A theoretical model of the interaction between plastic distortion and configurational stress on the phase transformation front

We discuss a phenomenological model that describes the influence of plastic deformation on the evolution of an interface between martensite and the parent matrix. In development of the model it has been assumed that the rate of change of plastic distortion in the direction normal to the interface exhibits a functional relationship, which in general involves critical magnitudes of thermodynamic forces complemented by forces of pure mechanical character that originate from the mechanical stress fluxes acting on the interface. We have established a general theoretical model based on the fundamental principles of continuum mechanics in accord with the crystallographic theory of martensitic transformations. By using a special type of an asymptotic expansion procedure and homogenization technique we were able to derive an explicit constitutive relationship among the rate of plastic distortion, mechanical stress, crystallographic transformation tensor, and change of thermodynamic potential.