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

Abstract

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. Polym. Eng. Sci. 44:2274–2287, 2004. © 2004 Society of Plastics Engineers.

Numerical simulation of polymer foaming process in extrusion flow

“…The growth of bubbles increases with the distance from the die, which is similar to experimental observations (Arefmanesh and Advani, 1995). Studies of the effect of concentration of the foaming agent on bubble growth during foaming processes and final foam densities have been carried out by other researchers (Osorio and Turng, 2004;Park and Cheung, 1997;Shimoda et al, 2001;Upadhyay, 1985). Their results are in good agreement with experiments and show general trends, including that the rate of bubble growth increases with the concentration of foaming agent and that the final foam density decreases with an increase of foaming agent concentration.…”

Morphology and flow effect of microinjection‐molded plastic microgears

“…For the simulation of mold cavity filling phase, a custom finite element code developed by El‐Otmani et al was used. For the rheological properties of the polymer, the 7‐parameter Cross‐Willam–Landel–Ferry model, given in Eqn was employed. where n is the power‐law index, τ * is the threshold shear stress at which shear thinning starts, and η 0 ( T , p ) is the zero shear rate viscosity.…”

“…For the simulation of mold cavity filling phase, a custom finite element code developed by El-Otmani et al [8] was used. For the rheological properties of the polymer, the 7-parameter Cross-Willam-Landel-Ferry model, [9] given in Eqn 1 was employed.…”

Visual observation and numerical studies of N2 vs. CO2 foaming behavior in core‐back foam injection molding

“…However, their model also did not incorporate bubble nucleation rate. Osorio and Turng [4] developed mathematical models for simulating non‐isothermal bubble growth behavior in injection molding of microcellular plastics and compared the predictions with experimental data where N 2 was used as a blowing agent. Teramoto et al [5], Barzegari and Rodrigue [6], and Lee et al [7] investigated microcellular foam injection processes to optimize process design and operating conditions so as to control the cell structure of the foam.…”