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7/29/2019 4.Mechanical Properties of Metals
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Chapter 3: Mechanical Properties of Metals
0.0100.0080.0060.0040.0020.0000
100
200
300
400
500
CONTINUED
Stress(MPa)
Strain
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Mechanical Properties Stiffnessis the ratio of the force required to create a specified
deflection or movement of a part. Elastic Modulus or Youngs Modulus (MPa)
Strength - is defined as the stress at which a predetermined
amount of permanent deformation occurs.
Yield, Ultimate, Fracture, Proof, Offset Yield. Measured asstress (MPa),
Ductility - Measure of ability to deform plastically without
fracture - Elongation, Area Reduction, Fracture Strain - (no units
or mm/mm) Toughness, Resilience - Measure of ability to absorb energy
(J/m3).
Hardness - Resistance to indentation/abrasion (Various scales,
e.g.; Rockwell, Brinell, Vickers.)
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Stress and Strain
In a simplistic sense, stress may be thought
of as Load/Area.
Similarly, strain is the deformation of thecomponent/original length.
A stress may be direct, shear, ortorsional -
leading to corresponding deformations. Stress cannot be measured directly, but
deformation can be.
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Direct Stress Examples
Load, P
P
Area
Ao
Lo
L/2
L/2
Direct Stress - Tension
Load, P
P
AreaAo
Lo
L/2
L/2
Direct Stress - Compression
SP
Ao
e L
Lo
Engineering Stress
Engineering Strain
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Tension Test
Typical Universal
Testing Machine
ExtensometerMeasures L
Measures P
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Modern Materials Testing System
Hydraulic
Wedge
Grips
SpecimenExtensometer
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ASTM Tension Test Specimen
0.505" Dia
2 Gauge Length
Ao=0.20 in2
Lo
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Stressstrain graph for typical metal
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Definition of terms Proportional limit: The greatest stress which a material
is capable of sustaining without deviation fromproportionality of stress and strain (Hooke's Law) or the
point on the stress-strain curve at which stress ceases to
be proportional to strain.
Yield point: the stress at which a predetermined amountof permanent deformation occurs.
Tensile strength: The resistance of a material to a force
tending to tear it apart, measured as the maximum
tension the material can withstand without tearing. Sample break: The point which material breaks.
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Raw Data Obtained
Load,
P(kN)
Elongation, L (mm)
Uniform Deformation
Total Elongation
Elastic
Deformation
X
Maximum
Load, Pmax
Load,
Pf
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Engineering Stress-Strain Curve
Elongation
0.2% offset
yield stress
Proportional Limit
E
E
(Ultimate)
Engineering Strain, e = L/Lo)
Eng
ineeringStre
ss,
S=P/Ao Sy
Su
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Express Load in Newtons (N) and Area in
mm2 to get Stress in MPa.
Mechanical properties of metals are almost
always given in MPa or ksi.
Imperial units: Load in kips (1000 lbf) &
Area as in2 givesStress in ksi (kips/in2)
1000 psi = 1 ksi = 6.89 MPa
N
mm2 MPa
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Hookes Law
Elastic Deformation Elastic deformation is not permanent; it means that when
the load is removed, the part returns to its original shape
and dimensions.
For most metals, the elastic region is linear. For some
materials, including metals such as cast iron, polymers, and
concrete, the elastic region is non-linear.
If the behavior is linear elastic, or nearly linear-elastic,
Hookes Law may be applied:
Where E is the modulus of elasticity (MPa)
S Ee
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Modulus of Elasticity - Stiffness
0.0100.0080.0060.0040.0020.0000
100
200
300
400
500
CONTINUED
Stress
(MPa)
Strain
ESe
(300 0)MPa(0.015 0.0)
2x105MPa
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Atomic Origin of Stiffness
Strongly B onded
Weakly Bonded
NetInteratomicForce
Interatomic Distance
E
dF
dr
ro
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Shear Stress and Strain
Shear Stress,ShearStrain,
shear stress, = Shear Load / Area
shear strain, = angle of deformation (radians)
shear modulus, G = /(elastic region)
ShearStress
Shear Strain
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The force per unit area is referred to as the
shear stress, denoted by the symbol
(Greek letter tau), where
When shear stress is applied, there will be
an angular change in dimension, just asthere is a change in length when materials
are under tension or compression. Shear
strain, denoted by the symbol (Greekletter gamma), is defined by
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Elastic Properties of Materials
Poissons ratio: When a metal is strained inone direction, there are corresponding
strains in all other directions.
For a uniaxial tension strain, the lateral strains are
constrictive.
Conversely, for a uniaxial compressive strain, the
lateral strains are expansive.
i.e.; the lateral strains are opposite in sign to theaxial strain.
The ratio of lateral to axial strains is known as
Poissons ratio, n.
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Poissons Ratio,n
n ex
ez
ey
ezFor most metals,
0.25 < n< 0.35
in the elastic range
Furthermore:
E 2G(1n)
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Plastic Deformation
Stres
s
Strain0.002 0.002 0.002
Sy
Sy
Sy
Elastic Plastic
Most Metals - Al, Cu Clad Al-Alloys Low carbon Steel
Elastic Plastic
Elastic Plastic
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Microstructural Origins of Plasticity
Slip, Climb and Slide of atoms in the crystal structure. Slip and Climb occur at Dislocations and Slide occurs
at Grain Boundaries.
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Elastic and Plastic Strain
Stre
ss
StrainPlastic
Elastic
eeep
P
Total Strain
(e,S)
e ee ep
ee S
Eep e ee
The 0.2% offset yield stress
is the stress that gives a plastic
(permanent) strain of 0.002.
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Elastic Recovery
Strain
Stre
ss
Loading
Unloading Loading
Unloading
Reloading
elastic strainStrain
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Ductility - EL% & AR%
Elongation
Area Reduction
EL%
Lf Lo
Lo x 100
AR% Ao AfAo
x 100
Lo
Ao
Lf
Af
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Ductile Vs Brittle Materials
Only Ductile materials will exhibit necking. Ductile if EL%>8% (approximately)
Brittle if EL% < 5% (approximately)
Enginee
ringStress
Engineering Strain
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Toughness & Resilience
Toughness: A measure of the ability of amaterial to absorb energy without fracture.
(J/m3 or N.mm/mm3= MPa)
Resilience:A measure of the ability of amaterial to absorb energy without plastic or
permanent deformation.
(J/m3
or N.mm/mm3
= MPa) Note: Both are determined as
energy/unit volume
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Toughness, Ut
Engineering Strain, e = L/Lo)
EngineeringStre
ss,
S=P/Ao
Ut Sdeo
ef
(Sy Su )
2
EL%
100
SuSy
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X
Resilience, Ur
Engineering Strain, e = L/Lo)
EngineeringStre
ss,
S=P/Ao
Ur Sdeo
ey
Sy ey
2
Sy2
2E
SuSy
E
ey
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Typical Mechanical Properties
Material Yield Stress
(MPa)
Ultimate
Stress (MPa)
Ductility
EL%
Elastic Modulus
(MPa)
Poissons
Ratio
1040 Steel 350 520 30 207000 0.30
1080 Steel 380 615 25 207000 0.30
2024 Al Alloy 100 200 18 72000 0.33
316 Stainless Steel 210 550 60 195000 0.30
70/30 Brass 75 300 70 110000 0.35
6-4 Ti Alloy 942 1000 14 107000 0.36
AZ80 Mg Alloy 285 340 11 45000 0.29
Metals in annealed (soft) condition