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**Mechanical Properties of Metals**

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**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.)

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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.

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**Direct Stress Examples**

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

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**Tension Test Typical Universal Testing Machine Measures P Extensometer**

Measures DL Typical Universal Testing Machine

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**Modern Materials Testing System**

Hydraulic Wedge Grips Specimen Extensometer

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**ASTM Tension Test Specimen**

Ao=0.20 in2 2” Gauge Length Lo

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**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)

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**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)

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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

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**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)

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**Modulus of Elasticity - Stiffness**

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**Atomic Origin of Stiffness**

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**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)

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**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.

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**Poisson’s Ratio, n For most metals, 0.25 < n < 0.35**

in the elastic range Furthermore:

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**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

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**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

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**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

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**Elastic Recovery Stress Strain Strain elastic strain Loading Loading**

Reloading Stress Unloading Unloading Strain Strain elastic strain

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Ductility - EL% & AR% Elongation Area Reduction Lo Ao Lf Af

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**Ductile Vs Brittle Materials**

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

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**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

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**Toughness, Ut Su Sy Engineering Stress, S=P/Ao**

Engineering Strain, e = DL/Lo)

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**Resilience, Ur Su Sy ey Engineering Stress, S=P/Ao E**

Engineering Strain, e = DL/Lo)

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**Typical Mechanical Properties**

Metals in annealed (soft) condition

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Hooke’s Law and Modulus of Elasticity ( )

Hooke’s Law and Modulus of Elasticity ( )

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