Applicability of solutions for periodic intralaminar crack distributions to non-uniformly damaged laminates
Résumé
Stiffness reduction simulation in laminates with intralaminar cracks is usually performed assuming that cracks are equidistant and crack density is the only parameter needed. However, the crack distribution in the damaged layer is very non-uniform, especially in the initial stage of multiple cracking. In this article, the earlier developed model for general symmetric laminates is generalized to account for non-uniform crack distribution. This model, in which the normalized average crack-opening and crack-sliding displacements are the main characteristics of the crack, is used to calculate the axial modulus of cross-ply laminates with cracks in internal and surface layers. In parametric analysis, the crack-opening displacement and crack-sliding displacement are calculated using finite element method, considering the smallest versus the average crack spacing ratio as non-uniformity parameter. It is shown that assuming uniform distribution, we obtain lower bond to elastic modulus. A `double-periodic' approach presented to calculate the crack-opening displacement of a crack in a non-uniform case as the average of two solutions for periodic crack systems is very accurate for cracks in internal layers of cross-ply laminates, whereas for high crack density in surface layers, it underestimates the modulus reduction.