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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
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 2
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)
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 3
Types of Loading
TensileCompressive
Shear
Torsion
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 4
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.
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 5
Strain(For Tension and Compression)
Strain: = l / lo ( 100 %)
l: change in length
lo: original length.
Stress / strain = /
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 6
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
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 7
Torsion
Torsion: like shear.
Load: applied torque, T
Strain: angle of twist, .
ShearTorsion
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 8
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.
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 9
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”
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 10
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
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 11
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
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 12
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).
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 13
Poisson’s ratio
Tension shrink laterally Compression bulge.
Ratio of lateral to axial strain called Poisson's ratio .
Unloaded Loaded
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 14
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
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 15
Shear Modulus
Zo
y
Unloaded
Loaded
Shear stress to shear strain:
= G ,
= tan = y / zo
G is Shear Modulus (Units: N/m2)
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 16
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.
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 17
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)
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 18
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
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 19
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.
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 20
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.
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 21
Tensile properties: Ductility
percent elongationor
percent reduction in area
Ductility Deformation at Fracture
100l
llEL%
0
0f
100A
AARA%
0
f0
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 22
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.
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 23
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).
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 24
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
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 25
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
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 26
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).
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 27
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
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 28
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
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 29
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:
Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 30
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