chapter 3 plasticity l.
Skip this Video
Loading SlideShow in 5 Seconds..
Chapter 3: Plasticity PowerPoint Presentation
Download Presentation
Chapter 3: Plasticity

Loading in 2 Seconds...

play fullscreen
1 / 59

Chapter 3: Plasticity - PowerPoint PPT Presentation

  • Uploaded on

Chapter 3: Plasticity. Tests for Mechanical Strength of Materials. Common tests used to determine the monotonic strength of metals. (a) Uniaxial tensile test. (b) Upsetting test. (c) Three-point bending test. (d) Plane-strain tensile test. (e) Plane-strain

I am the owner, or an agent authorized to act on behalf of the owner, of the copyrighted work described.
Download Presentation

PowerPoint Slideshow about 'Chapter 3: Plasticity' - andrew

An Image/Link below is provided (as is) to download presentation

Download Policy: Content on the Website is provided to you AS IS for your information and personal use and may not be sold / licensed / shared on other websites without getting consent from its author.While downloading, if for some reason you are not able to download a presentation, the publisher may have deleted the file from their server.

- - - - - - - - - - - - - - - - - - - - - - - - - - E N D - - - - - - - - - - - - - - - - - - - - - - - - - -
Presentation Transcript

Tests for Mechanical Strength of Materials

Common tests used to determine the monotonic strength of metals. (a) Uniaxial tensile test.

(b) Upsetting test. (c) Three-point bending test. (d) Plane-strain tensile test. (e) Plane-strain

compression (Ford) test. (f)‏ Torsion test. (g) Biaxial test.


Mechanical Testing: Servohydraulic Machine

A servohydraulic

universal testing machine linked to

a computer. (Courtesy of MTS

Systems Corp.)‏


Stress-Strain Curves at Different Heat Treatments

Stress–strain curves for

AISI 1040 steel subjected to

different heat treatments; curves

obtained from tensile tests.


Uniaxial Stress-Strain Curve

Idealized shapes of

uniaxial stress–strain curve. (a)‏

Perfectly plastic. (b) Ideal

elastoplastic. (c) Ideal elastoplastic

with linear work-hardening. (d)‏

Parabolic work-hardening (σ =

σo + Kεn).



Ludwik-Hollomon equation

Voce equation

Johnson-Cook equation


True Stress and True Strain Curve


representation of the change in

Poisson’s ratio as the deformation

regime changes from elastic to



Stress-Strain Curve

True- and

engineering-stress–strain curves

for AISI 4140 hot-rolled steel. R.

A. is reduction in area.


Engineering Stress and Engineering Strain

Engineering- (or nominal-) stress–strain curves (a) without and (b) with a yield



Tensile tests

Tensile specimen being tested; arrows show onset of necking.


Work hardening vs. Strain

Log dσ/dε versus log ε

for stainless steel AISI 302.

(Adapted with permission from A.

S. de S. e Silva and S. N. Monteiro,

Metalurgia-ABM, 33 (1977) 417.)‏



Correction factor for

necking as a function of strain in

neck, ln(A0/A), minus strain at

necking, εu. (Adapted with

permission from W. J. McGregor

Tegart, Elements of Mechanical

Metallurgy (New York: MacMillan,

1964), p. 22.)‏

Stress–strain curves for Fe–0.003% C alloy wire, deformed to increasing

strains by drawing; each curve is started at the strain corresponding to the prior

wire-drawing reduction. (Courtesy of H. J. Rack)‏


Strain Rate Effects

(a) Effect of strain rate

on the stress–strain curves for

AISI 1040 steel. (b) Strain-rate

changes during tensile test. Four

strain rates are shown: 10−1,

10−2, 10−3, and 10−4 s−1.


Plastic Deformation in Compressive Testing

(a) Compression

specimen between parallel platens.

(b) Length inhomogeneity in



Stress-Strain Curve for Compression

(a) Stress–strain

(engineering and true) curves for

70–30 brass in compression. (b)‏

Change of shape of specimen and



Finite Element Method

(a) Distortion of Finite Element Method (FEM) grid after 50% reduction in

height h of specimen under sticking-friction conditions. (Reprinted with permission from H. Kudo and S. Matsubara, Metal Forming Plasticity (Berlin: Springer, 1979),p. 395.) (b) Variation in pressure on surface of cylindrical specimen being



Bauschunger Effect

Ratio of compressive

flow stress (0.2% plastic strain) and

tensile flow stress at different

levels of plastic strain for different

steels. (After B. Scholtes, O.

