Size Effects on the Translaminar Strength and Toughness of Fibre-reinforced Composites Seminar

Size effects on the tensile strength and fracture toughness of fibre-reinforced composite materials are widely reported in the literature, and offer a significant challenge for the design of large composite structures. However, the physical mechanisms involved in this process are not fully understood yet, and a broadly accepted modelling strategy is still to be developed.

The failure process of a 2-fibres composite bundle under uniform tensile stresses is analysed, considering the probabilities associated with several possible sequences of fibre-break events. The presence of the matrix is considered through a simplified shear-lag model, which confines stress concentrations near fibre breaks and delays final fracture. This allows the definition of a recursive scaling law relating the strength distribution of a bundle to that of its sub-bundles. This is then used to predict tensile strength distributions of UD composites, with any number of fibres (and therefore for different sizes).

The size effect on the toughness of UD composites is addressed considering that fracture develops through stochastic variations of a fractal pattern, being the pull-out length at each fractal level the main variable. This length is solved by calculating the local stresses seen by unbroken bundles, which are subsequently coupled with the proposed strengthmodel to calculate the probability for formation of specific pull-out lengths. The toughness is then calculated from the debonding and pull-out energies associated with such fractal fracture surfaces.

It is shown that the proposed model predicts a size effect on the tensile strength and toughness of UD composites in good agreement with experimental results available in the literature. The model also explains the experimental observation of different trends for strength distributions (linear, convex and bi-linear in a Weibull plot), as a function of specimensize and micromechanical properties. The model correctly predicts that the fracture toughness of composites depends on the stochastic character of fibre strength, calculating higher toughnesses for composites with fibres with higher strength variability.