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

Abstract

The flow behavior of Ti-6Al-4V alloy in superplastic forming (SPF) is studied, and a simple constitutive model is established based on the hyperbolic-sine equation. The constant strain rate high temperature tensile tests were performed at 890, 920, and 950℃, the selected strain rates 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℃ or strain rate is above 10-3/s; (ii) GBS and diffusion creep if the temperature is above 920℃ 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 reduced from 11.10% to 5.52%. A new modeling method of strain compensation is provided, which is based on stress hardening and softening. The term K is introduced to describe the effects of strain on flow behavior in SPF, and a good agreement between the predicted results and experimental data can be obtained. In summary, the simple hyperbolic-sine constitutive model established in this work with parameter optimization can achieve high prediction accuracy.