Linear viscoelastic property measurement and its significance for some nonlinear viscoelasticity models

Three linear viscoelastic properties of an Ashland neat urethane adhesive were measured. Dynamic tensile compliance was found using a novel extensometer. The results were considerably more accurate and precise than standard DMTA testing. Dynamic shear compliance was determined using an Arcan specimen. Dynamic Poisson's ratio was extracted from strain gage data that was corrected to include gage reinforcement effects. Experiments spanned three frequency decades and isothermal data was shifted by time-temperature superposition to create master curves spanning thirty decades. Master curves were fit to Prony series that originated in the time domain. Dynamic shear compliance inferred from dynamic tensile compliance and dynamic Poisson's ratio compared well with measured values. This established the validity of the time temperature shifting and interconversion procedures that were developed for this isotropic material in its linear range. Dynamic tensile compliance and dynamic Poisson's ratio were then used to obtain the dynamic bulk compliance, which was in turn converted to the time domain along with the dynamic shear compliance. The shear and dynamic creep compliance functions thus obtained formed the basis of the nonlinear viscoelastic models. Two nonlinear viscoelastic models based on free volume considerations (modified to include distortional effects) were considered as constitutive models. One was based on the effect of the state of strain on the free volume through the Doolittle equation, while the other incorporated the effect of state of stress via the Tait equation. Ramp loading experiments conducted in tension and shear at strain rates spanning three decades were reasonably well predicted. Contrary to expectations based on previous work with less precise small strain data, the strain-based model proved to be more applicable than the stress-based one. This means that the shear modified free volume model of Popelar and Liechti (2003) has now been shown to be applicable to two structural adhesives, one an epoxy and the other a urethane, under certain loading conditions. There were also notable differences in the predicted responses to cyclic loading under strain and load control. However, neither matched the data in tension or in shear once the first unloading occurred, although the strain-based model again provided better predictions.