material used in manufacturing phase is driving the auto industry to adopt lightweight materials and manu-facturing and assembling technologies capable to meet such ambi-tious targets. It is worth of notice that constant automakers efforts in development and adoption of design approaches that pursue se-lection and use of easy-to-recycle materials and assembling tech-nologies is not only limited to decrease the environmental impact of product life cycle, but it is also an effective way to mitigate costs of manufacturing cycles for new products made of higher unitary price materials (i.e. dollars per kg of material used).

Cost. One of the most important consumer driven factors in auto-motive industry is the cost. Since the cost of a new material is al-ways compared to that presently employed in a product, it is one of the most important variables that determines whether any new ma-terial has an opportunity to be selected for a vehicle component. Cost includes three components: actual cost of raw materials, man-ufacturing value added, and the cost to design and test the product. This test cost can be large since it is only through successful vehi-cle testing that the product and manufacturing engineers can achieve a ‘level of comfort” to choose newer materials for applica-tion in a high-volume production program. For these reasons steels with their wide range of yield strength combined with high modu-lus together with ease of manufacture and low cost have largest share of the market. The higher unitary cost of alternative materials such as aluminum or composites mean that steel’s position as the first-choice material could be still secure for years [Corus Automo-tive Eng. 2010]. As historic lightweight materials, aluminum and magnesium alloys are the usual solutions for replace steels and cast

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irons. As already mentioned, the ability to approach the total cost of the competition, therefore, must be associated with lower compo-nent manufacturing costs. For this reason, notwithstanding alumi-num and magnesium have much higher unitary price (i.e. dollars per kg), compared to cast irons, a well-designed and properly sized part in either cast aluminum or magnesium components are poten-tially less costly. This is based on their reduced manufacturing cy-cle times, better machinability, ability to have thinner and more variable wall dimensions, closer dimensional tolerances, reduced number of assemblies, more easily produced to near net shape thus decreasing finishing costs, and less costly melting/metal-forming processes. This suggests not to refer to unitary price of materials in viability studies conducted by a R&D department, but an economic assessment based on the entire product value chain for the conven-tional and alternative scenarios should be conducted to evaluate (actualized) costs of new products, accordingly to New Product Development (NPD) best practices today employed. In any case wrought aluminum and magnesium components are almost always more costly to produce than their ferrous counterparts, but lighter and usually competitive in terms of GHGs emissions over the product life (refer to Figure 7.2). Since cost may be higher, deci-sions to select light metals must be justified on the basis of im-proved functionality, weight saving objectives and environmental impact capability. Government regulations mandate reductions in exhaust emissions, improved occupant safety, enhanced fuel econ-omy, reductions in workplace emissions, increased safety require-ments, and requirements for toxic materials handling and disposal. Also the high manufacturing costs, the lower productivity (a carbon fiber composite manufactured part requires batch process hardly to automate) and the reduced recyclability is one of the major barriers in use of the carbon fiber composite materials.

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Figure 7.2 - Total Greenhouse Gas Emissions during Various Phases of the Vehicle Lifecycle.

Safety, crashworthiness. The ability to absorb impact energy and be

survivable for the passengers is called the ‘‘crashworthiness’’ of the structure in vehicle. There are two important safety concepts in automotive industry to consider, crashworthiness and penetration resistance. Crashworthiness is defined as the potential of absorption of energy through controlled failure modes and mechanisms that provides a gradual decay in the load profile during absorption. The current legislation in design of the automobiles requires that, in the case of an impact at speeds up to 15.5 m/s with a solid, immovable object, the occupants of the passenger compartment should not ex-perience a resulting force that produces a net deceleration greater than 20g. The current trend of materials in car industry is towards replacing metal parts more and more by polymer composites in or-der to improve the fuel economy and reduce the weight of the vehi-cles. The behavior of composite failure in compression is the oppo-site to metals. Most composites are generally characterized by a brittle rather than ductile response to load. While metal structures collapse under crush or impact by buckling and/or folding in accor-dion (concertina) type fashion involving extensive plastic defor-mation, composites fail through a sequence of fracture mechanisms involving fiber fracture, matrix crazing and cracking, fiber-matrix de-bonding, de-lamination. The actual mechanisms and sequence of damage are highly dependent on the geometry of the structure, lam-ina orientation, and type of trigger and crush speed, all of which can be suitably designed to develop high energy absorbing mecha-nisms. Several aspects are considered in design for improved crashworthiness including the geometrical and dimensional aspects

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which have key role in different stages of crash. However the mate-rials deformation and progressive failure behavior in terms of stiff-ness, yield, strain hardening, elongation and strain at break are also very important in the energy absorption capacity of the vehicle. [Witteman, 1999].

Recycling and life cycle considerations. One of the major growing

concerns in all the industries including automotive, is an increased awareness for environment. Issues such as ‘protection of re-sources’, ‘reduction of CO2 emissions’, and ‘recycling’ are increas-ing the topics of consideration. While the United States has not is-sued regulations concerning automotive end-of-life requirements, European Union (E.U.) and Asian countries have released stringent guidelines. European Union legislation implemented in 2006 dic-tates that a significant percentage of the vehicle should be re-used or recycled. The End of Life Vehicles (ELV) Directive from envi-ronment agency aims to reduce the amount of waste produced from vehicles when they are scrapped. Around two million vehicles reach the end of their life in the UK each year. These vehicles are classed as hazardous waste until they have been fully treated. The directive requires ELV treatment sites to meet stricter environmen-tal standards. This would mean that the last owner of a vehicle must be issued with a Certificate of Destruction for their vehicle and they must be able to dispose of their vehicle free of charge. Vehicle manufacturers and importers must cover all or most of the cost of the free take-back system. It also sets higher reuse, recycling and recovery targets and limits the use of hazardous substances in both new vehicles and replacement vehicle parts. [Environment agency, 2010]. As the results of the new legislations, no discussion of new materials in the automotive industry should conclude without a consideration of recycling. Considerable R&D efforts are now fo-cused on developing materials with greater potential of recycling and re-use or developing ways of recycling and re-use of the cur-rent materials. This includes both metal and composite materials. The composition and forming processes of the metal materials are changing to accommodate this recycle and re-use demand. This al-so justifies the great attention towards natural fiber based compo-sites and new high temperature resistant thermoplastic resins. Tra-ditionally the design of the part/components has mainly been the responsibility of the OEMs. Recently, however, manufacturers have begun to shift design responsibility to part/component suppliers. After the manufacturing stage, the vehicle spends a long period of time in the use phase of the life cycle. In the past, the median life of

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a vehicle has been reported to be 12–13 years [Libertiny,1982, 1993]. Lately, the median life has increased to around 16 years with as many as 5% of the vehicles still remaining on the road after 30 years of operation [Davis, 2004].

Roskill UK, leader in international metals and minerals research, estimates that consumption of magnesium reached a new peak in 2012, 1.1Mt, with demand having grown by 5.5%py over the last decade. The largest end-uses for magnesium are die-cast magnesium and aluminum alloys, each accounting for a third of total consumption. On the other hand, the trans-portation industry is the largest consumer of die-cast magnesium and the second largest consumer of aluminum-magnesium alloys behind packag-ing.

