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Chapter6c - Chapter Outline Introduction To understand and...

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1 1 MSE 2090: Introduction to Materials Science Chapter 6, Mechanical Properties Mechanical Properties of Metals How do metals respond to external loads? Stress and Strain ¾ Tension ¾ Compression ¾ Shear ¾ Torsion Elastic deformation Plastic Deformation ¾ Yield Strength ¾ Tensile Strength ¾ Ductility ¾ Toughness ¾ Hardness Chapter Outline Optional reading (not tested): details of the different types of hardness tests, variability of material properties (starting from the middle of page 174) 2 MSE 2090: Introduction to Materials Science Chapter 6, Mechanical Properties To understand and describe how materials deform (elongate, compress, twist) or break as a function of applied load, time, temperature, and other conditions we need first to discuss standard test methods and standard language for mechanical properties of materials. Introduction Stress, σ (MPa) Strain, ε (mm / mm) 3 MSE 2090: Introduction to Materials Science Chapter 6, Mechanical Properties Types of Loading Tensile Compressive Shear Torsion 4 MSE 2090: Introduction to Materials Science Chapter 6, Mechanical Properties Concepts of Stress and Strain (tension and compression) To compare specimens of different sizes, the load is calculated per unit area. Engineering stress: σ = F / A o F is load applied perpendicular to speciment cross- section; A 0 is cross-sectional area (perpendicular to the force) before application of the load. Engineering strain: ε = Δ l / l o ( × 100 %) Δ l is change in length, l o is the original length. These definitions of stress and strain allow one to compare test results for specimens of different cross- sectional area A 0 and of different length l 0 . Stress and strain are positive for tensile loads, negative for compressive loads
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2 5 MSE 2090: Introduction to Materials Science Chapter 6, Mechanical Properties Concepts of Stress and Strain (shear and torsion) Shear stress: τ = F / A o F is load applied parallel to the upper and lower faces each of which has an area A 0 . Shear strain: γ = tg θ ( × 100 %) θ is strain angle Torsion is variation of pure shear. The shear stress in this case is a function of applied torque T, shear strain is related to the angle of twist, φ . Shear Torsion θ F Ao 6 MSE 2090: Introduction to Materials Science Chapter 6, Mechanical Properties Stress-Strain Behavior Elastic Plastic Stress Strain Elastic deformation Reversible : when the stress is removed, the material returns to the dimensions it had before the loading. Usually strains are small (except for the case of some plastics, e.g. rubber). Plastic deformation Irreversible : when the stress is removed, the material does not return to its original dimensions. 7 MSE 2090: Introduction to Materials Science Chapter 6, Mechanical Properties Stress-Strain Behavior: Elastic Deformation E is Young's modulus or modulus of elasticity , has the same units as σ , N/m 2 or Pa In tensile tests, if the deformation is elastic, the stress- strain relationship is called Hooke's law: Stress Strain Load Slope = modulus of elasticity E Unload σ = E ε Higher E higher “stiffness” 8
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