This paper is a collection of various analytical methods for predicting some of the properties of laminated fibre reinforced composites that can be used when designing composite laminates, or when validating numerical methods of estimating these properties. To begin, convenient methods are given to estimate the properties of undamaged single plies and undamaged symmetric laminates. Methods of predicting fracture in homogenized anisotropic materials are then described, which exploit some very useful properties of orthogonal polynomials. Example solutions are given which are compared with known accurate solutions. The problem is then considered of quantifying, using analytical methods, the dependence of the effective thermoelastic properties of a damaged laminate on the density of ply cracks in the 90
ply of a cross-ply laminate. Many very useful inter-relationships are given showing how most of the effective properties of damaged laminates depend on a single damage function. Some example predictions are given for a typical carbon fibre reinforced laminate. Finally, a model is described for predicting the progressive degradation of a unidirectional fibre reinforced composite that is degraded by an aggressive environment causing defect growth in the fibres and eventually the catastrophic failure of the composite. It is also shown how the time dependence of residual strength may be estimated. An example is given of a normalised failure/time curve, and some associated residual strength curves that can be the basis of design methods to avoid the failure of composites that will be exposed to aggressive environments.
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