Constitutive Equations for Describing the Hot Compressed Behavior of TC4-DT Titanium Alloy

A New Constitutive Model Based on Taylor Series and Partial Derivatives for Predicting High-Temperature Flow Behavior of a Nickel-Based Superalloy

Ni-based superalloys are widely used in aerospace applications. However, traditional constitutive equations often lack the necessary accuracy to predict their high-temperature behavior. A novel constitutive model, utilizing Taylor series expansions and partial derivatives, is proposed to predict the high-temperature flow behavior of a nickel-based superalloy. Hot compression tests were conducted at various strain rates (0.01 s-1, 0.1 s-1, 1 s-1, and 10 s-1) and temperatures (850 °C to 1200 °C) to gather comprehensive experimental data. The performance of the new model was evaluated against classical models, specifically the Arrhenius and Hensel-Spittel (HS) models, using metrics such as the correlation coefficient (R), root mean square error (RMSE), sum of squared errors (SSE), and sum of absolute errors (SAE). The key findings reveal that the new model achieves superior prediction accuracy with an R value of 0.9948 and significantly lower RMSE (22.5), SSE (16,356), and SAE (5561 MPa) compared to the Arrhenius and HS models. Additionally, the stability of the first-order partial derivative of logarithmic stress with respect to temperature (∂lnσ/∂T) indicates that the logarithmic stress-temperature relationship can be approximated by a linear function with minimal curvature, which is effectively described by a second-degree polynomial. Furthermore, the relationship between logarithmic stress and logarithmic strain rate (∂lnσ/∂lnε˙) is more precisely captured using a third-degree polynomial. The accuracy of the new model provides an analytical basis for finite element simulation software. This helps better control and optimize processes, thus improving manufacturing efficiency and product quality. This study enables the optimization of high-temperature forming processes for current superalloy products, especially in aerospace engineering and materials science. It also provides a reference for future research on constitutive models and high-temperature material behavior in various industrial applications.

Finite Element Analysis of Dynamic Recrystallization Model and Microstructural Evolution for GCr15 Bearing Steel Warm-Hot Deformation Process

Warm deformation is a plastic-forming process that differs from traditional cold and hot forming techniques. At the macro level, it can effectively reduce the problem of high deformation resistance in cold deformation and improve the surface decarburization issues during the hot deformation process. Microscopically, it has significant advantages in controlling product structure, refining grain size, and enhancing product mechanical properties. The Gleeble-1500D thermal-mechanical physical simulation system was used to conduct isothermal compression tests on GCr15 bearing steel. The tests were conducted at temperatures of 600-1050 °C and strain rates of 0.01-5 s^-1. Based on the experimental data, the critical strain model and dynamic recrystallization model for the warm-hot forming of GCr15 bearing steel were established in this paper. The model accuracy is evaluated using statistical indicators such as the correlation coefficient (R). The dynamic recrystallization model exhibits high predictive accuracy, as indicated by an R-value of 0.986. The established dynamic recrystallization model for GCr15 bearing steel was integrated into the Forge^® 3.2 numerical simulation software through secondary program development to simulate the compression process of GCr15 warm-hot forming. The dynamic recrystallization fraction was analyzed in various deformation regions. The grain size of the severe deformation zone, small deformation zone, and difficult deformation zone was compared based on simulated compression specimens under the conditions of 1050 °C and 0.1 s^-1 with the corresponding grain size obtained with measurement based on metallographic photos; the relative error between the two is 5.75%. This verifies the accuracy of the established dynamic recrystallization and critical strain models for warm-hot deformation of GCr15 bearing steel. These models provide a theoretical basis for the finite element method analysis and microstructure control of the warm-hot forming process in bearing races.

