Adhesive joint computations using cohesive zones

Abstract

Background: The cohesive zone approach has gained increasing success in recent years for simulating debonding and fracture via finite element methods and is ideally suited for simulating adhesive joints, the potential crack paths being generally known in advance in most cases. In the paper the determination of the size of the so-called cohesive process zone is discussed, i.e. the region wherein the stress and damage state have to be correctly resolved in order to properly quantify the dissipated energy and the load bearing capacity of the structure. An a priori estimate for the size of the active process zone is provided based on the beam on elastic foundation model in which the material parameters of the cohesive law are incorporated. Methods: The formulation of the cohesive model in a damage mechanics format is first provided. The beam on elastic foundation model is then recalled and an approximate solution for the cohesive zone length is found that depends on a material length and a geometric parameter as well. Results and discussion: Numerical results are presented for a Double Cantilever Beam (DCB) geometry with varying thickness for which bilinear and exponential cohesive laws are considered. The influence of the geometry and of the shape of the cohesive law are put forward in terms of global response and evolution of the cohesive process zone. Conclusions: The size of the process zone is found to be quite sensitive to the specimen characteristic size, whose influence is well captured even using a simplified modeling wherein the original cohesive law is changed into an ideal perfectly brittle one. This leads to fairly good estimates of the size of the cohesive zone compared to finite element results.