Chapter6 Mechanical Properties

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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals

University of Virginia, Dept. of Materials Science and Engineering

Mechanical Properties of Metals

How do metals respond to external loads?

Stress and Strain

Tension

Compression

Shear

Torsion

Elastic deformation

Plastic Deformation Yield Strength

Tensile Strength

Ductility

Toughness Hardness

Chapter 6 Outline

Not tested: true stress-true stain relationships, resilience, detail

f the different types of hardness tests, variability of materia

roperties


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How materials deform as a function o

applied loadTesting methods and language for

mechanical properties of materials.

Introduction

Stress,

(MPa)

Strain, (mm / mm)


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Types of Loading

TensileCompressive

Shear

Torsion


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Stress(For Tension and Compression)

To compare specimens , the load i

alculated per unit area.

Stress: = F / AoF:is load

A0: cross-sectional area

A0 perpendicular to F before

application of the load.


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Strain(For Tension and Compression)

Strain: = l / lo ( 100 %)l: change in lengthlo: original length.

Stress / strain = /


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Shear and Torsion

Shear stress: = F / AoF is applied parallel to upper and

lower faces each having area A0.

Shear strain: = tan ( 100 %) is strain angle

Shear Torsion


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Torsion

Torsion: like shear.

Load: applied torque, T

Strain: angle of twist, .

ShearTorsion


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Stress-Strain Behavior

(Tension)

Elastic Plastic

Stress

Strain

Elastic deformation

Reversible:

( For small strains)

Stress removed material returns to

original size

Plastic deformation

Irreversible:

Stress removed material does not return

to original dimensions.


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Elastic deformation

E = Young's modulus or modulus of elasticity

(same units as , N/m2 or Pa)

Gives Hooke's law for Tensile Stress

Stress

Strain

Load

Slope = modulus ofelasticity E

Unload

= E

Higher E higher stiffness


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University of Virginia, Dept. of Materials Science and Engineering 1

Nonlinear elastic behavior

n some materials (many polymers

oncrete...), elastic deformation is noinear, but it is still reversible.

Definitions of E

/ = tangent modulus at

/ = secant modulusbetween origin and 1


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Elastic Deformation: Atomic scale

Chapter 2: Potentials and Force

High

modulus

Low

modulus

E ~ (dF/dr) at ro

F= (sign) dV/drE~ curvature of potential

at equilibrium, r0

Separation,

Weaklybonded

Strongly

bonded

Force,F

Attractive is

positive here


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Anelasticity(time dependence of elastic deformation)

Have assumed elastic deformation is tim

independent

(applied stress produces instantaneoustrain)

Elastic deformation takes time; can

continue even after load release.

This behavior is known as anelasticity.

Small effect in metals; can be significanfor polymers (visco-elastic).


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Poissons ratio

Tension shrink laterallyCompressionbulge.

Ratio of lateral to axial strain called

Poisson's ratio .

Unloaded Loaded


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Poissons ratio

z

y

z

x

dimensionless.

Sign:

ateral strain opposite to longitudinal

train

Theoretical value:for isotropic material: 0.25

Maximum value: 0.50,

Typical value: 0.24 - 0.30


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Shear Modulus

Zo

y

Unloaded

Loaded

Shear stress to shear strain:

= G , = tan = y / zo

G is Shear Modulus(Units: N/m2)


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Elastic Modulus

Poissons Ratioand

Shear Modulus

For isotropic material:

E = 2G(1+) G ~ 0.4ESingle crystals are usually elastically

anisotropic

Elastic behavior varies with

crystallographic direction.


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Plastic deformation(Tension)

Plastic deformation:

stressnot proportional tostrain

deformation is not reversible

deformation occurs by breaking and re-

arrangement of atomic bonds (crystalline

materials by motion of defects)


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Tensile properties: Yielding

Elastic Plastic

Stress

StrainYield strength: yPermanent strain= 0.002

Yield point: PWhere strain deviates frombeing proportional to stress

(the proportional limit)

A measure of resistance

to plastic deformation

P

y

0.002


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Tensile properties: Yielding

Stress

Strain

For a low-carbon steel, the stress vs. strain

urve includes both an upper and loweield point.

