The effect of inelastic deformation on crack loading

Licentiate thesis, 2016

Rolling contact fatigue (RCF) cracks in rails are among the most detrimental railway track defects, in relation to reliability and cost. The cracks grow in a mixed mode II & III, which in combination with the rotating stress field in the neighborhood of the crack-tip, large plastic deformations on the rail surface, crack face friction due to the compressive stresses from the wheel load and anisotropic crack growth resistance, add to the complexity related to the study of RCF cracks. In contrast, most existing criteria for RCF crack propagation in the literature feature quantities that are susceptible to limitations, such as small scale yielding (see e.g. stress intensity factors), pure mode I growth, unloaded crack faces. Consequently, the range of validity (and precision) of existing criteria may be questioned. The current work focuses on one of the complicating factors: the role of inelastic deformation on the crack loading. At the first part, a qualitative assessment is performed of the mechanisms that accompany elastoplastic deformations of multi-axially loaded cracks. For this purpose, numerical simulations are carried out in pre-cracked tubular specimens subjected to torsional and axial loading in various load configurations. Elastoplastic deformations are quantified here via the relative deformation of initially aligned crack faces, here denoted as crack face displacement. The range of the crack face displacement over each load cycle accounts for the severity of the crack situation (in a manner analogous to the range of the stress intensity factor). Results are identified as shakedown and ratcheting effects and compared to experimental trends in literature. The work continues with the study of configurational (or material) forces for gradient-enhanced inelasticity. The severity of the crack loading is here measured via energy release rates (a generalization of the J-integral for inelasticity with material dissipation), which stem from the computed material forces. The mesh sensitivity of the energy release rates is investigated for the cases of a smooth interface and an embedded discrete singularity. Results highlight that the proposed gradient-regularized scheme provides sufficient regularity for the computation of material forces. Obtaining a rather mesh insensitive material force field for inelasticity, is considered a necessary step towards the development of a criterion for RCF crack propagation based on material forces.