The Optimized Quasi-Planar Approximation for Predicting Fiber Orientation in Injection-Molded Composites1

Abstract

Abstract Fiber filled injection-molded plastic parts contain complex fiber orientation patterns. This fiber orientation state affects material properties, including both elastic modulus and strength, and the calculation of shrinkage and warpage. Several models are available for predicting fiber orientation, which are based on the theory of Folgar and Tucker [1]. A particular simplification of these models, here called the quasi-planar (QP) approximation, was introduced by Gupta and Wang [2]. Here we develop a substantially improved version of that model, which we call the optimized quasi-planar (OQP) approximation. The OQP approximation is formed by optimizing the QP approximation against a more general fiber orientation model. Details of the current and improved models are discussed, and the typical behavior of the old and new models is explored. In addition, simulations are performed using C-MOLD, a commercial software package that implements the QP approximation, to determine the final fiber orientation state in an end-gated strip. The resulting fiber orientation data is then used to predict the elastic modulus as a function of position, and both predictions are compared to available experimental data for fiber orientation and elastic modulus. The results show that the OQP approximation improves the fiber orientation prediction and the subsequent elastic modulus prediction compared to the QP model, though the OQP approximation is still less accurate than the full three-dimensional model.