An Incremental Cohesive Law for Delamination Under a Mixed Mode Loading - Zhu, Man; Gorbatikh, Larissa; Lomov, Stepan V. (Frontiers in Materials, 2020)
Cohesive zone models rely on the formulation of a cohesive constitutive law. The latter describes the relation between displacement and traction in a cohesive element at an integration point. Cohesive constitutive laws in the presence of opening and shearing modes are less studied in comparison with those formulated for a single mode, particularly when the mode mixity changes. The mode mixity at an integration point is determined by the load history at the point. In this study, a formulation of the cohesive constitutive law is proposed for a mixed mode loading condition with the ability to deal with the variation in mode mixity. The proposed law is constructed incrementally and takes into account the load history. The validation is performed by simulating delamination in carbon fibre/epoxy composites in the mixed-mode bending test that is commonly used to characterize the inter-laminar fracture toughness. Although the mode mixity is fixed in this test at the specimen level, it varies locally at the element level. Cohesive constitutive laws proposed in the literature predict macroscopic delamination behaviour that is dependent on the strength of the interface, while, according to the analysis of linear elastic fracture mechanics, the dependence is expected to be only on the fracture toughness. Predictions with the current formulation, where the cohesive law is updated incrementally, show low sensitivity to the interface strength. The structural response simulated with it had a good agreement with the analytical solution of linear elastic fracture mechanics.