Measurement of stress–strain behaviour of human hair fibres using optical techniques

Synopsis Many studies have presented stress–strain relationship of human hair, but most of them have been based on an engineering stress–strain curve, which is not a true representation of stress–strain behaviour. In this study, a more accurate ‘true’ stress–strain curve of human hair was determined by applying optical techniques to the images of the hair deformed under tension. This was achieved by applying digital image cross‐correlation ( DIC ) to 10× magnified images of hair fibres taken under increasing tension to estimate the strain increments. True strain was calculated by summation of the strain increments according to the theoretical definition of ‘true’ strain. The variation in diameter with the increase in longitudinal elongation was also measured from the 40× magnified images to estimate the Poisson's ratio and true stress. By combining the true strain and the true stress, a true stress–strain curve could be determined, which demonstrated much higher stress values than the conventional engineering stress–strain curve at the same degree of deformation. Four regions were identified in the true stress–strain relationship and empirical constitutive equations were proposed for each region. Theoretical analysis on the necking condition using the constitutive equations provided the insight into the failure mechanism of human hair. This analysis indicated that local thinning caused by necking does not occur in the hair fibres, but, rather, relatively uniform deformation takes place until final failure (fracture) eventually occurs.