Statistical Properties of Hybrid Composites. I. Recursion Analysis

An adaptation of the chain-of-bundles probability model for unidirectional intraply hybrid composites consisting of two types of fibres is given. Local load sharing, which is sensitive to the different elastic moduli of the fibres, is assumed for the non-failed fibre segments in each bundle. A sequence of tight upper bounds is developed for the probability distribution of strength for the hybrid. The upper bounds are based upon the occurrence of k or more adjacent broken fibre segments in a bundle; this event is necessary but not sufficient for bundle failure. This development allows for a description of a critical crack size k*, dependent upon the load on the hybrid, which is a characterization of the length of a crack that catastrophically propagates causing bundle failure with virtual certainty. The upper bound developed with k*, based upon the hybrid median strength, is essentially identical to the true probability distribution of hybrid strength. It is also shown that the strength distribution for the hybrid composite has a weakest link structure in terms of a characteristic distribution function that is highly dependent upon the local load sharing rule, the fibre properties, and the geometrical structure of the hybrid. Numerical results from the model show that typically there is a negative 'hybrid effect' for hybrid breaking strain, but there is a positive 'hybrid effect' for hybrid tensile strength.