Analysis of a Crack in a Thin Adhesive Layer between Orthotropic Materials: An Application to Composite Interlaminar Fracture Toughness Test

Abstract

The problem of a crack in a thin adhesive layer is considered. The adherents may have orthotropic elastic behavior which allows composite laminates to be modeled. In the present work a linear elastic-brittle constitutive law of the thin adhesive layer, called weak interface model, is adopted, allowing an easy modeling of crack propagation along it. In this law, the normal and tangential stresses across the undamaged interface are proportional to the relative normal and tangential displacements, respectively. Interface crack propagation is modeled by successive breaking of the springs used to discretize the weak interface. An important feature of the BEM approach developed is that the behavior of the springs is independent of the boundary element mesh, (i.e. distance between springs and boundary element types used). This fact allows, for example, an easy mesh refinement to be performed. The present model allows not only the crack propagation but also the crack initiation to be studied. The problem of two linear elastic half-planes bonded by a cracked thin adhesive layer is considered first. A formulation of the new governing integral equation for two identical orthotropic half-planes bonded along a straight weak interface including a finite interface crack under constant pressure is presented, introducing a new dimensionless characteristic structural parameter d. A parametric study of this problem by BEM is presented, verifying the correct implementation of the weak interface model. Then, the Interlaminar Fracture Toughness (GIc) Test is analyzed by the BEM code developed. The crack propagation is studied by a new Energy Release Rate criterion. It is shown that the weak interface model of the adhesive layer, used in the 2D Boundary Element Method (BEM) code developed, provides a good representation of the actual adhesive behavior by comparing numerical and experimental results.