An evaluation of mode-decomposed energy release rates for arbitrarily shaped delamination fronts using cohesive elements

Computing mode-decomposed energy release rates in arbitrarily shaped delaminations involving large fracture process zones has not been previously investigated. The J-integral is a suitable method for calculating this, because its domain-independence can be employed to reduce the integration domain to a cohesive interface, and reduce it to a line integral. However, the existing formulations for the evaluation of the mode-decomposed J-integrals rely on the assumption of negligible fracture process zones. In this work, a method for the computation of the mode-decomposed J-integrals in three-dimensional problems involving large fracture process zones and using the cohesive zone model approach is presented. The formulation is applicable to curved fronts with non-planar crack faces. A growth driving direction criterion, which takes into account the loading state at each point, is used to render the integration paths and to decompose the J-integral into loading modes. This results in curved and non-planar integration paths crossing the cohesive zone. Furthermore, its implementation into the finite element framework is also addressed. The formulation is validated against virtual crack closure technique (VCCT) and linear elastic fracture mechanics (LEFM)-based analytical solutions and the significance and generality of the formulation are demonstrated with crack propagation in a three-dimensional composite structure.