In order to thoroughly understand the quantitative relationships between the flow stress and deformation conditions for Ti₂AlNb-based alloys at elevated temperatures, the Arrhenius and Johnson–Cook constitutive models are analyzed and identified on the basis of the uniaxial tensile tests. The Johnson–Cook model is modified so that the referenced temperature range can be randomly adjusted. By experimental verification, the Arrhenius model (including the Backofen model) is suitable for the deformation at relatively low strain-rate deformation, such as the superplastic forming, and the modified J–C model is applicable for the deformation within a wide range of strain rates. For deformation at high temperatures, the constitutive model enables a more precise description of the effect of strain on the flow stress through introducing as train-softening factor exp(sε).

The deformation behavior of a 2024 aluminum alloy sheet at elevated temperatures was studied by uniaxial hot tensile tests over the nominal initial strain rate range of 0.001–0.1 s⁻¹ and temperature range of 375–450 °C. In order to analyze the deformation behavior with higher accuracy, a digital image correlation (DIC) system was applied to determine the strain distribution during hot tensile tests. Local stress-strain curves for different local points on the specimens were calculated. The strain rate evolution of each point during the tensile tests was investigated under different deformation conditions. Then, an improved Fields–Backofen (FB) model, taking into account the local strain rate evolution instead of the fixed strain rate, was proposed to describe the constitutive behaviors. It has been found that obvious non-uniform strain distribution occurred when the true strain was larger than 0.3 during hot tensile tests. The strain rate distribution during deformation was also non-uniform. It showed increasing, steady, and decreasing variation tendencies for different points with the increasing of strain, which led to the local flow stress being different at different local points. The flow stresses predicted by the improved FB model showed good agreement with experimental results when the strain rate evolutions of local points during tensile tests were considered. The prediction accuracy was higher than that of traditional FB models.