Progressive Damage of a Spalling Rod

Abstract

A phenomenological theory describing the process of gradual damage of brittle rods leading to their ultimate rupture is developed and applied to the problem of spatial and temporal evolution of damage in a free-free rod subjected to a pressure pulse at one of its ends. As a result of nucleation, growth and coalescence of voids, de-cohesions and dislocations, irreversible structural changes occur in a polycrystalline material subjected to certain types of loading. A special internal variable is introduced to characterize the gradual loss of mechanical strength or stiffness. A system of quasi-linear partial differential equations describing the problem is solved numerically using the method of characteristics. Numerical results of damage evolution, energy dissipation, etc. are presented and discussed.