Metrological characterization of porosity graded β-Ti21S triply periodic minimal surface cellular structure manufactured by laser powder bed fusion

April 07, 2023

Lorena Emanuelli (1), Raffaele De Biasi (2), Huijuan Fu (1), Anton Du Plessis (3) (4), Carlo Lora (5), Alireza Jam (2), Matteo Benedetti (2), Massimo Pellizzari (2)
International Journal of Bioprinting. Volume 9 (7 April 2023). DOI:


Functionally graded porous structures, Ti-21S, skeletal-based triply periodic minimal surface structure, metrological characterization, laser powder bed fusion, additive manufacturing


The design of a functionally graded porous structure (FGPS) for use in prosthetic devices is crucial for meeting both mechanical and biological requirements. One of the most commonly used cellular structures in FGPS is the triply periodic minimal surface (TPMS) structure due to its ability to be defined by implicit equations, which allows for smooth transitions between layers. This study evaluates the feasibility of using a novel β-Ti21S alloy to fabricate TPMS-based FGPS. This beta titanium alloy exhibits low elastic modulus (53 GPa) and good mechanical properties in as-built condition. Two TPMS FGPSs with relative density gradients of 0.17, 0.34, 0.50, 0.66, and 0.83 and unit cell sizes of 2.5 mm and 4 mm were designed and fabricated using laser powder bed fusion (LPBF). The as-manufactured structures were analyzed using scanning electron microscopy (SEM) and X-ray micro-computed tomography (μ-CT), and the results were compared to the design. The analysis revealed that the pore size and ligament thickness were undersized by less than 5%. Compression tests showed that the stabilized elastic modulus was 4.1 GPa for the TPMS with a 2.5 mm unit cell size and 10.7 GPa for the TPMS with a 4 mm unit cell size. A finite element simulation was performed to predict the specimen’s elastic properties, and a lumped model based on lattice homogenized properties was proposed and its limitations were explored.

How Our Software Was Used

Wall thickness computations were used to measure ligament thicknesses and pore size distributions. In addition, overlapping of as-manufactured and of as-designed samples was performed with the align function and generation of a contour mesh in Dragonfly.

Author Affiliation

(1) INSTM (Operative center: University of Trento), Trento, 38123, Italy
(2) Department of Industrial Engineering, University of Trento, Trento, Italy
(3) Research Group 3D Innovation, Stellenbosch University, Stellenbosch, South Africa
(4) Object Research Systems, Montreal, Canada
(5) SISMA SpA, Piovene Rocchette, Vicenza, Italy