On the structure of metal plasticity constitutive equations and the physical origin of the plastic spin

The macroscopic elastic-plastic response of a metal polycrystal is analyzed here by homogenizing the response of a representative volume element. With this purpose, the theory developed in Hill(1967)(The essential structure of constitutive laws for metal composites and polycrystals. J. Mech. Phys. Solids, 15, 79-95) is extended so that the structural changes caused by plastic deformation are taken into account. It is found that the type of evolution assigned to the slip systems of a constituent crystal influences significantly the structure of the constitutive system characterizing the overall response. In particular, the classical normality structure is obtained only if slip systems are assumed to convect with the crystal lattice. Any other type of slip system evolution induces a deviation of the macro-rate of plastic deformation from the exterior normal to the yield surface. This provides a physical explanation and also a rigorous definition for the much debated concept of plastic spin.