Constitutive equations with varying parameters for superplastic flow behavior of Al–Zn–Mg–Zr alloy

In order to precisely describe superplastic flow behavior of Al–Zn–Mg–Zr alloy, a phenomenological constitutive equation and an empirical constitutive equation were established based on the experimental data, which were obtained from the constant strain rate tensions (1.0 × 10 −4 to 8.0 × 10 −2 s −1 ) at 530 °C. Through verification of the two constitutive equations with the experimental data in constant strain rate tensions, constant velocity tensions and constant load tensions, it was indicated that the phenomenological constitutive equation has very high accuracy in the local range of some strain rates and strains. The empirical constitutive equation has higher accuracy and more comprehensive reliability in a wide range of strain rates (1.0 × 10 −4 to 8.0 × 10 −2 s −1 ) and strains (0–2.0) due to considering the coupling effects of strain and strain rate on stress, compared with the phenomenological constitutive equation. In addition, both the phenomenological constitutive equation and the empirical constitutive equation have a good ability to model the superplastic flow behavior of Al–Zn–Mg–Zr alloy at 530 °C under other deformation conditions besides constant strain rate tension.