A family of weakest link models for fiber strength distribution

It is well known that the most widely used distribution function for fiber tensile strength, the two-parameter Weibull distribution, does not always adequately describe the experimentally observed fiber strength scatter and the strength dependence on fiber length. To remedy this discrepancy, modifications of the Weibull distribution have been proposed that, while providing a good empirical fit to the strength data, sometimes lack the theoretical appeal of the weakest link models. We derive a family of weakest link models based on the assumption of a two-stage failure process incorporating explicitly the probabilities of flaw initiation and the fiber fracture due to the largest flaw (i.e. the weakest link). The model is verified against a sample of E-glass fiber strength data at different gauge lengths and shown to provide a reasonably good fit to the test results.