Mechanical Properties of Hair 226 linear region of the dry (50% RH) fiber. There was little difference in post-yield slopes between the 50% RH and wet curves. The curve in the linear region (A-B) can be used to calculate Young’s Modulus of Elasticity, E. The elastic modulus is the stress divided by the strain, so the cross-sectional dimensions of the fiber must be measured accurately. For Caucasian or Asian hair, E is typically about 1.5 GPa in water and 3.5–4.5 GPa at 50–65% RH. African hair exhibits a somewhat lower value of E.19 For an example calculation of E and a description of the various units that have been used to report it see Appendix B of this book. The yield region: At ~ 3% strain the stress/strain curve “turns over” into the yield region (B-C in Figure 1). Past this point the stress does not increase markedly until about 30% extension. The mechanical properties of a fiber extended into the yield region can be recovered by relaxing the fiber in water for a few hours. This fact has been utilized to design protocols to measure the effect of treatments on hair strength as will be discussed below. Data from hair strained into the yield region are usually reported as either force at a given extension such as 15% or 20% or the work (energy) to extend a hair to a given extension, obtained by integrating the area under the stress strain curve from zero strain to the extension of interest. For an example of calculating area under the curve to obtain work, see Breuer.20 The post-yield region: The region from C-D in Figure 1 is known as the post yield region. Speakman2 found the post-yield slope of the wool stress/strain curve to be independent of the water content of the fiber, and the slopes of the C-D region are approximately equivalent at 50% RH and in water. The increased stiffness in the post-yield region apparently results from stress in the network of cysteine disulfide bonds, as the post-yield slope has been found to be dependent on the disulfide content of the hair.13,21,22 Cannell and Carothers reported data on the effect of disulfide bond cleavage with sodium bisulfite on the post-yield slope.21 Disulfide bond cleavage was measured by amino acid analysis.23 Slopes were normalized to the cross-sectional areas of the fibers. Their results are plotted in Figure 2.