Chapter 8 255 The S-N curve: Instinctively we may expect the tendency for failure to be related to the magnitude of the repeating stimulus. That is, faster failure may be predicted when encountering higher repeated stresses. In fatigue testing this relationship is commonly represented by what is termed an S-N Curve, where the stress is plotted against the logarithm of the number of cycles to failure. Figure 2 shows such a plot for Caucasian hair equilibrated at 60% RH. While a reasonable amount of scatter is observed, results confirm the earlier supposition and show how repeated application of stresses at the high end of this range tend to cause breakage after a few hundred cycles, while a few hundred-thousand cycles are required at the low end. Note on the magnitude of the stress relative to the “Hookean region” of hair: When performing this testing, it is possible to encounter two distinctly different occurrences. In theory, application of stresses within the “Hookean region” should result in a commensurate deformation, with full recovery being attained upon removal of the deformation. However, if an applied force exceeds that of the linear-like region, the fiber yields, becomes Figure 2. S-N Curve, Caucasian hair at 60% RH