Linear Viscoelastic Property Measurement and Its Significance for Some Nonlinear Viscoelasticity Models

Abstract

Three linear viscoelastic properties of an Ashland neat urethaneadhesive were measured. Dynamic tensile compliance was found using anovel extensometer. The results were considerably more accurate andprecise than standard DMTA testing. Dynamic shear compliance wasdetermined using an Arcan specimen. Dynamic Poisson's ratio wasextracted from strain gage data that was corrected to include gagereinforcement effects. Experiments spanned three frequency decades andisothermal data was shifted by time-temperature superposition to createmaster curves spanning thirty decades. Master curves were fit to Pronyseries that originated in the time domain. Dynamic shear complianceinferred from dynamic tensile compliance and dynamic Poisson's ratiocompared well with measured values. This established the validity of thetime temperature shifting and interconversion procedures that weredeveloped for this isotropic material in its linear range. Dynamictensile compliance and dynamic Poisson's ratio were then used to obtainthe dynamic bulk compliance, which was in turn converted to the timedomain along with the dynamic shear compliance. The shear and dynamiccreep compliance functions thus obtained formed the basis of thenonlinear viscoelastic models.

Two nonlinear viscoelastic models based on free volume considerations(modified to include distortional effects) were considered asconstitutive models. One was based on the effect of the state of strainon the free volume through the Doolittle equation, while the otherincorporated the effect of state of stress via the Tait equation. Ramploading experiments conducted in tension and shear at strain ratesspanning three decades were reasonably well predicted. Contrary toexpectations based on previous work with less precise small strain data,the strain-based model proved to be more applicable than thestress-based one. This means that the shear modified free volume modelof Popelar and Liechti (2003) has now been shown to be applicable to twostructural adhesives, one an epoxy and the other a urethane, undercertain loading conditions. There were also notable differences in thepredicted responses to cyclic loading under strain and load control.However, neither matched the data in tension or in shear once the firstunloading occurred, although the strain-based model again providedbetter predictions.