The use of principal spatial tensor to predict anisotropic fiber orientation in concentrated fiber suspensions

Abstract

The Phelps-Tucker anisotropic rotary diffusion (ARD) equation constitutes an important development in relation to concentrated fiber suspension rheology and is significant in its ability to predict transient, flow-induced fiber orientation, especially for long fiber composites in the industry. Within this model, a critical spatial tensor was assumed to be a polynomial tensor-valued function depending on both the orientation tensor and the rate-of-strain tensor. However, it can be difficult to derive a large number of fitting ARD parameters. For simplification, we newly defined the spatial tensor as coaxial with the orientation tensor's principal directions, while the spatial tensor's principal components are to control anisotropic changes in the orientation tensor. Such a principal spatial tensor used in the Phelps-Tucker ARD model is demonstrated in accurately predicting the shell-core structure of fiber orientation distributions for injection molding simulation of long fiber composites, supported with e...