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Magnesium Alloys for Structural Applications Magnesium has the lowest density (1.738 g/cm3) of the structural metals, with a density of approximately 2/3 that of aluminum and 1/4 that of steel. Although magnesium alloys have only moderate tensile strengths, in the range of 140 to 345 MPa, and a modulus of elasticity of only 45 GPa, due to their low densities, they exhibit favorable specific strengths (tensile strength/density) and specific moduli (modulus/ density) comparable to other structural metals. Magnesium and its alloys are used in a wide varie-ty of structural applications, such as automotive, industrial, materials han-dling equipment, kitchen appliances, hand-held tools, luggage frames, computer housings, cellular phones, and ladders. Magnesium is relatively inexpensive38 and easy to cast, machine, and weld; its electrical and ther-mal conductivity and heat capacity are relatively high. Magnesium alloys have very good damping capacity, and castings have found applications in high vibration environments. Over the years, one of the major drawbacks39 of magnesium alloys has been corrosion. Magnesium occupies the highest anodic position on the

38 Despite magnesium is commonly thought as an expensive metal, unitary price of magnesium over time periods varies so much to be either less expensive of or more expen-sive of its direct competitor in lightweighting transport sector strategy. The problem is more precisely related to high volatility of magnesium price, instead of its temporary shock uni-tary price. Magnesium price has been varying since first appearance on market and it is strictly related to availability on marketplace of magnesium supplying to satisfy current demand. Prior to World War I, Germany was the only significant producer of magnesium, but during the war other countries recognized the strategic importance of this metal and built plants to meet their inner military demands. The interest of governments in magnesi-um production during wartime caused relatively prolonged stable price. The use of expen-sive Mg metal decreased after World War I; the beginning of World War II resulted again in increased Mg demand: the consequence was higher prices since low availability on mar-ket. U.S. Government implemented plant production in the period 1943-1945, thus stabiliz-ing the price. Various other period of fluctuant price of magnesium were therefore due to mismatch between demand and supply: high unitary price are expected when magnesium is recognized as strategic, primarily by automotive sector, but recent low demand period have led to reduced production, thus low supplying capacity of magnesium producers. Low magnesium price periods were due to over production of magnesium against current request on market; thus, highly fluctuant unitary prices are direct consequence of a microeconomics economic model that determine price of any goods by supply and demand relationships.

39 One other major drawback that has been considered over the years is the supposed

high ignitability of magnesium. If it is dust or fine particles of magnesium are highly ignit-able in air, due to high reactivity of magnesium to oxygen, it is not quite different from the affinity and reactivity of aluminum fine powders or dust to oxygen. What is really different and more hazardous for magnesium is that, when ignited, it cannot be extinguished simply removing heat sources that has brought magnesium to melt point and flame ignition condi-

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galvanic series and, as shown in Fig. 2.56 of Chapter 2 can be subject to rather severe corrosion. The corrosion problem is mainly due to the impurity elements iron, nickel, and copper that act as galvanic microcells (refer to Chapter 2). However, the use of higher-purity magnesium alloys has led to corrosion resistance ap-proaching that of some of the competing aluminum casting alloys. Basics of Magnesium Metallurgy Pure magnesium has a hexagonal close-packed crystalline structure that re-stricts slip at room temperature to the basal planes (see Fig.7.3). Magnesi-um alloys work harden rapidly at room temperature, and their ductility is low. Since additional slip planes become operative at elevated temperature, wrought magnesium alloys are normally formed at temperatures greater than 205°C, normally in the range of 345 to 510°C, depending on the spe-cific alloy.

Figure 7.3 – The hexagonal close-packed crystalline structure, schematic represen-tation on the left, actual spatial occupancy of Mg atoms o the right. Magnesium also has a rather low melting point (650°C), which increases its susceptibility to elevated-temperature creep. However, through im-

tion. However, recent developments by Koreans researchers has led to put onto marketplace new magnesium series added with CaO that make magnesium alloy self-extinguishable in case of flame ignition. These magnesium modified alloy series are called Eco-Magnesium and when they are produced by adding over 0.5~0.7wt% CaO they can be considered fire-retardant and fire-proof.

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proved alloying techniques, the creep resistance of magnesium alloys has been significantly improved. Alloying Elements The most important alloying additions are aluminum, zinc, and zirconium. Aluminum provides solid-solution strengthening and widens the freezing range, making the alloy easier to cast. As aluminum is added to magnesi-um, the strength continuously increases as the aluminum content is in-creased up to 10 wt% Al, but the elongation peaks at approximately 3 wt% Al. Mg alloys with 3 wt% Al have the highest ductility, and those with 9% Al have the best strength, but those with approximately 6 wt% provide the best combination of strength and ductility. This phenomenon is explained by the Mg-Al phase system, as it is shown in Fig.7.4. This system is an eutectic system between the α solid solution and a brittle intermetallic compound β (Mg17Al12).

Figure 7.4 - The magnesium-rich end of the magnesium-aluminum phase diagram.

In the magnesium-aluminum phase diagram (Fig. 7.4), there is a eutectic between the terminal solid solution and the brittle intermetallic compound b (Mg17Al12). The eutectic structures contain more compound than a solid

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solution, and since the compound is brittle, alloys with a eutectic network are also brittle. When the aluminum content exceeds 8%, discontinuous precipitation of the β phase occurs at the grain boundaries as shown in Fig.7.5, leading to a decrease in ductility. The phase diagram also shows that aluminum has a maximum solubility of 12.7 wt% at 436°C, which de-creases down to approximately 2 wt% at room temperature. While this type of solubility would seem to indicate that these alloys would be ame-nable to precipitation hardening, unfortunately the resulting precipitate is coarse and results in only moderate hardening. While many of the alloying additions to magnesium form eutectics with decreasing solid solubility that lead to precipitation hardening, the strength that results from this harden-ing mechanism is much less than that observed with the precipitation hard-ened aluminum alloys. Since the response to precipitation heat treatment is poor, most of these alloys are used in either the as-cast. Zinc behaves in a manner similar to aluminum; the ductility reaches a maximum at a 3 wt% addition, and a good combination of strength and ductility occurs with 5 wt% Zn. It also improves the corrosion resistance by combining with the harmful impurities iron and nickel. Zinc is also used in conjunction with zirconium, rare earths40, or thorium to produce precipitation-hardenable alloys. Zirconium is a powerful grain refiner. However, zirconium cannot be used in combination with aluminum or manganese because it forms brittle intermetallic compounds that destroy ductility. Harmful elements The elements iron and nickel are harmful impurities that greatly reduce corrosion resistance. Copper is also often considered, along with iron and nickel, as an impurity but is actually used as an alloying addition in some magnesium alloys. Iron is by far the most troublesome of the three, be-cause nickel and copper are more readily controlled by selecting the purity of the starting materials. The ASTM designation of Mg alloys and most used Mg alloys In the following, an example of ASTM designation of magnesium alloys is shown and thus commented as practical example (all magnesium alloys are designated by this scheme):

AZ91D

40 Rare earth (RE) elements are potent solid solution strengtheners in magnesi-um alloys.

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The code above shown represent:

The first two letters, A and Z in the example, indicate respectively the alloying elements with higher content. The Table 7.2, first col-umn, gathers all the possibilities for codifying the two alloying el-ements added in chemical composition;

The two following numbers indicate respectively the round per-centage of two elements (in the example, 9% and 1% for Al and Zn respectively).

Third letter indicates different type of same alloy (in terms of pu-rity).

Fourth letter indicates supplying condition.

Table 7.2 - ASTM International designation for magnesium alloys.

In the following, most used commercial alloys are mentioned. Casting Alloys Magnesium has excellent die-filling properties and large, thin-walled and complex components can be cost-effectively produced by casting rather than by joining smaller parts together made of wrought Mg alloy parts.We mention among variety:

Mg-Al casting alloys, the AM series. When higher ductility is re-quired, a low aluminum content is pursued in order to decrease

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amount of β phase around α grains there are some alloys with lower aluminum contents, such as AM20 (Mg-2Al-0.5Mn), AM50 (Mg-5Al-0.3Mn), and AM60 (Mg-6Al-0.2Mn).

The Mg-Al-Zn casting alloys, the AZ series. They are Mg-Al-Zn casting alloys. Addition of Zn also helps to strengthen the alloys by a combination of solid solution - like Al effect - and precipita-tion hardening, thanks to Zn capability in refining precipitates that form during ageing treatment (after solution treatment). The addi-tion of zinc must be balanced by a concurrent decrease in the alu-minum content to keep the total below approximately 11 wt%. For example, comparing the AZ63 (6%Al-3%Zn) to AZ91 (9%Al-1%Zn), both them containing less than 11% of Al and Zn. Both AM and AZ series can be used at temperatures less than 120 °C, since they are susceptible of low-temperature creep phenome-na. Creep in magnesium alloys occurs primarily by grain-boundary sliding: as the temperature in these alloys increases, the β phase at the grain boundaries softens and it cannot prevent grain-boundary sliding.