V¨ohringer, and E. Macherauch,

Proc. ICMA6, Vol. 1 (New York:

Pergamon, 1982), p. 255.)‏

The Bauschinger effect.


Plastic Deformation of Polymers

Schematic of the

different types of stress–strain

curves in a polymer.

Effect of strain rate

and temperature on stress–strain curves.


Glassy Polymers

Schematic of necking

and drawing in a semicrystalline polymer.


Neck Propagation in Polyethylene

(a) Neck propagation

in a sheet of linear polyethylene.

(b) Neck formation and

propagation in a specimen, shown in schematic fashion.


Plastic Deformation of Glasses


stress–strain curves for

Pd77.5CU6Si16.5. (Adapted with

permission from C. A. Pampillo and H. S. Chen, Mater. Sci. Eng., 13 (1974) 181.)‏


Shear Steps

Shear steps

terminating inside material after

annealing at 250◦C/h, produced by (a) bending and decreased by (b)‏

unbending. Metglas

Ni82.4Cr7Fe3Si4.5B3.1 strip. (Courtesy of X. Cao and J. C. M. Li.)‏



(a) Gilman model of

dislocations in crystalline and

glassy silica, represented by

two-dimensional arrays of polyhedra. (Adapted from J. J. Gilman, J. Appl. Phys. 44 (1973)‏

675) (b) Argon model of displacement fields of atoms (indicated by magnitude and

direction of lines) when

assemblage of atoms is subjected to shear strain of 5 × 10−2, in

molecular dynamics computation. (Adapted from D. Deng, A. S.

Argon, and S. Yip, Phil. Trans. Roy. Soc. Lond. A329 (1989) 613.)‏


Viscosity of Glass

Viscosity of

soda–lime–silica glass and of

metallic glasses (Au–Si–Ge,

Pd–Cu–Si, Pd–Si, C0P) as a

function of normalized

temperature. (Adapted from J. F.

Shakelford, Introduction to Materials

Science for Engineers, 4th ed.

(Englewood Cliffs, NJ: Prentice

Hall, 1991), p. 331, and F. Spaepen

and D. Turnbull in Metallic Glasses,

ASM.) 1P=0.1 Pa · s.

Viscosity of three

glasses as a function of

temperature. 1 P=0.1 Pa · s.


Rankine, Tresca, and von Mises

Maximum-stress Criterion

Maximum-Shear-Stress Criterion

Maximum-Distortion-Energy Criterion


Comparison of the Rankine, von Mises, and Tresca

(a) Comparison of the

Rankine, von Mises, and Tresca

criteria. (b) Comparison of failure

criteria with test. (Reprinted with

permission from E. P. Popov,

Mechanics of Materials, 2nd ed.

(Englewood Cliffs, NJ:

Prentice-Hall, 1976), and G.

Murphy, Advanced. Mechanics of

Materials (New York: McGraw-Hill,

1964), p. 83.)‏


Displacement of the Yield Locus

Displacement of the

yield locus as the flow stress of the

material due to plastic

deformation. (a) Isotropic

hardening. (b) Kinematic



Mohr-Coulomb failure criterion

Griffith Failure Criterion

McClintock-Walsh Crtierion


Failure Criteria for Brittle Material

(a) Simple model for solid with cracks. (b) Elliptical flaw in elastic

solid subjected to compression loading. (c) Biaxial fracture

criterion for brittle materials initiated from flaws without (Griffith)‏

and with (McClintock and Walsh) crack friction.


von Mises Ellipse

Translation of von

Mises ellipse for a polymer due to

the presence of hydrostatic stress.

(a) No hydrostatic stress, (b) with

hydrostatic stress.


Shear Yielding and Crazing for Amorphous Polymer

Envelopes defining

shear yielding and crazing for an

amorphous polymer under biaxial

stress. (After S. S. Sternstein and L.

Ongchin, Am. Chem. Soc., Div. of

Polymer Chem., Polymer Preprints, 10

(1969), 1117.)‏


Failure Envelope

Failure envelope for unidirectional E-glass/epoxy composite under biaxial

loading at different levels of shear stress. (After I. M. Daniel and O. Ishai, Engineering Mechancis of Composite Materials (New York: Oxford University Press, 1994), p. 121.)‏


Plane-Stress Yield Loci for Sheets with Planar Isotropy

Plane-stress yield loci

for sheets with planar isotropy or

textures that are rotationally

symmetric about the thickness

direction, x3. (Values of R indicate

the degree of anisotropy =



Hardness Tests

Comparison of the impression sizes produced by various hardness tests on

material of 750 HV. BHN = Brinell hardness number, HRC = Rockwell hardness

number on C scale, HRN = Rockwell hardness number on N scale, VPN = Vickers

hardness number. (Adapted with permission from E. R. Petty, in Techniques of Metals

Research, Vol. 5, Pt. 2, R. F. Bunshah, ed. (New York: Wiley-Interscience, 1971), p. 174.)‏



Impression caused by

spherical indenter on metal plate.


