Kinetics of solid-solid phase transformations in shock waves

This research is focused on the development of a microstructural model for phase transformation kinetics in shockwaves. It is assumed that the Hugoniot state lies in the region of metastability around an equilibrium solid-solidphase boundary, hence this model applies to transformations occurring through nucleation and growth. The modelaccounts for both homogeneous (thermally driven) and heterogeneous (catalyzed by crystal defects) nucleationin the shock front, the subsequent growth of the nuclei, and their eventual coalescence. The spatiotemporal de-pendence of the volume fraction is calculated using KJMA kinetic theory. An explicit expression for the interphaseinterface speed, which appears in the Avrami equation, is provided by a phase fi eld model [1]; the thermodynam-ic driving force for interface propagation includes the free energy difference of the phases, the transformationwork, and an athermal threshold associated with crystal defects [2]. The transformation work accounts for shearstresses due to the shock wave as well as residuals associated with the two-phase microstructure. The plasticconstitutive relation of the two-phase material, which is computed using the KJMA-based volume fraction andnow standard results from the literature (Crisfi eld, Eshelby, and Hill), and the heat transport equation are coupledto the thermoelastic equations. The solution of this coupled set of equations yields a nonsteady, two-wave shockprofi le. We relate the evolution of this shock profi le to the nucleation rate and interface speed. Several examples ofshock-induced microstructure evolution are presented. REFERENCES[1] Levitas, V.I., Preston, D.L. Phys. Rev. B. 2002, 66, 134206, 134207.[2] Levitas, V.I., Lee, D.-W., Preston, D.L. 2010. Int. J. Plasticity. 2010, 26, 395.