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 mu m. 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 similar to 110, similar to 69, similar to 61 and similar to 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 (alpha = 1 and n = 2.5) for the cp-Ti foams and Knudsen-Spriggs model (b = 3.06) for the TTM, TT and TTS foams.