Abstract
The shock response of metallic single crystals can be captured using a micro-mechanical description of the thermoelastic–viscoplastic material response; however, using a such a description within the context of traditional numerical methods may introduce a physical artifacts. Advantages and disadvantages of complex material descriptions, in particular the viscoplastic response, must be framed within approximations introduced by numerical methods. Three methods of modeling the shock response of metallic single crystals are summarized: finite difference simulations, steady wave simulations, and algebraic solutions of the Rankine–Hugoniot jump conditions. For the former two numerical techniques, a dislocation density based framework describes the rate- and temperature-dependent shear strength on each slip system. For the latter analytical technique, a simple (two-parameter) rate- and temperature-independent linear hardening description is necessarily invoked to enable simultaneous solution of the governing equations. For all models, the same nonlinear thermoelastic energy potential incorporating elastic constants of up to order 3 is applied. Solutions are compared for plate impact of highly symmetric orientations (all three methods) and low symmetry orientations (numerical methods only) of aluminum single crystals shocked to 5 GPa (weak shock regime) and 25 GPa (overdriven regime). For weak shocks, results of the two numerical methods are very similar, regardless of crystallographic orientation. For strong shocks, artificial viscosity affects the finite difference solution, and effects of transverse waves for the lower symmetry orientations not captured by the steady wave method become important. The analytical solution, which can only be applied to highly symmetric orientations, provides reasonable accuracy with regards to prediction of most variables in the final shocked state but, by construction, does not provide insight into the shock structure afforded by the numerical methods.
Highlights
An understanding of the thermomechanical response of metallic crystals at high strain rates and high pressures is important for research and development of technologies involving impact, as occurring in crashworthiness applications and ballistic collisions, Lloyd et al Adv
Because the steady wave (SW) method approximates strain as uniaxial, it is expected to give highly accurate solutions for impact problems wherein the target is shocked along a direction that possesses twofold or greater rotational symmetry, and give approximate solutions for problems of lower symmetry
The finite difference (FD) method is able to model weak shock loading problems without an artificial viscosity given a mesh resolution that can sufficiently resolve the shock width; in the strong shock regime viscous regularization is used to damp the large jump in velocity that precedes plastic deformation [6]
Summary
Three methods of modeling the shock response of metallic single crystals are summarized: finite difference simulations, steady wave simulations, and algebraic solutions of the Rankine–Hugoniot jump conditions. For the former two numerical techniques, a dislocation density based framework describes the rate- and temperature-dependent shear strength on each slip system. For the latter analytical technique, a simple (two-parameter) rate- and temperature-independent linear hardening description is necessarily invoked to enable simultaneous solution of the governing equations. The same nonlinear thermoelastic energy potential incorporating elastic constants of up to order 3 is applied
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