# Fabrication and Analysis of a Ti6 Al4V Implant for Cranial Restoration
## 2 Methodology
### Modeling
The properties of materials designated to the FEA model are presented in Table 1. The different material properties were assigned to different regions on the skull [32]. The attributes of cortical bone were designated to the cranium, while Ti6 Al4V ELI was assigned to the customized cranial implant [33; 34]. Before analyzing the FEA model, the 3D model was fixed for minor geometrical errors, including the removal of very small faces and edges on both the implant and bone section. The skull (or the cortical bone section) was fixed at four positions at the bottom as shown in Figure 7a. A static force of 50 N was applied in the center region of the implant over an area of 550 mm\({}^{2}\). Moreover, the mesh-independent fasteners were used to model the joining between the implant and bone section. It is an effective approach to define an explicit connection between two or more surfaces in the same manner with a spot weld or rivet joint. Four fasteners were utilized at selected reference positions. The continuum tetrahedral quadratic elements with ten nodes (C3D10) were selected for the model as shown in Figure 7b. To avoid mesh distortion and improve element quality, the fine mesh was generated resulting in a total of 280000 elements for the implant and bone section. The ABAQUS/STANDARD was selected as the finite element solver with static general procedure. To ensure mesh-independent results, a finer mesh model was developed and checked with the original one. The results obtained after executing the FEA model can be realized in Figure 8. The Von Mises stress distribution is shown in Figure 8a and the maximum value was around 2.5 MPa which was well below the Yield strength (930 MPa) of the titanium alloy (Ti6 Al4V ELI) thus ensuring the absence of any plastic deformation in the implant. Moreover, the maximum principal strain distributions in Figure 8b marked comparatively high strained regions around fasteners and load areas. However, the overall strain levels were very low and the maximum value was around \(1.49\times 10^{-4}\). Similarly, Figure 8c shows the deformation pattern in the implant due to the applied load. As expected, maximum deformation occurred at the load area, however, the magnitudes were very low i.e., around \(3.26\times 10^{-6}\) mm. In conclusion, the results showed that the implant design could be used satisfactorily for the replacement of the defected skull region. \begin{table}
\begin{tabular}{c c c c} \hline \hline
**Materials** & **Young’s Modulus (MPa)** & **Poisson’s Ratio** & **Yield Strength (MPa)** \\ \hline Cortical Bone & 13700 & 0.3 & 122 \\ Cranial reconstruction plate, (Ti6 Al4V ELI) & 120000 & 0.3 & 930 \\ \hline \hline \end{tabular}
\end{table} 
Table 1: Properties of materials utilized in FEA model [18; 35]. Figure 6: (**a**) Cranial implant with fixation plates; (**b**) Implant fixed on the prototype. The fabrication of the cranial implants was preceded by the elimination of errors in the STL file as described in Figure S1. The errors such as overlapping, intersecting triangles, bad edges, and other defects were resolved in Magics(r). The purpose of this stage was the processing of the STL file and determining the best position and orientation for fabrication. Once the STL models were flawless, appropriate supports were generated on the overhanging structures as shown in Figure S2. The most suitable supports were essential to precisely build the prototype without any aberration. The support also helped in the straightforward ejection of the prototype from the building table. The support structures were also required for efficient heat transfer to minimize any distortion and to facilitate the fabrication of overhanging parts. Moreover, the support structures were attached to the cranial implant with teeth at the top and bottom for their easy removal. Figure 8: FEA Results illustrating: (**a**) stress distribution; (**b**) strain distribution; (**c**) maximum displacement. Figure 7: (**a**) Loading area and boundary conditions; (**b**) Mesh generation.