Simulation of the Influence of the Radial Graded Porosity Distribution on Elastic Modulus of γ/β Phase Ti-Based Alloy Foams for Bone Implant

Abstract

This research aims to examine how a radial graded porosity distribution affects the elastic modulus by conducting simulations on Ti-based alloy foams with face-centered cubic and body-centered cubic crystal structures. Four types of foams were analyzed; commercially pure-Ti, Ti-13Ta-6Mn (TTM), Ti-13Ta-(TT) and Ti-13Ta-6Sn (TTS), (all in at.%). Four radial graded porosity distribution configurations were modeled and simulated using the finite element analysis (FEA). The radial graded porosity distribution configurations were generated using a Material Designer (Ansys) with a pore range of 200 to 600 μm. These radial graded porosity distributions had average porosity values of 0, 20, 30 and 40%. The consolidated samples that were obtained through a powder metallurgy technique in two step samples were synthesized using a powder metallurgy technique, with the elastic moduli values of the aforementioned Ti based alloys being measured by ultrasound using ~110, ~69, ~61 and ~65 GPa, respectively. The results showed that the modulus decreased as a function of porosity level in all simulated materials. The TTM, TT and TTS foams, with average porosities of 20, 30 and 40%, exhibited an modulus smaller than 30 GPa, which is a requirement to be used as a biomaterial in human bones. The TT foams showed the lowest modulus when compared to the other foams. Finally, certain theoretical models were used to obtain the modulus, the best being; the Gibson–Ashby model (α = 1 and n = 2.5) for the cp-Ti foams and Knudsen–Spriggs model (b = 3.06) for the TTM, TT and TTS foams.