Comparative study of metamodeling methods for modeling the constitutive relationships of the TC6 titanium alloy

It is important to model the flow behavior of materials before the design and optimization of the forming process. In this work, the TC6 titanium alloy was subjected to a temperature range of 800 °C to 1000 °C and a strain range of 0.01 s−1 to 10 s−1 in isothermal compression experiments, after which friction and temperature corrections were performed. Based on the corrected data, three metamodeling methods—the response surface method, the Kriging method, and the BP neural network—were used to model the constitutive relationships of the TC6 titanium alloy. The results show that the three models can better predict the flow stress of the TC6 titanium alloy than the Arrhenius model. In addition, by comparing the fitting accuracy of the three methods using different numbers of training samples, we found that the accuracy of the BP neural network method is very dependent on the number of training samples, while the fitting accuracy of the response surface method and the Kriging method is always maintained at a high level; when the number of training samples is between 30 and 240, the curved surfaces fitted by these two methods do not change significantly. Compared with the Arrhenius model, the response surface method and the Kriging method can reach higher accuracy with fewer training samples, which is significant for reducing the number of experiments and calculation time required to model the constitutive relationship.