A fast method to estimate the multiaxial non-proportional elastic–plastic stress–strain in rail rolling contact fatigue problems

Abstract

This paper aims to propose a new and fast method to estimate the multiaxial non-proportional elastic–plastic stress and strain time histories developed in rails due to rolling contact and evaluate its accuracy for fatigue analysis. The method has the pseudo-elastic stress time history as input, which is obtained by a coupled analytical and numerical method. Therefore, a method originally proposed for notch-root elastic–plastic stress–strain analysis was extended to the Rolling Contact Problem (RCF). The problem is solved incrementally and is established considering a set of equations composed by constitutive and multiaxial notch correction equations. Additionally, a kinematic cyclic plasticity model was included. An equivalent model based on the Finite Element Method was used for comparison purposes. The comparison was made in terms of multiaxial fatigue damage parameters in critical planes, according to fatigue analysis models developed by Matake and Brown & Miller. The more relevant advantage of the method over the non-linear FEM analysis is the possibility to readily obtain long elastic–plastic stress and strain histories and to perform material parameter and load case studies. The method proposed agrees with the equivalent FEM and proved to be a powerful tool for fast wheel-rail failure analysis, especially in RCF problems.