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Manufacturing Processes for Engineering Materials, 4th ed.

Kalpakjian Schmid

Prentice Hall, 2003

Chapter 2

Fundamentals of the

Mechanical Behavior ofMaterials

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Kalpakjian Schmid

Prentice Hall, 2003

Types of Strain

FIGURE 2.1 Types of strain. (a) Tensile, (b) compressive, and (c) shear. All deformation

processes in manufacturing involve strains of these types. Tensile strains are involved in

stretching sheet metal to make car bodies, compressive strains in forging metals to maketurbine disks, and shear strains in making holes by punching.

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Kalpakjian Schmid

Prentice Hall, 2003

Tension Test

Figure 2.2 (a) Original and final shape of a standard tensile-test specimen. (b) Outline of a

tensile-test sequence showing stages in the elongation of the specimen.

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Kalpakjian Schmid

Prentice Hall, 2003

Mechanical Properties of Materials

METALS (WROUGHT) E (GPa) Y (MPa) UTS (MPa) ELONGATION(%) in 50 mm

POISSONSRATIO (n)

Aluminum and its alloysCopper and its alloysLead and its alloysMagnesium and its alloysMolybdenum and its alloysNickel and its alloysSteelsStainless steels

Titanium and its alloysTungsten and its alloys

69-79105-150

1441-45

330-360180-214190-200190-200

80-130350-400

35-55076-1100

14130-30580-2070105-1200205-1725240-480

344-1380550-690

90-600140-1310

20-55240-38090-2340345-1450415-1750480-760

415-1450620-760

45-565-350-921-540-3060-565-260-20

25-70

0.31-0.340.33-0.35

0.430.29-0.35

0.320.31

0.28-0.330.28-0.30

0.31-0.340.27

NONMETALLIC MATERIALS

CeramicsDiamondGlass and porcelainRubbers

ThermoplasticsThermoplastics, reinforcedThermosetsBoron fiberCarbon fibersGlass fibers (S, E)Kevlar fibers (29, 49, 129)Spectra fibers (900, 1000)

70-1000820-105070-80

0.01-0.1

1.4-3.42-50

3.5-17380

275-41573-8570-11373-100

----

--------

140-2600-140

-

7-8020-12035-1703500

2000-53003500-46003000-34002400-2800

0-0-

1000-510-1

00

1-25

3-43

0.2-0.240.5

0.32-0.40-

0.34-----

Note: In the upper table the lowest values forE, Y, and UTS and the highest values for elongation are for thepure metals. Multiply GPa by 145,000 to obtain psi, and MPa by 145 to obtain psi. For example, 100 GPa =

14,500 ksi, and 100 MPa = 14,500 psi.

Table 2.1 Typical mechanical properties of various materials at room temperature.

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Kalpakjian Schmid

Prentice Hall, 2003

Loading and Unloading

FIGURE 2.3 Schematic illustration of

loading and unloading of a tensile-test

specimen. Note that during unloading, the

curve follows a path parallel to theoriginal elastic slope.

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Kalpakjian Schmid

Prentice Hall, 2003

Total Elongation

FIGURE 2.4 Total elongation of aspecimen in a tension test as a

function of original gage length for

various metals. Because necking is

a local phenomenon, elongation

decreases with gage length.

Standard gage length is usually

50mm (2 in.), although shorterlengths can be used if larger

specimens are not available.

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Kalpakjian Schmid

Prentice Hall, 2003

True Stress-

True-StrainCurves in

Tension

FIGURE 2.5 (a) True stress-true-strain curve in tension. Note that, unlike in an engineering

stress-strain curve, the slope is always positive, and the slope decreases with increasing strain.

Although stress and strain are proportional in the elastic range, the total curve can be

approximated by the power expression shown. On this curve, Yis the yield stress and Yfis the

flow stress. (b) True-stress true-strain curve plotted on a log-log scale. (c) True stress-true-strain

curve in tension for 1100-O aluminum plotted on a log-log scale. Note the large difference in the

slopes in the elastic and plastic ranges. Source: After R. M. Caddell and R. Sowerby.

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Kalpakjian Schmid

Prentice Hall, 2003

Power Law Material Behavior

MATERIAL K (MPa) n

Aluminum, 1100-O2024-T45052-O

6061-O6061-T67075-O

Brass, 70-30, annealed85-15, cold-rolled

Bronze (phosphor), annealedCobalt-base alloy, heat treated

Copper, annealedMolybdenum, annealedSteel, low-carbon, annealed

1045 hot-rolled1112 annealed1112 cold-rolled4135 annealed4135 cold-rolled4340 annealed

17-4 P-H annealed52100 annealed304 stainless, annealed

410 stainless, annealed

180690210

2054104008955807202070

31572553096576076010151100640

120014501275

960

0.200.160.13

0.200.050.170.490.340.460.50

0.540.130.260.140.190.080.170.140.15

0.050.070.45

0.10Note: 100 MPa = 14,500 psi.

s= Ken

Table 2.3 Typical values

ofKand n in Eq. (2.11) at

room temperature.

