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.
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