Finite amplitude plastic shock wave treated with summed infinitesimal amplitude elastic-plastic waves through dislocation dynamics

Abstract

In the high strain rate region of a finite amplitude plastic shock wave constitutive equations need to be strongly history dependent and thus are difficult to use in the description of plastic deformation because the deformation is dominated by a dislocation dynamics which is far removed from quasi-equilibrium conditions. The Johnston-Cilman (1969) theory of the upper and lower yield point is the prototype of an analysis of a type of plastic flow that is more meaningfully described through dislocation dynamics than by setting up some sort of constitutive eqution which does not fully incorporate internal variables. In this paper it is shown that a finite amplitude elastic-plastic wave can be treated as a sum of infinitesimal amplitude elastic-plastic waves in which the plastic deformation rate is effectively linearized through a varying parameter η which is a measure of the relative strengths of the elastic and plastic strain rates. The waves treated are planar and the sum of their transverse elastic and plastic strains is always null. Dislocation dynamics determines the value of the η parameter. The plastic waves treated are of moderate amplitude (stress/bulk modulus small compared to 1).