J. Cosmet. Sci., 69, 383–395 (September/October 2018) 383 Quasi-Static Torsional Deformation of Single Hair Fibers: Application of a Modeling Approach and Results from Cosmetic Treatments REBECCA J. LUNN, YANN LERAY, STEVE. BUCKNELL, and DANIEL M. STRINGER, Dia-Stron Limited, Andover, Hampshire, UK (R.J.L., Y.L., S.B., D.M.S.) Synopsis To date, most single hair fi ber mechanical testing publications in the literature have focused on tensile deformation with torsional measurements receiving far less attention. However, there is much to be gained from the measurement of torsional properties of a single hair fi ber such as providing an insight into the shear stiffness changes that are associated with cuticle damage. This study outlines the potential use of torsional measurements to differentiate between cosmetic treatments where other modes of deformation do not. A core/shell modeling approach has also been applied to separate out the potential contributions of the cuticles and the cortex on the fi ber torsional modulus and the effect of relative humidity on hair fi ber structural components. INTRODUCTION Human hair is a highly complex material, biologically engineered to favor load bearing in a longitudinal direction while still preserving fi ber bending and twisting fl exibility. This is a result of the hair being an anisotropic material, exhibiting a change in the mechanical properties with direction. To gain a fuller understanding of hair fi bers’ mechanical properties, it is paramount not only to consider tensile deformations, but also to measure bending and torsional deformations. A more thorough understanding of the mechanical behavior of hair fi bers across the multiple modes of deformation could aid the development of hair care products, which may result in benefi ts to the consumer, such as improved manageability, ease of styling, and less breakage. The multiple substructural components of human hair infl uence the mechanical behavior of the fi ber to differing extents dependent on the mode of deformation. The tensile stiff- ness of hair fi bers arises from the crystalline intermediate fi laments (1,2) which are em- bedded within a sulfur-rich, cross-linked amphorous matrix. These fi laments are aligned in a parallel orientation to the longitudinal axis of the fi ber and along with the inter- and intramolecular interactions of the keratin-associated proteins within the matrix provide Address all correspondence to Rebecca Lunn at rebecca.lunn@diastron.com.

JOURNAL OF COSMETIC SCIENCE 384 resistance to tensile deformation. When hair fi bers are hydrated, the hydrogen bonds within the matrix are disrupted causing radial swelling of the fi ber and a weakening of the matrix. The intermediate fi laments are much less affected by the presence of water and therefore dominate the tensile stiffness (3,4). Under small levels of strain, typically less than 2%, the hair behaves as an elastic or “pseudo-elastic” material (5). Therefore, hair cuticles account for a low fraction area/volume of the whole fi ber and that the tensile deformation occurs solely in the longitudinal direction, the Young’s modulus can be as- sumed to be almost entirely associated with the cortex (6). Bending is a complex mode of deformation, and a number of theories describing the role the various substructures play have been proposed including the cuticles (7,8) and the cortex (9). The bending stiffness of a fi ber has a fourth power relationship with the fi ber diameter, and consequently, mate- rial further away from the fi ber center has a greater impact on the bending stiffness than material at the core of the fi ber. The torsional deformation of hair relates to the twisting of the fi ber around the longitu- dinal axis (Figure 1). When a fi ber is twisted, the shearing stress is not equally distributed throughout the fi ber (10) but increases from the central point to a maximum shear stress Figure 1. Shear deformation in an elliptical cylinder, where F is the force applied, θ is the deformation angle, and a, b are the major and minor radii, respectively.