JOURNAL OF COSMETIC SCIENCE 582 in the wet state if one blow dries the hair, we must consider the transition from the wet to the dry state and the number of grooming strokes, and fi nally we must consider the number of grooming strokes in the dry state. Therefore, to simply assign a number of grooming strokes per day without considering the state of the water content and the hair type is too simplistic. PHYSICAL DAMAGE OR WEAR BY ABRASION FROM SPECIFIC GROOMING DEVICES SUCH AS COMBS, PICKS, OR BRUSHES, AND FATIGUING OR PULLING THROUGH A TANGLE WITHOUT BREAKAGE Wear by abrasion occurs over the entire fi ber but more near the fi ber tip end because of a longer residence time, but even more so by high end peak forces when dry (3), as evi- denced by examination of many of the smaller fragments of short segment breaks (3,10). Combs or brushes with more space between the teeth or bristles can lead to fewer and less complex tangles and therefore to lower combing forces, less abrasion, less fatiguing, and fewer broken hairs some brushes provide more long segment breaks and fewer short seg- ment breaks than combs (18). Fatiguing occurs primarily between the root section of the fi ber and the brush or comb where the combing device encounters a snag, but only on the fi bers that are under tension at the snag, which generally is a very low percentage of the fi bers in the area being combed or in the brush. Therefore, fatiguing and impacting are related, but impact breakage is produced by a single impact however, fatiguing can produce breakage only by hundreds to thousands of impacts over the same section of the same fi ber. Therefore, for the same section of the same fi ber to be impacted suffi ciently thousands of times and each time to cause fatigue damage is a much lower probability occurrence than for a sin- gle hair under high tension to be impacted once and broken. The recent paper by Evans and Park (1) on hair breakage suggests that fatiguing is the primary reason for hair breakage and raises some important questions about hair break- age. Evans and Park used the combing wheel to brush hair repeatedly at a certain fre- quency, at 60% RH only, and collected the broken fi bers as a function of the number of brushing strokes up to 10,000 strokes. In Figure 4 of their paper, as expected of a good conditioner, we see a nearly 60% reduction in breakage. Then they proceeded to apply Weibull statistics to hair breakage data in Table I, assuming that combing or brushing amounts to fatiguing hair, eventually leading to catastrophic failure. It is true that in the past a signifi cant amount of work has been done on the mechanisms of the weakening of fi bers by fatiguing and the mechanism of protection of hair fi bers by conditioners using Weibull statistics (18). However, whether this approach can be used to interpret hair breakage in combing or brushing is questionable. The authors calculated the shape parameter and the characteristic life for virgin and bleached damaged hair, and for hair treated with conditioners. The defi nition of the characteristic life for hair breakage is the number of brushing strokes necessary for breaking 63.2% of the fi bers. For virgin hair, the characteristic life is given as 55.2 million brush strokes, and for the same hair after con- ditioning it increases to 1.04 billion brush strokes. But the data for these huge numbers are based on only 10,000 brush strokes and only 1.6% of the fi bers broken (326 of 20,000) as compared to 12,640 fi bers corresponding to the defi nition of characteristic life. These characteristic life values are so large relative to the actual data that they are of ques- tionable reliability. For example, assuming brushing at the rate of 1 stroke/s (the authors

HAIR BREAKAGE 583 have used 50 strokes/min), the two numbers correspond to 1.72 and 33 years, respec- tively, of continuous brushing to break 63.2% of the fi bers. Evans and Park (1) do admit, “Specifi cally, a prediction involving the outcome after tens of millions of cycles based on an experiment involving a few thousand cycles, is obviously dubious.” Nevertheless, they continue by saying “that together these two Weibull parameters describe the collected data,” and they proceed to calculate predicted probabilities for hair breakage with a “rea- sonable representation of real life conditions.” Furthermore, they suggest that longer fragment breaks can be “explained in terms of the gradual brushing out of snags and tangles,” which, because of the questionable characteristic life, may or may not have any- thing to do with the fatiguing process. The concept of pooling the data, which the authors adopted, though good for typical fi ber fatigue experiments conducted under precise conditions, is not desirable for a brushing or combing experiment for predicting hair breakage on heads because brushing 2500 fi bers in eight different experiments is not the same as brushing 20,000 fi bers in one experiment. This is also true of calculating failure probabilities on actual heads, based on the data col- lected by combing tresses containing 2500 hairs. Fatigue data are extremely sensitive to applied stress concentrations (1). The applied stress should be high enough to break a signifi cant fraction (~30–50%) of the test speci- mens. The brushing experiment described in this paper (or similar combing experiment) does not meet these criteria. The nature of the brushing force curve shows that the stress on the fi bers during the midlength traverse of the brush, the region where long segment breaks occur, is very low for the vast majority of the fi bers (because it is shared unequally by 2500 fi bers). Even the end peak force, which is higher than the midlength force, is likely to stress only a very few fi bers to signifi cant levels to cause signifi cant damage because the force per fi ber is likely to be very small and uneven. A brushing force curve for a tress will provide some idea of the stress levels in these ex- periments, and considering the large number of fi bers, they are likely to be very small. Therefore, the fracture mechanism based on fl aw propagation by fatiguing in real brush- ing and combing situations, which requires hundreds to thousands of high-stress fatigu- ing actions on the same region of the same fi ber, may occur with a few fi bers, but it is not the primary cause of hair breakage, especially for long segment breaks. The authors state correctly that in the studies on hair breakage by Robbins and Kamath (3–6) we focused heavily on the size of the broken hair fragments and that we related the effects primarily to fi ber looping and entanglements and thus to high localized stresses on a few fi bers rather than lower localized stresses on exactly the same regions on the same fi bers. But, Evans and Park then state an alternative mechanism (1): “In short, there is another breakage mechanism that involves progressive propagation of fl aws within the fi ber, and it does not require the presence and occurrence of tangles.” We cannot conceive of combing or brushing a full head of eight-inch or longer hair without any tangles. We believe that increasing long segment breaks with increasing curvature by the creation of fl aws by fatiguing only cannot explain hair breakage on live heads, and one cannot ignore direct breakage by fi ber looping and tangling with severe bending stresses that produce breakage by either impact or pulling the comb or brush through the tangle (1,10). This is especially true in a mechanical brushing process used by the authors, where the brush traverses the tress at relatively high speeds and impacting of looped and tangled fi bers becomes highly probable.