Stress redistribution around clusters of broken fibres in a composite

A key aspect of the longitudinal tensile failure of composites is the stress redistribution that occurs around broken fibres. Work on this topic has focussed mainly on the stress field surrounding a single broken fibre; however, this is an important limitation as unstable failure in carbon fibre bundles occurs when a cluster of about 16 or more broken fibres is formed. Therefore, we have developed a detailed Finite Element (FE) model to investigate how stress redistribution varies with the number of broken fibres in a cluster. The results show that both the recovery length and stress concentration factor increase significantly with increasing number of broken fibres in a cluster. We have also developed an analytical model, suitable to be included in existing or new fibre bundle models, that captures how the recovery length and stress concentration factor vary with the broken cluster size, and validated its predictions against our FE simulations. Finally, we extended our FE model to predict the survival probability of fibre bundles using Monte Carlo simulations, and found that these predictions were in good agreement with experimental and analytical results on microcomposites.