Constitutive Model for Hot Deformation Behavior of Fe-Mn-Cr-Based Alloys: Physical Model, ANN Model, Model Optimization, Parameter Evaluation and Calibration

The development and validation of constitutive models for high-temperature deformation are critical for bridging microstructure evolution with macroscopic mechanical behavior in materials. In this study, we systematically analyzed the hot deformation behavior of Fe-Mn-Cr-based alloys, compared the modeling processes of physical, phenomenological, and data-driven approaches in detail, and optimized their structural and predictive properties. First, the advantages, disadvantages, and applicability of three traditional models, namely the physical Arrhenius model, the phenomenological Johnson–Cook model, and the artificial neural network (ANN) model, are compared for flow stress prediction. Subsequently, traditional mathematical derivations and numerical optimization methods are evaluated. The parameters and architecture of the ANN model are then systematically optimized using optimization algorithms to enhance training efficiency and prediction accuracy. Finally, sensitivity analysis integrated with Bayesian posterior probability density functions enables the calibration of physical model parameters and uncertainty quantification. The results demonstrate that the ANN with optimized parameters and architecture achieves superior prediction accuracy (R2 = 0.9985, AARE = 3.01%) compared to traditional methods. Bayesian inference-based quantification of parameter uncertainty significantly enhances the reliability and interpretability of constitutive model parameters. This study not only reveals the strain–temperature coupling effects in the hot deformation behavior of Fe-Mn-Cr-based alloys but also provides systematic methodological support for constitutive modeling of high-performance alloys and a theoretical foundation for material processing technology design.