Modeling of injected pultrusion processes: A numerical approach

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Abstract
Injected pultrusion (IP) is an attractive process for high volume, high performance, and low cost manufacture of continuous fiber reinforced polymer matrix composites. In this work we focus our attention on development of a computer simulation model for the IP process. First, the governing equations for conservation of mass, momentum, and energy are developed using a local volume averaging approach. In turn, a computer simulation model of the IP process is developed using finite element/control volume (FE/CV) and finite difference techniques. Specifically, the equation of continuity and conservation of momentum are solved in 2‐D using a Galerkin FE/CV technique. The energy and chemical species balance equations are solved in 3‐D, where streamline upwind Petrov‐Galerkin (SUPG) or streamline upwind (SU) FE/CV are used to discretize the equations in two dimensions while finite differences have been used in the third dimension. The chemical species balance equation is solved in the Lagrangian frame of reference using finite differences. Different numerical formulations (Galerkin, Lagrangian, SU, and SUPG) are used to solve a number of benchmark problems to determine the best numerical formulation. It is shown that for coarse discretization, Streamline Upwind methods perform consistently better than the other methods. However, for refined meshes, the Lagrangian method produces the best solution for a given CPU time. Also, using the simulation model, the effect of fiber pull speed, reinforcement anistropy, and taper of the die on the quality of the product is studied. It is shown that the simulation model can be effectively used to design the die geometry as well as to optimize the operating conditions for a given product.

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