Fiber orientation in simple injection moldings. Part 1. Theory and numerical methods

This paper sets out the theory and numerical methods used to simulate filling and fiber orientation in 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 numerical scheme which 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 only predicted if the effects of the fountain flow and heat transfer are included in the simulation.