ABSTRACT
The linear relation between stress and strain, which describes the behavior of an elastic solid under load, holds up to a certain limit. This chapter provides the analysis of plastic deformation which is required in several engineering applications. To formulate a theory for plastic deformation of engineering materials, certain assumptions have to be made. The assumption of identical yield strength in tension and compression irrespective of the previous plastic deformation can therefore introduce errors in the analysis of problems involving reversed loading or metal-forming processes involving multistage working. The actual stress-strain curves for engineering materials as obtained from experiments are expressed by several empirical laws. The limit of elasticity, i.e., the yield strength under simple states of stress is directly obtained by means of mechanical testing of the material. The maximum difference in predicting yielding according to von Mises and Tresca is thus obtained from the ratio (0.577/0.5), which is equal to 1.155.
