Fiber Orientation in 3-D Injection Molded Features

Abstract

We present a finite element method for predicting the fiber orientation patterns in 3-D injection molded features, and compare the predictions to experiments. The predictions solve the full balance equations of mass, momentum, and energy for a generalized Newtonian fluid. A second-order tensor is used to describe and calculate the local fiber orientation state. A standard Hele-Shaw molding filling simulation is used to provide inlet boundary conditions for the detailed finite element models, which are limited to the local geometry of each feature. The experiments use automated image analysis of polished cross-sections to determine fiber orientation as a function of position. Predictions compare well with experiments on a transverse rib, where the detailed calculation can be 2-D. Results of a 3-D calculation for a flow-direction rib also show generally good agreement with experiments. Some errors in this latter calculation are caused by not simulating the initial filling of the rib, due to computational limits.

Exact tensor closures for the three-dimensional Jeffery's equation

“…This method should run at about the same speed as computing the orthotropic closure algorithms of Cintra & Tucker (1995) and VerWeyst et al (1999). The workload of this algorithm involves solving an ordinary differential equation in about 11 variables, where the main computational effort will be to diagonalize the matrices and perform the change of basis for the rank-two and rank-four tensors.…”

“…Hinch & Leal 1976;Altan et al 1989Altan et al , 1990Verleye & Dupret 1993;Cintra & Tucker 1995;VerWeyst et al 1999;Chung & Kwon 2002;Han & Im 2002;Jack & Smith 2005;Jack, Schache & Smith 2010) have proposed closures, that is formulae to calculate the fourth-order moment tensor A from the second-order moment tensor A. Many of the approximate closures involve coefficients obtained by fitting numerical data found by solving (1.2) using a finite-element method (see e.g.…”

Characterization of Velocity Profile of Highly-Filled GFRP-BMC through Rectangular Duct-Shaped Specimen during Injection Molding from SEM Fiber Orientation Mapping

“…10,11) This is done simply from the "skins" in Fig. 9 as: ¤ f,(L) and ¤ f,(R) = 0.14 and 0.27 mm, respectively, hence ¤ f,(avg) = 0.20 mm.…”

The Fast Exact Closure for Jeffery’s equation with diffusion

“…(2) and (3) when D r = 0 and when the orientation is isotropic at some time. Nevertheless it is reasonable to suppose that the exact closure should give a reasonable approximation in general, even when D r / = 0 as in Verweyst et al [1,13]. Their ORT closure is a polynomial approximation to the Exact Closure, and as we demonstrate below, gives answers that are virtually indistinguishable from that of the Exact Closure.…”