A dimensionless multi-size finite element model of a rolling contact fatigue crack

Considerations which should be taken in approaching a rolling contact fatigue (RCF) crack growth problem must cover the variety of possible configurations of geometrical parameters, material properties and loading conditions. The great variety of configurations occurring in engineering practice is probably a reason to the difficulties, which are usually encountered in finding the complete data concerning any particular problem from the discussed field. The purpose of the paper is to introduce a concept of a dimensionless multi-size finite element (FE) model, which can reduce the number of necessary models for a given problem of RCF. This concept is explained on the basis of the 2D version, in which the size of the crack is represented only by its length and the real contact load is applied in the form of traveling theoretical Hertz' pressure. Such a model assures the possibility of using only one FE mesh for analyzing a number of RCF crack lengths under moving contact load. The multi size feature of the model consists in introducing the two parameters of geometrical similarity to the 2D contact problem, i.e. the crack slope angle and the ratio of crack length to the half width of the theoretical Hertz' contact patch being called further the dimensionless crack length. These two parameters are sufficient for identifying the considered case. In the conventional approach, each crack length requires building a separate FE model, which can be used to determine the linear elastic fracture mechanics (LEFM) stress intensity factors (SIF) histories. This is very costly, time consuming and laborious, especially in 3D modeling. In the presented approach, the model of the member containing the crack is only one, whilst the different dimensionless crack lengths are realised by means of changing the contact patch instead of the crack length itself. The model was tested and the results obtained are in a good agreement with that obtained conventionally. Additionally, the functionality of the model was presented in conducting several series of analyses for the two crack slopes 15 and 20DG and the range of the dimensionless crack lengths from 0.5 to 15. On the basis of the results, the critical dimensionless crack lengths were determined, for which the crack tip is exposed to the highest ranges of the Modes I and II SIFs.