A coupling model of melting and damage evolution in the spallation of tin under shock loading

Abstract

To provide insight into the spallation characteristics in tin (Sn) while accounting for the melting effect induced by high pressure, a coupling model was developed utilizing a combination of equation of state (EOS), phase transition theory, damage theory, and percolation theory. Thermodynamic variables were derived by using a Hayes EOS, and melting rate and fraction were obtained by Andrews's phase transition method. To account for the temperature effect, a modified nucleation and growth model based on surface energy theory was introduced to describe the dynamic damage. The influence of melting on damage evolution was realized by using percolation theory. The model was then implemented into a one-dimensional finite element method to examine the mechanical spallation and micro-spallation behaviors of a Sn target subjected to various shock loadings. The calculated data, encompassing free surface velocity profile and spall strength, exhibit good agreement with experiments across an extensive range of load pressures up to 40 GPa. This work provides an inspiration for the study of the spall behavior of metals under varying levels of loading pressure and serves as a starting point for further investigations.