Macroscopic rate-variables in solids undergoing phase transformation

Abstract

Averaging rules are derived for the rates of deformation gradient and nominal stress in heterogeneous solids undergoing quasi-static deformation and displacive phase transformation with coherent interfaces. Infinitesimal increments in strain and stress in the bulk material are accompanied by the finite increments in growing layers of a transformed phase. Expressions for the rates of the macroscopic variables and their products are given in several equivalent forms. The transport theorem and rate compatibility conditions for moving interfaces are extended to the initial instant of non-smooth transformation when the standard kinematical condition of compatibility is not satisfied. As an application of the averaging formulae, it is shown that the continuous growth of parallel planar layers of a transformed phase at a meso-level results in macroscopic constitutive rate equations analogous to the theory of plasticity. The normality law is obtained if the propagation of a phase transformation front in an elastic material takes place at a prescribed value of the thermodynamic driving force.