Injection molding of dilute and semi-dilute fiber suspensions

Abstract

The focus of this paper is unsteady flow of semi-dilute fiber suspensions in complex geometries. These flows are typical of injection molding problems in which the raw material in granular form, usually plastic resin mixed with fibers of certain concentration and aspect ratio, is heated above the melting point, and forced into the mold cavity by means of pressure. When the mold cavity is filled, additional material is supplied to compensate for shrinkage due to cooling. The injection is then cut off, the mold is allowed to cool, and the piece is removed from the mold. The duration, temperature and pressure at each stage are adjusted to suit individual requirements. In this paper we used the theory developed by Dinh and Armstrong for semi-dilute fiber suspensions, although the theoretical background and numerical procedures developed in this paper can be extended to other theories as well. The constitutive equations are expressed in terms of the flow kinematics through the use of the Finger and Cauchy finite deformation tensors which are approximated numerically using a semi-implicit time integration scheme. The full unsteady form of the governing equations are formulated using a mixed Eulerian-Lagrangian description and solved using a classical Galerkin Finite Element Method. The accuracy of the numerical solution is compared to exact solutions for an equivalent radially diverging source flow. Results are shown for the filling of a two-dimensional cavity under various process conditions such as constant flow rate, constant pressure and at different fiber concentrations and fiber aspect ratio.