Numerical Approaches for Modeling Filling in Polymer Molding Processes

"Free boundary problems are a common occurrence in materials processing operations. An important example is the filling of material into molds. This paper looks at filling problems associated with polymer processing, in particular Resin Transfer Molding (RTM) and Compression Molding. A general, single governing equation is developed which on numerical solution provides predictions for the position of the polymer front in the mold during filling. Both fixed and deforming finite element solutions are developed. Application to polymer filling test problems reveal that the fixed and deforming grid scheme are accurate and compare closely with each other.IntroductionProblems arising from the analysis of material processing operations often involve the tracking of a moving boundary, on which a balance conditions needs to be met, or the locating of a free surface that defines the solution domain. Material processing examples of so called ""free and moving boundary problems"" include; the tracking of solidification/melting fronts[l], the tracking of the metal/gas interface during the filling of a mold[2] and location and shape of a skull (freeze line) in a melting furnace[3].Computational solution of free and moving boundary problems usually fit into one of two classes, viz.1. Fixed grid scheme: In which the spatial domain is covered by a fixed grid (mesh) of node points and the solution uses an auxiliary variable (e.g. a local liquid fraction) to track the moving boundary or locate the free surface.2. Deforming grid scheme: In which the grid in the spatial domain is continuously deformed (or adapted in a steady state problem) such that a specified set of grid points lie on the moving boundary or the free surface.Details on the basic underlying features in these two classes of solution can be found in the excellent monograph by Crank [4]."