The creep resistant Mg-Al-Si: the AS series. For better creep re-sistance, Si is added. It forms fine, hard particles of Mg2Si along the grain boundaries to help retard grain boundary sliding. Exam-ples are the alloys AS21 (Mg-2Al-1Si-0.4Mn) and AS41(Mg-4Al-1Si-0.3Mn). In any case they cannot compete with creep resistance of cast heat treated aluminum alloys.

The Mg-Zn-Zr casting alloys: the ZK series. The remarkable grain-refining ability of zirconium led to development of high strength and high ductility alloys such as ZK51 (Mg-4.6Zn-0.75Zr) and ZK61 (Mg-6Zn-0.7Zr). Both ZK51 and ZK61 produce fairly high strength levels when heat treated to the T5 (i.e. part is cooled from an elevated temperature shaping process then artificially aged to form precipitates) or T6 (i.e. part is solution heat treated, then arti-ficially aged) tempers, respectively.

The Mg-Rare Earth-Zn-Zr casting alloys: the ZE series. RE ele-ments (La, Ce, etc.) are added. On aging during precipitation heat treatments, fine precipitates can be formed. They enhance creep resistance due to the combined strengthening effects of grain-boundary phases and precipitates within the grains. One common alloy is ZE41 (Mg-4Zn-1.3RE-0.7Zr), which has moderate strength in the T5 condition that is maintained up to 150 °C.

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The Magnesium-Yttrium casting alloys: the WE43 series. Most recently developed high-temperature alloys that contain approximately 4 to 5 wt% Y, they exhibit high strength with good creep resistance at temperatures up to 300 °C and superior corrosion resistance comparable to some alumi-num-base casting alloys. However Y is very expensive and hard to mix in melting phase. For this reason a mischmetal containing 75 wt% Y in REs is used instead of pure yttrium. An example is the alloy WE43 (Mg-4Y-3.25RE-0.5Zr) that keep strength high up to 200°C. Recent commercial type Elektron 21 has been introduced by Magnesium Electron UK. Wrought Magnesium Alloys Wrought magnesium alloys are produced as sheet and plate, extruded bars, billets, shapes, and, to some limited extent, forgings. Despite the hexago-nal close-packed structure and its low number of active slip planes, when forming process is conducted at recommended temperatures (345 to 510 °C), Mg alloys exhibit very high formability. In fact, a number of slip planes become active at this temperature interval and a number of standard forming processes can be used with such correct forming temperatures. Among variety, the AZ31B (Mg-3Al-1Zn-0.3Mn) is the most widely used sheet and plate alloy. This alloys is strengthened by a combination of solid-solution strengthen-ing, grain size control, and cold working. Some advantages of hot forming of Mg are:

– forming process can usually be conducted in one step without the need for intermediate anneals;

– parts can be made to closer tolerances; – hardened steel dies are not necessary for most forming processes.

Box – Manufacturing operations Machining operations. Mg is the easiest of all of the metals to machine. Ma-chining is usually conducted dry, using large depths of cut and high feed rates. Very tight dimensional tolerances are easily achieved, with surface finishes. Although machining is usually conducted dry, cutting fluids can be used to reduce the chances of distortion and minimize the danger of fire when chips are fine, as during finish machining. When magnesium chips ig-nite, they burn with a brilliant white light and flame is not self-extinguishing. It is very important to remind that water cannot be used for extinguish flame, since Mg melt react with hydrogen contained in water with explosive reaction. Joining techniques. Mg alloys are welded by traditional techniques that use

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gas-shielded arc welding processes (MIG/TIG), although processing param-eters and equipment used for aluminum welding have to be modified. In au-tomotive sector, the most promising method for welding thin Mg sheets is laser or electron beam, while friction stir welding is a more recent develop-ment suitable for joining materials that are more difficult to weld or even for joining dissimilar materials like magnesium or aluminum alloys. Corrosion protection. For ordinary outdoor applications, substantial im-provement over the earlier alloys are sufficient. On other side, seacoast loca-tions involving direct contact with salts are definitely corrosive to magnesi-um alloys. The optimal corrosion protection (in terms of thickness and resistance) is provided by an anodizing treatment, followed by the applica-tion of an organic paint system chemical conversion coatings or anodizing treatments, are required. A number exist, such as the older Dow 17 and HAE and the newer and improved Tagnite, Keronite, and Magoxid treatments. In many cases it is sufficient to simply coat the counterpart and leave the mag-nesium uncoated (if it is no view part). This to prevent a defect in a coating on magnesium would result in an enhanced localized corrosion attack of the magnesium component. No contact corrosion of magnesium is caused by anodized AlMg3 alloy. Conventionally galvanized steel bolts can be at-tached to magnesium by using a silicate sealing. The silicate sealing of gal-vanized steel bolts was successfully applied by Audi and VW at the B80 magnesium gear housing.

Box – Alternative manufacturing processes for Mg parts to compete with Al parts for lightweighting Despite enormous market share of aluminum, a continuous request for using further lighter materials in several sectors like automotive, aeronautics, transportation in generals, has been pushing to adoption of magnesium al-loys, being magnesium 30% lighter than aluminum. Traditional magnesium die-casting is however not practicable for safe and structural related reasons since:

lower ductility and toughness than cast aluminum, not acceptable for several sector standards;

lower elastic modulus and lower strength of conventional magnesi-um casting alloys than aluminum cast alloys, not compensated by magnesium lower density, in structural component;

complex and expensive equipment is necessary because of using cover gases to prevent hazardous reactions of molten magnesium with air (it is well known that the continuous oxidation and result-ant burning of Mg alloy occur, at high temperature over 500 ºC).

However, impressive advancements have been recently introduced by: i.

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adding CaO to conventional Mg alloys; ii. a non SF6 (and other GHGs cover gases) die-casting is possible; iii. just safe and clean nitrogen enriched at-mosphere is required for prolonged time, while for short process cycle time casting can be done in air. These novel Mg-CaO added alloys are available on the market, known as Eco-Magnesium alloys. As alternative shaping technology, semisolid processes have been research-ing to produce parts that can compete with die-cast aluminum parts. A semisolid process relies on the behavior of metals that, stirred in interme-diate liquid and solid phase, exhibit a remarkable decrease of its viscosity [1]. Scientifically referred as thixotropic behavior [2-6], this phenomenon in metals is well explained because spheroidal rather than a dendritic micro-structure forms during agitation of semisolid slurry [7]: rounded solid parti-cles are suspended in the liquid fraction, thus viscosity drops. Consequently, a laminar not turbulent flow is possible to fill semisolid material into high complexity cavities with smooth mold filling preventing air entrapment, as it is usual in conventional die-casting. The absence of air/gas entrapment re-sults in:

higher integrity of the parts, due to absence of internal gas porosi-ties, with superior mechanical properties;

possibility to conduct post-heat treatments to increase furthermore mechanical properties, not possible for the cast alloys (gas en-trapped causes blistering phenomena during heat).

