Application of the complex cohesive zone model to the edge mi xed-mode crack problem for orthotropic media - Selivanov, M.F.; Chornoivan, Y.O. (Reports of the National Academy of Sciences of Ukraine, 2019)
The elasticity problem for a semiinfinite orthotropic body with an edge crack that is normal to the boundary is studied. The crack is aligned with one of the orthotropic material axes, and a biaxial stress field is applied at infinity. The multiple cohesive zone model developed to study the mixed-mode fracture is used to determine the critical stress parameters, as well as the cohesive stress field. The difference of mode I and mode II cohesive lengths is inherent to the model. The problem is formulated in terms of integral equations for the unknown displacement discontinuity along the crack line. The collocation method, which is applied to two singular integral equations with generalized Cauchy kernel, gives the equations for critical loads and respective discrete cohesive tractions and separations. These equations are non-linear, as a dependence of cohesive stresses on the crack opening is taken according to the potential-based traction—separation law. An algorithm for determining the parameters of limiting equilibrium of a mixed-mode crack is constructed. An iterative procedure is used to enforce the smooth crack closure for the two pure fracture modes, and two cohesive lengths can be determined with the precision of a mesh size. An example of calculating the critical state parameters and the corresponding cohesive stress field is given. The numerical example is built for the traction–separation law based on the trapezoidal laws of pure modes that are coupled without parameters of mode-mixity.