Tensile and Flexure Strength of Unidirectional Fiber-Reinforced Composites: Direct Numerical Simulations and Analytic Models

A Local Load Sharing (LLS) model recently developed by Curtin and co-workers for the numerical simulation of tensile stress-strain behavior in fiber-reinforced composites is used to predict the tensile strength of metal matrix composites consisting of a Titanium matrix and unidirectionally aligned SiC fibers. This model is extended to include the effects of free boundary conditions and non-constant load gradients and then used to predict the strength of a Ti-6Al-4V matrix reinforced with Sigma SiC fibers under 4-point flexure testing. The predicted tensile and flexure strengths agree very well with the values measured by Gundel and Wawner and Ramamurty et al. The composite strength of disordered spatial fiber distributions is investigated and is shown to have a distribution similar to the corresponding ordered composite, but with a mean strength that decreases (as compared to the ordered composite) with increasing Weibull modulus. A modified Batdorf-type analytic model is developed and similarly extended to the case of non-uniform loading to predict the strength of composites under tension and flexure. The flexure model is found to be inappropriate for application to the experimental materials, but the tensile model yields predictions similar to the Local Load Sharing models for the experimental materials. The ideas and predictions of the Batdorf-type model, which is essentially an approximation to the simulation model, are then compared in more detail to a simulation-based model developed by Ibnabdeljalil and Curtin to more generally assess the accuracy of the Batdorf model in predicting tensile strength and notch strength versus composite size and fiber Weibull modulus. The study shows the Batdorf model to be accurate for tensile strength at high Weibull moduli and to capture general trends well, but it is not quantitatively accurate over the full range of material parameters encountered in various fiber composite systems.