Universal multi-objective function for optimising superplastic-damage constitutive equations

Based on the dominated deformation mechanisms of superplastic materials, an assumption for micro-damage evolution is presented. Then, a set of unified viscoplastic-damage constitutive equations is proposed to model material hardening due to the increase of dislocation density and grain growth, as well as material softening due to intergranular void nucleation and growth. The effects of the hardening and softening state variables on superplastic flows are characterised. To overcome the difficulties associated with the difference between predicted and experimental life spans and the variation in scales during multi-objective optimisations of material constants arising in the constitutive equations from experimental data, a unitless objective function has been formulated. This enables all experimental data to be involved in the optimisation. The constitutive equation set has been characterised for two superplastic alloys from experimental data using evolutionary programming (EP) optimisation techniques and the proposed method for formulating objective functions.