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.