A three-dimensional finite element solution of frictional wheel–rail rolling contact in elasto-plasticity

Wear, rolling contact fatigue, and plastic deformation are the major failure modes of railway wheels and rails. Proper analyses of the failure mechanisms as well as improvement in design and maintenance require an accurate evaluation of the stress and strain states. Solution of frictional rolling contact between wheel and rail in elasto-plasticity seems, however, still to lack in the literature. This paper presents a model for such a solution. A 3D finite element model is built up to simulate the rolling contact. The focus is on the tangential problem, namely the distributions of surface shear stress and micro-slip as well as the distinction of areas of adhesion and slip in the contact patch. With the presented model the assumptions of half space, linear elasticity and quasi-static or steady state, which are often employed in existing solution of rolling contact, are dropped. A bilinear elasto-plastic material with isotropic hardening is employed to examine the effects of plasticity on frictional rolling. It is found that when plastic flow occurs, the contact patch in the rail top changes from an ellipse into an egg shape; the cross influence between the normal and tangential contact problems become stronger: the normal solution is not independent of the tangential solution any more, and the tangential solution is greatly affected by the normal solution. The model can be applied to investigation of the relationships between material properties, plastic deformation, frictional work, wear, and crack initiation. Such relationships may help in better understanding the occurrence of corrugation, head checks, and squats, and may further be used for design of fatigue resistant materials and profiles of wheel and rail.