Material Science and Metallurgy (BTME 402)

Dr. Ankitendran Mishra

Department of Mechanical Engineering

Oriental University, Indore

Unit-IIImperfections in crystals are categorized as:

1. Point imperfections

2. Line imperfections

3. Surface imperfections

4. Volume imperfections.

Point imperfections also referred to as zero-dimensional imperfections

• One or two atomic diameters is the typical size of a point imperfection.

1. Vacancy refers to an atomic site from where the atom is missing

• Substitutional impurity is a point imperfection.

• It refers to a foreign atom that substitutes for or replaces a parent atom in the

crystal,

Eg: Aluminium and phosphorus doped in silicon are substitutional impurities in the

crystal.

• Interstitial impurity is also a point imperfection. It is a small sized atom occupying

the void space in the parent crystal, without dislodging any of the parent atoms

from their sites.

• For example, carbon is an interstitial solute in iron.

• Why is solubility of Carbon in FCC iron limited to 2wt%?

• In ionic crystals, the formation of point imperfections is subject to therequirement that the overall electrical neutrality is maintained.

• An ion displaced from a regular site to an interstitial site is called aFrenkel imperfection.

• A pair of one cation and one anion can be missing from an ioniccrystal. The valency of the missing pair of ions should be equal tomaintain electrical neutrality. Such a pair of vacant ion sites is called aSchottky imperfection.

Line Defects

Line imperfections are called dislocations.

(i) the edge dislocation, and

(ii) the screw dislocation.

• Edge dislocations are symbolically represented by _or _ , depending on whether the incomplete plane starts from the top or from the bottom of the crystal.

• The plane ABCD is

called a slip plane

• The magnitude and

the direction of the

displacement are

defined by a vector

called the Burgers

vector (BV),

Equilibrium Concentration• n/N= exp (-Hf/RT)

Pb) Find the equilibrium constant of the vacancies in Aluminium and Nickle at 0,300 and 600K.

Plastic deformation in crystalline materials

• In crystalline materials, at temperatures lower than ~0.4Tm, where

Tm is the melting point in kelvin, the permanent deformation is called

plastic deformation.

• At temperatures above ~0.4Tm, permanent deformation continues as

a function of time, following the application of the load. This

behaviour is termed creep.

• Plastic deformation can occur under tensile, compressive or torsional

loads

The Tensile Stress-Strain Curve

• The load at the yield point divided by the initial cross-sectional areaof the test specimen is called the yield stress or the yield strength of amaterial.

• Beyond the yield point, the linear elastic region is followed by anonlinear plastic region. In this region, the load required to causefurther deformation increases with increasing strain. Thisphenomenon is called work hardening.

• The engineering stress corresponding to the maximum load is calledthe ultimate tensile strength (UTS) of the material.

• Beyond this maximum, a neck forms somewhere in the middle of thespecimen, where the cross-sectional area locally decreases.

• The applied load decreases up to the point of fracture, where thespecimen breaks into two pieces across the reduced cross-section ofthe neck.

Plastic Deformation by Slip

• During plastic deformation, even though more imperfections are introduced, the atom movements are such that the crystal structure remains the same before and after plastic deformation.

• There are two basic modes of plastic deformation called slip and twinning.

• Slip is a shear deformation that moves atoms by many interatomic distances relative to their initial positions

• Steps are created at the surface of the crystal during slip, but the orientation of all parts of the crystal remains the same before and after slip.

• Twinning, on the other hand, changes the orientation of the twinned parts.

• Here, the movement of an atom relative to its neighbours is only a fraction of an interatomic distance.

Hall-Petch equation

• The yield stress of a polycrystalline material.

• The grain diameter can be approximately calculated from the ASTMspecification for grain size. For an ASTM number n, the number of grainsper square inch (per 645 mm2) at a magnification of 100 is equal to 2n–1.Grain size number ASTM 1 corresponds to 1 grain per square inch at amagnification of 100.Pb) The yield strength of a polycrystalline material increases from 120MN m–2 to 220 MN m–2, on decreasing the grain diameter from 0.04mm to 0.01 mm. Find the yield stress for a grain size of ASTM 9.