Rockwell Hardness Tester

Procedure in using

Rockwell hardness tester.

(Reprinted with permission from

H. E. Davis, G. E. Troxel, and C. T.

Wiscocil, The Testing and Inspection

of Engineering Materials, (New

York: McGraw-Hill, 1941), p. 149.)‏


Vickers Hardness Test

Relationships Between Yield Stress and Hardness


Hardness Distance Profile

(a) Hardness–distance

profiles near a grain boundary in

zinc with 100-atom ppm of Al and

zinc with 100-atom ppm of Au

(1-gf load). (b) Solute

concentration dependence of

percent excess boundary

hardening in zinc containing Al, Au,

or Cu (3-gf load). (Adapted with

permission from K. T. Aust, R. E.

Hanemann, P. Niessen, and J. H.

Westbrook, Acta Met., 16 (1968)‏



Knoop Indenter

Some of the details of

the Knoop indenter, together with

its impression.


Nanoindenter apparatus

A schematic of a

nanoindenter apparatus.


Topographic Feature of the Berkovich Indentation

An impression made

by means of Berkovich indenter in

a copper sample. (From Deng,

Koopman, Chawla, and Chawla,

Acta Mater., 52 (2004) 4291.) (a)‏

An atomic force micrograph,

which shows very nicely the

topographic features of the

indentation on the sample surface.

The scale is the same along the

three axes. (b) Berkovich

indentation as seen in an SEM.


Load vs. Indentation Displacement

A schematic

representation of load vs. indenter



Simple Formability Tests for Sheets

Simple formability

tests for sheets. (a) Simple bending

test. (b) Free-bending test. (c)‏

Olsen cup test. (d) Swift cup test.

(e) Fukui conical cup test.


Plastic Anisotropy

“Ears” formed in

deep-drawn cups due to in-plane

anisotropy. (Courtesy of Alcoa,




Effect of “fibering” on formability. The bending operation is often an integral

part of sheet-metal forming, particularly in making flanges so that the part can be

attached to another part. During bending, the fibers of the sheet on the outer side of

the bend are under tension, and the inner-side ones are under compression. Impurities

introduced in the metal as it was made become elongated into “stringers” when the

metal is rolled into sheet form. During bending, the stringers can cause the sheet to fail

by cracking if they are oriented perpendicular to the direction of bending (top). If they

are oriented in the direction of the bend (bottom), the ductility of the metal remains

normal. (Adapted with permission from S. S. Hecker and A. K. Ghosh, Sci. Am., Nov.

(1976), p. 100.)‏


Punch-Stretch Test

Sheet specimen

subjected to punch–stretch test

until necking; necking can be seen

by the clear line. (Courtesy of S. S.



Punch-Stretch Test

Schematic of sheet

deformed by punch stretching. (a)‏

Representation of strain

distribution: ε1, meridional strains;

ε2, circumferential strains; h, cup

height. (b) Geomety of deformed



Forming-Limit Curve

Construction of a

forming-limit curve (or

Keeler–Goodwin diagram).

(Courtesy of S. S. Hecker.)‏


Different Strain Patterns in Stamped Part

Different strain

patterns in stamped part. (Adapted

from W. Brazier, Closed Loop, 15,

No. 1 (1986) 3.)‏


Strength of Biological Materials

Stress–strain response

fore a number of biological



Stress-Strain Response of Elastin

Stress–strain response

for elastin; it is the ligamentum

nuchae of cattle (Adapted from Y.

C. Fung and S. S. Sobin, J. Biomech.

Eng., 1103 (1981) 121. Also in Y.

C. Fung, Biomechanics: Mechanica

properties of Living Tissues

(NewYork: Springer, 1993) p. 244.)‏


Stress-Strain Response of Cortical Bone

Tensile and

compressive stress–strain curves

for cortical bone in longitudinal

and transverse directions.

(Adapted from G. L. Lucas, F. W.

Cooke, and E. A. Friis, A Primer on

Biomechanics (New York: Springer,



Strain Rate Response of Cortical Bone


dependence of tensile response of

cortical bone. (Adapted from J. H.

McElhaney, J. Appl. Physiology,

21(1966) 1231.)‏