Mode I fracture in adhesively-bonded joints: A mesh-size independent modelling approach using cohesive elements

Abstract

In recent years cohesive elements, coupled with a finite-element analysis (FEA) approach, have become increasingly popular for simulating both delamination in composite materials and fracture in adhesively-bonded joints. However, the industrial application of Cohesive Zone Models to model large and complex structures has been hindered by the requirement of extremely fine meshes along the crack propagation path. In the present work two-dimensional linear and quadratic (i.e. second-order) cohesive elements to model crack initiation and growth have been implemented in Abaqus using a user subroutine. These elements, which have a modified topology that allows a user-defined number of integration points, have been employed to model the fracture response of various mode I test specimens consisting of metallic substrates bonded with a structural film-adhesive. The effects of the mesh-density, element order and number of integration points on the numerical solution have been investigated. Whilst the linear models have shown the typical mesh-size dependent behaviour, the results obtained with their quadratic counterparts have been found to be independent of the element size. Furthermore, it is shown that increasing the number of integration points improves the stability, convergence and smoothness of the solutions. The mesh-size independent response obtained with the quadratic models arises from more accurate simulation of the deformed profile of the substrates and a more accurate calculation of the energy dissipated in the process zone due to damage. Overall, it is demonstrated that the quadratic cohesive-element formulation enables the use of much coarser meshes, resulting in shorter simulation times, and will therefore allow an increase in the industrial application of Cohesive Zone Models.