# FEM Analysis of Superplastic-Forming Process to Manufacture a Hemispherical Shell
## 5 Conclusions  
This work, through numerical and experimental activities, aimed to design the superplastic-forming process to manufacture a hemispherical shell characterised by an almost uniform final thickness distribution. The experimental activity was conducted using the superplastic magnesium-based alloy AZ31.  
Figure 11: Comparison between experimental results obtained from a constant thickness blank and a conical section blank.  
Figure 10: Comparison between the results obtained through FEM and those from the experimental tests for (**a**) a constant-thickness blank and (**b**) a conical section profile blank.  
Therefore, this work aimed to:  
* Model, through finite element analysis, the superplastic-forming process, conducted at a constant forming temperature and pressure, for the production of a hemispherical shell, both through a 3D scheme and a simplified 2D scheme;
* Verify, through a numerical-experimental comparison, the quality of the results achieved in the numerical simulation in terms of the final thickness distribution of the hemispherical shell;
* Show, starting from a blank with a conical section profile, an original procedure, based on a series of appropriately conducted numerical simulations; it allows for obtaining a more uniform final thickness distribution of the hemispherical shell. At the end of the work, the following conclusions were obtained: 1. The 2D scheme, which requires less computational time and a greater ease of preparation, can replace the 3D scheme. This comparison was made in terms of the thickness distribution of the formed hemispherical shell; the maximum deviation was of less than 2%;
2. The results of the numerical analysis were compared with the results from the experimental activity conducted on the superplastic magnesium-based alloy AZ31. The FEM results underestimate the final thickness distribution of the hemispherical shell, even if the maximum deviation from the experimental results was of less than 10%;
3. It is possible to produce a hemispherical shell characterised by an almost uniform thickness distribution. In this work, parameter A% was defined to measure the uniformity of the thicknesses of the manufactured hemispherical shell. In particular, this parameter tends to zero as the uniformity of the thicknesses increases. The uniformity of the thicknesses of the hemispherical shell is reduced if a constant thickness blank is used (it corresponds to a value of \(A\)% equal to 29%) and increases (\(A\)% = 20%) if a blank with a conical section profile is used.  
Future research is related to the study of blanks with sections shaped differently to make the thickness of the final product more uniform.  
Conceptualisation, G.G.; methodology, G.G.; validation, G.G. and W.P.; formal analysis, G.G.; writing--original draft preparation, W.P.; writing--review and editing, G.G. and W.P. All authors have read and agreed to the published version of the manuscript. This research received no external funding. Not applicable. Not applicable. Not applicable. Not applicable. Data Availability Statement: The raw data supporting the conclusions of this article will be made available by the authors on request. The authors declare no conflicts of interest.