Transition of Plastic Behavior From Single Crystal to Polycrystal Under Pure Tension, and the Effect of Multislip

Abstract

Based on a series representation the tensile stress-strain relation of a polycrystal is derived explicitly in terms of the plasticity of its constituent grains. This derivation assumes Taylor’s linear isotropic hardening law for slip systems and Berveiller and Zaoui’s modification of Hill’s self-consistent relation for grain interactions. It is taken that Taylor’s theory implies equal shears for the active systems, and this assumption leads to a simple micro equation for each grain. With the aid of self-consistent relation the average of these micro equations readily gives rise to a macro one for the aggregate, which is given analytically in terms of crystalline structure νij, slip modulus h and the number of active systems n. At a given n it is shown that, although the behavior of a polycrystal under partial yielding is sensitive to the interaction, or self-consistent model selected, the asymptotic state under full yielding is not. This simple theory is also shown to be in line with the classical ones of Taylor, Bishop and Hill, Hershey and Kocks. Comparison with Jaoul’s experiments on the hardening modulus further suggests that most crystals tend to deform with 2∼4, but not 5, active slip systems in the fully plastic range.