Efficient derivation of a nonlinear cohesive bridging law for numerical delamination simulations under static and fatigue loading

Delamination is a frequent and critical type of damage that occurs in composite structures under static and fatigue loading. This work presents a novel method to derive a nonlinear traction–separation law (TSL) for a cohesive zone model (CZM) used for delamination simulations. By solving an ordinary differential equation (ODE) resulting from the energy balance of the cohesive zone, a nonlinear TSL is directly derived from R-curves that were determined experimentally in standard quasi-static double cantilever beam (DCB) tests. A superimposed conventional bilinear TSL is required to match the initial energy release rate of the R-curves. This bilinear TSL is intended to model brittle fracture while the nonlinear part models the R-curve effects mainly caused by fiber bridging. In order to consider R-curve effects under fatigue loading conditions as well, an established fatigue CZM is embedded into both parts of the TSL using the same set of four required input parameters. The fatigue parameters are determined inversely by means of cyclic DCB tests. It is demonstrated that the numerical model is able to reproduce the force–displacement curves of the conducted quasi-static DCB tests with a higher accuracy, if the TSL is derived by the new method instead of the preexisting and commonly used J-integral approach. Furthermore, the model is able to reproduce experimental data from conducted cyclic DCB test with a limited number of input parameters which significantly decreases the effort of inverse parameter identification.