Statistics of single-fibre tensile strength incorporating spatial distribution of microcracks

The random distribution of single-fibre tensile strength has been commonly characterized by the two-parameter Weibull statistics. However, the calibrated Weibull model from one set of strength data at a given gauge length cannot accurately predicts the strength variation of the fibre at different gauge lengths. Instead of presuming the two-parameter Weibull distribution or any other specific statistical distribution for the single-fibre strength to begin with, this work proposes an approach to incorporating the appropriate spatial flaw distribution within a fibre and synchronizing multiple sets of tensile strength data to evaluate the single-fibre strength distribution. The approach is examined and validated by published single-fibre strength data sets of glass, ceramic and synthetic and natural carbon fibres. It is shown that the single-fibre strength statistics does not necessarily always follow the two-parameter Weibull distribution.