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.

JOURNAL OF COSMETIC SCIENCE 584 In the second paper of our series (3), an attempt was made to show some integration of the different factors (Introduction section) involved in hair breakage, rather than to sug- gest that one precludes the other as suggested by the following statement in the synopsis: “Extension or impacting hair fi bers with fl aws or damaged hair sections such as damaged wrapped ends produces short fi ber fragmentation, while longer segment breaks may be produced in fi bers with natural fl aws (19) such as fi ber twists, cracks or badly abraded (3,10,13,14) or chemically weakened hair or even knots (3,4).” (Reference citations in this quotation refer to references in the current paper.) CONCLUSION The phenomenon of hair breakage is a complex phenomenon involving multiple factors including progressive damage and the progressive propagation of fl aws within the fi ber as stated by Evans and Park, but more importantly it involves high localized stresses created in tangles. We believe that the literature clearly shows that the primary factors involved in hair breakage are the occurrence of tangles created by combing or brushing where one or more hair fi bers are severely bent around at least one other hair. Therefore, high local- ized stresses are created by impact or pulling through that tangle. As a result, one or more hair breaks, either with or without fl aws, under this condition. Other variables are clearly involved to determine the actual number of broken hairs and the type of fractures. These variables include hair type (primarily curvature), hair condition (treatments and wear), relative humidity or water content of the hair, and the specifi c grooming device as ex- plained in the Discussion section. Brushing and combing certainly play a role in weaken- ing hair, but they are unlikely to lead to pure fatigue breaks as claimed by the authors, especially under the low load levels experienced by the fi bers. REFERENCES (1) T. A. Evans and K. Park, A statistical analysis of hair breakage. II. Repeated grooming experiments, J. Cosmet. Sci., 61, 439–456 (2010). (2) A. C. Brown and J. A. Swift, Hair breakage: The scanning electron microscope as a diagnostic tool, J. Soc. Cosmet. Chem., 26, 289–297 (1975). (3) C. Robbins, Hair breakage during combing. II. Impact loading and hair breakage, J. Cosmet. Sci., 57, 245–257 (2006). (4) N. P. Khumalo, R. P. R. Dawber, and D. J. P. Ferguson, What is normal black African hair? A light and scanning electron-microscopic study, J. Am. Acad. Dermatol., 43, 814–820 (2000). (5) C. Robbins, in Chemical & Physical Behavior of Human Hair, 4th Ed. (Springer Verlag, Berlin, Heidelberg, New York, 2002), pp. 399–401. (6) C. Robbins, Ibid, pp. 398–399. (7) C. M. Pande, L. Albrecht, and B. Yang, Hair photoprotection by dyes, J. Cosmet. Sci., 52, 377–390 (2001). (8) Y. K. Kamath, S. Hornby, and H. D. Weigmann, Effect of chemical and humectants treatments on the mechanical and fractographic behavior of Negroid hair, J. Soc. Cosmet. Chem., 36, 39–52 (1985). (9) R. Beyak et al. Elasticity and tensile properties of human hair. II. Light radiation effects, J. Soc. Cosmet. Chem., 22, 667–678 (1971). (10) C. Robbins and Y. K. Kamath, Hair breakage during combing. III. The effects of bleaching and condi- tioning on short and long segment breakage by wet and dry combing of tresses, J. Cosmet. Sci., 58, 477–484 (2007). (11) J. Epps and L. J. Wolfram, Letter to the Editor, J. Soc. Cosmet. Chem., 34, 213–214 (1983). (12) T. A. Evans, Fatigue testing of hair—A statistical analysis of hair breakage, J. Cosmet. Sci., 60, 599–616 (2009).