Revisiting the Power Law Characteristics of the Plastic Shock Front under Shock Loading

Under uniaxial shock compression, the steepness of the plastic shock front usually exhibits power law characteristics with the Hugoniot pressure, also known as the "Swegle-Grady law." In this Letter, we show that the Swegle-Grady law can be described better by a third power law rather than the classical fourth power law at the strain rate between 10^{5}-10^{7}  s^{-1}. A simple dislocation-based continuum model is developed, which reproduced the third power law and revealed very good agreement with recent experiments of multiple types of metals quantitatively. New insights into this unusual macroscopic phenomenon are presented through quantifying the connection between the macroscopic mechanical response and the collective dynamics of dislocation assembles. It is found that the Swegle-Grady law results from the particular stress dependence of the plasticity behaviors, and that the difference between the third power scaling and the classical fourth power scaling results from different shock dissipative actions.