Superplastic pressure forming of a metal sheet into a long die with an isosceles trapezoid cross section

Superplastic deformation of thin sheets is widely used in aerospace, automotive and other industries. In this paper, a mathematical model of plane strain superplastic pressure forming of a sheet specimen into a die is proposed. A die under consideration has a shape of a long box with an isosceles trapezoid cross section, but the model can be generalized for more complex die shapes. It is assumed that sticking happens between a shell and a die and thickness remains unchanged once contact occurs. The process of forming was divided into different phases, which are determined by the die geometry. For each phase, ordinary differential equations for thickness were derived along with the initial conditions. Solutions of obtained ODEs allow estimating the shell thickness at any point of a specimen as a function of coordinate along walls of the die and to determine the duration of each superplastic pressure forming phase for a given pressure-time function. Norton’s power law was used as a constitutive equation. Due to the simplicity of Norton`s law it is possible to solve some of ODEs analytically. The proposed model can be used with other types of constitutive relations, in particular with relations that include microstructure parameters etc. The superplastic forming of a Ti-6Al-4V titanium alloy sheet for the piecewise pressure-time function has been modelled. Some special cases of die geometry are analyzed.