JOURNAL OF COSMETIC SCIENCE 138 This is a common fi nding, with single-fi ber fatigue experiments frequently showing much larger differences among test samples, and potentially suggesting that traditional stress–strain curves have been providing underestimates as to the effects of various insults on hair breakage. In the above example, it is hypothesized that increased plasticization of hair at elevated humidity results in a common force inducing greater deformation of the sample, and repeated application of this increased strain leads to faster breakage. Cor- roboration for this postulate has been obtained by determining that other treatments/ conditions that plasticize hair also give rise to similar effects. Figure 1. Decrease in break strength of hair with increasing relative humidity. Figure 2. Cycles-to-break for single hair fi bers as a function of applied stress and relative humidity.

VISUALIZING THE CAUSES OF HAIR BREAKAGE 139 DISCUSSION The traditional stress–strain approach for assessing hair strength probes the underlying tensile properties of hair fi bers, including average one-time stresses and strains to induce breakage. However, materials break at their weakest point, and the presence of any fl aw represents a nucleation site that can be propagated to failure by repeating deformations. Therefore, by fatigue theory the tendency for failure lies with both the presence and propagation rate of fl aws within a sample. A variety of parameters can be conceptualized as contributors to the presence of fl aws in hair: condition of the hair exposure to chemical treatments, UV, etc. mechanical fl aws caused by ponytails, braids, etc. hair type hair length etc. Similarly, factors can be identifi ed that are expected to infl uence fl aw propagation rates. Figure 2 shows how application of higher stresses produces an exponential increase in the tendency for hair breakage. There- fore, repeated applications of higher (grooming) forces or application of comparable forces to thinner fi bers should quicken fl aw propagation. The effect of the hair’s mechanical properties on propagation rates has already been discussed. Factors outlined earlier relating to the presence of fl aws are those traditionally cited when discussing reasons for increased hair breakage, whereas those associated with propagation rates have not traditionally been considered. Yet, modeling work based around extensive experimental data suggests that factors associated with propagation rate of fl aws have a markedly stronger infl uence on the tendency for breakage. To this end, our industry already possesses the means for slowing fl aw propagation, namely, surface lubrication provided by traditional conditioning products lowers grooming forces, which reduces the magnitude of fatiguing forces and results in an exponentially slower tendency for fi ber breakage (see Figure 2). This occurrence can be demonstrated in a more consumer-relevant manner by performing repeated grooming experiments, where hair tresses are continuously brushed with periodic counting of broken fi bers. Figure 3 shows Figure 3. Decreased hair breakage as a result of applying traditional products in a repeated grooming experiment.