A novel theory of effective mechanical properties of closed-cell foam materials

In this paper a new theory of effective mechanical properties of foam materials is proposed. A cell volume distribution coefficient is introduced to modify the original Gibson-Ashby equations of effective mechanical properties of foam materials. The constants that influence the effective modulus are replaced by the coefficient. Based on the modified distribution coefficient, the yield stress is also recalculated. Using X-ray microtomography, the internal structures of different samples of polypropylene-nanoclay foam are obtained. The cell volume distributions of these samples are derived from the experiment by image analysis and the fitting curves are plotted. The distribution coefficient is acquired using the parameters from the theoretical model of the distribution curves. The results of the improved theory are compared with the experimental values and show good fitting quality. It was found that the precision of the improved theory is high and the cell volume distribution has an impact on the effective mechanical properties that would lead to the optimization of the synthesis procedure.