A physics-based model and simple scaling law to predict the pressure dependence of single crystal spall strength

Abstract

A homogenized framework for ductile damage accounting for the effect of void growth on the thermomechanical response of single crystals under dynamic loading (CPD-FE) is developed. The current framework extends our prior work (Nguyen et al., 2017) by incorporating the yield function of Han et al. (2013) for porous single crystals to govern the degradation of the macroscopic critical resolved shear stress. Validation of the model against direct numerical simulations shows a significant improvement in accuracy under conditions of macroscopic shear loading. The model parameters are calibrated to Kolsky bar (split-Hopkinson pressure bar) and plate impact experiments, and utilized to predict spall strength of single crystal copper in ⟨100⟩ orientation. Simulation results exhibit favorable agreement with single crystal plate impact tests over a range of strain rates and shock compression pressures. These simulation results are used to further interpret previous experimental observations on the rate and pressure sensitivity of spallation. Lastly, a simple analytical model for spall strength depending on the temperature, strain rate and pressure is proposed, which shows agreement with molecular dynamics (MD) simulations and experimental results. This analytical model of spall strength concisely captures the physical mechanisms governing the effects of pressure, strain rate, and temperature on spall strength.