Phenomenological improvements to predictive models of fiber orientation in concentrated suspensions

Abstract

The standard Folgar-Tucker (FT) orientation equation is a useful method for theoretically determining isotropic fiber orientation in concentrated suspensions. However, when quantitatively compared with related experimental observations, this equation demonstrates an over-prediction inaccuracy. Recently, the Phelps-Tucker anisotropic rotary diffusion (ARD) model has shown an ability to handle primary anisotropic fiber orientation. Nevertheless, the ARD tensor depending upon Hand's tensor is difficult to apply in general, because numerous parameters themselves are so sensitive as to affect the stability of any numerical results. To address these critical problems in predicting fiber orientation, this study proposes an improved ARD tensor combined with a new retardant principal rate (iARD-RPR) model. The RPR model is a coaxial correction of the orientation tensor for the FT equation. In addition, the iARD tensor, consisting of an identity tensor and a dimensionless fiber-rotary-resistance tensor, is more concise with two available parameters. As a validation, the iARD-RPR model nicely fits the orientation tensor components measured in transient simple shear flows. Of particular importance is the good agreement between the predictive fiber orientation distribution and the practical core-shell structure for the center-gated disk of injection molding of fiber-reinforced thermoplastics.