The spall strength of condensed matter

Abstract

Two conditions are proposed which place constraints on the processes of dynamic spall in condensed media, and determine inequalities which bound the spall strength, fragment size, and failure time. Spall is defined as rupture within a body due to stress states in excess of the tensile strength of the material. The first is a horizon condition which establishes a domain of communication, consistent with the time to failure, within which spall must be independent of the surrounding environment. The second is an energy condition which requires that the potential and kinetic energy associated with the tensile loading process exceed the fracture energy of the material. Equality in the relations established from these conditions corresponds to energy-limited spall and provides specific analytic expressions for the spall properties. Inequality implies flaw-limited spall and requires more detailed material property information before spall can be characterized. Energy-limited spall is determined by the material fracture toughness in brittle solids and the material flow stress in ductile solids. Calculated spall properties, assuming energy-limited spall, compare well with experimental spall data for various materials. Under certain conditions, a transition from brittle to ductile spall (definition in text) with increasing strain rate is predicted. Comparison is made with spall data on 6061-T6 aluminum for which a brittle-to-ductile transition is predicted to occur at a critical strain rate of approximately 4 × 10 5 s −1. Energy-limited spall in liquids within their range of Newtonian fluid behavior is governed by surface energy and viscosity. Spall is predicted to be dominated by surface energy at low strain rates and viscous dissipation at high rates. Examples of each appear to exist within the scant experimental spall data available for liquids.