The state-of-the art recognizes for aluminium alloys two semisolid routes, “Rheocasting” and “Thixocasting”, while for magnesium alloys, only a commercial semisolid process route is possible, and it is called “Thixomold-ing”:

i. Thixocasting: consists in the manufacture of billets of the desired globular microstructure - usually by continuous casting and induc-tion stirring. The billet are fully solidified in globular shaped mi-crostructure and used as feedstock material for a subsequent reheat-ing in semisolid state and final shaping.

ii. Rheocasting: the semisolid slurry is prepared directly by spilling out from furnace into a heated crucible equipped with a stirrer; once the semisolid slurry is ready, it is gravity poured into the die or pressure injected. The advantage against Thixocasting is that avoids the re-heating of thixotropic state billet, as happens in the Thixocasting process. The advantage is reduced energy per kg of finished product.

iii. Thixomolding: employs a machine similar to injection molding of polymers. Room temperature magnesium alloy feedstock (i.e. chips) are fed into the a heated barrel through feeder. A screw in-side the barrel agitates and shears chips while they are heated up to semi-solid temperature range. The semisolid slurry once ready is

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injected into die. References [1] Z. Fan, International Materials Reviews, vol. 47, no. 2, pp. 49–85, 2002. [2] M. C. Flemings, Metallurgical Transactions A, vol. 22, no. 5, pp. 957–981, 1991. [3] A. R. A. McLelland et all, Materials Science and Engineering A, vol. 232, no. 1-2, pp. 110–118, 1997. [4] M. Modigell et all, Journal of Materials Processing Technology, vol. 111, no. 1–3, pp. 53–58, 2001. [5] D. Brabazon et all, Materials Science and Engineering A, vol. 356, no. 1-2, pp. 69–80, 2003. [6] B. P. Gautham et all, Materials Science and Engineering A, vol. 393, no. 1-2, pp. 223–228, 2005. [7] A. Blanco et all, Transactions of Nonferrous Metals Society of China, vol. 20, no. 9, pp. 1638–1642, 2010. [13] D. Liu et all, Acta Materialia, vol. 53, no. 14, pp. 3807–3819, 2005. [8] Kim, S. et all, Magnesium Conference (IMA-2009), San Francisco, May 2009, IMA, USA [9] R.Burapa et all, Trans. Nonferrous Met. Soc. China 20(2010) s857-s861

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Chapter 8–Titanium Alloys41

The primary advantages of titanium alloys are their combination of rela-tively low densities 4.5 g/cm3 (approximately half as heavy as steel and nickel-base superalloys), high strengths that are aligned with steels (yield strengths vary from 480 MPa of pure titanium to 1100 MPa for structural Ti alloys). Low density and high strength place titanium specific strength (i.e. strength versus density) at very high value, so it is qualified as light metal. Furthermore titanium alloys have much better fatigue strength than the other lightweight alloys, such as those of aluminum and magnesium. Titanium alloys can be used at moderately elevated temperatures, as high as 370 to 595°C, depending on the specific alloy. In addition, some alpha titanium alloys (refer to section Metallurgy of Titanium), especially the low interstitial grades, can be used in cryogenic applications because they do not exhibit a ductile-to-brittle transition. As a result of their attractive combination of properties, titanium alloys are used extensively in aerospace for both airframe and engine components. In commercial passenger aircraft engines, titanium alloys are used for the fan, the low pressure compressor, and approximately 2/3 of the high-pressure compressor. Although titanium is a highly reactive metal, a very stable and highly ad-herent protective oxide film forms on its surface. This oxide film, which forms instantly when fresh metal surfaces are exposed to air and/or mois-ture, provides the excellent corrosion resistance of titanium that can be su-perior to austenitic stainless steels. For this reason, Titanium alloys are frequently used in chemical processing equipment as a result of their ex-cellent corrosion resistance. They also have outstanding biocompatibility42 with the human body and are used for prostheses and dental implants. The biggest disadvantage of titanium alloys is their relatively high cost. Since titanium is a very reactive metal with a high melting point (1720°

41 Main reference: F.C. Campbell, Elements of Metallurgy and Engineering Alloys, ASM International, 2008 (Chapters 28).

42 Titanium is considered the most biocompatible of all metals due to its ability to withstand attack from bodily fluids, stay inert in the human body, be compatible with bone growth and stay strong and flexible during use. The TiO2 protective film that forms onto titanium metal when titanium is exposed to air (i.e. oxygen in air) is insoluble and chemically non transportable so that it makes such titanium highly resistant to body environments, preventing any immune reaction from oc-curring.

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C), ingot casting and primary fabrication procedures are complicated and expensive. Secondary fabrication processes, such as forming and machin-ing, are also usually more costly than those for other competing metals. Titanium Metallurgy Pure titanium at room temperature has an alpha (α) hexagonal close-packed (hcp) crystal structure, which transforms to a beta (β) body-centered cubic (bcc) structure at a temperature of approximately 885°C. This transformation temperature, known as the beta-transus temperature, can be raised or lowered depending on the type and amount of impurities or alloying additions. As a result of the hcp crystalline structure, alloys with appreciable amounts of alpha must be formed at elevated temperatures, while those with pre-dominantly bcc structures exhibit varying degrees of room temperature formability. At room temperature, commercially pure titanium is com-posed primarily of the alpha phase. As alloying elements are added to tita-nium, they tend to change the amount of each phase present and the beta-transus temperature in the manners shown in Fig. 8.1.

Fig.8.1 - Phase diagrams for binary titanium alloys.

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Specifically: Addition of alpha-stabilizer elements, such as aluminum, oxygen, nitro-

gen, and carbon, increases the beta-transus temperature by stabilizing the alpha phase (see Fig.8.1, upper left box);

Addition of beta-stabilizer elements, such as molybdenum, vanadium, tantalum, and niobium, that are miscible in the beta phase decreases the decrease the beta-transus temperature and stabilizes the beta phase (see Fig.8.1, upper right box);

Addition of eutectoid-forming elements, such as manganese, iron, chro-mium, cobalt, nickel, copper and silicon, that forms an eutectoid reaction with Ti (see Fig.8.1, bottom left box).

Titanium has a great affinity for interstitial elements, such as oxygen and nitrogen, and readily absorbs them at elevated temperatures, which increases strength and reduces ductility. Hydrogen has detrimental effect, and it always must be minimized in titanium al-loys because it causes hydrogen embrittlement by the precipitation of hydrides. The maximum limit allowed is approximately. 0.015 wt% (~100 ppm). Absorp-tion of several hundred ppm of hydrogen results in embrittlement (Fig. 8.2) and the possibility of stress cracking. Note that the addition of 20 ppm does not cause embrittlement, but when the hydrogen content goes up to 250 ppm, the reduction in area is seriously impaired.

Figure 8.2 - Effect of hydrogen content (ppm) on ductility of alpha titanium.

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Titanium Alloys Titanium alloys are classified according to the amount of alpha and beta retained in their structures at room temperature. Classifications include commercially pure, alpha and near-alpha, alpha-beta, and metastable beta. While these classifications are useful, many of them are actually very close to each other in the total amount of beta stabilizer present, as illustrated in the Fig. 8.3 phase diagram. For example, Ti-6Al-4V is classified as an alpha-beta alloy, and Ti-6Al-2Sn-4Zr-2Mo is classified as a near-alpha al-loy, yet they differ little in the total amount of beta stabilizer concentra-tion. The properties of a number of commercially important alloys are given in Table 8.1.

Fig. 8.3 - Pseudobinary titanium phase diagram.

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Table 8.1 - Properties of selected titanium alloys.

