Assessment of the Debonding Failure in Multi‐Layer Structures Using a Closed‐Form Analytical Model

In mechanical engineering, aerospace engineering and civil engineering, there are many situations where multi‐layer structures are applied. This can, for instance, be the overlap region of an adhesive joint, a local patch reinforcement on a substrate or a substrate with a protective layer. Under given mechanical or thermal loading, due to the dissimilar material properties, stress concentrations will typically arise at the ends of the involved layers, which might lead to the onset of debonding cracks and a subsequent debonding failure. In order to assess such situations in the framework of linear elasticity theory a closed‐form analytical approach is suggested based on layer‐wise displacement representations that take into account singular stress concentrations. From this, by means of the principle of minimum potential energy, an approximate closed‐form description of the resultant deformation and stress distribution can be derived and validated by accompanying finite element calculations. In order to assess potential failure in the framework of finite fracture mechanics, debonding cracks of finite length are introduced, and the corresponding incremental energy release is identified. Using the hybrid failure criterion suggested by Leguillon, it can be clearly concluded whether such debonding failure will happen in reality or not. By a corresponding optimization problem, the minimal critical loading leading to failure can also be determined. This is of high significance for the practical application.