The yield strength is defined in this case a

he average stress at the lower yield point.


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Tensile Strength

Tensile strength =

max. stress

(~ 100 - 1000 MPa)

If stress maintained specimen will break

Fracture

Strength

NeckingStress,

Strain,

Yield stress, y , usually more important thanensile strength. Once yield stress has been passed

tructure has deformed beyond acceptable limits.


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Tensile properties: Ductility

ercent elongationr

ercent reduction in

rea

DuctilityDeformation at Fracture

100l

llEL%

0

0f

10

A

AARA%

0

f0


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Mechanical Properties of Metals

Yield strength and tensile strength vary

with thermal and mechanical treatment

mpurity levels, etc.

Variability related to behavior o

dislocations (Elastic moduli are relatively

nsensitive)

Yield and tensile strengths and modulus o

lasticity: Decrease with increasing

emperature.

Ductility increases with temperature.


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Toughness

Toughness: ability to absorb energy up to

racture(Area under the strain-stress curveup to fracture)

Units: the energy per unit volume, e.g. J/m3

Can be measured by an impact test (Chapter 8).


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True Stress and Strain

True stress: load divided by actual area in thecked-down region, continues to rise to the poin

f fracture, in contrast to the engineering stress

= F/Ao = (li-lo/lo)

T = F/Ai T = ln(li/lo)

True Strain

True Stress


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Elastic Recovery During Plastic Deformation

Deformed plastically, stress released, material ha

ermanent strain.

f stress is reapplied, material again respondlastically at the beginning up to a new yield poin

hat is higher than the original yield point.

Elastic strain before reaching the yield point i

alled elastic strain recovery.

yy


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Hardness (I)

Hardness measure of materials resistanc

o localized plastic deformatione.g. dent or scratch)

Mohs scale ability of a material to scratchnother material: from 1 (softest = talc) to 10

hardest = diamond).

Variety of hardness tests

(Rockwell, Brinell, Vickers, etc.)

Small indenter (sphere, cone, o

pyramid) forced into surface o

material under controlled

magnitude and rate of loading.

Depth or size of indentation i

measured.

Tests are approximate, bu

popular because they are easy and

non-destructive (except for th

small dent).


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Hardness (II)

Tensile strength and hardness degree oesistance to plastic deformation.

Hardness proportional to tensile strength

roportionality constant depends on material.

Tensilestreng

th(MPa)

Tensilestrength

(103p

si)

Brinell hardness number


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What are the limits of safe deformation?

Design stress:

d

= Nc

: c

= maximum anticipated stress,

N the designfactor > 1.

Make sure d < y, safe or working stress:w = y/N where N is factor ofsafety > 1.

For practical engineering design,

the yield strength is usually the

important parameter

Strain

Stre

ss


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Summary

Anelasticity Ductility

Elastic deformation

Elastic recovery

Engineering strain

Engineering stress

Hardness

Modulus of elasticity

Plastic deformation

Poissons ratio

Proportional limit

Shear

Tensile strength

Toughness

Yielding Yield strength

Make sure you understand language and concepts:


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Reading for next class:

Chapter 7:Dislocations and Strengthening Mechanism

Dislocations and Plastic Deformation

Motion of dislocations in response to stress

Slip Systems

Plastic deformation in

single crystals

polycrystalline materials

Strengthening mechanisms

Grain Size Reduction Solid Solution Strengthening

Strain Hardening

Recovery, Recrystallization, and Grain Growth

Optional reading (Part that is not covered / not tested):

7 Deformation by twinning

n our discussion of slip systems, 7.4, we will not get into

Chapter6 Mechanical Properties

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