A micromechanics constitutive theory for forward transformation plasticity with shear and dilatation effect: I, nonproportional loading history

A micromechanics constitutive theory which takes into account both the dilatation and shear effects of the transformation is proposed to describe the macroscopic plastic behavior of structure ceramics during forward transformation under different temperatures. Under some basic assumptions, the analytic expressions of the Helmholtz and complementary free energy of the constitutive element are derived in a self-consistent manner by using the Mori-Tanaka's method which takes into account the interaction between the transformed inclusions. In the framework of Hill-Rice's internal variable constitutive theory, the forward transformation yield function and incremental stress strain relations, in analogy to the theory of metal plasticity, for non-proportional loading histories are obtained.