Chia-Hsiang Hsu

Phenomenological improvements to predictive models of fiber orientation in concentrated suspensions

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 Hands 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 con...

An objective tensor to predict anisotropic fiber orientation in concentrated suspensions

The improved anisotropic rotary diffusion (iARD) model was previously regarded as a suitable description of anisotropic orientation states for long fibers in concentrated suspensions. However, the iARD tensor does not pass the classic rheological rule of Euclidean objectivity, namely, material frame indifference. It is hard to ignore the nonobjective effect due to the fact that different coordinate systems may yield different answers. Such an issue can be attributed to the iARD tensor related to the nonobjective velocity-gradient tensor. We therefore proposed a new iARD tensor, which depends on the square of the objective rate-of-deformation tensor. It is important to differentiate between the original Phelps–Tucker anisotropic rotary diffusion tensor and the objective iARD tensor via computing their first invariants. Furthermore, we validated this new iARD models accuracy in predicting a distinct, broader core-shell orientation structure of injection-molded long-fiber composites through careful experime...

Effect of the packing stage on fiber orientation for injection molding simulation of fiber-reinforced composites

During the packing or post-filling stage, a significant flow of polymer inside the cavity may result due to the compressibility of the polymer melt under the higher packing pressure of the injection molding process. In the meantime, the effect of the packing stage on the shell–core structure of the fiber orientation for the fiber-reinforced composites has always been a concern. Even though certain commercial packages have undergone unified simulations of the filling and packing stages, fiber orientation has usually been determined at the end of the filling stage. A recently proposed mathematic model, Improved Anisotropic Rotary Diffusion and Retarding Principal Rate, having incorporated the state-of-the-art technology of 3D injection molding simulation, has demonstrated its ability to provide reliable predictions of fiber orientation. The present numerical results concentrate on comparing and analyzing the difference in fiber orientation between the filling and packing stages, while the important effects of packing time and packing pressure are further revealed. A qualitative comparison of core thickness widths in related experimental investigations is discussed herein.

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

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 tensors principal directions, while the spatial tensors 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...

Comparison of recent fiber orientation models in injection molding simulation of fiber-reinforced composites

In the structural analysis of automotive products made of lightweight fiber-reinforced thermoplastics (FRT), the primary mechanical requirement is their relation to the orientation states of fibers. The famous Folgar–Tucker equation of fiber orientation has hitherto been used to predict the skin–shell–core structure of fiber orientation patterns for injection-molded fiber composites. However, this model results in inaccurate predictions regarding the thinner core width. To enhance the reliability of fiber orientation predictions, Tucker and coworkers rigorously derived the reduced strain closure and anisotropic rotary diffusion (ARD) models in relation to the theoretical rheology of fiber suspension. More recently, the improved ARD and retarding principal rate model and the Moldflow rotational diffusion model were developed and made available in the industry dealing with the state-of-the-art software of injection molding simulation. A deep understanding of these fiber models is important for achieving successful FRT structural analysis. In this work, we therefore investigate the accuracy of these fiber orientation models, as well as the changes in fiber orientation distribution related to model parameters and model objectivity.

Predictions of fiber concentration in injection molding simulation of fiber-reinforced composites

The microstructures of injection-molded short fiber composites, involving fiber orientation and fiber concentration, strikingly influence flow behaviors and mechanical properties. Through the use of certain commercial software, reported numerical predictions of fiber orientation for the shell–core structure have been obtained to date. However, no work has been done on fiber concentration prediction available in processing simulations. In the theoretical field of suspension rheology, the suspension balance (SB) model has proven successful in capturing particle migration behavior under the simple Couette shear flow of “spherical” particle suspension, hence the attempt to verify the SB model applied in the “like-rod” suspensions. To predict flow-induced variations of fiber concentration, the SB model is implemented in 3-D-injection molding simulation with more general flows. It is remarkable for the shell–core structure is explored to reflect the relationship between fiber orientation and fiber concentration.