An extension of the time–temperature superposition principle to non-linear viscoelastic solids

An experimental data treatment is introduced to manage with the tensile test responses of highly non-linear viscoelastic solids such as solid propellants. This treatment allows the representation of a set of strain–stress curves by a single intrinsic non-linear response which is found independent of the experimental conditions of rate and temperature. To obtain this result, two independent normalization factors are applied both on the stress and strain axis. The requirement of a normalization factor applied to the strain measure produces a pseudo-strain which is found to be viscoelastic in nature. It is believed that the existence of such a viscoelastic strain measure is the characteristic feature of non-linear viscoelasticity. To confer some generality to the principle, the validity is also checked for volumetric and multiaxial stress response of solid propellant. To illustrate the potential application of the principle, it is applied to build up an idealized material database upon which numerical identification of constitutive non-linear models can be easily performed. Finally, generalization is extended to other filled elastomers such as a carbon black filled SBR.