Consider a plane–strain tension test (Figure 5.12) in which the tensile stress is applied along the x-direction. The strain, εy, is zero along the transverse direction, and the stress in the z-direction vanishes. Assuming the von Mises criterion, write expressions for

A.  as a function of σx, and

B. dε as a function of dεx.

C. Using the results of parts A and B, write an expression for the incremental work per volume, dw, in terms of σx and dεx.

D. Derive an expression for σx as a function of εx in such a test, assuming that the strain hardening can be expressed by  = Kn


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