Mechanical and statistical analyses of fracture of whisker-reinforced ceramic-matrix composites

This paper analyzes the fracture toughness of short-fiber reinforced ceramic-matrix composites (CMC). The effects of crack deflection and fiber pullout on matrix cracking are examined using a combination of mechanical and statistical models. First, the stress intensity factors of a deflected crack subjected to closure stress due to fiber pullout are analyzed based upon the mechanical model. Distributed dislocation method is used for the elastic analysis. Since the deflected crack is subjected to biaxial loading, a mixed mode fracture criterion in linear elastic fracture mechanics is applied to calculate the fracture toughness. Secondly, the number of pullout fibers on the fracture surface is treated as a random variable, and the statistical distribution of these fibers has been determined. The pullout force acting on a deflected crack is also obtained as a random variable by assuming a simple mechanism of fiber pullout. The probability of failure of CMC can thus be estimated from the strength characteristics of the fiber and matrix as well as the interface between these two.