An analytical model for the translaminar fracture toughness of fibre composites with stochastic quasi-fractal fracture surfaces

•An analytic model for the translaminar tensile toughness of composites is proposed.•Idealised fracture surfaces are quasi-fractal, with pulled-out fibres and bundles.•Energy is dissipated by interfacial debonding and pull-out friction at all levels.•Fracture mechanics and fibre strength statistics define debond and pull-out lengths.•Predicted fracture toughnesses and size-effects are validated against experiments.

The translaminar fracture toughness of fibre-reinforced composites is a size-dependent property which governs the damage tolerance and failure of these materials. This paper presents the development, implementation and validation of an original analytical model to predict the tensile translaminar (fibre-dominated) toughness of composite plies and bundles, as well as the associated size effect. The model considers, as energy dissipation mechanisms, debonding and pull-out of bundles from quasi-fractal fracture surfaces; the corresponding lengths are stochastic variables predicted by the model, based on the respective bundle strength distributions and fracture mechanics. Parametric studies show that composites are toughened by stronger fibres with large strength variability, and intermediate values of interfacial toughness and friction. Predictions are validated against four different composite ply systems tested in the literature, proving the models ability to capture not only size effects, but also the influence of different fibres and resins.

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