Keywords: shakedown map, wheel/rail contact, elastic limit, elliptical contact patches, two-crossed cylinders model, finite element simulation.

Wear, fatigue, and material deformation are the most common material damages caused by rolling contact fatigue (RCF) in the wheel/rail contact patch. Two important physical quantities in railway engineering, contact pressure and creepage, can be used to predict the material behavior of the wheel/rail contact region. The shakedown map is an important assessment tool used in the railway sector to predict damage caused by RCF. This paper presents a method to calculate the elastic limit of a shakedown map for different wheel/rail contact areas. The study focuses not only on the point and line contacts but also on different elliptical contacts. The focus of this paper is to investigate the influence of different elliptical contact patches on the elastic limit that separates the purely elastic material behavior from the elastic shakedown behavior. Based on an existing Abaqus rollover plugin, a new 3D finite element model representing two-crossed-cylinder is developed to generate elliptical contact areas for continuous rollover simulations. The mentioned model is validated with the Hertzian contact theory. The resulting elastic limit for the point contact is validated with Ponter’s analytical solution. The 3D FE model is then used to determine the elastic limits for the rail steel material R350HT, where the semi-axis elliptical ratio of the contact patch is varied.

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