Mesoscale finite element analysis of cracked composite laminates under out-of-plane loads using 3D periodic boundary conditions

The behavior of composite materials under out-of-plane loads is strongly affected by the presence of transverse ply cracks. The cracks perturb the distribution of stresses leading to large out-of-plane shear stiffness reductions. It is crucial to include these effects in the damage material models to improve their accuracy. Therefore, the stress transfer and stiffness reduction in cracked laminates have been studied with a mesoscale finite element model (FEM) under general in-plane, out-of-plane normal and shear loads. A symmetric laminate containing ply cracks in a single orientation has been considered under the hypothesis of periodicity using a novel relaxed three-dimensional formulation of Periodic Boundary Conditions (PBCs). The local stresses have been verified versus different analytical and numerical methods. In addition, the degraded effective thermo-elastic constants involving out-of-plane properties have been calculated as a function of crack density. Both uniform and non-uniform distributions of cracks have been considered for different lay-ups including angle-ply and unbalanced laminates. The effect of contact between the crack surfaces has been studied for specific loading conditions. It is shown that a single formulation based on three-dimensional periodic boundary conditions is sufficient to determine the interfacial stresses and the complete thermo-elastic constants under in-plane and out-of-plane loads accurately.