On the analysis of cross-ply laminates with micro-cracks and inelastic deformation

For cross-ply laminates micro-matrix cracks in the 90 ° plies and inelastic deformation in the 0 ° and 90 ° plies are two major forms of damage which affect the long-term durability of the materials. It is crucial to develop a mechanics based approach to incorporate both micro-cracks and inelastic deformation of the composite materials based on the response of the 0 ° and 90 ° plies in order to accurately predict the response of the materials in service environments and to assist in optimizing the materials system for best performance. However, such a task leads to severe mathematical difficulties, primarily due to the zero traction conditions on the crack surfaces, the complicated constitutive relations governing the inelastic deformation and the interaction between the cracks and the inelastic deformation. In this paper, a general framework for the analysis of crossply laminates with micro-matric cracks and inelastic deformation is proposed. For this purpose admissible stress fields are constructed which satisfy equilibrium and all boundary and interface conditions. The principle of minimum complementary energy is utilized to derive a differential equation for the stress function from which the stress field of the composite can be derived. The inhomogeneous terms of the differential equation involve the inelastic strains which are loading history dependent. The Greenʹs function of the differential equation is then obtained. Using the Greenʹs function and a constitutive equation, two-dimensional stress and strain states in the composite at any time are represented by an integral of the Greenʹs function and the inelastic strains accumulated up to that time. This new analysis takes into consideration the microcrack-microcrack interaction, as well as the interaction between the microcracks and the inelastic deformation, and provides a point-wise variation of the stress field instead of average stress field as most of the analytical approaches yield. The interactions of matrix cracks and creep deformation of an eight-harness satin weave (8HSW) Nextel 610/Aluminosilicate ceramic matrix composite is studied using the proposed model. The predicted creep strain of the composite shows good correlation with experimental data at different levels of temperature and stress conditions. The distribution of stresses and strains provides important information on the response of the composite. © 1997 Elsevier Science Ltd