Plasticity in Shock Compression

Much of what we currently understand about the micromechanics of shock-induced plastic flow comes from macroscale measurement of wave profiles (sometimes) combined with pre- and post-shock microscopic investigation. This combination obviously results in nonuniqueness of interpretation. By this we mean that more than one micromechanical model can be consistent with all observations. In spite of these shortcomings, wave profile measurements can tell us much about the underlying micromechanics, and we describe here the relationship between the mesoscale and macroscale. 

In the following development we consider a plane wave of infinite lateral extent traveling in the positive Xj direction (the wave front itself lies in the Xj, Xj plane). When discussing anisotropic materials we restrict discussion to those propagation directions which produce longitudinal particle motion only i.e., if u is the particle velocity, then Uj = Uj = 0. The 100 , 110 , and 111 direction in cubic crystals have this property, for example. The derivations presented here are heuristic with emphasis on the essential qualitative features of plastic flow. References are provided for those interested in proper quantitative features of crystal anisotropy and nonlinear thermoelasticity. 

The total strain rate in the material is assumed to be the sum of elastic and plastic contributions 

The entropy production terms in (7.4) and (7.5) come from plastic deforma-tional heating. Following Wallace [15] 

If the maximum resolved shear stress r and the plastic shear strain rate y are defined according to (it is assumed that the Xj and Xj directions are equivalent) 

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