A Variational Approach to Analyzing Laminates with Cracks and Viscoplasticity—The Model and its Validation

Abstract

For cross-ply laminates, matrix cracks and viscoplasticity of the 90 degree ply are two major forms of damage which affects the performance of the composite laminates, especially at high temperatures and under complicated loading patterns. To predict the durability of such kinds of materials, one of the tasks is to analyze stress distribution in each ply of the laminates taking into the interaction between the cracks and viscoplastic deformation. A unified viscoplasticity model is utilized together with the principle of minimum complementary energy to establish a general framework for cross-ply laminates containing cracks and undergoing general viscoplastic deformation. The problem is reduced to an ordinary differential equation for a stress function with an inhomogeneous "force" term related to the viscoplastic strain accumulation. An algorithm to solve the equation for the stress function is presented. The results are compared with those from the finite element method to validate the proposed approach. It is found that although the variational approach, like most of the analytical solutions, does not represent the near crack tip stress singularity field, it does provide fairly accurate through-thickness average stress within the 0 and 90 degree plies. In reality, local inelastic deformation occurs near the crack tip so that the stress is finite. If the local inelastic deformation near the crack tip is taken into consideration, the results from the variational approach match more closely with the finite element solution. Furthermore, the variational approach yields rather accurate in-plane shear stress along the interface between the 90 and 0 degree plies.