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 shock waves. It is assumed that the Hugoniot state lies in the region of metastability around an equilibrium solid‑solid phase boundary, hence this model applies to transformations occurring through nucleation and growth. The model accounts for both homogeneous (thermally driven) and heterogeneous (catalyzed by crystal defects) nucleation in the shock front, the subsequent growth of the nuclei, and their eventual coalescence. The spatiotemporal dependence of the volume fraction is calculated using KJMA kinetic theory. An explicit expression for the interphase interface speed, which appears in the Avrami equation, is provided by a phase field model [1]; the thermodynamic driving force for interface propagation includes the free energy difference of the phases, the transformation work, and an athermal threshold associated with crystal defects [2]. The transformation work accounts for shear stresses due to the shock wave as well as residuals associated with the two-phase microstructure. The plastic constitutive relation of the two-phase material, which is computed using the KJMA-based volume fraction and now standard results from the literature (Crisfield, Eshelby, and Hill), and the heat transport equation are coupled to the thermoelastic equations. The solution of this coupled set of equations yields a nonsteady, two-wave shock profile. We relate the evolution of this shock profile to the nucleation rate and interface speed. Several examples of shock-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