Commercially Pure Titanium Commercially pure titanium wrought products are used primarily for ap-plications requiring corrosion resistance (such as corrosion-resistant tub-ing, tanks, and fittings in the chemical-processing industry.). They are also useful in applications requiring high ductility for fabrication but relatively low strength in service (yield strengths range from 170 to 480 MPa). In the higher strength grades, oxygen and iron are intentionally added to the re-sidual amounts already in the sponge to provide extra strength. On the oth-er hand, carbon and nitrogen usually are held to minimum residual levels to avoid embrittlement. Conversely, when good ductility and toughness are desired, the extra-low interstitial (ELI) grades are used. In ELI grades, car-bon, nitrogen, oxygen, and iron must be held to acceptably low levels, be-cause they lower the ductility of the final product. Alpha and Near-Alpha Alloys Aluminum is the principal alloying element in the alpha and near-alpha al-loys. Aluminum provides solid-solution strengthening and oxidation re-sistance and reduces density. They are slightly less corrosion resistant but higher in strength than unalloyed titanium. They have medium formability and are weldable. Actually the Ti-5Al-2.5Sn is the only true alpha alloy that is commercially produced (the remainder of the commercially availa-ble alloys are near-alpha alloys). Since it is a single-phase alloy containing

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only alpha, it cannot be strengthened by heat treatment. Except for cryo-genic applications, the use of Ti-5Al-2.5Sn has declined as alloys with bet-ter forming properties and higher creep resistance have been developed. Near-alpha alloys contain small amounts beta phase dispersed in an other-wise all-alpha matrix and they generally contain 5 to 8 wt% Al. The amount of aluminum that can be added as an alloying element is limited43 since an excess of aluminum content forms the brittle intermetallic com-pound α-2 (Ti3Al) forms, which adversely affects ductility. The near-alpha alloys (such as Ti-6Al-2Sn-4Zr-2Mo-0.25Si) retain their strength to high temperatures and have good creep resistance in the range of 315 to 595°C; furthermore they have good cryogenic behavior. Alpha-Beta Alloys They contain both the alpha and beta phases. Again, aluminum is the prin-cipal alpha stabilizer that strengthens the alpha phase but beta stabilizers, such as vanadium, are added and they also provide strengthening and al-low these alloys to be hardened by solution heat treating and aging. An ex-ample is the widely commercial available Ti-6Al-4V, which is the work-horse of the aerospace industry. Although the metallurgy of titanium heat treatment is complex, the re-sponse to heat treatment of alpha-beta alloys is a result of the instability of the high-temperature beta phase at lower temperatures. You may refer again to Fig.8.3, and consider the Ti-6Al-4V as major example. Heating such an alloy, to the solution treating temperature (above martensite start, Ms, line), produces a higher ratio of beta phase. During rapid cooling44, i.e. quenching, the beta is transformed to beta and titanium martensite or α’ phase, the acicular structure shown in Fig.8.4a. During subsequent aging (i.e. reheating at low temperature) treatment, strengthening effects may occur together45:

a. the decomposition of the unstable martensite into beta-plus-alpha microstructure (it is defined as the first stage of hardening) visible in Fig.8.4b;

43 The maximum aluminum content is actually calculated considering other elements that promote a-2 phase formation; thus, the maximum aluminum content must be account considering the aluminum equivalent content that is determined by summing the following weight percentages of alloying elements: Aleq = Al+1/3Sn+1/6Zr+10 (O+C+2N).

44 Since the response to heat treatment is a function of cooling rate from the solution temperature, the section sizes that can be through hardened are limited.

45 The martensite formed in titanium alloys is not like the extremely hard and strong martensite formed during the heat treatment of steels.

.

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b. The precipitation of ordered α2 particles (type Ti3Al) in the alpha phase, that is also defined second stage of hardening.

(a) (b)

Figure 8.3 - Microstructure of Ti-6Al-4V: a) after quenching from solution treat-ing temperature; b) after aging treatment. The weldability of the alpha-beta alloys is not as good as the near-alpha al-loys, but their formability is better. The alloys that contain smaller per-centages of beta stabilizers, known as “lean” alloys, are more weldable. As the amount of beta stabilizers increases, the weldability decreases. Beta Alloys Beta alloys are sufficiently rich in beta stabilizers and lean in alpha stabi-lizers that the beta phase can be completely retained with appropriate cooling rates. Beta alloys are metastable, thus the precipitation of alpha phase in the metastable beta is usual and it is also a method used to strengthen the alloys. Beta alloys contain small amounts of alpha stabiliz-ing elements as strengthening agents, such as Ti-10V-2Fe-3Al. such alloys are high-strength alloys that can be heat treated to tensile strength levels approaching 1380 MPa. Heat treatment consists in solution treating and aging hardening treatment, as for the alpha-beta alloys. Since their better response to solution and aging treatment than the alpha-beta alloys, heavier sections can be treated. The aging sequence, including temperature and time, is important in producing a uniform precipitation without the occur-rence of grain-boundary alpha. In fact, an excessive grain-boundary alpha precipitation is detrimental to alloy ductility, fatigue strength, and stress-corrosion cracking resistance.

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They exhibit better room-temperature forming and shaping characteristics than alpha-beta alloys; higher strength than alpha-beta alloys at tempera-tures where yield strength, instead of creep. Basics of fabrication of titanium alloys Titanium is difficult to form at room temperature and exhibits a high degree of shrinking due to its yield-strength-to-modulus ratio. To compensate for the shrink, titanium must be extensively overformed or, as is done most frequently, hot sized after cold forming. Hot forming, conducted at temperatures from 595 to 815°C, is normally used to form titanium alloys. Hot forming allows the material to deform more readily, simultaneously stress relieves the deformed material, and minimizes shrinking. Titanium also tends to creep at elevated temperature, and therefore, creep forming, performed by holding the part under load at the forming temperature, is another al-ternative for achieving the desired shape without having to compensate for exten-sive shrinking. Heating or plastic deformation at temperatures above the normal aging tempera-ture for solution-treated Ti-6Al-4V causes overaging to occur, and, as a result, mechanical properties decrease. Titanium is difficult to machine because of its high reactivity, low thermal con-ductivity, relatively low modulus, and high strength at elevated temperatures. When machining titanium, it is important to use slow speeds, maintain high feed rates, use flood cooling, maintain sharp tools, and use rigid setups. Adhesive bonding, mechanical fastening, metallurgical bonding, and welding are used to join titanium and its alloys. The first three processes do not affect the properties of these metals as long as joints are properly designed. Titanium alloys can be welded by gas tungsten arc welding in an inert atmosphere or electron beam or laser welded. Electron beam and laser welds are normally made without filler metal, and weld beads have high depth-to-width ratios. This combination al-lows excellent welds to be made in heavy sections, with properties very close to those of the base metal.

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Chapter 9 – Steelmaking process: basics of primary fabrication and secondary operations46

Introduction

A general diagram for the production of steel from raw materials to finished mill products is shown in Fig. 9.1. Steel production may start either with the reduction of iron ore in a blast furnace into pig iron by employing as main additional raw material coal, to produce pig iron47, to be refined and purify into steel in a second step (refer to “Steelmaking furnaces – Basic Oxygen Furnace”) and thus it is pro-cessed in an electric arc furnace to refine steel to desired chemical composition, also reducing the carbon content of less than 1 wt%. The main differences in primary metallurgy process for steel making is clearly shown in the left part of the scheme in Fig.9.1, that shows the upstream process steps from raw materials to primary steel products, i.e. blooms, billets and slabs. If any primary steelmaking processes conduct to same primary products (i.e. blooms, billets and slabs), this final output is achieved in two different pattern, depending on plant architecture and by raw materials used:

Primary steelmaking production from iron ore. If steelmaking process starts from iron ore, plant is equipped to satisfy the necessary steps to re-duce iron ore with carbon (provided in the form of coke) into pig iron; in this case a blast furnace (Fig.9.2, unit identified by “1”) is present. It is essentially a tall, hollow, cylindrical structure with a steel outer shell lined on the inside with refractory brick. In such a vertical furnace, liquid metals in form of pig iron (highly carbon content liquid with many impu-rities) by the reaction of: 1) a flow of heated air (i.e. oxygen) introduced under pressure into the bottom of the furnace with a mixture of metallic ore, coke, and flux fed into the top to process according to general equa-tion (eq. 9.1) Fe2O3 + 3COÆ 2Fe + 3CO2 where the CO necessary is pro-duced by high temperature reaction between coke and oxygen. After the pig iron is produced, it is necessary to be converted into steel, thus car-bon content must be reduced to level of steel, before it is cast into ingots or continuously cast into billets. This secondary conversion process is conducted outside the blast furnace into a Basic Oxygen Furnace or BOF (see Fg.9.1, refer to unit “2”), where main process of reducing carbon content takes place; as result, steel is produced with acceptable carbon content so to be ultimately refined to final chemical composition (also in

46 Main reference: F.C. Campbell, Elements of Metallurgy and Engineering Alloys, ASM International, 2008 (Chapter 28).

47 Pig iron is in the range of 3 to 4.5 wt% of carbon, thus exceeding the maximum 2.11 wt% carbon content of steels. This requires pig iron must be further refined (and purify in terms of inclusions) in a basic oxygen furnace, or BOF, as described in the following.

