Fiber orientation in simple injection moldings. Part I: Theory and numerical methods

Abstract

This paper sets out the theory and numerical methods used to simulate filling and fiber orientation is simple injection moldings (a film‐gated strip and a center‐gated disk). Our simulation applies to these simple geometry problems for the flow of a generalized Newtonian fluid where the velocities can be solved independently of fiber orientation. This simplification is valid when the orientation is so flat that the fibers do not contribute to the gapwise shear stresses. A finite difference solution calculates the temperature and velocity fields along the flow direction and through the thickness of the part, and fiber orientation is then integrated numerically along pathlines. Fiber orientation is three‐dimensional, using a second‐rank tensor representation of the orientation distribution function. The assumptions used to develop the simulation are not valid near the flow front, where the recirculating fountain flow complicates the problem. We present a numerrical scheme that includes the effect of the fountain flow on temperature and fiber orientation near the flow front. The simulation predicts that the orientation will vary through the thickness of the part, causing the molding to appear layered. The outer “skin” layer is predicted only if the effects of the fountain flow and heat transfer are included in the simulation.

Rheology Effects on Predicted Fiber Orientation and Elastic Properties in Large Scale Polymer Composite Additive Manufacturing

“…Note that the second order orientation tensor A has seen widespread use for statistically describing the orientation of suspended fibers in narrow gap shear dominant applications [8][9][10]13]. In this study, flow within the nozzle has a significant shear component; however, there is considerable extensional flows within the converging section of the nozzle, and also just outside the nozzle exit where die swell begins to form.…”

“…Following Fu et al, we define β = 0.9802 (corresponding to α = 10 in Equation (19)). Bay and Tucker [9] defined an empirical formula for evaluating C I , which depends on the values of the fiber volume fraction and aspect ratio as…”

“…A computationally more efficient approach that is often employed is a one-way weakly coupled formation that ignores the effect of the fiber suspension on viscosity. This approach has been effective in applications having shear dominant narrow gap flows such as injection and compression modelling simulations [8][9][10], and is the approach we use in this study. Fiber orientation studies in polymer composite AM applications have recently become of interest.…”

Effect of plant fiber content on velocity field in extensional flow

“…There are some literatures dealing with the dynamics of polymer-fiber composites by experimental, numerical and analytical methods for decades, such as [1][2][3][4][5]. Huang et al [6][7] investigate the orientation distribution of fiber suspensions based on shear-planar extensional force field and equibiaxial extensional flow.…”

Influence of Hygrothermal Aging on Poisson’s Ratio of Thin Injection-Molded Short Glass Fiber-Reinforced PA6

“…Furthermore, the number of components of the tensor can be reduced due to symmetry conditions from 9 to 6; the components a xy , a xz and a yz are not considered due to negligible results [1]. represented by the tensor second stage TFOD as shown in Equation (1) based on the angles Φ and Θ (from polar coordinate system, see Figure 1), which describes the average glass fiber orientation in a defined region in the Cartesian coordinate system according to Advani and Tucker as well as Bay and Tucker [6][7][8]. Equation (1) is based on the probability distribution function of fiber orientation state at a point in space by Advani and Tucker [8].…”