Assessment of the time-dependent behavior of dislocation multiplication under shock loading

In this study, we proposed a method, which is a combination of qualitative analysis and quantitative analysis, to establish dislocation-based plasticity model, and assessed the time-dependent behavior of dislocation multiplication under shock loading. First, the dimensional analysis method is applied to generate the governing equation of dislocation multiplication rate, and ten potential governing equations are derived. Second, through the theoretical analysis of the mechanical response on the shock front, each time-dependent governing equation is directly integrated on the shock front, and the explicit expression of dislocation density with respect to the applied stress is derived, which is further quantitatively connected to the power scaling characteristics of the plastic front. It`s found that only three of the ten equations, including two common equations and one newly derived equation via the dimensional analysis method, can predict the appropriate scaling coefficient of the plastic front. Third, three common equations and the newly derived equation are implemented into a dislocation-based constitutive model, and we compared results, including the velocity profiles and dislocation densities, calculated using the model associated with each equation and experimental results to evaluate the accuracy and efficiency of each equation. Through the comparison of the quantitative relation of the power scaling characteristics of the plastic front, and the elastic precursor decay, it`s concluded that the newly derived stress-dependent governing equation is more suitable for shock-loading process than the commonly used equations by previous constitutive models.