Measurement of the dynamic Young’s modulus of porous titanium and Ti6Al4V

The dynamic Young’s modulus of porous titanium and Ti6Al4V with various porosities was measured using the electromagnetic acoustic resonance method. The dependence of Young’s modulus (E) on the porosity (P) has been analysed in detail based on Phani–Niyogi relation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left(E = E_0 \left(1 - \frac{P} {{P_C }}\right)^n\right ) $$\end{document} and Pabst–Gregorová relation \documentclass[12pt]{minimal} \usepackage{amsmath} \usepackage{wasysym} \usepackage{amsfonts} \usepackage{amssymb} \usepackage{amsbsy} \usepackage{mathrsfs} \usepackage{upgreek} \setlength{\oddsidemargin}{-69pt} \begin{document}$$ \left(E = E_0 (1 - aP)\left(1 - \frac{P} {{P_C }}\right)\right) $$\end{document}. We find that both Phani–Niyogi relation and Pabst–Gregorová relation with fixed material constant n = 2 or a = 1 but varying PC can correctly account for the dependence of Young’s modulus on the porosity for porous titanium and Ti6Al4V.