A sigmoidal model for superplastic deformation

A new phenomenological model, designed to capture the sigmoidal nature of stress dependency on strain rate for superplastic deformation, is presented. The model is developed for the Ti-6Al-2Sn-4Zr-2Mo alloy using data obtained under controlled strain-rate tensile tests spanning a range of strain rates and temperatures, from 930 to 980°C. The sigmoidal model performance is compared with that of a more conventional double-power law, strain, and strain-rate hardening model using time-dependent finite element and theoretical analyses. The primary intended application of the sigmoidal model is for more accurate simulation of the effects of strain-rate variation within test specimens and sheet during superplastic deformation. Analysis of this variation within two designs of tensile test specimens is presented to illustrate this aspect.