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terms of chemical alloying elements) into further furnace, the Ladle Fur-nace or LF (see again Fig.9.1, refer to unit “3”);

Primary steelmaking production from steel scraps. Because the raw ma-terial used is already steel, the upstream stages conducted into Blast Fur-nace and Basic Oxygen Furnace are not necessary. The steelmaking pro-cess in this case starts from the melting of steel scraps into an Electric Furnace (EF); melt steel is therefore spilled out to the Ladle Furnace (see again Fig.9.1, refer to unit “3”), where chemical composition refinement takes place.

Note from above that, despite two different steelmaking processes are required if you start from either iron ore or recycling scraps, the steps that follow the unre-fined steel production in either BOF or EF are the same: the unrefined steels shall be turned into desired chemical composition in the Ladle Furnace. When steel is refined, it can be cast into ingots or continuously cast into billets, blooms or slabs, depending on section shape and size48 (see again the scheme in Fig.9.1). Cast semifinished products are therefore hot worked to improve homogeneity, re-fine the as-cast microstructure, and fabricate desired product shapes. All these downstream steps are those we call secondary steelmaking process and, by gener-alizing, they start from initial hot deformation processes (e.g. forging or rolling) can proceed in further refinement of section, shape and size of products. Some products therefore derives directly from hot rolling operations, and they are used in the hot rolled condition, some others are heat treated to obtain specific proper-ties. Some other steel products are fabricated by secondary working by hot forging into semifinished shapes or hot extruding. For some other products thin sections, close clearances and good surface quality is required for example to fabricate cold drawn pans, wound cold springs, etc. In this case the hot deformed semifinished products are further cold worked to achieve final shape, size and surface quality. In the following sections, some further details on main units of the upstream pri-mary steelmaking production for both the iron-ore and recycled steel scraps pat-tern routes are provided.

48 Continuous casting process can produce semifinished products that can be: a) billets, namely long semifinished products with round or square cross-section and with section ar-ea less than 230 cm2; b) blooms, similar to billets except the cross-sectional area that is greater than 230 cm2; c) slabs, long semifinished product with rectangular cross-section ar-ea.

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Primary production from steel scraps Primary production from iron-ore Secondary production

Fig.9.1 - Principal steps in steelmaking..

1 2

3

Box – Brief History of Steel Steel started to replace bronze in approximately 1200 B.C. Cast iron alloys predate steel because cast iron, with its higher carbon content, melts at lower temperatures. Early steel alloys were produced by solid-state smelting that produced iron with a low carbon content and high density of entrapped slag inclusions. Heavy hammering or forging was used to fragment and disperse the inclusions. In approximately 350 B.C., wootz steel was produced in In-dia by adding carbon to wrought iron and then carburizing it in crucibles with charcoal. During this period, similar processes evolved in other parts of the world. Since these early processes provided both an economic and mili-tary advantage, they were closely guarded secrets. Despite the drawbacks of these early processes, early blacksmiths produced remarkable objects, such as the Damascus and Japanese swords that had sharp cutting edges, high hardness and strength, good fracture resistance, and were also objects of great beauty. Damascus swords, first produced in approximately 500 A.D., were forged from blocks of high-carbon wootz steel and were known for their highly decorative surface patterns caused by fine bands of dispersed al-loy carbides. Japanese swords, which evolved about the same time, were made by welding alternating layers of low- and high-carbon steel together in multiple forging steps. However, it was not until the middle of the 19th cen-tury that a large-scale process emerged for making steel, when, in 1856, Bessemer patented a process in which hot air was blown through molten pig iron to reduce the carbon and silicon contents. In 1858, Siemens first suc-cessfully operated an openhearth furnace in which liquid pig iron and scrap were melted with a hot gas flame. The key factor in both the Bessemer and Siemens processes was the oxidation and removal of carbon, silicon, and other impurities by oxides, such as CO in the case of carbon.

Blast Furnace As mentioned, the first step in making steel from iron ore is to make iron by chemically reducing the ore (iron oxide) with carbon, in the form of coke, according to the general equation: (eq. 9.1) Fe2O3+3CO Æ2Fe+3CO2 This reaction takes place in a blast furnace, shown schematically in Fig. 9.2.

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Blast furnace main units - 1: Iron ore + Calcareous sinter; 2: coke; 3: conveyor belt; 4: feeding open-ing, with a valve that prevents direct contact with the internal parts of the furnace; 5: Layer of coke; 6: Layers of sinter, iron oxide pellets, ore; 7: Hot air (around 1200°C); 8: Slag; 9: Liquid pig iron; 10: Mixers; 11: Tap for pig iron; 12: Dust cyclon for removing dust from exhaust gasses before burning them in 13; 13: air heater; 14: Smoke outlet (can be redirected to carbon capture & storage (CCS) tank); 15: feed air for Cowper air heaters; 16: Powdered coal 17: cokes oven 18: cokes bin 19: pipes for blast furnace gas.

Fig.9.2 – Scheme of blast furnace Blast Furnace as it is placed in an installation. For a video describing Blast Furnace operation click here. The stack inside the blast furnace is kept full with alternating layers of coke, ore, and limestone admitted at the top during continuous operation (see Fig.9.2, details “1”, “2” and “4”). Coke is ignited at the bottom and burned rapidly with the forced air from the tuyeres49 (see Fig.9.2, detail “7”). The iron oxides in the ore are chemically reduced to molten iron by carbon and carbon monoxide from the coke. The slag formed consists of the limestone flux, ash from the coke, and substances formed by the reac-tion of impurities in the ore with the flux; it floats in a molten state on the top of the molten iron; see the detail “8” in Fig.9.2, as it represents the slag that floats – it is lighter than metal - onto upper part of molten metal. The slag is periodically purified from molten metal by the opening outlet in “8”, thus eliminated for recycling by “8”. On the opposite side, from the

49 From the French, tuyer is an opening water-cooled nozzle through which air is blown into a blast furnace to facilitate combustion.

https://www.youtube.com/watch?v=z2pk2XorD7w%23t=28

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http://www.britannica.com/EBchecked/topic/95021/carbon-monoxide

http://www.britannica.com/EBchecked/topic/548015/slag

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outlet “9” the molten pig iron is spilled out and loaded onto torpedo cars (see Fig.9.2, detail “11”) for transferring it quickly to the next station, the Basic Oxygen Furnace, where conversion from pig iron into steel takes place. Hot gases rise from the combustion zone, heating fresh material in the stack and then passing out through ducts near the top of the furnace. Finally exhaust gases must be captured by pipes (see Fig.9.2, detail “19”), cleaned by dust by use of cyclone for removing dust (see Fig.9.2, detail “12”) so to burn them in an air heater (see Fig.9.2, detail “13”) and finally trans-ferred to smoke outlet (in modern plant, this can be redirected to carbon capture & storage CCS tank to reduce CO2 emissions). Modern blast furnaces range in size from 20 to 35 m, have hearth diame-ters of 6 to 14 m, and can produce from 1,000 to almost 10,000 tons of pig iron daily. Basic Oxygen Furnace Basic Oxygen Furnace (BOF) or Basic Oxygen Converter is a steel making furnace, in which molten pig iron and steel scrap convert into steel due to oxidizing action of oxygen blown into the melt under a basic slag. Typical basic oxygen furnace is shown in fIg.9.3a. It has a vertical vessel lined with refractory lining. Actually only 8-12% of the furnace volume is filled with the treated molten metal. A careful balance between the relative amounts of pig iron and scrap charged into the converter is maintained as a means of controlling the temperature and to ensure that steel of the re-quired specification is produced. A water-cooled lance is then lowered into the vessel (see Fig.9.3), through which very pure oxygen is blown at high pressure. The oxygen interacts with the molten pig iron to oxidize undesirable elements, including excess carbon, manganese, and silicon from the ore, limestone, and other impuri-ties such as sulfur and phosphorus. Oxidation of the molten metal and the slag is complicated process proceed-ing in several stages and occurring simultaneously on the boundaries be-tween different phases (gas-metal, gas-slag, slag-metal), however finally the reactions may be presented as follows. The lance "blows" 99% pure oxygen over the hot metal, igniting the carbon dissolved in the steel, to form carbon monoxide and carbon dioxide, and causing the temperature to rise to about 1700°C. This melts the scrap, lowers the carbon content of the molten iron and helps remove unwanted chemical elements. After a sample has been taken to verify the chemical composition of the steel, the vessel is tilted to allow the molten steel to flow out. The steel is

