Effect of T-Stresses on Kinking and Branching of the Crack Path

The direction of propagation of a straight-line plane crack in structurally inhomogeneous (grainy) materials under the combined effect of loading corresponding to fracture modes I and II is studied. The theoretical curve of the material strength or the Coulomb–Mohr curve type is assumed to be known. Based on the Neuber–Novozhilov force (integral) criterion relations are derived, which allow one to determine the angles of kinking (branching) of the crack path in the case of an arbitrary generalized stress state. Asymptotic presentations of the stress components in the vicinity of the crack tip take into account nonsingular terms (\(T\)-stresses). It is found that the crack can develop: 1) normal to the maximum stress direction if there are no shear stresses near the crack tip (Erdogan–Sih hypothesis) in the case of brittle fracture; 2) along the maximum shear direction if there are no normal stresses near the crack tip in the case of viscous fracture (in this case, a dislocation is emitted); 3) along a certain direction corresponding to a mixed stress state in the case of quasi-brittle or quasi-viscous fracture. The crack propagation direction depends on the ratio of the stress intensity factors for fracture modes I and II, sign of \(T\)-stresses, and shape of the theoretical curve of strength on the plane of the critical states.