On the propagation of elastic-viscoplastic waves in damage-softened polycrystalline materials

Abstract

Abstract Theories for uniaxial wave propagation as, for example, along the longitudinal axis of slender rods composed of materials that behave elastically or plastically with hardening, encounter difficulty when confronted with softening material. For such theories, onset of softening causes the value of the wave speed to become complex thereby transforming the governing partial differential equations from hyperbolic to elliptic, implying no further possibility for wave-like motion in the softened material. The purpose of this paper is to show how an elastic-viscoplastic-damage type of constitutive theory together with the equation of motion produce a system of governing partial differential equations that can be shown to be hyperbolic. As an outgrowth of the calculation for the characteristics of the system, an expression relating the elastic dilatational wave speed with material damage and softening can be derived, demonstrating positive value for all phases of the material deformation including material softening that terminates in fracture. The paper also shows how experimental data from plate impact spall fracture tests can illustrate the reality of wave motion through damage-softened polycrystalline material.