Physics-Informed Residual Deep Learning for Constitutive Modeling of Hot Deformation and Dynamic Recrystallization in a Mo-Rich $α+β$ Titanium Alloy
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 $α+β$ 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 = 11.62 MPa, MAE = 4.73 MPa, R^2 = 0.9852, and a cross-validated RMSE of 12.74 +/- 0.38 MPa. The learned JMAK parameters converged to k = 2.03 and n = 1.99, remaining close to the conventional values while being inferred directly from the data. The model effectively mirrored flow curves influenced by temperature, DRX development, and Zener Hollomon correlations under interpolation scenarios while preserving physically coherent constitutive behavior.