An extended multi-linear cohesive zone model for mixed-mode I/II delamination growth simulation in composite laminates with R-curve effects

In this paper, the multi-linear cohesive zone model has been extended to simulate the mixed-mode I/II delamination growth in composite laminates. In the extended multi-linear cohesive zone model, inclined spring elements have been used to consider the fracture process zone effects so that when the crack starts to grow, the spring stiffness changes based on the material’s traction–separation curve with any arbitrary shape of softening law. To apply mode II loading in addition to mode I, the angle of spring elements in each desired mixed-mode ratio has been calculated using analytical equations and applied in the finite element model. The simulation results as load–displacement curves at different mixed-mode ratios are compared with the available experimental results to investigate the validity and accuracy of the newly proposed model. The maximum load values in three different mixed-mode ratios have been well predicted with an average error of less than 6%. After that, the applicability of the extended multi-linear cohesive zone model is evaluated to estimate the mixed-mode I/II delamination R-curve behavior and an analytical relation for the R-curve is presented based on the spring elements’ energy. A good agreement has been obtained between the R-curves extracted by the new model and the available experimental R-curves. The results show that the extended multi-linear cohesive zone model in combination with the proposed analytical R-curve can accurately predict the mixed-mode I/II delamination growth in composite laminates by considering the effects of the fracture process zone.