Physics of the Stress Overshoot and Chain Stretch Dynamics of Entangled Polymer Liquids under Continuous Startup Nonlinear Shear

We construct a new theory for transient aspects of the shear rheology of entangled chain liquids. Within an established tube model constitutive equation framework, four new physical features are introduced: a tension blob scaling derivation of the interchain grip force that generates chain stretch, a force imbalance condition for the termination of affine stretch deformation, a delayed chain retraction process that after loss of grip is accelerated for fast deformations, and a distribution of tube diameters. Nonclassical predictions are made for the stress-strain curve to just beyond the overshoot, the existence of a master curve, and fractional power law scaling of the overshoot strain and stress at high shear rates, all in good agreement with experiment and simulation. Testable new predictions are made for chain stretch dynamics.