Prefracture zones in quasibrittle materials with branched and kinked cracks

The paper is concerned with regularly structured solids. A two-stage solution is proposed for the nonlinear problem of fracture mechanics where branching or kinking of an initial mixed-mode crack is possible. First, the kink and branch angles are found, and then the critical fracture parameters for chosen directions are determined; in so doing, necessary and sufficient fracture criteria of the Neuber-Novozhilov type are used respectively. The critical fracture parameters (the lengths of prefracture and loads) are found with a modified version of the classical Leonov-Panasyuk-Dugdale model for prefracture zones confined in rectangles along crack branches. Simple expressions for the critical fracture parameters are derived using stress intensity factors for cracks with infinitesimal branches and for those with a branch on which normal and shear stress simulative of the plastic zone are specified. The stress intensity factors for a branched crack are obtained from solving the problem of uniaxial tension of a plate with a double-symmetric crack branch by the finite-element method. The stress intensity factors are calculated for mode I and II cracks in relation to the branch angle.