Optimal design of section profile in a circular blank to superplastic form a hemispherical shell with a more uniform thickness

This paper presents a new methodology to optimise the design of the section profile of a circular blank to be submitted to a superplastic forming process to obtain a hemispherical shell. The optimisation aims to plan the blank section to minimise the difference among the thickness values of the formed shell to have a more uniform thickness. The considered section profile has a part near the blank axis with a constant thickness equal to a maximum value and a part with a thickness varying linearly from the maximum to a minimum value, whereas the minimum value is near the blank end. This means the blank has a truncated cone section and, therefore, a variable thickness. Keeping constant the metal volume, the constant thickness part of the section was varied between two limit conditions: a conical section of the blank (the constant thickness part of the section is zero) and a constant thickness blank (the entire blank has a constant thickness). The results show that the proposed design methodology allows defining a section profile of the blank to form that allows superplastic forming a hemispherical shell with a thickness more uniform than that due to the profiles proposed by the literature, i.e. conical or rectangular profiles. The difference in the thickness values of the formed hemispherical shell is 9.7% instead of 16% or 55% for conical or rectangular profiles.