Modelling grain growth evolution and necking in superplastic blow-forming

A stability analysis is carried out to investigate necking in superplastic materials characterised by the sinh-law constitutive equation ε̇p∝sinh(βσ). The effects of load and the strain rate sensitivity parameter β on necking are quantitatively studied and a necking map is obtained for conditions of uniaxial loading. Finite element simulations of a superplastic blow-forming process are carried out in order to investigate both non-uniform thinning and grain size distribution which result from the use of the sinh-law constitutive equation. The pressure cycle required to ensure a target maximum strain rate is not exceeded in the material is obtained. The effects of strain rate and the magnitude of the parameter β on the grain size and through-thickness strain distributions for the formed part are investigated.