1.0 0.B 0.6 0.4 477 STIFFNESS OF HUMAN HAIR FIBERS L._.•.D. MEASURED ß K FIBER 102 IN W,.•• z• H FIBER 54 o H FIBER 34 IO HOOK DIA. '•-- ZO 30 40 50 60 70 80 % RELATIVE HUMIDITY Figure 5. Effect of relative humidity on the stiffness index 90 100 EFFECT OF RELATIVE HUMIDITY influence of humidity is shown in Figure 5 for three fibers of The ' ß ß t fibers were measured without experimen"stiffnessdifficuthicknthedifferent changes while the thinnest fiber is limited in the amount of change index" value in water is less than twice the wire diameter. immersiwetrequusedtestingbesincecan additional study to select optimum conditions. Smaller weights since fibers bend more easily and the fiber mass is diminished by buoyancy- RELATION TO ELASTIC EXTENSION An objective here was to test the strength of unaltered stretching to see how well one measurement predicts the Fourteen fibers were measured for linear density and the stretched with Instron equipment under conditions suitable or Hookean slope portion of the extension curve. When data showed a good, straight-line relationship to linear densitiesslolinestrethewereandHooktheAsindexdetermforplotted,other.byandbendibyfibersstiffness expec increased with thickness of fibers. In Figure 6, stiffness indices and the show linear relationship- The prediction = the mensions used. Thus, tensile measurementdi-toforusedsatisI4abemay0.0151fibersDfibers14forunalteredapproximaonisslopesequationHookean an extent, to estimate bending strengths.

478 JOURNAL OF THE SOCIETY OF COSMETIC CHEMISTS x la.I 1.0 0.8 0.6 - 0.2 I0 20 30 40 50 60 70 80 HOOKEAN SLOPE g/rnrn EXTENSION Figure 6. Relation of the stiffness index to the Hookean slope ELASTIC MODULI During bending, one side of a fiber is extended and the other side is compressed. For homogeneous elastic fibers with perfectly round cross sections, bending and tensile moduli would be identical and predict each other. For natural fibers such as wool or hair, however, the degree to which this identity holds is a matter of controversy (2-6, 11, 13). This is not surprising since hair fibers are oil-containing, viscoelastic, anisotropic materials which are nonuniform in cross-sectional shape and of variable thickness along their length. Results are shown in Table II for fibers, measured at 60% RH, 75øF, and arranged ac- cording to linear densities (approximate thicknesses). The elastic moduli for bending (En) are calculated from eq 7 and those for stretching (Es) from eq 8. For both calcula- tions, the fibers are assumed to be round in cross section. The larger spread of values for bending moduli is ascribed to greater dependence on shape factors. It is interesting that the averages for EB and Es are approximately equal even though the EB/Es ratio varies widely for the individual fibers. The modulus values in Table II are calculated by assuming all fiber cross sections are circular. Correction for shape would increase Eu values since, in the Balanced Fiber method, bending occurs preferentially across the fiattest cross section. Higher Eu values may therefore more closely represent circular fibers and truer Eu values. Ac- cordingly, the data favors an hypothesis (4, 6) that the bending modulus is greater than the stretching modulus. The logic is that outer layers of a fiber are stiffer and play a greater role in bending than in stretching.