# FEM Analysis of Superplastic-Forming Process to Manufacture a Hemispherical Shell
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In [11; 12; 13; 14], the influence of the pre-forming phase on the final thickness distribution of superplastic domes was analysed. In this case, different superplastic materials were used. In [15], it was shown that the multi-phase process does not bring improvements to the uniformity of the thicknesses if there is no contact between the sheet metal and the die. The effect of the geometry of the pre-forming dies was analysed in [16]. In [17; 18; 19], the pre-forming process consisted of a hot drawing. Due to this process, the draw-in material feeds the material into the die cavity, making the subsequent superplastic-forming phase less aggressive. In [20], by means of a two-stage process, it was possible to reduce the thinning in the finished product, but the process was too long. The long times required by the use of the multi-stage forming technique have shifted the research towards the use of blanks characterised by a variable thickness profile. Some papers in the literature demonstrated that circular blanks with a variable thickness profile can achieve greater thickness uniformity in the half-shell. An analytical procedure characterised by simplified assumptions was proposed to make the thicknesses of a hemispherical dome uniform in [21]. On the contrary, in [22], numerical simulation coupled with an optimisation technique was used. The cases examined are related to both a hemispherical and a conical product. The optimal blank presented a thickness profile varying in a non-linear way. Similarly, in [23], the thickness profile of the blank presented a sigmoidal shape and was discontinuous. Also, in [24], by applying a reverse simulation approach, the thickness profile of the optimal blank resulted in varying in a non-linear way. In [25], the authors employed finite element modelling included in an automatic procedure guided by the multi-objective genetic algorithm MOGA-11. The case studies analysed are represented by a hemispherical dome and a frustum of a cone. The thickness profile of the optimal blank was found to vary according to a second-order polynomial function. In any case, however, the calculation times were very long (in the order of tens of hours). Based on some simplifying hypotheses, an optimal blank, in which the thickness profile varies linearly (conical thickness profile), was proposed in [2]. In [26; 27], the authors showed that the sole reduction in the thickness of the blank in the peripheral region allowed for reaching greater breaking heights in a free forming test. The same authors, using a circular blank with thickness varying linearly between the pole and the edge of the sheet metal, were able to create a hemispherical product [28] and a product with a more complex geometry [29] characterised by a more uniform thickness distribution. They reduced both the forming time and the weight of the component. A review on thickness control techniques in superplastic forming is reported in [30]. This work highlights that the finite element simulation results are independent of using a 3D scheme versus an axisymmetric 2D scheme. Furthermore, it suggests the opportunity to uniform the thickness distribution of the produced hemispherical shell by using a circular blank characterised by an initial conical thickness profile.