*2.4. SPF Process Design and Prosthesis Manufacturing*

The optimal conditions (in terms of temperature and strain rate) in which the Ti alloy exhibits the emphasized superplastic behaviour were determined in a previous experimental campaign [15]. The SPF process could be thus designed by means of an FE-based approach implementing the previously evaluated material modelling, with the aim of: (i) defining the geometry of the tool; (ii) calculating the gas pressure profile able to form the blank in the above-mentioned optimal conditions. ‐

Starting from the CAD bone reconstruction (as discussed in Section 2.2), the SPF process was simulated using the commercial software Abaqus. The tool geometry (i.e., the die to be copied by the blank) was modelled using two different approaches, briefly labelled as convex and concave (see Figure 9). − 

**Figure 9.** Different types of dies used for the SPF simulation: (**a**) convex and (**b**) concave.

As reported in Figure 9, to obtain the prosthesis geometry (green area), an additional area had to be added to deform the blank and to allow the blankholder action. In addition, 4 protrusions were included in the tool to obtain, on the formed blank, the reference positions to create the anchoring holes. Both the types of the die were modelled as a rigid body, meshing the surface with 1 mm element (R3D3 and R3D4 shell rigid element); the blank was modelled as a shell deformable body using S4R and S3R shell elements (average size equal to 0.5 mm) and considering 5 integration points in the thickness direction. The friction between the die and the blank was modelled using the Coulomb's formulation and setting the coefficient to 0.1 [20]. The gas pressure profile was calculated by means of an internal subroutine (CREEP STRAIN RATE CONTROL) by specifying that the blank portion in contact with the die surface (the one highlighted in green in Figure 9) had to be deformed under a strain rate target level of 5 <sup>×</sup> <sup>10</sup>−<sup>4</sup> 1/s.

As concerns the prostheses manufacturing, an INSTRON 4485 universal testing machine (INSTRON, Norwood, MA, USA) controlled by a ZwickRoell software (version, ZwickRoell, Ulm, Germany) and equipped with a specifically designed equipment was used. The experimental set-up is composed of a load cell, which allows to control the Blank Holder Force (BHF) during the tests, an upper tool which applies the BHF, and which is connected to the pneumatic circuit for the argon supply, a lower tool and the die. The tools and the die are embedded into an electric split furnace. The starting blank was a 1 mm thickness sheet with a circular shape having a radius of 75 mm. In order to simplify the extraction of the sheet after the forming process, a thin layer of graphite was applied on the external part of the sheet (the one in contact with the blankholder). The temperature of the furnace was set at 850 ◦C. After the target temperature was reached in the forming chamber, the blank was placed between the tool and the die, and a BHF of 22 kN was applied. Then, the argon gas was inflated into the forming chamber according to the pressure profile calculated by the FE simulations, while the BHF was kept constant by the control system for the whole forming time. As forming tool, a specific ceramic insert placed into a cylindrical steel frame, was used for each prosthesis (customized to the specific anatomy); such a ceramic was manufactured by investment casting using the pattern shown in Figure 10a (created by stereolithography) having the negative geometry of the ceramic insert.

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**Figure 10.** CAD model of (**a**) the photopolymeric base and (**b**) the upper bracket of the mould used for manufacturing the ceramic insert for the die; (**c**) assembled mould.

The mould for pouring the ceramic material (Figure 10b) was obtained by Fused Deposition and was assembled putting it on the pattern, as shown in Figure 10c. The mould is composed of two parts (as highlighted by the different colours) in order to simplify the extraction of the ceramic insert after the casting and autoclave curing operations.
