Fig.1 Schematic representation of the topology of studied cellular structures, XY view; (a) Cubic regular, (b) Cubic irregular, (c) Star regular, (d) Star irregular, (e) Cross regular, (f) Cross irregular, (g) Trabecular.
In the present study, 7 different topologies with a target strut thickness of 500 µm and a target pore size of 1100 µm were selected. The XY view of the topologies considered are as shown in Fig. 1, and the samples were printed along the Y direction. The regular structures were named as cubic, star and cross. The irregular structures were named as cubic irregular, star irregular and cross irregular. Irregular structures were been obtained by using an algorithm to misalign the nodes of the regular structures in random directions and distances to induce irregularity. Trabecular is a modified version of the Voronoi tessellation with a narrow pore distribution. This structure is able to mimic the trabecular human bone and consists of 4 to 6 struts joined at a node and oriented in random directions. The number of struts at a node and their orientation depend on the cell topology.
Cylindrical test specimens of 15mm diameter (d) and 17mm height (h) (h/d>1) were used both for quasi-static and fatigue tests. The top and bottom surfaces of the specimens were polished to make sure the contact surface is flat for fatigue testing.

Experimental Procedure

Microstructure

The microstructure of the specimen was observed along the XZ plane (parallel to printing plane) and XY plane (perpendicular to the printing direction). One cubic regular specimen was cut along two planes and subjected to polishing process with SiC abrasive papers of different girt size from 220 to 2400, 3-micron diamond solution, and finally polished with alumina suspension to give it a mirror finish. The samples were then etched using a Kroll’s reagent to reveal the microstructure.

Porosity and Geometrical Deviation

The porosity was calculated on the compression test samples (5 specimens) using equation 1, where ρs is the density of the specimen and ρo is the theoretical density of Ti6Al4V alloy (4.42 g/cm3)48. Specimen density was calculated using the mass of the specimen obtained from gravimetric precision balance (XS Balance (BL 224), Italy) and the nominal volume calculated using the height and diameter of the specimen.
\(Porosity=\frac{\rho_{o}-\rho_{s}}{\rho_{o}}\) …… (1)
The geometrical deviation of structures was carried out to obtain the thickness of different struts. The struts in all seven topologies can be categorized into horizontal struts, vertical struts, oblique (inclined struts) (struts in regular structures), random and irregular struts (struts in irregular structures). The images of the different topologies were captured using a stereo optical microscope (Nikon SMZ25) as shown in Fig.2. The strut thickness was measured from end to end including the roughness on the surface using ImageJ® software. To obtain a statistically significant data, 100 measurements were captured for all the different catogeries of struts mentioned above.