Estimation of fracture toughness of sic fiber and statistical analysis of change in fracture strength distribution with notch size

Distribution of fracture toughness value of amorphous SiC fiber (Tyranno ZMI, Ube Industries, Ltd.) and statistical feature of distribution of fracture strength at various notch sizes were studied analytically. The fracture toughness values, estimated for the fiber specimens with mode I type straight-fronted edge notch introduced with focused-ion-beam, were almost independent of the fiber diameter and notch depth. The distribution of the fracture toughness was described by the three-parameter Weibull distribution function. The distributions of fiber diameter and original fracture strength were described by a normal distribution function and fiber diameter-incorporated three-parameter Weibull distribution function, respectively. These distribution functions and a Monte Carlo method were used to simulate the change in fracture strength distribution with notch depth. With this simulation, the experimental results were well described. Also the statistical features in notch size-dependence of distribution of fracture strength, arising from the decrease in fraction of intrinsic-defect fractured fiber specimens to all specimens and hence the increase in the fraction of notch-fractured specimens with increasing notch size, were elucidated.