Numerical prediction of the foam structure of polymeric materials by direct 3D simulation of their expansion by chemical reaction based on a multidomain method

• Published in: Journal of materials science Vol. 40; no. 22; pp. 5875 - 5881
• Main Authors: Bikard, J, Bruchon, J, Coupez, T, Vergnes, B
• Format: Journal Article
• Language: English
• Published: New York Springer Nature B.V 01.11.2005; Springer Verlag
• Subjects: Automobile industry; Automotive components; Automotive engineering; Automotive parts; Bubbles; Carbon dioxide; Chemical reactions; Computer simulation; Conversion; Engineering Sciences; Finite element method; Foams; Ideal gas; Irreversible processes; Materials; Materials science; Mathematical analysis; Mathematical models; Numerical prediction; Organic chemistry; Parameters; Plastic foam; Polymers; Polyurethane foam; Porosity; Rheological properties; Rheology; Shear thinning (liquids); State variable; Viscous fluids; Wall thickness; DYNAMICS
• ISSN: 0022-2461; 1573-4803
• DOI: 10.1007/s10853-005-5022-9

The quality of thermosetting polymer foams (like polyurethane foam, used for example in automotive industry) mainly depends on the manufacturing process. At a mesoscopic scale, the foam can be modelled by the expansion of gas bubbles in a polymer matrix with evolutionary rheological behaviour. The initial bubbles correspond to germs, which are supposed quasi-homogeneously distributed in the polymer. An elementary foam volume (∼1 mm3) is phenomenologically modelled by a diphasic medium (polymer and immiscible gas bubbles). The evolution of each component is governed by equations resulting from thermodynamics of irreversible processes: the relevant state variables in gas, resulting from chemical reaction creating carbon dioxide (assimilated then to a perfect gas), are pressure, temperature and conversion rate of the reaction. The number of gas moles in each bubble depends on this conversion rate. The foam is considered as a shear-thinning viscous fluid, whose rheological parameters evolve with the curing reaction, depending on the process conditions (temperature, pressure). A mixed finite element method with multidomain approach is developed to simulate the average growth rate of the foam during its manufacture and to characterize the influence of the manufacturing conditions (or initial rheological behaviour of the components) on macroscopic parameters of the foam (cell size, heterogeneity of porosity, wall thickness).