Elastic-Plastic Fracture Mechanics and RCF in Rails

Abstract: This thesis concerns issues regarding the modeling and numerical simulation of singular cracks and their propagation in the context of Rolling Contact Fatigue (RCF) in rails. Typically, such cracks are associated with squats and head-checks in the rail head. One characteristic feature, which is of particular concern in the thesis (and in the CHARMEC project MU17), is that the propagation of RCF-related cracks takes place under significant influence of large plastic deformations. Another feature is that several cracks interact in a complex fashion due to the rotating stress state during each single over-rolling. The work is reported in two papers submitted for international publication: In Paper A the objective is to investigate geometric and material parameters that effect the interaction of multiple preexisting (initiated) cracks due to RCF loading conditions. Parameters of interest are: initial crack angle, initial crack spacing, distribution of initial crack length, load/contact zone in relation to spacing, FE-mesh sensitivity, and material properties (in particular the friction coefficient). An open question of particular interest is the effect of crack interaction, e.g. shielding, on the prevailing crack spacing. In view of all uncertainties of the material model as well as the three-dimensional geometric complexity of the RCF-problem, it is important to obtain a good understanding of the sensitivity of parameters. This is achieved in the presented investigation, although it is carried out using simplifying assumptions such as plane strain, linear elasticity, Hertzian pressure distribution, etc. Paper B focusses on the proper definition and computation of the ”crack-driving force” to be used in crack propagation modeling. The crack-driving force is defined in the context of ”material forces” (or configurational forces), which is a vectorial measure of the energy release rate due to a (virtual) variation of the position of the crack tip. A particular issue is the role of material dissipation that is induced by configurational changes, such as crack advancement. In this paper, we introduce two approximations for the relation between the rate of internal variables and the given rate of change of material configuration. We consider convergence from mesh refinement for the two different assumptions for the simple model problem of a plate with a pre-existing edge crack in a setting of small strains and isotropic hardening.