Attenuation of the Dynamic Yield Point of Shocked Aluminum Using Elastodynamic Simulations of Dislocation Dynamics

Abstract

When a metal is subjected to extremely rapid compression, a shock wave is launched that generates dislocations as it propagates. The shock wave evolves into a characteristic two-wave structure, with an elastic wave preceding a plastic front. It has been known for more than six decades that the amplitude of the elastic wave decays the further it travels into the metal: this is known as "the decay of the elastic precursor". The amplitude of the elastic precursor is a dynamic yield point because it marks the transition from elastic to plastic behaviour. In this letter we provide a full explanation of this attenuation using the first method of dislocation dynamics to treat the time dependence of the elastic fields of dislocations explicitly. We show that the decay of the elastic precursor is a result of the interference of the elastic shock wave with elastic waves emanating from dislocations nucleated in the shock front. Our simulations reproduce quantitatively recent experiments on the decay of the elastic precursor in aluminum, and its dependence on strain rate.The dynamic behaviour of crystalline solids subjected to shock compression plays a central role in diverse applications, including bird strikes in aerospace [1], crashworthiness in the automobile industry [2], and manufacturing processes such as laser shock peening [3], amongst many others. Upon being shocked within a range of strain rates and pressures of typically 10 6 − 10 10 s −1 and 5 − 50GPa [1], the shock front in crystalline materials often displays a characteristic two-wave structure near the loading surface: the plastic wave front leading to the Hugoniot shocked state is preceded by an elastic precursor wave [1]. The amplitude of the elastic precursor wave decays as the wave front advances[1, 4]-a phenomenon known as the 'decay of the elastic precursor'. The amplitude of the elastic wave marks the onset of plasticity, i.e. it is the dynamic yield point. The subsequent plastic wave is commonly ascribed to the generation and motion of dislocations, the agents of plasticity in crystalline solids [9].The cause of its attenuation remains unclear after six decades [4][5][6][7][8]. Clifton and Markenscoff [4] calculated analytically the amplitude attenuation of a planar elastic shock wave caused by the destructive interference of elastic wavelets emanating from pre-existing dislocations set into motion by the passage of a shock wave of infinite strain rate; dislocation generation by the shock was neglected. Consequently, the elastic precursor decay was attributed to the density and initial velocity of pre-existing dislocations. Armstrong et al.[10] studied the dislocation relaxation mechanisms during high strain rate shock loading, concluding that dislocation generation dominates plastic relaxation under shock loading. This is because the number of pre-existing dislocations is about two to three orders of magnitude less than that generated during the shock [1,4,7].In this letter we show that we can account for the experimentally observed residual disloca...

Analysis of nonlinear elastic aspects of precursor attenuation in shock-compressed metallic crystals

“…This numerical work improves existing (quasi-static) discrete dislocation plasticity simulations wherein spurious dislocations can appear ahead of a shock wave front because stress fields are transmitted instantaneously, violating the causality principle. Application of the method to a study of precursor decay in aluminum [26] demonstrated reasonable agreement of stress relaxation in shock fronts at various strain rates, considering only effects of nucleation of new dislocations (i.e., no pre-existing defects) in a linear elastic medium. It was noted how cumulative effects of shielding dislocations exceed those of anti-shielding dislocations, and defect morphologies reminiscent of Smith-Hornbogen interfaces [29][30][31][32] were predicted by the simulations.…”

“…Given a constitutive model for the stress dependence of dislocation velocity υ D , values of initial dislocation density, b, and θ, and linear elastic properties G=G 0 , c l =c l0 , the differential equation (2.9) [or even more simply (2.7) with (2.8)] can be integrated numerically to predict precursor decay, i.e., stress P at the front versus time t or propagation distance X. The recent numerical study of [26] invokes dynamic discrete dislocation mechanics and analytical expressions from [16,22,24,43] to compute effects of injected and subsequently moving and interacting dislocations, with potentially complex morphologies, on precursor decay.…”

“…Both [16] and [26] omit the possible contributions of hydrodynamic attenuation and effects of dislocation nucleation, motion, and interactions occurring at a finite distance behind the precursor front since all stress waves are assumed to propagate at the linear elastic sound speeds of the undeformed medium. The longitudinal speed c l0 is equal to U in the linear approximation invoked in such studies, so trailing rarefaction waves never reach the shock front and thus cannot contribute to its decay.…”

“…Recent work [24][25][26][27][28] has extended the elastodynamic analyses of Markenscoff and Clifton [16,22] to consider injection and subsequent non-uniform motion of edge dislocations. This numerical work improves existing (quasi-static) discrete dislocation plasticity simulations wherein spurious dislocations can appear ahead of a shock wave front because stress fields are transmitted instantaneously, violating the causality principle.…”

An atomistic study of the effect of micro-structure on the HEL evolution in a nanocrystalline aluminum

“…It is the material yield stress under compression and is also called the elastic shock precursor. Several researchers studied the precursor decay phenomenon in a variety of metallic materials using experiments [1,2] and the molecular dynamics approach [3,4]. Its decay along the shock direction is linked to the evolution of defects such as interfaces, stacking faults, dislocations, twins, vacancies, and interstitials in the shock fronts and to the rise of plasticity in materials.…”