Mechanical Properties of Hair 244 the matrix is composed of keratin associated proteins63 packed around the microfibrils which combine to form macrofibrils. (The reader is referred back to Chapter 1 for more details.) The composite is modeled as a fixed spring in parallel with a spring and viscous dashpot in series (Figure 14) the fixed spring (K 0 ) represents the water-impenetrable microfibrils and contributes about 1.4 GPa to the elastic modulus. The main resistance to extension of the microfibrils probably comes from the hydrogen bonded network of the α-helical keratin proteins.14,15,64 The matrix phase, M, primarily contributes viscous forces which decay with time as the matrix proteins flow, causing stress relaxation by releasing the stress on spring K 1 . The matrix is considered to make a small contribution to the equilibrium modulus (spring K 0 ). The viscosity of the matrix (η) decreases as the water content of the fiber increases, thereby increasing viscous loss in dynamic experiments and the rate of stress relaxation at fixed extension. Rapid extension of the hair by X units will require a force of (K 0 + K 1 )X which will decay to K 0 X due to flow of the matrix proteins constituting the dashpot. The initial dry modulus of ~4 GPa will relax to the equilibrium modulus of about ~1.4–1.6 GPa with time. Stress relaxation can be analyzed using Figure 14. Stress decays exponentially to an equilibrium level following the equation: F(t) = K0X + K1Xe-t/τ where K0, K1 and X are defined above and τ= η/K1 thus stress relaxation will be much faster in water when the matrix proteins are plasticized greatly reducing η. The equation above represents a simple linear model of viscoelasticity. It is useful to illustrate the application of viscoelastic theory to stress relaxation, but more complex models with more springs and dashpots may be required under many Figure 14. Mechanical model representing the two phase model of keratin fibers