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Model to Predict the Effect of Through-Thickness Loading on Ply Cracking in General Symmetric Laminates


 For the case of the combined in-plane biaxial and shear loading of a general symmetric laminate having ply cracks in a single orientation, a stress transfer model has been developed that can predict the stress and displacement distributions at all points in the laminate provided that generalised plane strain conditions prevail, as expected in such laminates in regions away from free edges. For the special case of cross-ply laminates, the modelling of the effects of a uniform through-thickness loading has led to an extensive set of inter-relationships between the thermo-elastic constants, whose validity has been verified by solutions to the stress transfer model. These interrelationships have been used to develop a very simple crack formation criterion that involves a scalar effective stress that is able to take account of the general in-plane loading of the laminate. The paper will investigate the extension of these results to general symmetric laminates with ply cracks subject to a uniform through-thickness load combined with general in-plane loading involving both biaxial and shear stresses.
 The paper will describe the assumptions on which the model is based, and the representation for the stress and displacement field that has been shown to be consistent with the Reissner variational principle whose application to composites has been pioneered by Pagano. Following Pagano, ply refinement techniques will be used to improve the accuracy of predictions, and indicate the nature of the singularity that exists at the tips of the ply cracks. The model will be used to predict the dependence of the thermoelastic constants on crack density, and to investigate the validity of new inter-relationships between the predicted constants. The inter-relationships will be used to develop a relatively simple crack formation criterion that generalises the known cross-ply criterion to the important case of general symmetric laminates.
 Evidence will be presented showing how the new model has been validated by comparison of predictions with finite element analysis for cracked laminates (e.g. quasi-isotropic laminates), and with experimental data.