Continuum nonlinear dynamics of unstable shock waves induced by structural phase transformations in iron

Abstract Iron is the predominant metal in the interior of the Earth and other rocky planets and has also received substantial consideration in materials science and engineering due to its technological importance. Here, a finite deformation continuum framework for combining nonlinear elasto-viscoplasticity with multivariant phase-field theory is used to investigate shock-induced polymorphic phase transitions in single-crystal iron. A large number of low- and high-pressure variants with explicit anisotropic pressure-dependent stiffnesses are included with respect to the point-symmetry groups of cubic and hexagonal crystal lattices. Using the element-free Galerkin method with high-performance computing resources, the three-dimensional nonlinear calculations accurately describe some important features reported by the experimental literature, and strongly complement our understanding of the phase-change dynamics in iron at larger time and length scales than hitherto explored by molecular dynamics simulations in the last two decades. The numerical model is able to reproduce unstable shock waves (which break up into elastic, plastic and phase-transition waves), providing new stress-informed insights into the coupling between the high strain-rate plasticity and microstructure evolution during the displacive phase transitions. The analyses of time-position diagrams indicate that the prompt plastic relaxation to a nearly hydrostatic state from uniaxial shock-compression is responsible for the peculiar multiphase microstructure with an unexpected gradient selection of high-pressure variants behind the phase-transition wave front. The existence of two-zone sequential sets of ”release” and ”reload” variants that results from a heterogeneous nucleation instability leads to a specific microstructural fingerprint of the nonlinear dynamics of phase transitions, thus offering novel guidelines for future experimental diagnostics of shock wave propagation in iron.