THE PLASTIC GROWTH OF A CAVITY NUCLEATED AT A SHEAR-BAND

In this paper, the dynamic expansion of a spherical cavity nucleated at a shear band is theoretically investigated. To this end, the voided solid is represented in the vicinity of the band by a model consisting of a rigid-plastic thick hollow sphere which experiences an expansion characterized by a radial velocity field with spherical symmetry plus an additional pure shear distortional field representing localized shear deformation within a thickness 2h. The selected shear strain rate field enables us to cope with localized deformation within a band of arbitrary thickness, oriented parallel to the direction of the imposed macroscopic shear strain. Expressions for the macroscopic deviatoric and volumetric stresses required to deform the material with voids located at shear bands were then computed. Furthermore, the dynamic void growth equation was also derived. The formulation was applied to the dynamic fracture of a thermal softening material in discrete steps, and the influence of the model parameters on the fracture strength of the material was assessed.