Physics-Informed Residual Deep Learning for Constitutive Modeling of Hot Deformation and Dynamic Recrystallization in a Mo-Rich $\alpha+\beta$ Titanium Alloy

Abstract

Accurate constitutive modeling of hot deformation behavior is essential for designing thermomechanical processes in advanced structural alloys. Conventional Arrhenius-type and empirical models do not adequately capture the combined effects of strain hardening, dynamic recovery (DRV), and dynamic recrystallization (DRX) across broad processing conditions. In this study, two Stacked Residual Physics-Informed Neural Networks (STAR-PINNs) were developed to simulate the hot deformation response of a Mo-rich $\alpha+\beta$ titanium alloy (Ti-6Al-4Mo-1V-0.1Si). The Enhanced STAR-PINN incorporated thermomechanical constitutive constraints, while the DRX-Aware STAR-PINN employed a dual-output architecture to account for recrystallization kinetics. Both models used a shared residual encoder trained on experimental flow stress data collected at temperatures from 800 to 1050 degrees C and strain rates between 0.01 and 10 per second. Physics-informed constraints, including thermal softening, strain-rate sensitivity, strain hardening, and post-peak softening, were enforced through automatic differentiation. The DRX-Aware model further integrated JMAK-Avrami regularization, DRX saturation constraints, and Arrhenius-based consistency with tunable parameters, directly linking the predicted DRX fraction to stress output via latent-feature fusion. The DRX-Aware STAR-PINN achieved RMSE = 11.69 MPa, MAE = 4.83 MPa, R^2 = 0.9850, and a cross-validated RMSE of 12.47 +/- 0.26 MPa. This model accurately reproduced temperature-dependent flow curves, DRX kinetics, and Zener-Hollomon relationships, while maintaining physically consistent constitutive behavior. These results demonstrate that physics-informed deep learning provides a robust and interpretable framework for constitutive modeling, offering a practical approach for advanced process modeling of titanium alloys.