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Kalpakjian Schmid

Prentice Hall, 2003

True Stress -

True StrainCurves for

Various Metals

FIGURE 2.6 True-stress-true-strain curves in tension at room temperature for various metals.

The point of intersection of each curve at the ordinate is the yield stress Y; thus, the elastic

portions of the curves are not indicated. When the Kand n values are determined from these

curves, they may not agree with those given in Table 2.3, because of the different sources from

which they were collected. Source: S. Kalpakjian.

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Kalpakjian Schmid

Prentice Hall, 2003

Idealized Stress-Strain Curves

FIGURE 2.8 Schematic illustration of various types of idealized stress-strain curves. (a)

Perfectly elastic. (b)Rigid, perfectly plastic. (c) Elastic, perfectly plastic. (d) Rigid, linearly

strain hardening. Ep is referred to as the plastic modulus and is the slope of the stress-strain

curve after yielding. (e) Elastic, linearly strain hardening. The broken lines and arrows indicateunloading and reloading, respectively, during the test. Most engineering metals exhibit a

behavior similar to that shown in curve (e).

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Kalpakjian Schmid

Prentice Hall, 2003

Strain-Hardening and Temperature Effects

FIGURE 2.9 The effect of the strain -

hardening exponent, n, on the shape of true-

stress-true-strain curves. When n = 1, the

material is elastic, and when n = 0, it is rigidand perfectly plastic.

FIGURE 2.10 Typical effects of

temperature on engineering stress-

strain curves. Temperature affects the

modulus of elasticity, yield stress,ultimate tensile strength, and

toughness of materials.

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Kalpakjian Schmid

Prentice Hall, 2003

Range of Strain, Speed and Strain Rate

in Manufacturing ProcessesPROCESS TRUE STRAIN DEFORMATION SPEED (m/s) STRAIN RATE (s

-1)

Cold workingForging, rollingWire and tube drawing

Explosive formingHot working and warm working

Forging, rolling

ExtrusionMachiningSheet-metal formingSuperplastic forming

0.1-0.50.05-0.5

0.05-0.2

0.1-0.5

2-51-100.1-0.50.2-3

0.1-1000.1-100

10-100

0.1-30

0.1-10.1-1000.05-2

10-4

-10-2

1-103

1-104

10-105

1-103

10

-1

-10

2

103-10

6

1-102

10-4

-10-2

Table 2.4 Typical ranges of strain, deformation speed, and strain rates in metalworking

processes.

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Kalpakjian Schmid

Prentice Hall, 2003

Strain Rate Sensitivity

FIGURE 2.11 The effect of strain rate on the

ultimate tensile strength of aluminum. Note

that as temperature increases, the slope

increases thus, tensile strength becomes more

sensitive to strain rate as temperature increases.Source: After J. H. Hollomon.

FIGURE 2.12 Dependence of the strain-rate sensitivity

exponent m on the homologous temperature T/Tm for

various materials. Tis the testing temperature, and Tm

is

the melting point of the metal, both on the absolute scale.

The transition in the slopes of the curve occurs at aboutthe recrystallization temperature of the metals. Source:

After F. W. Boulger.

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Kalpakjian Schmid

Prentice Hall, 2003

Strain Rate Effects

Table 2.5 Approximate range of values for Cand m in Eq. (2.16) for various annealed

materials at true strains ranging from 0.2 to 1.0.

C

MATERIAL TEMPERATURE, C psi x 103 MPa m

Aluminum

Aluminum alloysCopperCopper alloys (brasses)LeadMagnesiumSteel

Low-carbonMedium-carbon

StainlessTitaniumTitanium alloysTi-6Al-4V

*

Zirconium

200-500

200-500300-900200-800100-300200-400

900-1200900-1200

600-1200200-1000200-1000815-930200-1000

12-2

45-535-360-2

1.6-0.320-2

24-723-7

60-5135-2130-59.5-1.6120-4

82-14

310-35240-20415-1411-2

140-14

165-48160-48

415-35930-14900-3565-11830-27

0.07-0.23

0-0.200.06-0.170.02-0.30.1-0.2

0.07-0.43

0.08-0.220.07-0.24

0.02-0.40.04-0.30.02-0.30.50-0.800.04-0.4

* At a strain rate of 2 x 10-4

s-1

.Note: As temperature increases, Cdecreases and m increases. As strain increases, Cincreases and m may

increase or decrease, or it may become negative within certain ranges of temperature and strain.Source: After T. Altan and F.W. Boulger.

