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A Thermomechanical Instability in the High Rate Extension of Textile Fibers

The effect of thermomechanical coupling arising from fiber plasticity on the stability of homogeneous straining deformation in fibers extended at high strain rates is investigated using a simple analytical approach. A constitutive model is assumed for the fiber's plastic deformation, incorporating linear thermal softening and linear strain hardening. The behavior of solutions to the coupled equations of motion and energy balance under adiabatic conditions is studied for small initial disturbances to the velocity field associated with homogeneous straining. Homogeneous straining motion is shown to be stable for particular values of a parameter involving the fiber's thermophysical and constitutive properties. For other values of the parameter, unstable strain localization leading to fiber rupture is demonstrated to be likely. The implications of these results with regard to high strain rate behavior of textile materials are discussed.