Modelling shocks using molecular dynamics

Abstract

The study of shocks in solid, crystalline metals has been ongoing since the early works of Rankine and Hugoniot in the latter half of the 19th century. However, the understanding of the behaviour of such materials under these extreme conditions remains an area of active research because of the paucity with which models can predict experimental observations. The modern era has seen a huge increase in the ability to solve many of the problems of this area of study by numerical, rather thatn analytic, means. One of these tools has been the use of computers to provide a numerical solution to the many–body problem posed by consideration of the medium as being composed of interacting atoms. The issue, then, has been transferred from one of dealing with many particles (which remains a problem for some aspects) to one of being able to develop a model which correctly describes the atomic interactions. However, it has been found that approximately correct models provide sufficient fidelity to enable qualitative studies to be undertaken. The study undertaken here has used this advantage to consider the behaviour of metallic materials under weak shock conditions. A comparison with some previous studies is given, which shows that, in order to avoid certain behaviours not observed experimentally, the simulation must contain thermal motion equivalent to at least room temperature. This thermal motion, and its resultant misalignment of the atoms, prevents spurious transfer of uni-directional momentum into rebounding translational supersonic waves. Further examination of the initial generation of dislocations indicates differences in the behaviour of not only the three high symmetry directions, but in the way that shear stress is relieved initially in low symmetry crystals as well. This behaviour gives some indication as to how the elastic precursor, commonly observed in weak shock experiments, decays from the level predicted by the Rankine–Hugoniot conservation relations to the much lower level observed experimentally. However, a very large discrepancy exists between the amplitude of the elastic wave observed in these simulations and that of experiments. It is shown that the existence of defects within the crystal can account for at least some of this discrepancy. However, computational limitations not only prevent the creation of realistic sample sizes, but also prevent the simulation of realistic defect densities and microstructures. This computational limtation, then, means that it is not currently possible to recreate the low Hugoniot elastic limits observed experimentally. The inability of atomistic simulations to recreate experimental data notwithstanding, useful analysis of shock behaviour is demonstrated. This fortuity is used to examine the behaviour of bicrystals under shock loading. It is shown that the difference in shock speed, together with the difference in response of the two crystal orientations leads to an interaction which modifies the behaviour from that observed in single crystal simulations. Further use is made of the ability of modern simulation methods to recreate salient features of dynamic processes to examine the behaviour of metallic substrates under high–speed impact from nanometer sized particles. Here the plasticity of the substrate is shown to be vital to ensuring that the simulation results are faithful to experiment, and hence to space science work. In order to capture this behavioour correctly, issues of substrate size and boundary behaviour are seen to be key.