Solving Some Problems of Crack Mechanics for a Normal Edge Crack in Orthotropic Solid Within the Cohesive Zone Model Approach

A problem of an edge crack with a fracture process zone in semi-infinite orthotropic planes under the pure- and mixed-mode loading (I and II modes) was studied. A cohesive zone with different cohesive lengths in opening and sliding modes (multiple cohesive zone) was used to simulate the fracture process zone. The smooth crack closure condition defines cohesive lengths of the two fracture modes. The problem of an edge crack that is normal to the plate edge was formulated in terms of integral equations for the unknown displacement discontinuity along the crack. A collocation method applied to two singular integral equations with Cauchy kernel gave the equations for critical loads and respective discrete cohesive tractions and separations. These equations are non-linear since a dependence of cohesive tractions on crack opening was taken according to potential-based traction–separation law. An iterative procedure was used to satisfy the condition of smooth crack closure. A generalization of the potential, well-known in the literature, was used to generate the cohesive traction field. The potential combines pure-mode laws without mode-mixity parameters. Two types of generalized potential functions were considered, and a critical analysis was carried out. Numerical solutions were presented for the cohesive tractions and separations in critical state when both pure-mode cohesive laws were trapezoidal shaped. Comparison of the fracture loci obtained for two types of generalized potentials allowed us to conclude that the type strongly influences the critical state parameters.