Time, temperature, and linear viscoelasticity

Abstract Linear viscoelastic bodies satisfy the Boltzmann superposition principle which permits the calculation of the effect of arbitrary stress or strain history in terms of creep or stress relaxation parameters, respectively. In such calculations, the temperature is not considered as an independent variable; rather, the temperature must be constant, and the stress relaxation and creep parameters used are for the given temperature. By assuming the validity of the time‐temperature superposition principle, it is shown how an arbitrary thermal history may be included. By employing spring‐dashpot model methods, Boltzmann's principle is generalized, leading to the concepts of equivalent stress σ( t ) and equivalent time w ( t ), the latter concept having also been introduced for creep and stress relaxation by Hopkins. These quantities are defined by\documentclass{article}\pagestyle{empty}\begin{document}$\sigma(t)=\rho(0)T(0)S(t)/\rho(t)T(t),w(t)=\int_0^t dt^{\prime}/a[T(t^{\prime}),T(0)]$\end{document} where t = time, p = density, T = temperature, and a [ T ( t ), T (0)] is the time‐temperature shift factor between temperatures T (0) and T ( t ). In terms of the equivalent stress and equivalent time, Boltzmann's principle for shear remains the same as for the isothermal case with stress relaxation or creep parameters at the initial temperature, T (0). In the case of tensile experiments, the observed strain must be corrected for thermal expansion.