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tapped into a ladle where further composition adjustments are made. The process which takes place in BOF is the most powerful and effective steel making method. About 67% of the crude steel in the world is made in the Basic Oxygen Furnaces (BOF). The typical capacity of the Basic Oxy-gen Furnace is 250-400 t.

(a)

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Fig. 9.3 – A Basic Oxygen Furnace: a) scheme of equipment; b) the BOF, the converter, while it is loaded by pig iron transferred from torpedo car (see upper-right corner) and when steel is spilled out from converter to steel ladle, to reach the next station, the Ladle Furnace. For a video describing Basic Oxygen Furnace operation click here.

https://www.youtube.com/watch?v=OqCclE6kZQw

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Electric Arc Furnace Unlike the BOF, the electric arc furnace (Fig. 9.4) does not use molten pig iron but uses steel scrap50. Thus, this furnace is the primary stand of steelmaking process that use steel scrap as raw material, instead iron ore (refer to pattern route “Prima-ry production from steel scraps” in the scheme in Fig.9.1). Scraps are charged into the furnace from an overhead crane, and a lid is swung into position over the fur-nace. The lid holds graphite electrodes that are lowered into the furnace. An elec-tric current is passed through the electrodes to form an arc, which generates the heat necessary to melt the scrap. During melting, alloying elements are added to the steel to give it the required chemical composition51. After samples have been taken to check the chemical composition, the furnace is tilted to allow the floating slag to be poured off. The furnace is then tilted in the other direction, and the molten steel is tapped into a la-dle, where it either undergoes secondary steelmaking or is transported to the caster (see the phases in the scheme of Fig.9.5). The modern electric arc furnace typically makes approximately 136,000 kg of steel in about 90 min.

Fig. 9.4 – Scheme of an Electric Arc Furnace .

50 Since the electric arc furnace has a relatively low capital equipment cost and uses steel scrap, this process is used where local supplies of steel scrap are available and has given rise to what are known as “mini” mills.

51 The electric arc furnace is also used for producing alloy steels that contain apprecia-ble amounts of easily oxidized alloying elements, such as chromium, tungsten, and molyb-denum. It can also be used to make steels requiring very low sulfur and phosphorus con-tents. Special slags are used to lower the sulfur and phosphorus levels and to protect against oxidation of alloying elements.

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Fig. 9.4 – Electric arc furnace main operations. For a video describing Electric Arc Furnace gen Furnace operation click here.

Ladle Furnace Molten steel have to be refined to desired chemical composition in a de-vice called Ladle Furnace (LF). From BOF the unrefined steel is poured into a ladle that moved quickly to next stand, the Ladle Furnace, where it is placed under a cover equipped with three graphite electrodes connected to a three-phase arc transformer. The scheme of a Ladle Furnace stand is illustrated in Fig.9.5; notice the ladle visible under the cover with three electrodes.

(a) (b)

Fig.9.5 – (a) Scheme of a Ladle Furnace stand; (b) section of Ladle Furnace with main functions.

https://www.youtube.com/watch?v=1qnhXgqgWKc

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The ladle bottom has a porous refractory plug, which is connected to the argon supply pipe at the Ladle Furnace stand. The LF stand is also equipped with an addition hopper mounted on the cover and a lance for in-jection of desulfurizing agents. Fumes formed during the operation are ex-tracted through the cover. Molten steel treated in Ladle Furnace is covered by a layer of desulfurizing slag. The graphite electrodes are submerged into the slag, which protects the ladle lining from overheating produced by the electric arcs. The arcs are capable to heat the steel at the rate about 3°C/min. During the treat-ment process argon is blown through the bottom porous plug providing continuous metal stirring. Stirring results in distribution of heat produced by the arcs, chemical homogenization and desulfurization of the steel by the slag. Alloying elements are therefore added through the addition hop-per. Ladle Furnace primary functions are those to permit the secondary refining of molten steel before to final cast, such as: temperature homogenization or adjustment; chemical adjustments for carbon, sulfur, phosphorus, oxy-gen and precise alloying; inclusion control; degassing, and others. The function of the porous plug is to provide inert gas stirring of the mol-ten metal to promote homogenization. Normal stirring operations are per-formed by percolating argon gas through a purge plug arrangement in the bottom of the ladle. Vacuum degassing is also possible with the steel in a ladle, and argon lances can be used to stir the steel to make the composition more homoge-neous. Vacuum degassing produces ultra low-carbon steels, with carbon contents as low as 0.002 wt%. Vacuum degassing also removes hydrogen that can result in hydrogen flaking and porosity. From Ladle Furnace to Casting Process Whichever is the raw material used and relative patter route employed, ei-ther the iron-ore or recycled steel scrap, the ladle refining operations must be completed in the Ladle Furnace (such phase, crucial for steel refining, is also called ladle metallurgy). From the ladle furnace station, the liquid steel is moved by ladle to be cast to produce ingots or continuously cast long product (in a continuous cast-ing machine). Ingot Casting During ingot casting, the ladle is moved by an overhead crane so that is can be tapped or teemed into individual upright-standing molds on rail

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cars. The metal can be poured into the mold either from the top of the mold or from the bottom through a connecting channel. In the first case, the steel is poured from the ladle directly into the mold (Figure 9.6a). After the mold is filled, the ladle opening is closed and the ladle is moved by crane to the next mold, where the process is repeated. In bottom pouring, several molds (from two to 60) can be filled with steel simultaneously. Here, the molds are mounted on a stool having channels lined with refrac-tory brick. The steel from the ladle descends through the fountain into the channels of the stool and then enters the mold from the bottom (Figure 9-6 b). The pouring method used depends on such factors as the steel’s grade and weight and the intended use of the ingots.

(a) (b)

Fig.9.6 – Ingot casting through: (a) top-pouring and (b) bottom-pouring processes; (1) ladle with metal, (2) mold, (3) stool, and (4) fountain. Continuous Casting Although ingot casting has been the traditional method, continuous casting has rapidly evolved as the method of choice because of cost and quality advantages. In the continuous casting process (Fig. 9.7), the ladle of molten steel is transported to an elevated casting platform above the casting machine. The molten steel is poured into a rectangular trough, called tundish, which acts as a reservoir for the steel. From a spout in the bottom of the tundish, the molten steel is poured into a water-cooled mold with a movable temporary bottom. As the molten steel enters the mold, the metal at the surface of the mold solidifies, forming a thin skin. The skin thickens as the metal passes through the mold, and the temporary bottom is slowly lowered to allow

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metal to be continuously poured into the mold. The remaining metal in the center of the ingot is solidified by spraying cold water onto the ingot as it leaves the mold. The solid metal billet is pulled by rollers so that a long, continuous steel slab is produced. At the end of the machine, it is straightened and cut to the required length. Fully formed slabs, blooms, and billets emerge from the end of this con-tinuous process. The continuous casting process runs for days or weeks as ladle after ladle of molten steel feeds the casting machine. The advantages of the continuous casting process include reduced costs, improved quality, increased yield, lower energy costs, and less pollution. It is now the process of choice for high-volume, low-cost plain carbon steels. Quality improvements include less variability in chemical composition, both through the thickness and along the length of the continuously cast slab. The surface quality of the slab is also higher than for an ingot, having fewer surface defects such as seams and scabs. The yield for continuous casting is also higher, since it is not necessary to crop the ends of continuously cast slabs. Energy savings are achieved, since the continuously cast slabs are sent directly to rolling mills and do not require soaking pits for reheating. In addition, since the thickness of continuously cast slabs is approximately half the thickness of individual ingots, much less hot rolling is required.

