Fatigue failure testing of human hair: Weibull-analysis for constant strain experiments

Fatigue failure testing of materials is an important aspect of assessing their strength and resilience under long-term, oscillatory stresses and/or strains. This also applies to human hair. For this investigation, we decided to complement existing experience on cyclic tests at various levels of constant stress with those at various constant strains (4-30%). For the description and analysis of the data sets, we opted for a non-linear fit of the cumulative two-parameter Weibull distribution (CWD) to the survival data. This gives direct access to the numerical values of the parameters as well as to their standard errors (SE), as measures of precision. As relevant parameters, we identified the lifetime index ln(α) and the shape factor β. All fits showed very high coefficients of determination and normally distributed residuals. Accordingly, precision of the parameter values is very high. It only starts to drop for high constant strains, when significant grouping of data starts to occur. ln(α) drops and β increases both exponentially with strain. β exceeds the value of unity (β ≥ 1) at a strain of 4.3%, indicating a fundamental change of failure mode. The cross-over of the theoretical curves for ln(α) and β occurs around 45% strain, which coincides with the break strain for conventional tensile testing. This agreement supports the validity of our approach and suggests a more than just empirical nature of the CWD-function for modelling the fatigue failure data of human hair.