A semi-analytic method for crack kinking analysis at isotropic bi-material interfaces

Interface delamination is a key failure mechanism in numerous applications. Microscopic analysis illustrates that macroscopic delamination may contain both adhesive and cohesive cracking. As a result, the fracture pattern at this microscopic scale is inherently dependent not only on the adhesive interface properties but also on the cohesive properties of the bulk materials surrounding the interface. For this reason, this paper focuses on the competition between adhesive and cohesive crack propagation of an initial interface crack. A computationally efficient semi-analytic approach is presented to predict this competition. First, crack kinking theory is thoroughly reviewed explaining the use of solution coefficients to relate the energy release rate (ERR) of an interface crack and a kinking crack. It is found that the tabulated values of the imaginary part of the solution coefficients given for negative Dundurs’ parameters in [1] should be of opposite sign. Also, solution coefficients are calculated in a finite element (FE) framework based on previous work by Jakobsen et al. (2008) [2]. This method is validated by applying it to different geometries and loading conditions. In addition, the method is generalized for any arbitrary material combination by providing solution coefficients through Response Surface Modeling (RSM). This enables the semi-analytic approach, i.e. the analytic calculation of energy release rates for kinking cracks at interfaces solely based on the FE results for the interface crack itself. The accuracy of this method is validated by comparison to detailed FE simulations. Finally the relative size effect of the sample dimensions is scrutinized.