Elastoplastic fracture mechanics with application to fatigue crack propagation in rails

Other conference contribution, 2007

Fracture mechanics is of paramount importance for the life estimation of railway components. One particular class of fracture phenomena is associated with rolling contact fatigue in rails and wheels; a typical phenomen is head checks (pre-existing short surfacebreaking cracks in the rail) with a spacing of around 1mm. A significant characteristic for head checks, as well as several other fracture phenomena, is that the crack propagation takes place under very large local stresses and severely large inelastic deformations at the surface due to the large normal and tangential contact tractions. However, elastic-plastic fracture mechanics accounting for global plastic deformation is still a relatively virgin field, even from a more fundamental point of view, in particular in the context of fatigue crack propagation. The crack-driving force may be defined in the context of “material forces”, which is a measure of the energy release rate due to a (virtual) variation of the position of the crack tip. In fact, it is a generalization of the classical J-integral (as known from linear elastic fracture mechanics). A key issue is how to establish the appropriate variational, or energetic, setting in a thermodynamic context for a material with internal dissipation. In particular, it is necessary to account for changing plastic deformation due to the virtual extension of the crack. Although this task is of quite fundamental character, it is an important one in order to accomplish the ultimate goal of the project due to lack of established results in the literature. In this contribution, we discuss different possibilities for establish the crack-driving force. Furthermore, the pertinent computational procedure in a finite element setting is presented and illustrated by few numerical examples.