Combined analysis of fracture under stresses acting along cracks

Abstract

A joint approach to the study of two non-classical fracture mechanisms, namely fracture of cracked materials with initial (residual) stresses acting along the crack planes and fracture under compression along parallel cracks, is considered in the framework of three-dimensional linearized solid mechanics. Mathematical statements of problems for pre-stressed solids that contain interacting circular cracks are given. Problems for an infinite solid containing two parallel co-axial cracks and for a space with the periodical set of co-axial parallel cracks as well as for a half-space with near-the-surface crack are solved. Several patterns of loading on the crack faces (normal loading, radial shear and torsion) are considered. The effects of initial stresses on stress intensity factors are analyzed for highly elastic materials with some types of elastic potentials. Formulation of fracture criteria accounting effect of initial (residual) stresses is given. Critical parameters of fracture of solids containing interacting cracks under compression along the cracks are calculated. The influence of geometrical parameters of the problems as well as physical and mechanical properties of materials on these critical parameters is analyzed.