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The objective of this paper is to investigate geometric and material parameters that affect the interaction of multiple pre-existing (initiated) cracks due to rolling contact fatigue (RCF) loading conditions. In particular, the behaviour of short cracks (head checks) in railway rail is studied. Parameters of interest are initial crack angle and spacing, distribution of initial crack lengths, width of the load/contact zone, and the material properties (in particular, the friction coefficient). Furthermore, the sensitivity of the finite element (FE)-mesh density is investigated. 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 parameter changes. This is achieved in the presented investigation, although it is carried out using simplifying assumptions such as plane strain, linear elasticity, and Hertzian pressure distribution.

The thermodynamic framework for combined configurational and deformational changes was recently discussed by . One key ingredient in this setting is the (fixed) absolute configuration, relative to which both physical and virtual (variational) changes of the material and spatial configurations can be described. In the present paper we consider dissipative material response and emphasize the fact that it is possible to identify explicit energetic changes due to configurational changes for "frozen" spatial configuration (a classical view) and the configuration-induced material dissipation. The classical assumption (previously adopted in the literature) is to ignore this dissipation, i.e. the internal variables are considered as fixed fields in the material configuration. In this paper, however, we define configurational forces by considering the total variation of the total dissipation with respect to configurational changes. The key task is then to compute the sensitivity of the internal variable rates to such configurational changes, which results in a global tangent problem based on the balance equations (momentum and energy) for a given body. In this paper we restrict to quasistatic loading under isothermal conditions and for elastic-plastic response, and we apply the modeling to the case of a moving interface of dissimilar materials.

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