An objective model for slow orientation kinetics in concentrated fiber suspensions: Theory and rheological evidence

Abstract

Recent experiments suggest that short fibers in concentrated suspensions align more slowly as a function of strain than models based on Jeffery’s equation predict. We develop an objective model that captures the slow orientation kinetics exhibited by short-fiber suspensions. The standard moment-tensor equation of fiber orientation is used to find equations for the change rates of the eigenvalues and eigenvectors of the orientation tensor. As a phenomenological assumption, the growth rates of the eigenvalues are reduced by a constant scalar factor, while the rotation rate expressions for the eigenvectors are unchanged. The eigenvalue/eigenvector equations are then reassembled as a tensor equation. An equivalent kinetic theory is also developed. The new model is tested in a variety of flows, and found to exhibit slower kinetics than the standard model but similar steady-state orientations. The model provides an excellent fit to the shear stress transient in a shear reversal experiment with a 30% glass fiber filled polybutylene terephthalate resin melt, and we show how this experiment can be used to determine the parameters of the model.

A validation of the fibre orientation and fibre length attrition prediction for long fibre-reinforced thermoplastics

“…Recent studies could show that those materials show a slower rate of orientation development as predicted by the FT-model. To slow down the rate of orientation, Wang et al [3] developed a reduced strain closure (RSC) model which exhibits a slower orientation kinetic by use of a scalar damping parameter . Since the RSC-model retains the isotropic diffusion term of the FT-model, described by the fibre-interaction coefficient C i , the model shows the same orientation states as the FT-model for long times (or steady-state) but shows improved predictions elsewise.…”

Using startup of steady shear flow in a sliding plate rheometer to determine material parameters for the purpose of predicting long fiber orientation

“…In a later paper, Eq. (5) was modified to incorporate a method that allowed for the slowing of the orientation dynamics and is referred to as the reduced strain closure (RSC) model [Wang et al (2008)]. The RSC model is much more complex as compared to Eq.…”

Prediction of fiber orientation in injection-molded parts using three-dimensional simulations

“…To obtain an objective model with slow orientation kinetics, the growth rates of the eigenvalues λi are reduced by a phenomenological factor κ ≤ 1 while the rotation rates of the eigenvectors ei are kept unchanged, which is the essence of the RSC model [3]:…”

“…Wang et al [3] modified the F-T model by reducing the growth rates of the eigenvalues of the fiber orientation tensor by a constant scalar factor while keeping the rotation rates of the eigenvectors unchanged. Thus was developed the Reduced Strain Closure (RSC) model.…”