1. Mechanical Properties of Metals

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
Engineering Stress
Engineering Strain
Direct Stress - Tension
Direct Stress - Compression

5. Tension Test Typical Universal Testing Machine Measures P Extensometer
Measures DL
Typical Universal
Testing Machine

6. Modern Materials Testing System
Hydraulic
Wedge
Grips
Specimen
Extensometer

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

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

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

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

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)

12. Modulus of Elasticity - Stiffness

13. Atomic Origin of Stiffness

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

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 For most metals, 0.25 < n < 0.35
in the elastic range
Furthermore:

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

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. t t

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

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

21. Ductility - EL% & AR%
Elongation
Area Reduction 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 Su Sy Engineering Stress, S=P/Ao
Engineering Strain, e = DL/Lo)

25. Resilience, Ur Su Sy ey Engineering Stress, S=P/Ao E
Engineering Strain, e = DL/Lo)

26. Typical Mechanical Properties
Metals in annealed (soft) condition