Characterization of Dynamic Deformation Behavior and Constitutive Model of TB9 Titanium Alloy for Cryogenic-Ultrasonic Elliptical Vibration Cutting

In the cryogenic-ultrasonic elliptical vibration cutting (UEVC) of TB9 titanium alloy, high-strain-rate deformation occurs, and its cryogenic dynamic deformation behavior and constitutive model are crucial for analyzing the cutting process. Static stress–strain curves were obtained using an electronic universal testing machine, while dynamic stress–strain curves under different temperatures and strain rates were measured using a split Hopkinson pressure bar (SHPB) apparatus. Based on the Johnson–Cook (J-C) constitutive model, a modified J-C (M-J-C) constitutive model was developed by adjusting the strain rate sensitivity factor and temperature exponent. The results showed that TB9 exhibited certain strain rate sensitivity and temperature sensitivity. At low temperatures, the flow stress of TB9 titanium alloy first increased and then decreased with strain rate; as the temperature decreased, the flow stress of the material gradually increased. Compared to the original J-C model, the M-J-C curves showed closer descriptive agreement with the reported plastic stress–strain responses within the fitted domain. The proposed model was subsequently implemented in a finite element model of cryogenic-UEVC, and its predictive performance was evaluated through corresponding cutting experiments. Under machining parameter set No. 1, the experimentally measured surface residual-stress magnitude was approximately 355 MPa, whereas the original J-C and M-J-C models predicted 411 MPa and 391 MPa, respectively, reducing the prediction error from 15.7% to 9.8%. For parameter sets Nos. 2–4, the prediction errors of the M-J-C model were lower than those of the original J-C model by 9.4%, 4.2%, and 6.4%, respectively. These results demonstrate that incorporating the coupled effects of strain rate and temperature improves the description of the dynamic deformation behavior of TB9 titanium alloy and enhances the predictive capability of finite element simulations for cryogenic-UEVC.