Size-Dependent Behavior of Macromolecular solids II: Higher-Order Viscoelastic Theory and Experiments

Additional molecular rotations in long chained macromolecules lead to additional size dependence. In this investigation, we developed the higher order viscoelasticity framework and conducted experiments to determine the higher order material length scale parameters needed to describe the higher order viscoelastic behavior in the new framework. In the first part of the investigation of high order deformation behavior of macromolecular solids, the higher-order viscoelasticity theories for Maxwell and Kelvin-Voigt materials, and models of higher-order viscoelastic beam deflection creep are developed in this study. We conducted creep bending experiments with epoxy beams to show that the creep deflection behavior followed the conventional Kelvin-Voigt viscoelastic behavior when the beams are thick and that higher-order size dependences are present in both the time-independent elastic and time-dependent creep deflection when the beams are thin. The higher-order viscoelastic creep bending model with a higher-order material length scale parameter, 12, was shown to be in good agreement with the data. Furthermore, 12 is chain-based, instead of mechanism-based. Since each macromolecular solid has only a single set of chains, only a single 12 is needed to characterize its higher order behavior in the newly developed higher order viscoelasticity framework. The new single 12 higher order viscoelastic theory can be used to describe viscoelastic nanomechanical behaviors in nanostructured macromolecular solids.