A thermodynamically consistent level set approach for shock-induced α-γ phase transition of RDX

The mechanisms of strain energy dissipation in shocked crystalline solids include plastic slip and/or polymorphic transformation. While the anisotropic elastic-plastic response of single crystals at high strain rate has been studied, modeling the effects of phase transformation has received less attention. We employ the level set method [1] to study shock-induced α-γ phase transformation in RDX single crystals. Our approach is based on a regularization energy functional [2] that does not require explicit reinitialization. A diffusive regularization flux is introduced to maintain the signed distance property of the level set function. The diffusive flux enables incorporating the level set formulation within Galerkin finite element framework. The level set approach is evaluated using one-dimensional and three-dimensional models of a bar shocked on the (100) plane of RDX. The diffusive form of the flux ensures curvature based motion and hence the level sets around the interface evolve smoothly for both examples. We compared the interface evolution using the proposed scheme with the velocity extension method for the one-dimensional example. The time lag in the interface motion captured by the two schemes decreases along the direction of shock propagation as well as with the element size and the number of Gauss points used. The particle velocity time trace and the stress history compare well between the two schemes. The marginal lag in the particle velocity and stress can be reduced by appropriate choice of the regularization energy. The efficacy of the proposed level set method depends on the choice of the regularization energy and the applied Dirichlet boundary conditions. The parameter in the regularization energy should be carefully chosen to obtain desired results. For the three-dimensional example, the proposed approach is shown to capture the characteristic features associated with the α-γ phase transformation in RDX such as stress relaxation behind the phase interface. We did not observe any slip activity for loading on the (100) plane or due to the α-γ phase transformation. This is consistent with the experimental observations where RDX shocked on the (100) plane undergoes elastic deformation. There were no spatial disturbances observed in the evolution or distribution of the level set parameter, compressive stress, or temperature. The proposed level set approach has simulated a smooth evolution of the α-γ phase interface in shocked RDX.

References:
[1] Osher and Sethian, J. Comput. Phys. 79, 12 (1988).
[2] Li et al., IEEE Trans. Image Process. 19, 3243 (2010).