Elastic-plastic fracture mechanics - Application to rolling contact fatigue in rails
Doctoral thesis, 2010
Railway structures represent complex mechanical problems involving wave propagation, plastic deformations and material degradation. The wheel-rail contact loads subject the material to repeated cycles of complex stress states resulting in rolling contact fatigue (RCF). A significant problem is the development of "short" surface cracks called head-checks. These RCF cracks appear on the rail-head and are, typically, close-spaced and (almost) parallel. A parametric study of geometric and material properties that affect the interaction between surface cracks in a model that mimics the wheel-rail situation has been carried out, (Paper A). (Over)simplifying assumptions such as small trains, linear elasticity, plain strain, and Hertzian ressure distribution have been used in this study.
In reality, the propagation of RCF cracks takes place under very large local stresses and severe inelastic deformations. An important issue, which is focused in this thesis, is the role of material dissipation for the crack-driving force. Elastic-plastic fracture mechanics accounting for global plastic deformation is still a relatively virgin field. In this thesis the crack-driving force is defined in the context of material (or configurational) forces and computed numerically using finite element analysis. It is proposed that the driving force is defined as the variation of the total dissipation with respect to configurational changes. Material dissipation occurs as result of the configurational changes in addition to the local energy release from the propagating crack tip. As it turns out, the key task is then to compute the sensitivity of the rate of internal variables due to configurational changes, which results in a global tangent problem based on the balance equations.
In order to avoid solving this tangent problem, simplifying assumptions in the relation between the rate of spatial deformation and rate of internal variables can be introduced. A few different approaches have been introduced and assessed numerically for a plate with an edge crack, (Paper B). In this investigation, an elastic-plastic material model with isotropic hardening has been used. The development of the crack-driving force for a single crack in a wheel-rail situation has been compared as part of a parameter study, (Paper C). In particular, elastic-plastic material response is compared to purely elastic response. Even in this investigation, simplifying assumptions such as small strains, plain strain and Hertzian pressure distribution are adopted.
It is desirable to solve the sensitivity problem without introducing the simplifying assumptions mentioned above. As a first attempt, such an analysis is implemented for quite a simple discrete structure, (Paper D). The approach is extended to the problem of an interface separating parts with dissimilar material properties in a non-homogeneous plate, (Paper E).
rolling contact fatigue
Elastic-plastic fracture mechanics