Mathematical modeling and numerical simulation of cell growth in injection molding of microcellular plastics

A mathematical formulation and numerical simulation for non-isothermal cell growth during the post-filling stage of microcellular injection molding have been developed. The numerical implementation solves the energy equation, the continuity equation, and a group of equations that describe the mass diffusion of dissolved gas and growth of micro-cells in a microcellular injection molded part. The unit-cell model employed in this study takes into account the effects of injection and packing pressures, melt and mold temperatures, and super-critical fluid content on the material properties of the polymer-gas solution and the cell growth. The material system studied is a microcellular injection molded polyamide 6 (PA-6) resin. Two Arrhenius-type equations are used to estimate the coefficients of mass diffusion and solubility for the polymer-gas solution as functions of temperature. The dependence of the surface tension on the temperature is also included in this study. The numerical results in terms of cell size across the sprue diameter agree fairly well with the experimental observation. The predicted pressure profile at the sprue location has also been found to be in good agreement with the dynamics of the cell growth. Whereas for conventional injection molding the pressure of the system tends to decay monotonously, the pressure profile in microcellular injection molding exhibits an initial decay resulting from cooling and the absence of packing followed by an increase due to cell growth that expands the polymer-gas solution and helps to pack out the mold uniformly. (C) 2004 Society of Plastics Engineers.