Research on constitutive model of pure Nb under cold deformation conditions assisted by machine learning

Abstract In this paper, compression experiments on pure Nb were conducted using a Gleeble3500 thermal simulation machine to systematically investigate its thermal deformation behavior under conditions of 25–300 °C and 0.01–10 s −1 . The results indicated that the flow stress behavior of pure Nb was jointly dominated by work hardening caused by dislocation proliferation and softening due to dynamic recovery. To accurately describe this physical process, a Swift-Voce-Power function (SVP) piecewise combined constitutive model based on critical strain and saturation hardening stress was proposed. The model parameters were globally optimized by using the Differential Evolution (DE) algorithm and the Sigmoid function, reducing the average absolute relative error ( AARE ) of the average parameter prediction under full deformation conditions to 3.427%. To address the prediction deviation in the room-temperature high-strain-rate region, a partitioned modelling strategy was further proposed to adapt to different dominant mechanisms. Finally, the model was implanted into DEFORM as part of USRMTR user subroutine through finite element secondary development for verification. The simulation results were highly consistent with the experimental data ( AARE = 4.13%, R 2 = 0.947), demonstrateing good mesh independence, proving that the established model has high engineering applicability and prediction reliability.