The Dynamic Stress State of the Wheel-Rail Contact XIN ZHAO * , ZILI LI * , COENRAAD ESVELD * , ROLF DOLLEVOET # * Section of Road and Railway Engineering, Faculty of Civil Engineering and Geosciences Delft University of Technology Stevinweg 1, 2628 CN Delft THE NETHERLANDS x.zhao@tHttp://www.rail.tudelft.nl # Infra Management Railsystems, Department of Civil Technology, ProRail P.O. Box 2038, 3500 GA Utrecht THE NETHERLANDS Abstract: The rolling contact between wheels and rails is one of the key areas of studies in railway. Nowadays, the rolling contact fatigue (RCF) of rails, especially the surface-initiated RCF, is becoming one of the major concerns in the railway industry. In order to study the initiation and growth of RCF, the stress and strain states of the rails, particularly in the contact interface, have to be predicted accurately. In this paper, a three- dimensional dynamic vehicle-track finite element (FE) model has been created to investigate the dynamic stress state of the rail surface and the effects of the tangential contact force. The model is composed of the primary suspension of vehicle, half locomotive wheelset, one rail, rail pads, and ballast. The wheelset and the rail are modeled using constant stress solid element; the carbody and bogie sprung mass are lumped into one rigid body with suspension; the sleepers are modeled as lumped mass; the fastening and the ballast are modeled as springs and dampers. In addition, the bilinear isotropic elastic-plastic material is used in the rail contact surface, and an explicit integration method is used to solve the problem in the time domain. The results show that the dynamic effects are significant, even in the case with smooth rail contact surface, and the tangential force can greatly increase the shear stress level of the rail surface and reduce the oscillations of the contact stress. Key-words: Contact mechanics, Rolling contact, Dynamics, Finite element method, Stress 1 Introduction In studies of railway, wheel-rail rolling contact is one of the main issues. The contact forces developed in the contact are the most important external inputs to the vehicles and the track, and are also the direct cause of the damage of wheels and rails like wear, corrugation, fatigue and fracture. In recent years, with the continuous increase of the running speed and the axle load, the influence of the contact forces on the wheel-rail damage and the track deterioration has received more and more attention. Dynamic rolling contact has therefore attracted great interests. Although contact mechanics is dated back as early as 1882 with the advent of Hertz theory, the first treatment of rolling contact was done by Cater in the 1920s [1]. He handled the wheel and the rail as two half-spaces and the wheel as a cylinder for boundary conditions, so the contact area was rectangular. Johnson extended Carter's two- dimensional theory to a three-dimensional case of two rolling spheres in which the longitudinal and the lateral creepages were included, but the spin creep was not considered [2]. Further, Vermeulen and Johnson extended the theory for arbitrary smooth surface to the pure creepage without the spin creep [3]. Kalker [4] solved the three-dimensional frictional contact problems with arbitrary magnitudes of the creepages and the spin using a number of numerical methods developed by himself. The solution is basically of boundary element characteristics, and with Boussinesq[5]- Cerruti[6] formula for the influence number. The contact area can be any planar shape. The above-mentioned solutions are all based on the half-space approximation, and exclude the plasticity of the material and the dynamic effects of the system. In order to handle non-planar contact, such as encountered between the wheel flange root and the rail gage corner, Li [7] extended Kalker’s solution into the quasi-quarter space, and applied it to the wear simulation of wheel-rail contact, particularly the severe wear at the wheel flange and the rail gage corner. Except the contact theories mentioned above, there is another powerful tool for solving contact problem  finite element (FE) method. With FE Proceedings of the 2nd IASME / WSEAS International Conference on Continuum Mechanics (CM'07), Portoroz, Slovenia, May 15-17, 2007 127