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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) Three-point bending test. (d) Plane-strain tensile test. (e) Plane-strain 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 Stressstrain curves for AI SI 1040 steel subjected to different heat treatments; curves obtained from tensile tests. Stress-Strain Curves at Different Heat Treatments I dealized shapes of uniaxial stressstrain curve. (a) Perfectly plastic. (b) I deal elastoplastic. (c) I deal elastoplastic with linear work- hardening. (d) Parabolic work- hardening ( = o + K n ). Uniaxial Stress-Strain Curve Ludwik-Hollomon equation Plasticity Voce equation Johnson-Cook equation Schematic representation of the change in Poissons ratio as the deformation regime changes from elastic to plastic. True Stress and True Strain Curve True- and engineering-stress strain curves for AI SI 4140 hot- rolled steel. R. A. is reduction in area. Stress-Strain Curve Engineering- (or nominal-) stressstrain 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 / d versus log for stainless steel AI SI 302. (Adapted with permission from A. S. de S. e Silva and S. N. Monteiro , Metalurgia-ABM , 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, u . (Adapted with permission from W. J. McGregor Tegart, Elements of Mechanical Metallurgy (New York: MacMillan, 1964), p. 22.) Necking Stressstrain 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 wire-drawing reduction. (Courtesy of H. J. Rack) (a) Effect of strain rate on the stressstrain curves for AI SI 1040 steel. (b) Strain-rate 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) Stressstrain (engineering and true) curves for 7030 brass in compression. (b) Change of shape of specimen and barreling. Stress-Strain 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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