s= Cem

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Kalpakjian Schmid

Prentice Hall, 2003

Strain-Rate Sensitivity Effect on Total

Elongation

FIGURE 2.13 (a) The effect of the strain-rate sensitivity exponent m on the total elongation for

various metals. Note that elongation at high values ofm approaches 1000%. Source: After D. Leeand W. A. Backofen. (b) The effect of the strain-rate sensitivity exponent on the postuniform

(after necking) elongation for various metals. Source: After A. K. Ghosh.

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Kalpakjian Schmid

Prentice Hall, 2003

Hydrostatic

Pressure Effecton True Strain

for Various

Metals

FIGURE 2.14 The effect of hydrostatic pressure on true strain at fracture in tension forvarious metals. Note that even cast iron becomes ductile under high pressure. Source:

After H. L. D. Pugh and D. Green.

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Kalpakjian Schmid

Prentice Hall, 2003

Barreling In

Compression

FIGURE 2.15 Barreling in compression of a

round solid cylindrical specimen (7075-O

aluminum) between flat dies. Barreling is caused

by interfaces, which retards the free flow of the

material. See also Figs. 6.1 and 6.2. Source: K. M.

Kulkarni and S. Kalpakjian.

FIGURE 2.16 Schematic illustration of the

plane-strain compression test. The dimensional

relationships shown should by satisfied for this

test to be useful and reproducible. This test give

the yield stress of the material in plane strain, Y.

Source: After A. Nadai and H. Ford.

Plane Strain

Compression

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Kalpakjian Schmid

Prentice Hall, 2003

Aluminum Stress

Strain Curve

FIGURE 2.17 True-stress-true-strain curve in

tension and compression for aluminum. For

ductile metals, the curves for tension and

compression are identical. Source: After A. H.Cottrell.

Bauschinger Effect

FIGURE 2.18 Schematic illustration of the

Bauschinger effect. The arrows show loading and

unloading paths. Note the decrease in the yield

stress in compression after the specimen has beensubjected to tension. The same result is obtained if

compression is applied first, followed by tension,

whereby the yield stress in tension decreases.

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Kalpakjian Schmid

Prentice Hall, 2003

Disk Test

FIGURE 2.19 Disk test on a brittle material,

showing the direction of loading and the

fracture path. This test is useful for brittle

materials, such as ceramics, carbides, and

round specimens from grinding wheels.

Torsion-Test

FIGURE 2.20 A typical torsion-test

specimen. It is mounted between the two

heads of a machine and is twisted. Note the

shear deformation of an element in the

reduced section of the tubular specimen.

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Kalpakjian Schmid

Prentice Hall, 2003

Simple Shear and

Pure Shear

FIGURE 2.21 Comparison of (a) simple shear

and (b) pure shear. Note that simple shear is

equivalent to pure shear plus a rotation.

FIGURE 2.22 The effect of axial compressive stress on

the shear strain at fracture in torsion for various steels.

Note that the effect on ductility is similar to that ofhydrostatic pressure, shown in Fig. 2.14. Source: Based

on data in P. W. Bridgman, Large Plastic Flow and

Fracture, McGraw-Hill, 1952,

Compressive Stress

Effect on Ductility

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Kalpakjian Schmid

Prentice Hall, 2003

Bending Tests

FIGURE 2.23 Two bend test methods for brittle materials. (a) three-point bending; (b) four-

point bending. The lower sketches represent the bending moment diagrams. Note the region

of constant maximum bending moment in diagram (b), whereas the maximum bendingmoment occurs only at the center of the specimen in diagram (a).

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Kalpakjian Schmid

Prentice Hall, 2003

Hardness

Tests

FIGURE 2.24 General characteristics of hardness testing methods. The Knoop tst is knownas a microhardness test because of the light load and small impressions. Source: After H. W.

Hayden, W. G. Moffatt, and V. Wulff.

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Kalpakjian Schmid

Prentice Hall, 2003

Brinell Hardness

Test

FIGURE 2.25 Indentation geometry for

Brinell hardness testing: (a) annealed

metal; (b) work-hardened metal. Note thedifference in metal flow at the periphery of

the impressions.

Hardness vs. Yield

Stress

FIGURE 2.26 Relation between Brinell

hardness and yield stress for aluminum and

steels. For comparison, the Brinell hardness(which is always measured in kg/mm2) is

converted to psi units in the scale on the left.

