Rupture crack branching in solids with structural hierarchy

Abstract

Both growth and branching of sharp cracks in perfect single crystals are studied. Strength and deformation criteria of sharp crack branching are proposed. These criteria describe brittle, quasi-brittle, and ductile material behavior under fracture propagation. For inner cracks, simple relations have been obtained that describe crack branching when curves of Kolumb-Mohr type theoretical strength for the generalized deformation mode are known. Multiple crack branching, associated with a multiplicity of eigenvalues when the system is buckled, is discussed. It has been ascertained that the principle of local symmetry in the vicinity of a crack tip is valid for perfect single crystals if the symmetry axis of a crystal is in line with the crack axis. When asymmetric perturbations of an atomic lattice occur in the vicinity of a crack tip or the symmetry axis of a single crystal is inconsistent with the crack axis, the principle of local symmetry fails. Solids with a hierarchy of regular structures that are typical for Macro-, Micro- and Nano-scales are studied in the same way. The curves of theoretical strength (Kolumb-Mohr type) of every structural level of material are considered to be known for the generalized stress state.