Fracture, failure, and fragmentation

A general approach is required for describing matter of behavior when the failure is likely to involve growth and coalescence of a large number of fractures. Failures of this kind appear frequently in rapid dynamic processes, particularly in the formation of spall fragments. An approach to formulating constitutive relations that accounts for the opening, shear and growth of an ensemble of cracks is discussed. The approach accounts for plastic flow accompanying fragmentation. The resulting constitutive relations were incorporated into a Lagrangian computer program. A theoretical approach to coalescence is described. The simplest formulation uses a linear Liouville equation, with crack growth limited by the mean free path of cracks, assumed constant. This approach allows for an anisotropic distribution of cracks. An alternative approach in which the decrease of the mean free path with increasing crack size is accounted for, but the crack distribution is assumed isotropic is described. A reduction of the governing Liouville equation to an ordinary differential equation of third order is possible, and the result can be used to determine how mean free path decreases with increasing crack size.