FATIGUE TESTING OF HAIR 601 events. Such work is often termed reliability statistics or survival probability. In this work, the objective has been to model the propensity for hair breakage under repeated fatigu- ing forces—a process that is proposed to better mimic the stimuli received during conventional grooming. Applications of fatigue testing are known in the textile indus- try and in the evaluation of other fi brous materials (1), although the approach has re- ceived only minor attention in the hair science literature. Previously, members of our Institute described microscopic analysis of fracture patterns obtained after performing such tests on a homemade device (2). Meanwhile, a parallel can be drawn between re- peated application of an extensional force and the repeated application of a frictional force, as is used in fl exabraison experiments (3). It is also possible to think of repeated combing experiments (4–6) as a version of a fatigue experiment. The work described here relates to experiments performed on a commercially available unit, the Dia-stron CYC800 (Dia-stron Limited, Andover, UK). This equipment has been described previ- ously (7,8), in articles where the primary focus was to describe new commercial instru- mentation. The purpose of this paper is to provide guidance in designing and performing such experiments, in addition to describing and illustrating the novel na- ture of the data analysis. In similar applications of fatigue testing involving other fi brous materials, it is taken that breakage occurs as a result of propagating fl aws that ultimately result in failure of the fi - ber. Such fl aws are generally thought to be at the surface—that is, in a homogeneous fi - brous material, the surface represents a greater area than the bulk, and consequently there is a higher likelihood of these fl aws being present at the surface. As such, failure is taken to be virtually independent of fi ber thickness and, instead, the fi ber length is considered more important. That is, there is a higher likelihood for such fl aws to exist in a long fi ber compared to a shorter one. Some issues arise in thinking about hair in the same manner. First, unlike many synthetic fi bers, hair does not have a homogeneous structure. It is well recognized that the surface of hair consists of a hard, resistant cuticle layer that protects the inner portions but has no signifi cant contribution to the tensile strength (9). Instead, the inner cortex structure is responsible for the bulk of the strength. Therefore, propagat- ing surface cracks would not be expected to result in fi ber breakage and, consequently, failure must be considered a result of bulk fl aws. Microscopic analysis of fi bers that have been subjected to this repeated stimulus do frequently show the presence of propagating surface cracks (for example, see Figure 2), but these are not thought to be points that ultimately result in breakage. Hair also differs from many synthetic fi bers in that there is considerable variability in dimensions. Synthetic fi bers are often manufactured to high dimensional tolerance, which does not occur in natural fi bers. Therefore, use of a common fatiguing force on fi bers of varying dimension will result in a range in the applied stress (force per unit area). Fur- thermore, with differences in applied stress comes an infl uence on the number of cycles to break. That is, a fi ber is likely to fail earlier when exposed to repeated application of a higher stress. This occurrence is well recognized in fatigue testing, as will be discussed at some length. Ideally, there is the desire to apply a repeating force (or, more specifi cally, a repeating stress) that is representative of actual grooming conditions. However, this information is not readily available. As such, while these experiments appear to better simulate real-life conditions, it is not yet possible to replicate them. Nevertheless, it is possible to use the approach to compare the likelihood of breakage in hair of varying quality, or after specifi c

JOURNAL OF COSMETIC SCIENCE 602 treatments. Alternatively, by altering the applied stress, it becomes possible to model the impact of increasing or decreasing grooming forces on the propensity for breakage. Both of these areas will be addressed in this report. In designing and performing such experiments, the magnitude of the fatiguing force is by far the most signifi cant variable, and it requires consideration for a number of reasons. The fi rst involves timeliness, in that fatigue experiments can be very lengthy if relatively low repeating stresses are employed. Thus, when comparing samples under a common set of conditions, it may be prudent to select forces that do not make experiments too lengthy. However, while application of higher stresses leads to faster data generation, conditions may stray further from those presumed to accompany everyday grooming. Especially use- ful information may arise from performing experiments across a range of fatiguing forces, as this provides insight into the relationship between the magnitude of the external stim- ulus and the propensity for breakage. This may be useful to the manufacturers of condi- tioning products, where functionality lies primarily with the ability to provide surface lubrication and therefore lower grooming forces. There are other experimental variables that are worth noting from a fundamental view- point. In theory, the speed at which the fatiguing force is applied would be expected to have an effect. It is well recognized that hair is a viscoelastic material, and consequently dynamic mechanical properties will have frequency dependence that is, at higher fre- quencies hair appears more elastic (solid-like), while at lower frequencies there is more time for molecular relaxations that result in a higher viscous (liquid-like) component. In this work, a constant fatiguing rate was used, with no attempt being made to study this variable. As will be becoming clear, the distribution of such fl aws in a sample represents a statisti- cal consideration, and consequently necessitates a statistical analysis of the results. This is believed to be another uniqueness of the approach, in that testing produces predictions of the probability of breakage. Figure 2. Propagating cracks in the cuticle as a result of fatiguing.