Chapter 8 257 repeated application of a force approximately one-third lower than the “break force” will still induce fiber breakage after around 500 cycles. Similarly, a repeating stress that corresponds to half the “break stress” will still cause failure after around 22,000 cycles. Table 1. Average cycles-to-fail as a function of repeating stress for Caucasian hair at 60% RH Stress Range Force on 70um fiber Average # Breakage Cycles 0.0145 g/μm2 55.8 g 490 0.0135 g/μm2 52.0 g 1,280 0.0125 g/μm2 48.1 g 3,320 0.0115 g/μm2 44.3 g 8,600 0.0105 g/μm2 40.4 g 22,300 0.0095 g/μm2 36.6 g 57,800 0.0085 g/μm2 32.7 g 149,000 The forces and stresses encountered by single fibers during grooming are not readily available, but are likely to be below the values used in these experiments. However, as seen, use of lower forces will result in a further exponential increase in the cycles-to-fail and lead to unreasonably long experiments. Nonetheless, knowledge of this relationship begins to provide insight into the causes of breakage, and subsequently introduces strategies for mediating against this occurrence. For example, Figure 3 shows the same results, but this time plotted with a linear y-axis to better emphasize the exponential relationship between the magnitude of the repeating stress and the cycles- to-fail. One observes how higher grooming stresses (as may be associated with damaged hair) will result in exponentially higher fiber breakage, while the ability to lower these stresses (through using lubricating conditioner treatments) has the reverse effect. Moreover, the lower stresses encountered during grooming are likely to be within a yet steeper region of this curve, where the above influences yield even larger effects.