Numerical simulation of three-dimensional fiber orientation in short-fiber-reinforced injection-molded parts

In this paper, a second-order orientation tensor, orientation average of dyadic product of orientation vector, was adopted to describe three-dimensional orientation distribution of short fibers in injection-molded parts. For calculation of the fiber orientation tensor, a closure approximation is needed to reduce the higher fourth-order orientation tensor to the lower second-order. A modified hybrid closure approximation, which can accurately describe random-in-space, random-in-plane, and uniaxial distribution of fiber orientations, is introduced to yield better computational results than existing solutions available in references. Comparisons between numerical calculations of the second-order orientation tensor and the orientation distribution function (ODF) in simple flow field were made in order to demonstrate the accuracy of the closure approximation proposed. Orientation tensor equation currently introduced was incorporated into a finite-element/finite-difference program for injection molding analysis. In addition, new numerical technique was developed to reasonably calculate velocity gradients using constant velocity elements. The developed program was applied to simulation of injection molding for the thin cavity of a sector of spherical shell. The analysis showed that the currently proposed numerical approach enhances the solution accuracy of fiber orientation prediction in injection-molded parts made of short-fiber-reinforced thermoplastics.