Fundamental influence of irreversible stress–strain properties in solids on the validity of the ramp loading method

Abstract

The widely used quasi-isentropic ramp loading technique relies heavily on back-calculation methods that convert the measured free-surface velocity profiles to the stress–density states inside the compressed sample. Existing back-calculation methods are based on one-dimensional isentropic hydrodynamic equations, which assume a well-defined functional relationship P(ρ) between the longitudinal stress and density throughout the entire flow field. However, this kind of idealized stress–density relation does not hold in general, because of the complexities introduced by structural phase transitions and/or elastic–plastic response. How and to what extent these standard back-calculation methods may be affected by such inherent complexities is still an unsettled question. Here, we present a close examination using large-scale molecular dynamics (MD) simulations that include the detailed physics of the irreversibly compressed solid samples. We back-calculate the stress–density relation from the MD-simulated rear surface velocity profiles and compare it directly against the stress–density trajectories measured from the MD simulation itself. Deviations exist in the cases studied here, and these turn out to be related to the irreversibility between compression and release. Rarefaction and compression waves are observed to propagate with different sound velocities in some parts of the flow field, violating the basic assumption of isentropic hydrodynamic models and thus leading to systematic back-calculation errors. In particular, the step-like feature of the P(ρ) curve corresponding to phase transition may be completely missed owing to these errors. This kind of mismatch between inherent properties of matter and the basic assumptions of isentropic hydrodynamics has a fundamental influence on how the ramp loading method can be applied.