Mechanical Properties
of Metals
Stress (MPa)
500
CONT INUED
400
300
200
100
0
0.000 0.002 0.004 0.006 0.008 0.010
Strain
Mechanical Properties
• Stiffness - Elastic Modulus or Young’s Modulus (MPa)
• Strength - Yield, Ultimate, Fracture, Proof, Offset Yield.
Measured as stress (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.)
Stress and Strain
• In a simplistic sense, stress may be thought
of as Load/Area.
• Similarly, strain is the deformation of the
component/original length.
• A stress may be direct, shear, or torsional leading to corresponding deformations.
• Stress cannot be measured directly, but
deformation can be.
Direct Stress Examples
Load, P
L/2
Lo
Area
Ao
L/2
P
Engineering Stress
P
S
Ao
Load, P
L/2
Lo
L
e
Lo
Area
Ao
L/2
Engineering Strain
P
Direct Stress - Tension
Direct Stress - Compression
Tension Test
Measures P
Extensometer
Measures L
Typical Universal
Testing Machine
Modern Materials Testing System
Hydraulic
Wedge
Grips
Extensometer
Specimen
ASTM Tension Test Specimen
Ao=0.20 in2
0.505" Dia
2” Gauge Length
Lo
Raw Data Obtained
Load, P (kN)
Total Elongation
Uniform Deformation
X
Maximum
Load, Pmax
Elastic
Deformation
Elongation, L (mm)
Load,
Pf
Engineering Stress-Strain Curve
Engineering Stress, S=P/Ao
Elongation
Sy
0.2% offset
yield stress
(Ultimate)
E
Su
E
Proportional Limit
Engineering Strain, e = L/Lo)
Duke’s Quick Tip!
• Express Load in Newtons (N) and Area in
mm2 to get Stress in MPa.
N
2  MPa
mm
• Mechanical properties of metals are almost
always given in MPa or ksi.
• Imperial units: Load in kips (1000 lbf) &
Area as in2 gives Stress in ksi (kips/in2)
• 1000 psi = 1 ksi = 6.89 MPa
Hooke’s 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,
Hooke’s Law may be applied:
S  Ee
• Where E is the modulus of elasticity (MPa)
Modulus of Elasticity - Stiffness
Stress (MPa)
500
CONT I NUED
400
300
200
E
S (300  0)MPa

 2x10 5 MPa
e (0.015  0.0)
100
0
0.000
0.002
0.004
0.006
Strain
0.008
0.010
Atomic Origin of Stiffness
Net Interatomic Force
dF 
E   
 dr ro
Strongly Bonded
Weakly Bonded
Interatomic Distance
Shear
Strain,
Shear Stress,
Shear Stress
Shear Stress and Strain
Shear Strain
shear stress,  = Shear Load / Area
shear strain,  = angle of deformation (radians)
shear modulus, G =  /(elastic region)
Elastic Properties of Materials
• Poisson’s ratio: When a metal is strained in
one 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 the
axial strain.
• The ratio of lateral to axial strains is known as
Poisson’s ratio, n.
Poisson’s Ratio, n
ey
ex
n  
ez
ez
For most metals,
0.25 < n< 0.35
in the elastic range
Furthermore:
E  2G(1 n )
Plastic Deformation
Elastic Plastic
Elastic Plastic
Sy
Sy
Elastic Plastic
Stress
Sy
0.002
Most Metals - Al, Cu
0.002
Strain
Clad Al-Alloys
0.002
Low carbon Steel
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.


Elastic and Plastic Strain
P (e,S)
e  ee  e p
Stress
S
ee 
E
e p  e  ee
Total Strain
Strain
Plastic
ep
ee
Elastic
The 0.2% offset yield stress
is the stress that gives a plastic
(permanent) strain of 0.002.
Elastic Recovery
Loading
Reloading
Stress
Loading
Unloading
Unloading
Strain
elastic strain
Strain
Ductility - EL% & AR%
• Elongation
EL% 
L f  Lo
Lo
x 100
Lo
Lf
• Area Reduction
AR% 
Ao  A f
Ao
Ao
x 100
Af
Ductile Vs Brittle Materials
Engineering Stress
• Only Ductile materials will exhibit necking.
• Ductile if EL%>8% (approximately)
• Brittle if EL% < 5% (approximately)
Engineering Strain
Toughness & Resilience
• Toughness: A measure of the ability of a
material to absorb energy without fracture.
(J/m3 or N.mm/mm3= MPa)
• Resilience: A measure of the ability of a
material to absorb energy without plastic or
permanent deformation.
(J/m3 or N.mm/mm3= MPa)
• Note: Both are determined as
energy/unit volume
Engineering Stress, S=P/Ao
Toughness, Ut
Su
Sy
ef
Ut   S de
o
(S y  Su ) EL%



 100 
2
Engineering Strain, e = L/Lo)
Engineering Stress, S=P/Ao
Resilience, Ur
Su
Sy
ey
Ur   S de
o

E

ey
Sy e y
2
Sy 2
2E
Engineering Strain, e = L/Lo)
X
Typical Mechanical Properties
Metals in annealed (soft) condition
Material
1040 Steel
1080 Steel
2024 Al Alloy
316 Stainless Steel
70/30 Brass
6-4 Ti Alloy
AZ80 Mg Alloy
Yield Stress
(MPa)
350
380
100
210
75
942
285
Ultimate
Stress (MPa)
520
615
200
550
300
1000
340
Ductility
EL%
30
25
18
60
70
14
11
Elastic Modulus
(MPa)
207000
207000
72000
195000
110000
107000
45000
Poisson’s
Ratio
0.30
0.30
0.33
0.30
0.35
0.36
0.29