The Influence of Aspect Ratio of Voids on the Effective Elastic Moduli of Foamed Metals

Abstract

An analytical methodology is developed to study the influence of void's aspect ratio on the overall elastic behavior of foamed materials. The method developed for the prediction of the effective elastic moduli is based upon Eshelby's equivalent inclusion method and Mori-Tanaka theory. Analysis results with foamed aluminum as demonstration of the effectiveness of the proposed methodology indicate that the effective longitudinal elastic modulus Ē11, the effective shear moduli Ḡl2 and Ḡ13 and effective Poisson's ratio v̄12 appear to increase with the increment of void's aspect ratio. Meanwhile, the effective transverse elastic moduli Ē22 and Ē33, the effective out-plane shear modulus Ḡ23, and the effective Poisson's ratios v̄21 as well as v̄23 decrease with increasing aspect ratio of the void. The numerical results correlate well with experimental data, demonstrating the accuracy of the proposed methodology with respect to predicting elastic moduli of foamed materials.