Simulation of Impact-Induced Martensitic Phase-Transition Front Propagation in Thermoelastic Solids

Abstract

Most experiments in martensitic phase transformations are performed under quasi-static loading of a specimen. The results of the quasi-static experiments usually characterize the bulk properties of the material in the specimen, but not the local behavior of phase transition fronts. The only well-documented experimental investigation concerning the impact-induced austenite-martensite phase transformations is given by Escobar and Clifton [1, 2]. As Escobar and Clifton noted, measured velocity profiles provide a difference between the particle velocity and the transverse component of the projectile velocity. This velocity difference, in the absence of any evidence of plastic deformation, is indicative of a stress induced phase transformation that propagates into the crystals from the impact face. But the determination of this velocity difference is most difficult from the theoretical point of view. In fact, the above mentioned velocity difference depends on the velocity of a moving phase boundary. However, the extensive study of the problem of moving phase boundaries shows that the velocity of a moving phase boundary cannot be determined in the framework of classical continuum mechanics without any additional hypothesis [3]–[9]. What continuum mechanics is able to determine is the so-called driving force acting on the phase boundary. The propagation of a phase boundary is thus expected to be described by a kinetic relation between the driving traction and the rate at which the transformation proceeds.