Elastic constants of lotus-type porous magnesium: Comparison with effective-mean-field theory

Lotus-type porous (LTP) metals possess a markedly anisotropic porous structure, in which long straight pores are homogeneously aligned unidirectionally. In this paper, we first describe a procedure for the determination of reliable elastic constants of LTP metals with high porosity, and next apply the technique to LTP magnesium, and finally compare the measurement results with those from the effective-mean-field (EMF) theory that has been recently proposed by Tane and Ichitsubo [Appl. Phys. Lett. 85, 197 (2004)]. Young’s modulus in the direction parallel to the longitudinal axis of pores decreases virtually linearly with porosity p, i.e., E‖≈45.3(1−p)1.33, whereas the normal Young’s modulus E⊥, falls rapidly, i.e., E⊥≈45.3(1−p)2.64. The Mori-Tanaka mean-field theory yields values that are close to the measured elastic constants in a wide porosity range, but cannot explain this power-law behavior. In contrast, the EMF theory gives more accurate values in the high-porosity range, and can reproduce the power-law behavior.