Simplified Model of Elastic-Plastic Wheel/Rail Interactions

The results of numerical calculations, presented in the paper [1], demonstrate a significant role of plastic yield in the process of formation of the rail corrugations. Below, certain analytical solutions for a simplified model of wheel/rail interaction process are given. At first, normal and tangent loads of rails, assumed on the basis of the results presented in the paper [2], are analyzed. The corresponding elastic stress field is given in explicit form. Next, a complete solution for a thin, plastic surface layer of rail is pro­posed. The simple analytical expressions enable us to calculate the changes of the limit shear stress and residual stresses under the wheel/rail contact surface after successive passings of a wheel. Two cases are considered: a load moving with constant amplitude and a load moving with cyclically changing amplitude. Two important facts are proved. The first one – that the limit shear stress (K) and the longitudinal residual stress (R) under the running surface of rail converge to asymptotic values. The second one – that the final location of K peaks and R valleys corresponds to the positions of rail corrugations.