Closed-form formulae for prediction of homogenized ply-properties and laminate thermo-elastic constants in symmetric laminates containing ply cracks in multiple orientations

The aim of this study is to develop a novel model for predicting homogenized properties of a cracked ply in a symmetric laminate using the crack density and thickness of the ply. In doing so, the periodic boundary conditions are applied to the RVEs in a three-dimensional finite element model to calculate the thermo-elastic constants of symmetric laminates containing uniformly and non-uniformly spaced cracks under in-plane and out-of-plane loading conditions. On the other hand, homogenized material properties of the cracked ply are explicitly determined by averaging procedures for both stress and strain components. Using computed results and nonlinear least square fitting, an analytical formula is proposed to describe the mechanical properties of the cracked ply, which takes into account the effect of ply thickness, material properties and crack density. Different cracked laminates are tested to indicate the potential of the developed method in analyzing complex crack geometries in multiple orientations. Moreover, the applicability and accuracy of the suggested model are verified by comparing the results with those of experiments, variational approach and finite element method.