The simple hyperbolic-sine equation for superplastic deformation and parameters optimization

The flow behavior of Ti-6Al-4V alloy in superplastic forming (SPF) is studied, and a simpleconstitutive model is established based on the hyperbolic-sine equation. The constant strainrate high temperature tensile tests were performed at 890, 920, and 950 degrees C, the selected strainrates are 10(-2), 10(-3), and 10(-4)/s. The calculation results of strain rate sensitivity index (m) indicates there are two dominant mechanisms of deformation: (i) grain boundary sliding (GBS) when the temperature is below 920 degrees C or strain rate is above 10(-3)/s; (ii) GBS and diffusion creepif the temperature is above 920 degrees C and strain rate is below 10(-3)/s. Besides, the higher temperatures or the lower strain rates, the smaller void volume fraction. The genetic algorithm (GA) is applied to optimize the parameters in the constitutive model, the average absolute relative error (AARE) between the prediction results and experimental data of stress is reducedfrom 11.10% to 5.52%. A new modeling method of strain compensation is provided, whichis based on stress hardening and softening. The term K is introduced to describe the effectsof strain on flow behavior in SPF, and a good agreement between the predicted results andexperimental data can be obtained. In summary, the simple hyperbolic-sine constitutivemodel established in this work with parameter optimization can achieve high prediction accuracy. (C) 2020 The Author(s). Published by Elsevier B.V.