A finite element method for reconstruction of shakedown map in wheel–rail rolling–sliding contact

The classical shakedown map has served as the standard template for predicting rolling contact fatigue in wheel–rail systems. Its derivation is based on numerical analysis methods with idealized parameters, limiting generalizability and applicability to realistic conditions. To address this, an evaluation method for shakedown limits based on a finite element method was developed in this paper. A 3D shakedown map under rolling–sliding contact was reconstructed using a nonlinear kinematic hardening material. The effects of different rail materials and wheel–rail tangential load on the elastic shakedown limit were investigated. The results show that the classical shakedown map provides conservative estimates, while the reconstructed 3D shakedown surfaces are consistently higher. The elastic shakedown limit of the nonlinear kinematic hardening material lies between those of elastic-perfect plastic material and linear kinematic hardening material. The shakedown surfaces generally decrease with increasing coefficient of friction and traction coefficient, it elevates progressively for rail materials U75V, U71Mn, and U78CrV. The elastic shakedown limit also increases with the ratio of lateral to longitudinal load. The reconstructed shakedown map thus provides an effective framework for predicting the material mechanical response and rolling contact fatigue.