The hot deformation behavior of 21-4N heat-resistant steel was studied by hot compression test in a deformation temperature range of 1000–1180 °C, a strain rate range of 0.01–10 s⁻¹ and a deformation degree of 60%, and the stress-strain curves were obtained. The functional relationship between flow stress and process parameters (deformation degree, deformation temperature, strain rate, etc.) of 21-4N heat-resistant steel during hot deformation was explored, the constitutive equation of peak stress was established, and its accuracy was verified. Based on the dynamic material model, the energy dissipation maps and destabilization maps of 21-4N heat-resistant steel were established at strains of 0.2, 0.4 and 0.6, and processing maps were obtained by their superposition. Within the deformation temperature range of 1060~1120°C and a strain rate range of 0.01–0.1 s⁻¹, there is a stable domain with the peak efficiency of about 0.5. The best hot working parameters (strain rate and deformation temperature) of 21-4N heat-resistant steel are determined by the stable and instable domain in the processing maps, which are in the deformation temperature range of 1120–1180 °C and the strain rate range of 0.01–10 s⁻¹.

The Gleeble-1500D thermal simulation test machine was used to conduct the isothermal compression test on 21-4N at the strain rate ( $\dot{\epsilon }$ ) of 0.01–10 s⁻¹, the deformation temperature (T) of 1273–1453 K and the maximum deformation is 0.916. The data of the stress-strain (σ-ε) were obtained. Based on the σ-ε data, the Johnson-Cook (J-C), modified J-C, Arrhenius and Back-Propagation Artificial Neural Network (BP-ANN) models were established. The accuracy of four models were verified, analyzed and compared. The results show that J-C model has a higher accuracy only under reference deformation conditions. When the deformation condition changes greatly, the accuracy of J-C model is significantly reduced. The coupling effect of T and $\dot{\epsilon }$ of modified J-C model is considered, and the prediction accuracy is greatly improved The Arrhenius model introduces Zener-Hollomon (Z) to represent the coupling effect of T and $\dot{\epsilon }$ , it has a fairly high prediction accuracy. And it can predict flow stress (σ) accurately at different conditions. The accuracy of BP-ANN model is the highest, but its learning rate is low, the learning and memory are unstable. It has no memory for the weights and thresholds of the completed training. So, there are certain limitations of it in use. Finally, a Finite Element Method (FEM) of the isothermal compression experiment for four models were established, and the distribution of the equivalent stress field, equivalent strain field and temperature field with the deformation degree of 60% were obtained.