Estimate the Young's modulus of porous titanium with open pores using the Gibson–Ashby equation E* = Es(ρ*/ρs)². If the Young's modulus of dense titanium is Es = 110 GPa and the porosity is 60%, which value is closest to E*? ρ*/ρs is the relative density.

Answer: B. About 18 GPa

With a porosity of 60%, the relative density is ρ*/ρs = 1 − 0.60 = 0.40. E* = 110 × 0.40² = 110 × 0.16 ≈ 17.6 GPa, about 18 GPa, which falls within the range of the Young's modulus of cortical bone (about 10–30 GPa). Open pores also serve as a scaffold for bone to grow into, so porous metals are one way to reduce stress shielding. About 44 GPa forgets the square and uses 110 × 0.40, and about 40 GPa uses the porosity itself as 110 × 0.60². However, more porosity also lowers the strength, especially the fatigue strength, so the design is a balance between porosity and strength.