Mechanical Properties of Metals

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 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 Total Elongation Uniform Deformation Elongation, DL (mm) Load, P (kN) X Maximum Load, Pmax Elastic Deformation Load, Pf

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 givesStress 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 Stress 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. Elastic Plastic Elastic Plastic Elastic Plastic Plastic Deformation Sy Sy Sy Stress 0.002 Strain 0.002 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 P (e,S) Stress Total Strain The 0.2% offset yield stress is the stress that gives a plastic (permanent) strain of 0.002. Strain Plastic Elastic ee ep

20. Elastic Recovery 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 Engineering Stress, S=P/Ao E ey Engineering Strain, e = DL/Lo)

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