Recovery, Recrystallization and Grain growth

• Recovery, recrystallization and grain growth are phenomena intimately associated with the annealing of a plastically deformed crystalline material.

• Plastic working below 0.3–0.5Tm is called cold work.

• The density of point imperfections and dislocations increases with increasing amount of plastic deformation carried out at temperatures below the range 0.3–0.5Tm.

• Between 1 and 10% of the energy of plastic deformation is stored in the material in the form of this strain energy.

• On annealing, that is, on heating the deformed material to higher temperatures and holding the material tends to lose the extra strain energy and revert to the original condition before deformation, by the processes of recovery and recrystallization.

• During recovery, which takes place at low temperatures of annealing, the

excess point imperfections that are created during plastic deformation are

absorbed at the surface or the grain boundaries or at dislocations by the

climbing up process.

• Also, random dislocations of opposite sign come together and mutually

annihilate each other

• Dislocations of the same sign arrange themselves into lower energy

configurations, such as tilt and twist Boundaries

• However, the decrease in the dislocation density during recovery is not

substantial.

• Recrystallization is the process of nucleation and growth of new, strain-free

crystals, which replace all the deformed crystals of the worked material.

• It starts on heating to temperatures in the range of 0.3–0.5Tm, which is

above the recovery range.

• There is no crystal structure change during recrystallization.

• As such, recrystallization is not a phase transformation in a strict sense. The

free energy change during recrystallization arises from the excess strain

energy of the deformed material as compared to the undeformed material.

• The strain energy difference between the cold-worked and the strain-freematerial is known as the driving force for recrystallization.

• The recrystallization temperature is arbitrarily defined as that temperatureat which 50% of the material recrystallizes in 1 hr.

• Some well-known empirical laws of recrystallization are:

1. The higher is the degree of deformation, the lower is the recrystallizationtemperature.

2. The finer is the initial grain size, the lower is the recrystallization

temperature.

3. Increasing the amount of cold work and decreasing the initial grain size

produce finer recrystallized grains.

4. The higher is the temperature of cold working, the less is the strain energy

stored in the material. The recrystallization temperature is correspondingly

higher.

5. The recrystallization rate increases exponentially with temperature

• Grain growth refers to the increase in the average grain size on further

annealing, after all the cold worked material has recrystallized.

• As a reduction in the grain boundary area per unit volume of the material

occurs during grain growth, there is a decrease in the free energy of the

material.

• The atoms tend to jump across the boundary to increase their overall bond

energy.

• The state of binding on either side of a planar boundary is the same and,

therefore, a planar boundary tends to remain stationary

Fracture Failure• Materials subjected to alternating or cyclic loading (as in machines)

fail due to fatigue.

• Materials used at high temperatures can fail due to creep fracture.

Ductile Fracture

• Ductile fracture is the rupture of a material after a considerable amount of plastic deformation.

• Materials begin to neck beyond the ultimate tensile strength, which is at the maximum point in the load-elongation curve.

• The true stress in this region is increasing, in spite of the fall in the load and the engineering stress.

• Fully ductile materials will continue to neck down to an infinitesimally thin edge or a point and thus fail, as the cross-section at the neck becomes so small that it cannot bear the load any longer.

• Here, the cracks are found to nucleate at brittle particles: either the natural kind found in multiphase materials.

• If fracture initiates at pores in the neck region, then the voids are already present.

• The voids grow with increasing deformation and ultimately reach sizes of the order of a mm.

Brittle fracture

• Brittle fracture is the failure of a material without apparent plastic deformation.

• Brittle fracture is usually caused by the propagation of pre-existing cracks in a material. Griffith’s criterion gives the critical stress required to propagate a crack spontaneously

• If the broken pieces after a brittle fracture are fitted together, the original shape and dimensions of the specimen are restored.

• If we write an energy equation for the crack formation, the energy change U as the crack forms is given by

• The negative sign of the second term indicates that the elastic energy stored in the material is released, as the crack forms.

• The critical condition as a critical fracture stress:

Pb) A sample of glass has a crack of half length 2 m. The Young’s modulus of the glass is 70 GN m–2 and the specific surface energy is 1 J m–2. Estimate its fracture strength and compare it with its Young’s modulus.