Deformation Behavior, a Flow Stress Model Considering the Contribution of Strain and Processing Maps in the Isothermal Compression of a Near-α Ti–3.3Al–1.5Zr–1.2Mo–0.6Ni Titanium Alloy

In the present study, isothermal compression tests are conducted for a near-α Ti–3.3Al–1.5Zr–1.2Mo–0.6Ni titanium alloy at deformation temperatures ranging from 1073 K to 1293 K and strain rates ranging from 0.01 s⁻¹ to 10 s⁻¹ on a Gleeble-3500 thermomechanical compressor. The results show that, in the initial stage of the compression, the flow stress rapidly increases to a peak value because of elastic deformation, and then the alloy enters the plastic deformation stage and the flow stress slowly decreases with the increase in strain and tends to gradually stabilize. In the plastic deformation stage, the flow stress significantly decreases with the increase in the deformation temperature and the decrease in strain rate. A flow stress model considering the contribution of the strain is established, and the relative error between the calculated and the experimental values is 3.72%. The flow stress model has higher precision and can efficiently predict the flow behavior in the isothermal compression of the alloy. Furthermore, the processing map of the Ti–3.3Al–1.5Zr–1.2Mo–0.6Ni alloy is drawn. Based on the processing map, the influence of process parameters on power dissipation efficiency and stability parameters is analyzed, and the optimized hot working process parameters are pointed out.

Hot Deformation Behavior of the 25CrMo4 Steel Using a Modified Arrhenius Model

25CrMo4 steel is widely used in the manufacturing of high-speed train axles due to its excellent mechanical properties. The purpose of this study is to develop an accurate modified constitutive model to describe the hot deformation behavior of the steel. Isothermal compression experiments were performed at different strain rates (0.01, 0.1, 0.5, and 1 s⁻¹) and different temperatures (950, 1000, 1050, and 1100 °C) using a Gleeble-3800 thermal simulator. The microstructure after hot deformation was observed by the electron backscatter diffraction (EBSD), and the effects of temperature and strain rate were analyzed. The results showed that the coupling effect of temperature and strain rate on the dislocation density led to the change in the shape of the true stress–strain curve and that dynamic recovery (DRV) and dynamic recrystallization (DRX) caused the macroscopic softening phenomenon, with DRX being the main mechanism. Based on the true stress–strain curves, the strain-compensated Arrhenius constitutive model was calibrated. To improve prediction ability, a modified Arrhenius constitutive model was proposed, in which the temperature and strain rate coupling correction functions were incorporated. The original, modified Arrhenius models were evaluated according to the absolute relative error (ARE), the average absolute relative error (AARE), and the correlation coefficient (R²). Compared with the original model, the modified Arrhenius model has a higher prediction accuracy, with the ARE value mostly below 4%, the AARE value of 1.91%, and the R² value of 0.9958.

Prediction of Flow Stress of Annealed 7075 Al Alloy in Hot Deformation Using Strain-Compensated Arrhenius and Neural Network Models

Hot compression experiments of annealed 7075 Al alloy were performed on TA DIL805D at different temperatures (733, 693, 653, 613 and 573 K) with different strain rates (1.0, 0.1, 0.01 and 0.001 s⁻¹.) Based on experimental data, the strain-compensated Arrhenius model (SCAM) and the back-propagation artificial neural network model (BP-ANN) were constructed for the prediction of the flow stress. The predictive power of the two models was estimated by residual analysis, correlation coefficient (R) and average absolute relative error (AARE). The results reveal that the deformation parameters including strain, strain rate, and temperature have a significant effect on the flow stress of the alloy. Compared with the SCAM model, the flow stress predicted by the BP-ANN model is in better agreement with experimental values. For the BP-ANN model, the maximum residual is only 1 MPa, while it is as high as 8 MPa for the SCAM model. The R and AARE for the SCAM model are 0.9967 and 3.26%, while their values for the BP-ANN model are 0.99998 and 0.18%, respectively. All these reflect that the BP-ANN model has more accurate prediction ability than the SCAM model, which can be applied to predict the flow stress of the alloy under high temperature deformation.