Download Chapter 6. Mechanical Properties of Metals

Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
Chapter 6 Outline
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
Not tested: true stress-true stain relationships, resilience, details
of the different types of hardness tests, variability of material
properties
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
Introduction
Stress,  (MPa)
How materials deform as a function of
applied load 
Testing methods and language for
mechanical properties of materials.
Strain,  (mm / mm)
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
Types of Loading
Tensile
Compressive
Shear
Torsion
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
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
application of the load.
F
before
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
Strain
(For Tension and Compression)
Strain:  = l / lo ( 100 %)
l: change in length
lo: original length.
Stress / strain = / 
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
Shear and Torsion
Shear stress:  = F / Ao
F 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
Torsion
Torsion: like shear.
Load: applied torque, T
Strain: angle of twist, .
Torsion
Shear
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
Stress-Strain Behavior
(Tension)
Elastic Plastic
Elastic deformation
Reversible:
Stress
( For small strains)
Stress
removed
material
returns
original size

to
Plastic deformation
Irreversible:
Strain
Stress
removed

material does not return
to original dimensions.
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
Elastic deformation
Gives Hooke's law for Tensile Stress
 = E
E = Young's modulus or modulus of elasticity
(same units as , N/m2 or Pa)
Stress
Unload
Slope = modulus of
elasticity E
Load
Strain
Higher E  higher “stiffness”
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
Nonlinear elastic behavior
In some materials (many polymers,
concrete...), elastic deformation is not
linear, but it is still reversible.
/ = tangent modulus at 2
Definitions of E
/ = secant modulus
between origin and 1
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
Elastic Deformation: Atomic scale
Chapter 2: Potentials and Force
Force, F
High
modulus
Strongly
bonded
Attractive is
positive here
Separation, r
Low
modulus
Weakly
bonded
E ~ (dF/dr) at ro
F= (sign) dV/dr 
E~ curvature of potential
at equilibrium, r0
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
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).
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
Poisson’s ratio
Unloaded
Loaded
Tension  shrink laterally
Compression  bulge.
Ratio of lateral to axial strain called
Poisson's ratio .
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
Poisson’s ratio
y
x


z
z
 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
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
Shear Modulus
y
Zo
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
Elastic Modulus
Poisson’s Ratio
and
Shear Modulus
For isotropic material:
E = 2G(1+)  G ~ 0.4E
Single 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
Plastic deformation
(Tension)
Plastic deformation:
• stress not proportional to strain
• deformation is not reversible
• deformation occurs by breaking and rearrangement of atomic bonds (crystalline
materials by motion of defects)
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
Tensile properties: Yielding
Elastic Plastic
Stress
y
P
Yield point: P
Where strain deviates from
being proportional to stress
(the proportional limit)
Strain
Yield
strength:
y
0.002 Permanent strain= 0.002
A measure of resistance
to plastic deformation
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
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.
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
Tensile Strength
If stress maintained specimen will break
Stress, 
Fracture
Strength
“Necking”
Tensile strength =
max. stress
(~ 100 - 1000 MPa)
Strain, 
Yield stress, y , usually more important than
tensile strength. Once yield stress has been passed,
structure has deformed beyond acceptable limits.
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
Tensile properties: Ductility
Ductility  Deformation at Fracture
percent elongation
or
percent reduction in
area
 lf  l0 
 100
%EL  
 l0 
 A0  Af 
 100
%RA  
 A0 
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
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.
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
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).
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
True Stress and Strain
True Stress
T = F/Ai T = ln(li/lo)
 = F/Ao  = (li-lo/lo)
True 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.
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
Elastic Recovery During Plastic Deformation
y
y
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.
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
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).
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
Tensile strength (103 psi)
Tensile strength (MPa)
Hardness (II)
Brinell hardness number
Tensile strength and hardness  degree of
resistance to plastic deformation.
Hardness proportional to tensile strength
Proportionality constant depends on material.
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
Stress
What are the limits of “safe” deformation?
For practical engineering design,
the yield strength is usually the
important parameter
Strain
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.
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
Summary
Make sure you understand language and concepts:
















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
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Introduction To Materials Science, Chapter 6, Mechanical Properties of Metals
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
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