Extrapolation techniques at short gauge lengths based on the weakest link concept for fibres exhibiting multiple failure modes

In order to extrapolate the tensile strength of fibres at short gauge lengths corresponding, for instance, to the mean fragment length in a fragmentation test or the so-called load-transfer length for unidirectional composite failure models, four types of extrapolation techniques have been reviewed. The ability of these models to describe the tensile strength of fibres is checked on E-glass fibres exhibiting multiple modes of failure. It is shown that Weibull unimodal statistics as well as the bimodal Weibull cumulative distribution function model lead to underestimated results. The double box approach provides values having a physical meaning but remaining phenomenological. The need for modelling to take a trimodality into account is emphasized.