Wave propagation in a condensed medium with N transforming phases: Application to solid-I-solid-II-liquid bismuth

Abstract

Constitutive assumptions of local thermal and pressure equilibrium in a mixture of N transforming phases allow construction of a constitutive equation of a generalized Maxwellian form suitable for studying the kinetics of phase transformations induced by shock-wave loading. This equation relates the pressure rate to the strain rate and the phase change rate, the latter being expressed as the time derivative of a vector which has components equal to the mass fractions of the constituent phases. A separate kinetic equation is required for evolution of this composition vector. Coefficients appearing in the constitutive equation depend only on properties that the mixture displays with a frozen composition which in turn depend directly on properties of the pure-phase components of the mixture. The constitutive equation is applied to solid-I-solid-II-liquid bismuth (N=3). When wave propagation calculations on bismuth are compared to previous theory and experiments, a lower bound on the melting rate of 4 μsec-1 is found.