Modeling of the effect of porosity on the Young’s modulus of titanium powder alloys

Titanium powder alloys with superelasticity, corrosion resistance, and good biochemical and biomechanical compatibility have good prospects for use as materials for bone implants. The porous structure of such alloys has a great influence on their elastic characteristics — with increasing porosity, the Young’s modulus decreases, which makes it possible to obtain medical products in which the Young’s modulus is comparable to the corresponding value of bone tissue. For stable fixation of bone tissue in the pores of the implant, it is necessary to optimize the characteristics of the pore space (number, size, shape and roughness of pores), which depend on the morphology of the initial powder. When creating products with a given level of porosity, it is important to establish the effect of porosity on the Young’s modulus and shear modulus, which reflect the rigidity of the material. This is possible using analytical, experimental or numerical methods. A theoretical analysis of the effect of porosity on the Young’s modulus of sintered titanium powder alloys has been performed using numerical finite element modeling for a representative volume. Cells in the form of a unit cube are accepted as a representative volume. The dependences of the effective Young’s modulus on porosity are obtained for the two limiting cases of the porous structure of the alloy (spherical pores and spherical particles). The results of the numerical solution are compared with known approximate analytical dependencies. It is established that the effective Young’s modulus for the spherical particle model depends on porosity to a greater extent than for the spherical pore model.The study was conducted within the framework of the state task FEWG-2024-0002, as well as with the support of the Russian Science Foundation (grant No. 25-29-20055, https://rscf.ru/project/25-29-20055/) and the Tula Region Committee on Science and Innovation.