Q:Show that Equations 6.18a and 6.18b are valid when there is no volume change during deformation.Q:Demonstrate that Equation 6.16, the expression defining true strain, may also be represented bywhen specimen volume remains constant duringQ:Using the data in Problem 6.28 and Equations 6.15, 6.16, and 6.18a, generate a true stress–true strain plot for aluminum. Equation 6.18a becomesQ:A tensile test is performed on a metal specimen, and it is found that a true plastic strain of 0.20 is produced when a true stress of 575MPaQ:For some metal alloy, a true stress of 415MPa (60,175psi) produces a plastic true strain of 0.475. How much will a specimen of this material elongateQ:The following true stresses produce the corresponding true plastic strains for a brass alloy:What true stress is necessary to produce a true plasticQ:For a brass alloy, the following engineering stresses produce the corresponding plastic engineering strains, prior to necking:On the basis of thisQ:Find the toughness (or energy to cause fracture) for a metal that experiences both elastic and plastic deformation. Assume Equation 6.5 for elasticQ:For a tensile test, it can be demonstrated that necking begins whenUsing Equation 6.19, determine the value of the true strain at this onset ofQ:Taking the logarithm of both sides of Equation 6.19 yieldsThus, a plot of log σT versus log ∈T in the plastic region to the point of neckingQ:A cylindrical specimen of a brass alloy 7.5 mm (0.30 in.) in diameter and 90.0 mm (3.54 in.) long is pulled in tension with a force of 6000 NQ:A steel alloy specimen having a rectangular cross section of dimensions 12.7 mm × 6.4 mm (0.5 in. × 0.25 in.) has the stress–strain behaviorQ:(a) A 10-mm-diameter Brinell hardness indenter produced an indentation 1.62 mm in diameter in a steel alloy when a load of 500 kg was used.Q:Estimate the Brinell and Rockwell hardnesses for the following:(a) The naval brass for which the stress–strain behavior is shown in Figure 6.12.(b)Q:Using the data represented in figure, specify equations relating tensile strength and Brinell hardness for brass and nodular cast iron, similar toQ:Cite five factors that lead to scatter in measured material properties.