On the application of Weibull analysis to experimentally determined single fibre strength distributions

The application of Weibull theory to the analysis of experimental data obtained from the tensile testing of reinforcement fibres is widespread in composites research and development. One basic assumption implicit in the use of Weibull analysis is that all values of fibre strength described by any set of unimodal or multimodal Weibull parameters are accessible experimentally. However, this is not the case, as a minimum level of fibre strength is necessary in order to be able to isolate, prepare and test any fibre. In this paper the consequences of this experimental limitation are explored in terms of the commonly applied Weibull graphical analysis method. It is demonstrated that this can result in significant curvature in a standard Weibull plot at the low strength end of the data. Furthermore, at low sampling numbers this effect can be misinterpreted as evidence of multiple defect populations. The phenomenon significantly affects the values of the Weibull parameters obtained from the graphical analysis and also from the average strength versus gauge length analysis. The presence of this lower limit presents a serious challenge to those wishing to support conclusions on the physics and mechanics of fibre fracture from Weibull analysis of single fibre tensile data.