Hugoniot elastic limit of single-crystal tantalum at normal and elevated temperatures subjected to extreme strain rates

Large-scale nonequilibrium molecular dynamic simulations of impact-induced shock propagation in defect-free single-crystal Ta along the [001] direction is presented, paying particular attention to the formation of elastic-plastic two-wave structures. Plastic deformation and elastic limits of Ta single crystals for various crystal orientations were investigated in a recent paper [R. Ravelo et al., Phys. Rev. B 88, 134101 (2013)]. In the present paper, a comprehensive study on the Hugoniot elastic limit (HEL) and its dependence on associated physical parameters is reported. The observed attenuation of an elastic precursor in a stress-wave profile led to proposing wide-range scaling relations for HEL decay applicable for ultrahigh strain rates. The influence of a lateral dimension on the spatial profile of a stress wave and time profile of free surface velocity (FSV) in the distinct appearance of a spike-valley feature and its consequence on scaling relations is investigated. Further, it is shown that the commonly used method of calculating HEL from a FSV profile is inadequate for submicron-thick samples at high strain rates. The necessary modifications are incorporated that resulted in comparable HEL values by two complimentary approaches of stress and FSV profiles. Simulations carried out for increasing impact strength revealed a power law dependence of HEL with strain rate. A methodology based on extrapolation of stress decay law and strain rate scaling constructed by us is proposed here for prediction of HEL pertaining to larger length samples. Very good agreement between the predicted values and available experimental results makes the modeling robust and applicable for a wide range of strain rates and length scales. Finally, the study is extended for elevated sample temperatures up to melting. Interestingly, yield strength is shown to follow an increasing trend up to a certain temperature, beyond which it decreases. An empirical relation is proposed here for expressing temperature dependence of HEL that explains the observed yield strength anomaly. Results are justified through thermal analysis of shear stress and evolution of dislocation density.