Analytical micromechanical models for the prediction of multiple cracking in composites

Abstract
Because of the wide variety of composite materials that are available, and the expense involved in testing to measure properties for design purposes (such as their damage tolerance), there is a need to develop predictive methods that can readily be utilised on desk-top computers. It is inevitable that such methods will be based on analytical rather than finite element techniques. A review is given of recent progress that is being made with the use of analytical micromechanical models for the prediction of the dependence of thermoelastic constants on crack density, and for the prediction of multiple cracking in both unidirectional and laminated composites. Various stress transfer models for unidirectional and laminated composites are assessed for their quality by considering their ability (or otherwise) to satisfy the equations of equilibrium, stress-strain relations, interfacial boundary conditions, and external boundary conditions. Both shear-lag and variational models are considered. In addition, so-called complete solution models are described that provide the stress and displacement distributions in a composite. The characteristics of the various models are briefly described. A most important need is to be able to predict the dependence of the thermoelastic constants on the level of applied stress or strain rather than on crack density so that non-linear stress-strain behaviour can be predicted. A recently developed energetic method of predicting multiple cracking in laminated composites is described showing how it can deal with both the simultaneous and progressive formation of cracks during loading for combined biaxial and shear modes of loading. It is pointed out that the fracture criterion can be derived from energetic principles or from the application of the generalised plane strain model of stress transfer, thus demonstrating energetic consistency. The fracture criterion depends only on macroscopic parameters, namely, the thermoelastic constants of cracked laminates and it follows that micromechanical models are only needed to determine the dependence of these constants on crack density.