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7/29/2019 Chapter6 Mechanical Properties
1/30
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
7/29/2019 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
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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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering
Types of Loading
TensileCompressive
Shear
Torsion
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering
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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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering
Strain(For Tension and Compression)
Strain: = l / lo ( 100 %)l: change in lengthlo: original length.
Stress / strain = /
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering
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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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering
Torsion
Torsion: like shear.
Load: applied torque, T
Strain: angle of twist, .
ShearTorsion
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering
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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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering
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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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
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
7/29/2019 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 1
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
7/29/2019 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 1
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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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 1
Poissons ratio
Tension shrink laterallyCompressionbulge.
Ratio of lateral to axial strain called
Poisson's ratio .
Unloaded Loaded
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 1
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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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 1
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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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 1
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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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 1
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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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 1
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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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 1
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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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 2
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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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 2
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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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 2
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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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 2
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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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 2
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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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 2
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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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 2
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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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 2
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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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 2
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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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
University of Virginia, Dept. of Materials Science and Engineering 2
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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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
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