Ad-hoc modeling of closed-cell foam microstructures for structure-properties relationships

Abstract

During the formation of open-cell foams the relevant driving force besides gas pressure comes from surface tension which controls area minimization of the topology. Accordingly, the Surface Evolver software expressly developed to shape liquid surface by minimizing their energy given various constraints such as bubble volumes allows computing very realistic models of equilibrium foam microstructures. However, when considering non-equilibrium foam (dense foam) or the formation of closed-cell foams where films between adjacent cells are thick, a more complete model would have to consider the expansion process as a whole and include the viscous flow of the suspending fluid, which eventually solidifies to form the solid phase of the foam. This situation has not been investigated computationally because the problem size is too large and despite several attempts there remain significant challenges to integrate the foaming process knowledge into mathematical formulas. In a continuing effort to establish structure-properties relationships, an ad-hoc model is detailed to generate numerical closed-cell foam microstructures that resemble the real ones for a medium to a high porosity range. Inspired from a physical description of the manufacturing process making use of chemical blowing agent, a dynamic approach taking into account the influence of the temperature on the physical material characteristics is proposed. It allows the nucleation of cells, their growth through gas expansion, and the interactions between growing cells to be taken into account simultaneously. The large variety of generated microstructures with porosities spanning the few to 95 percents range is compared to real polymeric closed-cell foams whose microstructures were determined by X-ray microtomography at high spatial resolution. These structures are then used as templates to generate realistic finite element models and study the mechanical properties.