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Unformatted text preview: Chapter 3: Plasticity Common tests used to determine the monotonic strength of metals. (a) Uniaxial tensile test. (b) Upsetting test. (c) Threepoint bending test. (d) Planestrain tensile test. (e) Planestrain compression (Ford) test. (f) Torsion test. (g) Biaxial test. Tests for Mechanical Strength of Materials A servohydraulic universal testing machine linked to a computer. (Courtesy of MTS Systems Corp.) Mechanical Testing: Servohydraulic Machine Stress–strain curves for AI SI 1040 steel subjected to different heat treatments; curves obtained from tensile tests. StressStrain Curves at Different Heat Treatments I dealized shapes of uniaxial stress–strain curve. (a) Perfectly plastic. (b) I deal elastoplastic. (c) I deal elastoplastic with linear work hardening. (d) Parabolic work hardening ( σ = σ o + K ε n ). Uniaxial StressStrain Curve LudwikHollomon equation Plasticity Voce equation JohnsonCook equation Schematic representation of the change in Poisson’s ratio as the deformation regime changes from elastic to plastic. True Stress and True Strain Curve True and engineeringstress– strain curves for AI SI 4140 hot rolled steel. R. A. is reduction in area. StressStrain Curve Engineering (or nominal) stress–strain curves (a) without and (b) with a yield point. Engineering Stress and Engineering Strain Tensile specimen being tested; arrows show onset of necking. Tensile tests Log d σ / d ε versus log ε for stainless steel AI SI 302. (Adapted with permission from A. S. de S. e Silva and S. N. Monteiro , MetalurgiaABM , 33 (1977) 417.) Work hardening vs. Strain Correction factor for necking as a function of strain in neck, ln( A 0/ A ), minus strain at necking, ε u . (Adapted with permission from W. J. McGregor Tegart, Elements of Mechanical Metallurgy (New York: MacMillan, 1964), p. 22.) Necking Stress–strain curves for Fe– 0.003% C alloy wire, deformed to increasing strains by drawing; each curve is started at the strain corresponding to the prior wiredrawing reduction. (Courtesy of H. J. Rack) (a) Effect of strain rate on the stress–strain curves for AI SI 1040 steel. (b) Strainrate changes during tensile test. Four strain rates are shown: 10 − 1, 10 − 2, 10 − 3, and 10 − 4 s − 1. Strain Rate Effects (a) Compression specimen between parallel platens. (b) Length inhomogeneity in specimen. Plastic Deformation in Compressive Testing (a) Stress–strain (engineering and true) curves for 70–30 brass in compression. (b) Change of shape of specimen and barreling. StressStrain Curve for Compression (a) Distortion of Finite Element Method (FEM) grid after 50% reduction in height h of specimen under sticking friction conditions. (Reprinted with permission from H. Kudo and S....
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 Trigraph, Rockwell scale, Vickers hardness test, fr om

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