Mathematical modeling of superplastic forming of a long rectangular box section

The method to calculate the pressure time cycle for the case of superplastic forming of a long rectangular diaphragm is suggested in this paper. Simplified model of this process is developed by using the principal equations of the thin shell theory. The approach involved enables one to obtain the analytical expression for calculating gas pressure time dependency providing constant strain rate deforming of a shell. Material properties have been estimated by means of the same technological equipment which is exploited in the technological process under consideration. Such an approach provides the identity of the uniaxial test conditions and the conditions corresponding to the technological process under consideration. A good agreement between the results obtained and experimental data is found. The model involved can be used in calculating the pressure-time cycle as well as in estimating the thickness distribution and maximum thinning on the part. Furthermore, one can use this model for estimating the strain rate sensitivity of sheet materials to be formed on the basis of constant pressure testing forming.