A Distortion-Modified Free Volume Theory for Nonlinear Viscoelastic Behavior

Many polymeric materials, including structural adhesives, exhibit anonlinear viscoelastic response. The nonlinear theory of Knauss and Emri(Polym. Engrg. Sci. 27, 1987, 87–100) is based on the Doolittle conceptthat the free volume controls the mobility of polymer molecules and,thus, the inherent time scale of the material. It then follows thatfactors such as temperature and moisture, which change the free volume,will influence the time scale. Furthermore, stress-induced dilatationwill also affect the free volume and, hence, the time scale. However,during this investigation, dilatational effects alone were found to beinsufficient for describing the response of near pure shear tests of abisphenol A epoxy with amido amine hardener. Thus, the free volumeapproach presented here has been modified to include distortionaleffects in the inherent time scale of the material. The same was foundto be true for a urethane adhesive.The small strain viscoelastic responses of the two materials havebeen determined from master curves of uniaxial and bulk creep testing atvarious temperatures. The nonlinear free volume model, modified toinclude distortional effects in the reduced time, was incorporated inthe ABAQUS finite element code via a user-defined material subroutine.For the epoxy, validation of the modified theory (a strain-basedformulation of free volume) has been achieved through good agreementbetween the computational and experimental results of butterfly-shapedArcan specimens subjected to loadings ranging from near pure shear toshear with various amounts of superposed tension and compression. Inaddition to predicting the response under a variety of multiaxial stressstates, the modified free volume theory also accurately predicts theformation and growth of shear banding, or regions of highly localizeddeformation, which have been found to occur upon continued loading ofthe epoxy. The urethane did not appear to exhibit any localizeddeformation over the range of temperatures at which it was tested.As a result, a stress-based modified free volume approach was requiredto model its multiaxial and temperature-dependent behavior. Althoughfree volume was the unifying parameter for the two materials, the needfor a stress-based and strain-based formulation of the free volume forthe urethane and epoxy, respectively, could not be reconciled at thistime.