Elastic Modulus Distribution in Rigid PU Foams of Elliptically Graded Density

Structural and insulating components for automobiles, marine vessels, aircraft, spacecraft and other vehicles and technical devices are often manufactured by foaming rigid polyurethane foams in sealed molds; consequently, it is crucial to understand the physical and mechanical properties of the molded foams. The objective of the study is to evaluate the elastic modulus distribution in rigid polyurethane foams with an elliptically graded density that appears when foaming in a parallelepiped-shaped sealed mold at overpressure. The dependence of the modulus on the density was investigated experimentally under compression, and the constants of the model function were determined. Using the constants, the modulus values were calculated and corresponding distribution maps were plotted for vertical and horizontal cross-sections of the foam block. The results of numerical calculations showed that the modulus distribution is elliptical in vertical sections of the block and circular in horizontal cross-sections. It was concluded that the elliptical symmetry of the density distribution leads to symmetry of the same kind in the elastic properties. The modulus distribution maps are model-based predictions which require an independent experimental spatial validation. The dependence of the aspect ratio of the equidensity and equimodulus ellipses on the aspect ratio of the mold was estimated.