Effects of non-uniform strains on tensile fracture of fiber-reinforced ceramic composites
Effects of non-uniform strains on tensile fracture of fiber-reinforced ceramic–matrix composites have not been satisfactorily explained by existing mechanics-based models. In this paper, we use an exact model of fiber fragmentation under global load sharing conditions to predict fracture in three model problems in which non-uniform strains occur: (i) an end-constrained plate subject to a linear transverse temperature gradient; (ii) an internally-pressurized cylindrical tube with a linear through-thickness temperature gradient; and (iii) a rectangular beam under combined bending and tension. Fracture is assumed to occur when the global load reaches a maximum value. Approximations to the exact fragmentation model are also assessed, with the goal of decoupling the effects of two important parts of the computed stress–strain response: the rate of post-peak strain softening and the magnitude of the plateau “flow” stress once fiber fragmentation is complete. We find that for cases in which the fiber Weibull modulus is low and hence its plateau strength is high relative to its peak and the loading yields a sufficiently high strain gradient, the failure strain lies in the plateau regime. Consequently, the results can be predicted with good accuracy using a perfectly-plastic representation of the post-peak response. In contrast, for cases in which the fiber Weibull modulus is high, the failure strain lies in the softening portion of the curve. Here a linear-softening model is found to yield accurate results. A preliminary assessment of the model has been made by comparing predicted and measured bending/tension strength and failure strain ratios for one specific composite. The correlations appear good, though additional experiments are required in order to critically assess the model predictions over a range of loading scenarios.