Probabilistic Modelling of Fracture Toughness of Composites with Discontinuous Reinforcement

The results presented in the paper are related to the prediction of the effective fracture toughness of particulate composites (K(ICeff)). K(ICeff) was determined using a probabilistic model supported by a cumulative probability function qualitatively following the Weibull distribution. Using this approach, it was possible to model two-phase composites with an arbitrarily defined volume fraction of each phase. The predicted value of the effective fracture toughness of the composite was determined based on the mechanical parameter of the reinforcement (fracture toughness), matrix (fracture toughness, Young’s modulus, yield stress), and composite (Young’s modulus, yield stress). The proposed method was validated: the determined fracture toughness of the selected composites was in accordance with the experimental data (the authors’ tests and literature data). In addition, the obtained results were compared with data captured by means of the rule of mixtures (ROM). It was found that the prediction of K(ICeff) using the ROM was subject to a significant error. Moreover, a study of the effect of averaging the elastic–plastic parameters of the composite, on K(ICeff), was performed. The results showed that if the yield stress of the composite increased, a decrease in its fracture toughness was noticed, which is in line with the literature reports. Furthermore, it was noted that an increase in the Young’s modulus of the composite affected K(ICeff) in the same way as a change in its yield stress.