This document discusses the mechanical properties of metals, including: - Stiffness (elastic modulus), strength, ductility, toughness, and hardness, which are used to characterize metals. - Stress and strain relationships, including Hooke's law, yield strength, ultimate strength, and the stress-strain curve. - Elastic and plastic deformation behavior and the origins at the atomic and microstructural levels. - Other key concepts covered include modulus of elasticity, Poisson's ratio, toughness, resilience, and examples of properties for various metals.

1. Mechanical Properties
of Metals
0.010
0.008
0.006
0.004
0.002
0.000
0
100
200
300
400
500
CONTINUED
Stress
(MPa)
Strain

2. 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.)

3. 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.

4. Direct Stress Examples
Load, P
P
Area
Ao
Lo
L/2
L/2
Direct Stress - Tension
Load, P
P
Area
Ao
Lo
L/2
L/2
Direct Stress - Compression
S 
P
Ao
e 
L
Lo
Engineering Stress
Engineering Strain

5. Tension Test
Typical Universal
Testing Machine
Extensometer
Measures L
Measures P

6. Modern Materials Testing System
Hydraulic
Wedge
Grips
Specimen
Extensometer

7. ASTM Tension Test Specimen
0.505" Dia
2” Gauge Length
Ao=0.20 in2
Lo

8. Raw Data Obtained
Load,
P
(kN)
Elongation, L (mm)
Uniform Deformation
Total Elongation
Elastic
Deformation
X
Maximum
Load, Pmax
Load,
Pf

9. Engineering Stress-Strain Curve
Elongation
0.2% offset
yield stress
Proportional Limit
E
E
(Ultimate)
Engineering Strain, e = L/Lo)
Engineering
Stress,
S=P/Ao
Sy
Su

10. Duke’s Quick Tip!
• 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 gives Stress in ksi (kips/in2)
• 1000 psi = 1 ksi = 6.89 MPa
N
mm2  MPa

11. 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:
• Where E is the modulus of elasticity (MPa)
S  Ee

12. Modulus of Elasticity - Stiffness
0.010
0.008
0.006
0.004
0.002
0.000
0
100
200
300
400
500
CONTINUED
Stress
(MPa)
Strain
E 
S
e

(300 0)MPa
(0.015 0.0)
 2x105
MPa

13. Atomic Origin of Stiffness
Strongly Bonded
Weakly Bonded
Net
Interatomic
Force
Interatomic Distance
E 
dF
dr






ro

14. Shear Stress and Strain
Shear Stress,
Shear
Strain,
shear stress,  = Shear Load / Area
shear strain,  = angle of deformation (radians)
shear modulus, G =  /(elastic region)
Shear
Stress
Shear Strain

15. 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.

16. Poisson’s Ratio, n
n  
ex
ez
 
ey
ez
For most metals,
0.25 < n< 0.35
in the elastic range
Furthermore:
E  2G(1n)

17. Plastic Deformation
Stress
Strain
0.002 0.002 0.002
Sy
Sy
Sy
Elastic Plastic
Most Metals - Al, Cu Clad Al-Alloys Low carbon Steel
Elastic Plastic
Elastic Plastic

18. 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.



19. Elastic and Plastic Strain
Stress
Strain
Plastic
Elastic
ee
ep
P
Total Strain
(e,S) e  ee  ep
ee 
S
E
ep  e  ee
The 0.2% offset yield stress
is the stress that gives a plastic
(permanent) strain of 0.002.

20. Elastic Recovery
Strain
Stress
Loading
Unloading
Loading
Unloading
Reloading
elastic strain
Strain

21. Ductility - EL% & AR%
• Elongation
• Area Reduction
EL% 
Lf  Lo
Lo
x 100
AR% 
Ao  Af
Ao
x 100
Lo
Ao
Lf
Af

22. Ductile Vs Brittle Materials
• Only Ductile materials will exhibit necking.
• Ductile if EL%>8% (approximately)
• Brittle if EL% < 5% (approximately)
Engineering
Stress
Engineering Strain

23. 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

24. Toughness, Ut
Engineering Strain, e = L/Lo)
Engineering
Stress,
S=P/Ao
Ut  Sde
o
ef


(Sy  Su )
2
EL%
100






Su
Sy

25. X
Resilience, Ur
Engineering Strain, e = L/Lo)
Engineering
Stress,
S=P/Ao
Ur  S de
o
ey


Sy ey
2

Sy
2
2E
Su
Sy
E
ey

26. Typical Mechanical Properties
Material Yield Stress
(MPa)
Ultimate
Stress (MPa)
Ductility
EL%
Elastic Modulus
(MPa)
Poisson’s
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