Abstract
We present a mathematical model for elastoplasticity in the regime where the applied stress greatly exceeds the yield stress. This scenario is typically found in violent impact testing, where millimetre thick metal samples are subjected to pressures on the order of 10–102GPa, while the yield stress can be as low as 10−2GPa. In such regimes the metal can be treated as a barotropic compressible fluid in which the strength, measured by the ratio of the yield stress to the applied stress, is negligible to lowest order. Our approach is to exploit the smallness of this ratio by treating the effects of strength as a small perturbation to a leading order barotropic model. We find that for uniaxial deformations, these additional effects give rise to features in the response of the material which differ significantly from the predictions of barotropic flow.
Highlights
Most simulations of the mechanical response of a metal undergoing violent elastic–plastic deformation rely on knowledge of the equation of state (EoS) for the material under study
We have developed a one-dimensional model for elastoplasticity in the regime where the applied stress greatly exceeds the yield stress
Our model is valid in the absence of shocks, and this is important as isentropic compression experiments (ICEs) are designed in such a way that shock formation occurs outwith the lifetime of the experiment
Summary
Most simulations of the mechanical response of a metal undergoing violent elastic–plastic deformation rely on knowledge of the equation of state (EoS) for the material under study. Violent impact experiments reported by numerous authors have confirmed the existence of both elastic and plastic waves (Meyers, 1994; Clifton, 1985; Pack et al, 1948; Von Karman and Duwez, 1950; Whitley et al, 2011) The former propagate through the material as the stress increases toward the yield stress, and the latter as the material is compressed further beyond the yield surface. At realistic macroscopic length-scales, it is not feasible to track the motion of individual dislocations, and instead one must construct a continuum model that describes bulk elastoplastic deformation in an averaged way Many such models aim to encapsulate a broad range of phenomena by fitting parameters in the constitutive assumptions of the model. We show that the inclusion of elastic effects gives rise to significant distinctive features in the material response which cannot be resolved by barotropic flow alone
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