Mechanical Properties of Metals Mechanical Properties Stiffness Elastic

Mechanical Properties of Metals

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/m 3). • 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 Engineering Stress Engineering Strain Direct Stress - Tension Direct Stress - Compression

Tension Test Measures P Extensometer Measures DL Typical Universal Testing Machine

Modern Materials Testing System Hydraulic Wedge Grips Extensometer Specimen

ASTM Tension Test Specimen Ao=0. 20 in 2 2” Gauge Length Lo

Raw Data Obtained Load, P (k. N) Total Elongation Uniform Deformation X Maximum Load, Pmax Elastic Deformation Elongation, DL (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 = DL/Lo)

Duke’s Quick Tip! • Express Load in Newtons (N) and Area in mm 2 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 in 2 gives Stress in ksi (kips/in 2) • 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: • Where E is the modulus of elasticity (MPa)

Modulus of Elasticity - Stiffness

Atomic Origin of Stiffness

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)

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 For most metals, 0. 25 < n < 0. 35 in the elastic range Furthermore:

Plastic Deformation 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. t t

Elastic and Plastic Strain Stress P (e, S) Total 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 Strain elastic strain Strain

Ductility - EL% & AR% • Elongation Lo Lf • Area Reduction Ao 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/m 3 or N. mm/mm 3= MPa) • Resilience: A measure of the ability of a material to absorb energy without plastic or permanent deformation. (J/m 3 or N. mm/mm 3= MPa) • Note: Both are determined as energy/unit volume

Engineering Stress, S=P/Ao Toughness, Ut Sy Su Engineering Strain, e = DL/Lo)

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

Typical Mechanical Properties Metals in annealed (soft) condition