Generalized relations between metallurgical and process parameters for superplastic forming of titanium alloys were determined from a systematic characterization of the superplasticity indices for alpha-beta titanium alloys. The flow stress at a constant strain rate of different alpha-beta alloys is uniquely related to grain size, beta transus temperature, and volume fractions of constituent phases at the test temperature. The effects of different compositions and microstructural modifications are implicit in the ratio of the forming temperature T to the beta-transus temperature Tβ of a specific alloy. For a fixed T/Tβ ratio, regardless of the alloy composition, the logarithm of flow stress is a function of the logarithm of the product of strain rate and the average grain size. A constitutive equation for the stress, time, grain size, and temperature dependence of strain rate was obtained and the equation used to construct generalized, three-dimensional plots of the relation between flow stress, strain, strain-rate sensitivity, grain size, and temperature, with consideration given to the continuous change in alloy microstructure during superplastic deformation. The applicability of the constitutive equation and three-dimensional plots for predicting superplastic strain rates was confirmed by constant-stress superplastic forming tests.
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