introduction to materials science, chapter 6, mechanical properties of metals university of...

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

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

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, details

of the different types of hardness tests, variability of material

properties



How materials deform as a function of applied load Testing methods and language for mechanical properties of materials.

Introduction

Str

ess,

(

MP

a)

Strain, (mm / mm)



Types of Loading

TensileCompressive

Shear

Torsion



Stress(For Tension and Compression)

To compare specimens , the load is calculated per unit area.

Stress: = F / Ao

F: is load

A0: cross-sectional area

A0 perpendicular to F before application of the load.



Strain(For Tension and Compression)

Strain: = l / lo ( 100 %)

l: change in length

lo: original length.

Stress / strain = /



Shear and Torsion

Shear stress: = F / Ao

F is applied parallel to upper andlower faces each having area A0.

Shear strain: = tan ( 100 %)

is strain angle

Shear Torsion



Torsion

Torsion: like shear.

Load: applied torque, T

Strain: angle of twist, .

ShearTorsion



Stress-Strain Behavior(Tension)

Elastic Plastic

Str

ess

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.



Elastic deformation

E = Young's modulus or modulus of elasticity (same units as , N/m2 or Pa)

Gives Hooke's law for Tensile Stress

Str

ess

Strain

Load

Slope = modulus ofelasticity E

Unload

= E

Higher E higher “stiffness”



Nonlinear elastic behaviorIn some materials (many polymers, concrete...), elastic deformation is not linear, but it is still reversible.

Definitions of E

/ = tangent modulus at 2

/ = secant modulus between origin and 1



Elastic Deformation: Atomic scale

Chapter 2: Potentials and Force

High modulus

Low modulus

E ~ (dF/dr) at ro

F= (sign) dV/dr

E~ curvature of potential

at equilibrium, r0

Separation, r

Weaklybonded

Stronglybonded

For

ce, F

Attractive is positive here



Anelasticity(time dependence of elastic deformation)

• Have assumed elastic deformation is time independent

(applied stress produces instantaneous strain)

• Elastic deformation takes time; can continue even after load release.

This behavior is known as anelasticity.

• Small effect in metals; can be significant for polymers (visco-elastic).



Poisson’s ratio

Tension shrink laterally Compression bulge.

Ratio of lateral to axial strain called Poisson's ratio .

Unloaded Loaded



Poisson’s ratio

z

y

z

x

dimensionless.

Sign: lateral strain opposite to longitudinal strain

Theoretical value: for isotropic material: 0.25

Maximum value: 0.50, Typical value: 0.24 - 0.30



Shear Modulus

Zo

y

Unloaded

Loaded

Shear stress to shear strain:

= G ,

= tan = y / zo

G is Shear Modulus (Units: N/m2)



Elastic ModulusPoisson’s Ratio

andShear Modulus

For isotropic material:

E = 2G(1+) G ~ 0.4E

Single crystals are usually elastically anisotropic

Elastic behavior varies with crystallographic direction.



Plastic deformation(Tension)

Plastic deformation: • stress not proportional to strain• deformation is not reversible• deformation occurs by breaking and re-

arrangement of atomic bonds (crystalline materials by motion of defects)



Tensile properties: Yielding

Elastic Plastic

Str

ess

Strain

Yield strength: y Permanent strain= 0.002

Yield point: P

Where strain deviates from being proportional to stress

(the proportional limit)

A measure of resistance to plastic deformation

P

y

0.002



Tensile properties: Yielding

Stress

Strain

For a low-carbon steel, the stress vs. strain curve includes both an upper and lower yield point. The yield strength is defined in this case as the average stress at the lower yield point.



Tensile Strength

Tensile strength =

max. stress

(~ 100 - 1000 MPa)

If stress maintained specimen will break

Fracture Strength

“Necking”Stre

ss,

Strain,

Yield stress, y , usually more important than

tensile strength. Once yield stress has been passed, structure has deformed beyond acceptable limits.



Tensile properties: Ductility

percent elongationor

percent reduction in area

Ductility Deformation at Fracture

100l

llEL%

0

0f

100A

AARA%

0

f0



Mechanical Properties of Metals

Yield strength and tensile strength vary with thermal and mechanical treatment, impurity levels, etc.

Variability related to behavior of dislocations (Elastic moduli are relatively insensitive)

Yield and tensile strengths and modulus of elasticity: Decrease with increasing temperature.

Ductility increases with temperature.



Toughness

Toughness: ability to absorb energy up to fracture (Area under the strain-stress curve up to fracture)

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

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



True Stress and Strain

True stress: load divided by actual area in the necked-down region, continues to rise to the point of fracture, in contrast to the engineering stress.

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

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

True Strain

True Stress



Elastic Recovery During Plastic Deformation

Deformed plastically, stress released, material has permanent strain.

If stress is reapplied, material again responds elastically at the beginning up to a new yield point that is higher than the original yield point.

Elastic strain before reaching the yield point is called elastic strain recovery.

y

y



Hardness (I)Hardness measure of material’s resistance to localized plastic deformation (e.g. dent or scratch)

Moh’s scale ability of a material to scratch another material: from 1 (softest = talc) to 10 (hardest = diamond).

Variety of hardness tests

(Rockwell, Brinell, Vickers, etc.). Small indenter (sphere, cone, or pyramid) forced into surface of material under controlled magnitude and rate of loading.

Depth or size of indentation is measured.

Tests are approximate, but popular because they are easy and non-destructive (except for the small dent).



Hardness (II)

Tensile strength and hardness degree of resistance to plastic deformation.

Hardness proportional to tensile strengthProportionality constant depends on material.

Ten

sile

str

engt

h (M

Pa)

Ten

sile

str

engt

h (1

03 psi

)

Brinell hardness number



What are the limits of “safe” deformation?

Design stress:

d = N’c : c = maximum anticipated stress,

N’ the “design factor” > 1.

Make sure d < y, safe or working stress:

w = y/N where N is “factor of safety” > 1.

For practical engineering design, the yield strength is usually the important parameter

Strain

Stre

ss



Summary

Anelasticity Ductility Elastic deformation Elastic recovery Engineering strain Engineering stress Hardness Modulus of elasticity Plastic deformation Poisson’s ratio Proportional limit Shear Tensile strength Toughness Yielding Yield strength

Make sure you understand language and concepts:



Reading for next class:

Chapter 7: Dislocations and Strengthening Mechanisms

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):

7.7 Deformation by twinning

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

direction and plane nomenclature

introduction to materials science, chapter 6, mechanical properties of metals university of...

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