Numerical analysis of effect of material and processing parameters on thickness distribution during superplastic die bulging of cavity sensitive materials

Abstract

The superplastic bulging of circular sheets clamped against axisymmetrical cylindrical dies has been analysed numerically by means of a rigid–viscoplastic finite element method, in which four node quadrilateral isoparametric elements are used with a Newton–Raphson non­linear solution scheme. Both effects of normal anisotropy and strain hardening in the material are considered and a modified Coulomb friction law is adopted. At the same time, the yield criterion suited for the superplastic forming process and the cavity damage evolution model deduced from continuum damage mechanics are applied to a finite element formulation. The influences of material parameters (the strain rate sensitivity exponent m, the strain hardening exponent n, the coefficient of normal anisotropy R) and processing parameters (pressure cycle, lubrication condition, die geometry) on the inhomogeneity of the thickness distribution are studied and discussed. A selection of the simulated results is compared with the experimental results, with good agreement.