Using transient shear rheology to determine material parameters in fiber suspension theory

Abstract

Fiber suspension theory model parameters for use in the simulation of fiber orientation in complex flows are, in general, either calculated from theory or fit to experimentally determined fiber orientation generated in processing flows. Transient stress growth measurements in startup of shear flow and flow reversal in the shear rate range, γ̇=1–10 s−1, were performed on a commercially available short glass fiber-filled polybutylene terephthalate using a novel “donut-shaped” sample in a cone-and-plate geometry. Predictions using the Folgar–Tucker model for fiber orientation, with a “slip” factor, combined with the Lipscomb model for stress were fit to the transient stresses at the startup of shear flow. Model parameters determined by fitting at γ̇=6 s−1 allowed for reasonable predictions of the transient stresses in flow reversal experiments at all the shear rates tested. Furthermore, fiber orientation model parameters determined by fitting the transient stresses were compared to the experimentally determined evolution of fiber orientation in startup of flow. The results suggested that fitting model predictions to the stress response in well-defined flows could lead to unambiguous model parameters provided the fiber orientation as a function of time or strain at some shear rate was known.