Dynamic localized shear failure influenced by changing rates in brittle solids containing initial microcracks

Abstract

Dynamic microcracks growth has a great influence on macroscopic dynamic mechanical properties under impact loadings in brittle solids containing numerous initial microcracks. Confining pressure plays an important part in shear failure along with shear bands in brittle solids. However, the theoretical micro-macro relationship between shear failure and microcracks growth subjected to impact loadings is rarely proposed. Furthermore, evaluations of changing rates-dependent dynamic mechanical properties have a great meaning for engineering applications. In this study, a micro-macro dynamic localized shear failure model is proposed to explain the effects of changing rates on stress-deformation constitutive curves. A dramatic dynamic failure criterion is proposed by calculating zero crack velocity (ZCV) under constant strain rate during continuous deformation. The formulation of this micro-macro model is based on Ashby and Sammis's crack model, dynamic crack fracture propagation toughness law, a suggested physical correlation of the microcrack and deformation rates, and a deformation path function of changing rates. This suggested rate correlation of microcrack and deformation explains a unified correspondence of crack velocity, axial strain rate and shear velocity with increasing crack length, axial strain and shear displacement, which is established by unifying crack damage and deformation damage. The deformation path function of changing rates describes the step variation of crack velocity, strain rate and shear velocity with ascending crack length, axial strain, and shear displacement, respectively. Effects of parameters in this path function of changing rates on axial stress-crack curve, axial stress-strain, and shear stress-displacement curve are discussed. Rationality of the proposed model is verified by comparing with the published results. The theoretical results will provide an important help for evaluating the mechanical behaviors of applied brittle solids materials in engineering.