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Kalpakjian Schmid

Prentice Hall, 2003

Indentation Depth

FIGURE 2.27 Bulk deformation in mild steel under a spherical indenter. Note that the depth of

the deformed zone is about one order of magnitude larger than the depth of indentation. For a

hardness test to be valid, the material should be allowed to fully develop this zone. This

difference in depth is why thinner specimens require smaller indentations. Source: Courtesy of

M. C. Shaw and C. T. Yang.

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Kalpakjian Schmid

Prentice Hall, 2003

Fatigue Behavior

FIGURE 2.28 Typical S-Ncurves for two

metals. Note that, unlike steel, aluminum does

not have an endurance limit.

FIGURE 2.29 Ratio of endurance limit to

tensile strength for various metals, as a

function of tensile strength. The fatigue

strength of a metal can thus be estimated

from its tensile strength.

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Kalpakjian Schmid

Prentice Hall, 2003

Creep Behavior

FIGURE 2.30 Schematic illustration of a typical creep curve. The linear segment of the

curve (constant slope) is useful in designing components for a specific creep life.

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Kalpakjian Schmid

Prentice Hall, 2003

Impact Tests

FIGURE 2.31 Impact tests: (a) Charpy; (b) Izod.

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Kalpakjian Schmid

Prentice Hall, 2003

Residual Stresses Developed in Bending

FIGURE 2.32 Residual stresses developed in bending a beam made of an elastic, strain-

hardening material. Note that unloading is equivalent to applying an equal and opposite moment

to the bent part, as shown in diagram(b). Because of nonuniform deformation, most parts madeby plastic-deformation processes contain residual stresses. Note that for equilibrium, the forces

and moments due to residual stresses must be internally balanced.

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Kalpakjian Schmid

Prentice Hall, 2003

Residual Stress-Induced Distortion

FIGURE 2.33 Distortion of parts with residual stresses after cutting or slitting: (a) rolled sheetor plate; (b) drawn rod; (c) thin-walled tubing. Due to the presence of residual stresses on the

surfaces of parts, a round drill may produce an oval-shaped hole, because of relaxation of

stresses when a portion is removed.

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Kalpakjian Schmid

Prentice Hall, 2003

Elimination of Residual Stresses

FIGURE 2.34 Elimination of residual stresses by stretching. Residual stresses can be also

reduced or eliminated by thermal treatments, such as stress relieving or annealing.

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Kalpakjian Schmid

Prentice Hall, 2003

Stress State in

MetalworkingProcesses

FIGURE 2.35 The state of stress in various

metal working processes. (a) Expansion of a

thin-walled spherical shell under internal

pressure. (b) Drawing of round rod or wire

though a conical die to reduce its diameter;

see Section 6.5 (c) deep drawing of sheet

metal with a punch and die to make a metalcup; see Section 7.12.

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Kalpakjian Schmid

Prentice Hall, 2003

Stress Distribution

in Neck

FIGURE 2.36 Stress distribution in

the necked region of a tensile-test

specimen.

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Kalpakjian Schmid

Prentice Hall, 2003

States of StressFIGURE 2.37 Examples of states of

stress: (a) Plane stress in sheet stretching;

there are no stresses acting on the surfaces

of the sheet. (b) Plane stress in

compression; there are no stresses acting on

the sides of the specimen being

compressed. (c) Plane strain in tension; the

width of the sheet remains constant while

being stretched. (d) Plane strain in

compression (see also Fig. 2.16); the width

of the specimen remains constant, due to

the restraint by the groove. (e) Triaxial

tensile stresses acting on an element. (f)

Hydrostatic compression of an element.

Note also that an element on the cylindrical

portion of a thin-walled tube in torsion is in

the condition of both plane stress and plane

strain. (See also Section 2.11.7.)

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Kalpakjian Schmid

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Yield Criterion Comparison

FIGURE 2.38 Plane-stress diagrams for maximum-shear-stress and distortion-energy criteria;note that s2 = 0.

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Kalpakjian Schmid

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Stresses and Strains

FIGURE 2.39 Schematic illustration of a

true-stress-true-strain curve showing the

yield stress Y, the average flow stress Y, thespecific energy u1, and the flow stress Yf.

FIGURE 2.40 Deformation of grid patterns in a

workpiece: (a) the original pattern; (b) after ideal

deformation; (c) after inhomogeneous deformation.

Note that grid pattern (c) is basically the same as grid

pattern (b), but with additional shearing, especially atthe outer layers. Thus, grid pattern (c) requires higher

work of deformation than grid pattern (b). See also

Figs. 6.2 and 6.51.

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