A FINITE ELEMENT ANALYSES OF THE EFFECT OF HYDROSTATIC PRESSURE IN A THIN ADHESIVE LAYER ON ITS FRACTURE UNDER MIXED-MODE LOADING

Abstract

The problem of deformation of a sample, which is a composition of orthotropic bodies bound by an adhesive layer, realizing a mixed loading mode I + II for the layer material in the vicinity of a crack-like defect, is considered. A crack-like defect in a composite was considered both in the form of a mathematical section and a physical section, the thickness of which was considered as a linear parameter. A finite element solution with an elastic description of materials in a state of plane deformation is used. To find critical states, the values of specific elastic energy in the tip of a crack-like defect were analyzed. So, for the mathematical section, the values of energy were associated with stress intensity factors and for the physical section with the energy product in the form of the product of a linear parameter and the average specific free energy on the face of a dead-end finite element of the adhesive layer. Finding the characteristics averaged over the layer thickness was determined within the framework of the Neuber – Novozhilov approach. For a small finite value of the linear parameter the convergence of the energy product to the critical value of the specific elastic energy found for the crack model in the form of a mathematical cut is shown for equivalent loading of the sample with a physical cut and the linear parameter tends to zero. For an adhesive layer of finite thickness an energy fracture criterion is considered which takes into account the loosening of the material due to hydrostatic pressure. The loosening of the material was taken into account by the parameter which was determined from the solution of the problem of normal tension of the adhesive layer by the cantilevers of the two-cantilever beam taking into account the critical values of the specific elastic energy. A comparison is made of the calculated critical external load for the formulation of the problem using a layer of finite thickness and the classical representation of a crack-like defect in the form of a mathematical section and a layer of zero thickness under the appropriate failure criteria.