Separation process modeling of composite with adhesive layer
The deformation model of a composite with a thin adhesive layer is examined. The consideration of a layer’s stress state is based on the relationship between the average stresses by thickness and the stresses on the layer’s border. The layer’s medium strains are expressed in terms of its boundary displacements. The average stresses and strains are used to avoid the stress-strain state dependence on the shape of end faces. The variational condition for the equilibrium state of two bodies linked through an adhesive layer is obtained within small strains. The problem is considered in the framework of linear theory of elasticity. The Hooke’s law relates the strain and stress fields in the matched bodies. As a result, the system of variational equations is reduced to the equations with respect to the displacements fields in the matched bodies including the layer’s bounds. The system of variational equations with respect to displacements contains the adhesive layer thickness as a parameter. It is significant that the current equations system is not a discrete one since the displacement fields are supposed to be continuous. Various approximations for displacements may be used to obtain approximate solutions. In particular, the finite element method with a quadratic approximation for displacement fields is used for the case of plane strain. The influence of the characteristic size of a finite element on the convergence of the solution is studied. It is found that the numerical convergence is present when the ratio between the finite element faces and the layer’s thickness is four or more. The proposed approach allows to use the well-known local failure criteria under the absence of stress singularity at the points of conjugation of the adhesive layer with the bodies. The analysis of the possible forms of composite destruction due to the destruction of a material layer as well as due to bonds breaking between the layer and adjacent materials is carried out.