IN-SITU FIBER STRENGTHS IN CERAMIC-MATRIX COMPOSITES FROM FRACTURE MIRRORS
The in situ breaking stresses of pulled-out fibers on the fracture surface of a fiber-reinforced composite can be determined ex post facto from a measurement of the fracture mirrors on the surfaces of the fibers. Here, the relationship between the resultant distribution of breaking stresses and the true in situ fiber strength distribution, as characterized by a Weibull modulus m and characteristic strength sigma(c), is derived for composites that fail after the first matrix crack has propagated. Specifically, it is demonstrated that, if the true in situ parameters are m and sigma(c), then the distribution of breaking stresses is well approximated by a Weibull form with apparent Weibull modulus m* and apparent characteristic strength S*. The relationships between m* and m, and S* and sigma(c), are presented, and these results allow for the conversion of fracture mirror data, or any fracto-graphic determination of fiber strength, to the true strength parameters necessary for predicting/interpreting composite performance.