Abstract：The shakedown limit defines the critical load preventing sustained alternating plasticity or ratcheting deformation in elasto-plastic structures subjected to cyclic loading. This provides a vital theoretical guidance for improving rail load-bearing performance and optimizing design against rolling contact fatigue. However, previous shakedown analysis models neglect the temperature-dependent material properties, non-linear cyclic hardening behavior, stick-slip frictional regime, and non-Hertzian contact conditions arising from the complex wheel/rail tread surface and wheelset lateral motions. Consequently, they exhibit significant deviations from the actual service conditions of rails. Therefore, the standard wheel/rail tread geometry and a modified Abdel Karim-Ohno cyclic plasticity constitutive model with temperature-dependent elasto-plastic material properties are employed here. Moreover, the strip theory is applied to determine the tangential traction under partial stick/slip rolling contact conditions. The finite element simulations of three-dimensional cyclic elasto-plastic rolling contact of rails are performed to obtain the evolution of equivalent plastic strain with the loading cycle. And then, a shakedown criterion is developed to identify the rail’s shakedown state in combination with the fundamental shakedown definition. A bisection iteration of axle loads is implemented to search for the shakedown limit corresponding to the critical shakedown/non-shakedown condition. Parametric studies are conducted based on the developed model to examine the effects of wheelset lateral motion, creepage mode, and temperature dependence of elasto-plastic properties on the shakedown limit. Results show that wheelset lateral motion reduces the contact pressure, suppresses the plastic deformation, and consequently increases the shakedown limit, though this effect becomes slight under low friction coefficients with an opposite-direction motion; decreasing the normalized tangential loading coefficients expands the stick zone, reduces the tangential traction and total contact stress, weakens the plastic deformation, and thereby elevates the shakedown limit, particularly under high-friction conditions; a thermo-induced decrease in elastic modulus enhances the shakedown limit by reducing the structural stiffness and contact stress level, whereas the thermal decay of both isotropic resistance and hardening modulus promotes the plastic deformation and then reduces the shakedown limit.
2026, Vol. 47 
