ON THE PROPAGATION OF ELASTIC-VISCOPLASTIC WAVES IN DAMAGE-SOFTENED POLYCRYSTALLINE MATERIALS

Theories for uniaxial wave propagation as, for example, along the long itudinal axis of slender rods composed of materials that behave elasti cally or plastically with hardening, encounter difficulty when confron ted with softening material. For such theories, onset of softening cau ses the value of the wave speed to become complex thereby transforming the governing partial differential equations from hyperbolic to ellip tic, implying no further possibility for wave-like motion in the softe ned material. The purpose of this paper is to show how an elastic-visc oplastic-damage type of constitutive theory together with the equation of motion produce a system of governing partial differential equation s that can be shown to be hyperbolic. As an outgrowth of the calculati on for the characteristics of the system, an expression relating the e lastic dilatational wave speed with material damage and softening can be derived, demonstrating positive value for all phases of the materia l deformation including material softening that terminates in fracture . The paper also shows how experimental data from plate impact spall f racture tests can illustrate the reality of wave motion through damage -softened polycrystalline material. Copyright (C) 1996 Elsevier Scienc e Ltd