A new analytical formulation for contact stress and prediction of crack propagation path in rolling bodies and comparing with finite element model (FEM) results statically

Abstract

Rails fracture by the growth of fatigue crack or critical crack is one of the prevalent defects in railway. The rail fracture, failure and analysis of stress should be studied to prevent rail fracture and events. In this paper, new formulation of contact stress for two rolling bodies is presented, and its results are close to the hertz stress formulation. The analysis of stress is done by Finite Element Model (FEM) and it is compared with hertz stress and new stress formulation results. Then, the analysis of stress, fracture, prediction of fracture and path of crack motion in rail and wheel are studied, statically which plays an important role in this field. The methods of analysis of stress theory fracture with numerical and FEM are compared and consequently, it was proved that these approaches have acceptable results compared with other results. So we can rely on these methods and their results. The relation between maximum displacement and maximum stress is presented, and the path of crack growth and fracture is predicted. To analyze the pressure of collection of the wheel and rail instead of elliptical contact surface, quadrant of elliptical contact surface is assumed. With this assumption, acceptable results will be attained. Key words: Rail fracture, maximum stress, Hertz’s elliptic, reformation coefficients, negative discharge energy hole, crack growth.