Fig.9.7 – Continuous steel casting, architecture and main equipment for the opera-tions. For animation video describing all process steps from recycling scrap to continuous casting click here.

https://www.youtube.com/watch?v=nqzJk2836V8

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The cast product microstructure A metal cast into a mold, such as continuous casting rectangular shaped billet shown in Fig.9.8, can have up to two or three distinct zones: a chill zone, a zone containing columnar grains or dendritic grains, and a center-equiaxed grain zone.

Fig.9.8 – Freezing sequence for an alloy casting.

These zones form because of metallurgy phenomena which develop for rapid so-lidification that can be generalized by the scheme in Fig.9.9; the scheme illustrates which is basic phenomena that lead to formation of a series of columnar, or col-umn shaped, grains that are oriented almost parallel to the heat flow direction. Be-cause each metal grows more favorably in one principal crystallographic direction, only those grains favorably oriented with their growth direction most perpendicu-lar to the mold wall will grow into the center of the casting. The axes of the co-lumnar grains are parallel to the direction of heat flow, and they grow along spe-cific crystalline planes.

Fig.9.9 – Columnar growth from mold wall

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As freezing progresses, the thermal gradient decreases, and this causes the den-drites to become very long. Breakdown of columnar growth may occur as a result of fracturing of the very long dendrite grains by convection currents in the melt. These broken arms can then serve as nuclei for new grains, as shown in Fig. 9.10 that refers to typical ingot product that solidifies.

Fig.9.10 – Formation of equiaxed zone in alloy casting. The amount of the final cast structure that is columnar or equiaxed depends on the alloy composition and on the thermal gradient at the liquid-solid interface during solidification52. As freezing progresses, there is a buildup of the solute in the liquid that freezes last, such as at the center of the casting. Such long-range variations in composition are called macrosegregation. Normal segregation frequently occurs when the di-rection of growth is inward, as in columnar growth. Furthermore, solidification shrinkage occurs especially in ingot casting. Shrinkage porosity often forms in areas that the liquid metal from the risers cannot reach. For example, it is difficult to effectively feed metal into the interdendritic areas where shrinkage is occurring. Because this type of porosity occurs late in solidification,

52 It should be noted that all three zones do not always occur. For example, pure metals can exhibit a chill zone and a columnar zone but not contain a center-equiaxed zone. The amount of the final cast structure that is columnar or equiaxed depends on the alloy composition and on the thermal gradient at the liquid-solid interface during solidification. The thermal gradient is most easily controlled by controlling the rate of heat extraction from the casting, or the cooling rate.

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especially in alloys with wide freezing ranges and a large mushy zone, it is partic-ularly difficult to eliminate. The primary casting microstructure is thus made of:

Large grains; Non-equiaxic structure; Non homogeneous chemical composition due to macrosegrations and mi-

crosegregations; Gas porosities and shrinkage porosity.

As result, the mechanical properties of primary casting structure are: Very low mechanical strength (low YS and UTS); Very low toughness (low KV and KIc);

namely those features that do not allow products to be put in service directly cut-ting from ingots, blooms, slabs and billets.

Box - Solidification interfaces growing and morphology of industrial cast products The solidifying solid-liquid interface can exhibit one of three types of inter-facial growth in the liquid: planar, cellular, or dendritic. As shown in Fig. 9.11, the type of growth is controlled by the manner in which heat is re-moved from the system. When the liquid ahead of the solid-liquid interface, x0, has a positive temperature gradient, heat is removed from the liquid by conduction through the growing solid. Since the temperature gradient is lin-ear and uniform perpendicular to the interface, a smooth interface is main-tained, and the growth is planar into the liquid (Fig. 9.11a). When there is a temperature inversion and the temperature decreases ahead of the solid-liquid interface, then either dendritic (Fig. 9.11b, c and Fig.9.12) or cellular (Fig.9.13) will occur.

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Fig.9.11 – Effects of undercooling on solidification structures.

Fig.9.12 – Dendrite formation in succinonitrile-4% acetone solution.

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Fig.9.13 – Columnar cells formation in round billet continuously cast.

Primary metalworking hot processes: the bulk deformation processes

Primary metalworking processes, such as the bulk deformation processes used to conduct the initial breakdown of cast ingots, are always conducted hot. The term bulk deformation implies large amounts of material move-ment, such as in hot rolling or forging53. Bulk deformation changes the shape of a workpiece by plastic deformation through the application of compressive forces, as for the typical bulk de-formation processes in Fig. 9.14.

53 They have to be distinguished from secondary processes, which are used to produce the final product shape, that are conducted either hot or cold (such as sheet forming) and that do not involve large amounts of deformation.

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Fig.9.14 – Bulk deformation processes.

Bulk deformation has therefore a double intent: to change the shape of a workpiece by plastic deformation through the application of compressive forces and to refine the inhomogeneous structure resulting from semifin-ished steelmaking products, such as cast ingots and continuously cast slabs, billets and blooms. Such products are therefore typically hot worked by hot deformation processes (as those ones shown in Fig.9.14) into inter-mediate product forms, such as plates, bars, and sheet. Large plastic de-formation in combination with heat - bulk deformation processes are con-ducted at minimum 0.5Tm, in austenitic state - and they are necessary to:

Reduce dendritic structure, braking original dendrite structure and promoting dynamic recrystallization in fine grains;

Reduce inhomogeneity of microstructure, by promoting at high temperature the reflowing of metal and diffusion of chemical ele-ments, thus eliminating macro-segregations;

Close all residual porosities and shrinkage cavities;

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in order to enhance all mechanical properties of hot worked microstruc-ture. For processes such as hot rolling, hot extrusion, and hot forging, the time within the deformation zone is usually short, and grain refinement is usual-ly accomplished by (static) recrystallization after hot working. A high level of hot deformation followed by holding the workpiece at an elevated tem-perature causes static recovery and recrystallization, resulting in a fine grain size. The hot rolling scheme in Fig. 9.15 generalizes what happens when billet section is reduced under two rolling cylinders, and finally recrystallization occurs when it slowly cools to room temperature.

Fig.9.14 –Recrystallization during hot rolling. Similar phenomena occurs also for other bulk metalworking operations, such as rolling ring, forging of rolls, hot rolling mill (see Fig.9.15). Products from primary metalworking process may be suitable for its in-tended application, but in many cases, it provides the starting material for secondary deformation processes such as drawing, hot or cold forging, and sheet metalworking.

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Fig. 9.15 – Example of bulk hot metalworking: a) rolling mill plant for plate roll-ing (click on figure or click here for video); b) forging of primary continuously cast billet into rolls (click on figure or click here for video); c) ring rolling pro-duced from slab (click on figure or click here for video).

https://www.youtube.com/watch?v=AuuP8L-WppI

https://www.youtube.com/watch?v=sooeYRbJuyw

https://www.youtube.com/watch?v=jvfHNNXRiYk

https://www.youtube.com/watch?v=AuuP8L-WppI

https://www.youtube.com/watch?v=sooeYRbJuyw

https://www.youtube.com/watch?v=jvfHNNXRiYk

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Documents

Applied Metallurgy