Finite-element modeling of super-plastic forming processes

The present work is devoted to the development of the production of three-layered hollows structures made of VT6 titanium alloy by means of superplastic forming (SPF) and pressure welding. Finite-element modeling can be successfully applied to optimize the forming process, if the adequate constitutive relations would be defined and the friction at the contact surface of the material with the die would be specified. To find the friction coefficient and the parameters of the constitutive relations for metal forming process, test experiments are conducted to the forming of sheet into dies of various shapes. In such test experiments, a biaxial loading is realized, as in the actual processes of fabricating complicated structures from sheet by SPF. To this end, Finite-element modeling of the SPF process of sheet forming into dies of two types is performed: (i) into wedge die having cross section in the form of equilateral triangle, and (ii) cone die. Recommendations are given for the choice of the optimum angle at the vertex, determining the geometry of the dies, which results in the constancy of the stresses during forming at constant pressure.
The methodology for estimating the coefficient of friction on the contact surface between sheet and die is given. Finite-element modeling of the SPF process of three-layer hollow structures is carried out using the parameters of the constitutive relations obtained by the proposed methods. Technological constraints on the geometric parameters of structures, such as the angle of inclination of the stiffening ribs and the thickness ratio of outer to inner sheet thicknesses are established, which provides forming without the formation of folds on the shell and the minimum variability of ribs thickness.