A Review: Double Multivariate Nonlinear Regression Constitutive Model of High-Speed Train Axle Steel 40CrNiMo during Hot Tension

The constitutive model of metal materials can predict the change in flow stress with strain during deformation. This study aimed to establish the constitutive model of 40CrNiMo steel during hot tension. A Gleeble-3800 thermal simulation machine was used and the tensile conditions were set at three temperatures (1223K, 1323K, 1423 K) and four strain rates (0.5 s −1 , 1.0 s −1 , 5.0 s −1 , 10.0 s −1 ). Based on the double multivariate nonlinear regression model (DMNR), the relationship between the influencing factors ( ε , ε ˙ , T , ε - T , ε ˙ - T , ε - ε ˙ ) and the average stress σ ¯ was fitted, and the expression f of the contribution of each influencing factor on the stress change and weight was calculated. A new constitutive model of 40CrNiMo steel was established. The prediction accuracy of the model was evaluated by using standard statistical parameters. The constitutive model could predict the tensile flow stress of 40CrNiMo steel well when the strain rate was not higher than 5 s −1 in the temperature range of 1273–1373 K.