On the calibration of the cohesive strength for cohesive zone models in finite element analyses

•Fracture in FEA computed using local CZM depends on cohesive strength.•LEFM provides analytical solution, independent of cohesive strength.•Cohesive strength calibration fits FEA to LEFM on macroscale even for coarse meshes.•Calibrated setting depends on element size, geometry and material parameters.•Qualification of coarse meshed models possible via calibration. Cohesive zone models are commonly used to numerically model fracture phenomena on the microscale. Typical fracture processes are described experimentally via the Double Cantilever Beam (DCB) test and the End Notched Flexure (ENF) test on the macroscale. Analytical solutions, e.g. the LEFM-based beam theory, are used to evaluate these tests and to validate numerical models. However, some input parameters of cohesive zone models, i.e. cohesive stiffness and cohesive strength, are independent of the analytical solutions. In particular, the cohesive strength has a significant effect on the accuracy of the numerical model compared to the analytical solution and thus needs to be calibrated. This work extends the available literature by fitting the numerical to the analytical solution of the DCB and ENF models through calibration of their cohesive strength by using more suitable and generally applicable criteria. It considers the deformation, the applied load and the crack length of the models. The latter has been neglected so far in the existing literature. Via a parametric study, the derived criteria are minimised to find the best fit to the analytical solution. In addition, the effect of all input parameters and of the numerical element size on the calibrated cohesive strength is investigated. The obtained information can be used to qualify numerical models with coarse meshes to accurately compute the fracture of DCB and ENF models. Further, it provides a comprehensive understanding of the cohesive strength as a modelling parameter.