In this paper, the correlation between the cell density (the number of cells per unit volume remaining in the foamed polymethylmethacrylate (PMMA) resin) with the decompression time and foaming temperature will be discussed. The foaming was carried out by the following method. The solid PMMA resin was soaked in a blowing agent under high pressure at a temperature higher than the glass transition temperature of the resin. After the foaming agent reached its saturation state, cell nucleation and cell growth were induced by decompression at the elevated temperature. Cell growth was then halted by cooling. Using a device that could accurately control temperature and decompression rate, PMMA resins were foamed under various foaming temperatures and decompression times by the above-mentioned method. The following results were obtained.
(1) The cell density of the foamed PMMA increases when the decompression time is shortened at low foaming temperatures but decreases when the decompression time is lengthened at high foaming temperatures.
(2) The correlation between the cell density of foamed PMMA and the decompression time and foaming temperature can be expressed with a master curve, i. e., a time-temperature equivalence can be derived.
(3) The time-temperature shift factor obtained from the master curve shows Arrhenius type of activation behavior, similar to the viscoelastic behavior of the material.
(4) Based on these correlation, it is possible to predict the necessary foaming conditions to achieve arbitrary cell densities.

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Modeling of the polyurethane foaming flow process is difficult because the temperature, density, and thermal conductivity profiles change greatly due to the heat generation in the two-liquid mixture of polyol and polyisocyanate. The precise simulation of the polyurethane foaming flow process would be very effective for reducing the development period and production costs. In this study, the interdependence of heat generation reaction, density and thermal conductivity for polyurethane resin was determined experimentally. A foaming flow simulation was then developed by applying these relationships in a 3D flow simulation program. The following results were obtained by comparing the simulations with the experimental observations.
(1) The temperature of the polyurethane resin in the foaming flow process rises greatly from the initial temperature to about 100°C due to the heat generation reaction. The resin temperature can be calculated with a precision of ±10°C even as the wall thickness and mold temperatures change.
(2) The foaming flow analysis can reproduce (simulate) an increase in specific volume by 30-fold. The specific volume can be calculated with a precision of ±8% even as the wall thickness and mold temperatures change. At the end of the foaming flow process, however, the precision of the prediction becomes worse as the wall thickness changes.

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