Stiffness reduction and stress transfer in composite laminates with transverse matrix cracks

Abstract

Cross-ply laminates and angle-ply laminates with transverse plies containing through-width matrix cracks across the thickness of the transverse plies are studied using a variational, strain energy based approach, complementary to that of Hashin. An upper bound on the effective axial stiffness of the cracked laminates with a uniform distribution of transverse cracks, has been derived using the principle of minimum potential energy. The boundary value problem associated with the cracked body is solved using the principle of superposition. The equations governing the field variables in a typical representative volume element are derived using the layerwise laminate theory of Reddy. A finite element solution of the equations of the layerwise theory is also developed. The predicted reduction in the effective axial modulus is in very good agreement with experimental results, and was found to approach a fixed value with increase in crack density, for laminates with both staggered and non-staggered cracking. Laminates with staggered cracks showed a greater reduction in effective modulus at lower crack densities. The crack opening displacements at different crack densities were normalized in a way as to compare with the solution for an isolated crack in an infinite isotropic plane elastic body. The mechanics of load transfer has been examined in detail based on the stresses in the representative volume element.