Solving the problem on the subcritical state of an edge crack within the cohesive zone model approach




edge crack, cohesive zone model, integral equation with generalized Cauchy kernel, smooth crack closure, sucritical state of a crack


The problem of the subcritical state of a mode I crack in a semiinfinite isotropic plate is considered. The solution is obtained within the cohesive zone model approach based on the non-uniform dependence of the cohesive traction on the separation of the fictitious crack faces. This zone simulates the failure zone that appears near the crack front. The solving procedure uses a regularized singular equation with a generalized Cauchy kernel, which is solved by the collocation method. The introduction of the interval of growth in the traction-separation law ensures a smooth crack closure. A numerical example is illustrated for the smoothed trapezoidal law. The absence of oscillations of the solution is shown, and the appearance of a singularity due to the discontinuity of the boundary conditions on the contour of the fictitious crack in the case of the study of the subcritical state is shown. The difference between the solutions of the first- and second-kind equations for small cohesive lengths is indicated.


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How to Cite

Selivanov, M., & Protsan, V. (2022). Solving the problem on the subcritical state of an edge crack within the cohesive zone model approach. Reports of the National Academy of Sciences of Ukraine, (1), 39–47.