HAIR BREAKAGE: REPEATED GROOMING EXPERIMENTS 441 (Dia-stron CYC800, Dia-stron, UK), where experiments involve repeated application of a user-defi ned force until breakage. The propensity for breakage was found to depend strongly on the magnitude of the repeating stress (i.e., stress = force/unit area), meaning that the magnitude of the repeating force and the fi ber dimensions are major infl uences. This relationship is shown in Figure 1, in what is often termed an S-N curve. From Figure 1, one observes that an exponential relationship exists between the magni- tude of the repeating stress and the number of cycles to fail. Extrapolating these fi ndings into the world of hair care, one observes how lowering the stresses associated with groom- ing will signifi cantly reduce the likelihood of fi ber breakage, and it explains why many conditioning products produce dramatic effects in repeated grooming experiments. These single-fi ber experiments provide fundamental understanding, but the magnitude of the stresses experienced by individual fi bers during everyday grooming is not readily available. As such, while it is possible to model the propensity for breakage as a function of the applied stress, it is unknown where real-life conditions lie. Repeated grooming experiments represent the opposite scenario—in that real-life stresses and strains are pre- sumably replicated relatively well but the magnitude of these stimuli is unknown. Nev- ertheless, this comparision does introduce the idea of treating repeated grooming results by fatigue testing approaches. WEIBULL ANALYSIS OF FAILURE DATA In a fatigue test, failure is commonly attributed to the propagation of pre-existing fl aws within a material. Accordingly, with the distribution of such fl aws on a hair fi ber being statistical in nature, breakage also needs to be treated as a statistical var- iable. Therefore, modeling and characterization of breakage involves fi tting a statis- tical distribution to the data. A convenient approach involves utilization of the highly fl exible Weibull distribution (9). The fl exibility of this expression arises from the presence of the Weibull shape factor, β. By means of illustration, when β = 3.6, Figure 1. S-N curve showing failure data for virgin Caucasian hair at 60% relative humidity.

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