The prediction of time-dependent non-linear stresses in viscoelastic materials: I. Selection of constitutive equation and strain measure

The theories for the prediction of time-dependent, non-linear stresses in viscoelastic materials such as polymers are reviewed, and it is noted that the commonly observed stress non-linearity may be ascribed either, as is usually done, to memory-function non-linearity or, alternatively, to strain-measure non-linearity. To investigate the latter alternative whilst retaining a general memory-function non-linearity, a single-integral constitutive equation of the Bird—Carreau type is employed but with an arbitrary strain measure I in place of the normally employed Finger tensor F. This model includes as special cases a large proportion of the constitutive equations previously employed for predictive purposes and in particular with a linear memory function it is shown to be indistinguishable, with the normally conducted shear experiments, from the successful BKZ model.In the new model the shear component I₁₂ of the strain measure can be found from experimental results obtained in the startup of steady shear flow, without specification or restriction of memory-function non-linearity. The form of I₁₂ found from experiment is quite non-linear in shear a for ¦a¦> 2, and hence differs from the F tensor for which F₁₂ = a. The same form for I₁₂ found for a variety of polymer solutions and a polymer melt and consequently a simple function describing I₁₂ is proposed as a new, material-independent, strain measure.