Concept of ultimate fracture velocity in the analysis of spherical cavity expansion in brittle materials: Application to penetration problems

A new model of dynamic spherical cavity expansion with constant velocity in a brittle material has been developed on the basis of the hypothesis of an ultimate fracture front velocity proposed by Nikolayevskii. With the use o f this model, the Alekseevskii-Tate model is modified for long-rod penetrat ion into brittle materials. The ultimate fracture front velocities relative to the material moving before this front are considered as a physical char acteristic specific to every material and fracture mode. Therefore, fractur e front velocities (as well as crack propagation velocities) relative to un perturbed material depend on the cavity expansion velocity and can exceed t he Rayleigh wave velocity. Unlike the models based on the hypothesis of an ultimate fracture stress, this proposed model explains the possibility of s hort term "dynamic overloads" of the material: tensile in elastic precursor and shearing in the cracked material zone. (C) 1999 Elsevier Science Ltd. All rights reserved.