Analysis of cohesive failure in adhesively bonded joints with the SSPH meshless method

Adhesives have become the method of choice for many structural joining applications. Therefore, there is a need for improved understanding of adhesive joint performance, especially their failure, under a variety of loading conditions. Various numerical methods have been proposed to predict the failure of adhesive bonded material systems. These methods generally use a cohesive zone model (CZM) to analyze crack initiation and failure loci. The CZM incorporates a traction–separation law which relates the jump in surface tractions with the jump in displacements of abutting nodes of the cohesive segment; the area under the curve relating these jumps equals the energy release rate which is determined from experimental data. Values of parameters in the CZM are usually obtained through the comparison of results of numerical simulations with the experimental data for pure mode I and mode II deformations. Here a numerical approach to simulate crack initiation and propagation has been developed by implementing CZM in the meshless method using the symmetric smoothed particle hydrodynamics (SSPH) basis functions, and using the design of experiments technique to find optimal values of CZM parameters for mode I failure. Unlike in the finite element method where a crack generally follows a path between element boundaries, in the meshless method a crack can follow the path dictated by the physics of the problem. The numerical technique has been used to study the initiation and propagation of a crack in a double cantilever beam under mode I and mixed mode in-plane loadings. Computed results are found to agree well with the corresponding experimental findings. Significant contributions of the work include the determination of optimum values of CZM parameters, and simulating mode I, mode II and mixed mode failures using a meshless method with the SSPH basis functions.