Hot-deformation behaviour of rare earths (RE) containing 3Cr13MoNiVNb martensitic stainless steel based on constitutive equations and deep learning algorithm

The present constitutive model can accurately predict the flow stresses in materials during thermal deformation, which is of great significance for the formulation and improvement of hot working processes. This study performed hot deformation testing on rare earths-containing 3Cr13MoNiVNb martensitic stainless steel, using stress–strain data to develop traditional constitutive models, including modified Zerilli–Armstrong (ZA), optimised ZA, and Arrhenius models. A range of machine learning models, including gradient boosting regression, random forests, support vector regression, extreme gradient boosting, kernel ridge regression, decision tree, multilayer perceptron, and deep neural network (DNN), have been designed to relate stresses to strain rate, strain, and hot deformation temperature. Among all the constructed models, the DNN model demonstrated significantly higher accuracy than the other models in predicting experimental values, achieving mean squared errors of 11.647 and 12.648 on the training and test sets, respectively, and corresponding R 2 values of 0.999 and 0.997. Furthermore, the DNN model can accurately predict stress across dense temperature intervals, enabling the construction of more precise hot processing maps.