Finite element procedures for crack path prediction in multi-axial fatigue

Sammanfattning: Rolling Contact Fatigue (RCF) cracks in rails are among the most detrimental railway track defects regarding reliability and cost. The cracks typically grow in shear mode up to a certain length at which they might arrest or kink into a more tensile-driven growth. This growth scheme appears as a result of non-proportional loading, large plastic deformations at the rail surface and primary compression with crack-face friction. In contrast, most existing crack growth criteria in the literature feature quantities that are susceptible to the limitations of small-scale yielding, e.g. Stress Intensity Factors (SIFs), tensile-mode growth and unloaded crack-faces. Consequently, the range of validity of the existing criteria may be questioned in the non-linear crack growth setting of RCF. In a study of the role of inelastic deformation on the crack loading, elastic–plastic simulations are carried out in pre-cracked tubular specimens subjected to mixed-mode cyclic loading. The crack loading is quantified via the Crack-Tip Displacements (CTDs) in modes I and II. Shakedown and ratcheting effects in the ranges of the CTDs are compared to trends of crack growth curves from experiments in the literature. It is concluded that the ranges of the CTDs can be used for qualitative crack growth assessment in the examined load cases. In addition, a gradient-enhanced mixed variational formulation is developed for overcoming the numerical difficulties associated with the computation of Configurational Forces (CFs) for inelasticity. The mesh sensitivity of the CFs acting on an embedded discrete singularity is investigated. Results highlight that the proposed formulation provides sufficient regularity for the computation of CFs, which may then be used in the formulation of criteria for RCF crack propagation. Predictions of the multi-axial fatigue crack path are performed based on instantaneous crack growth direction criteria. To this end, a generic model for load cycle evaluation is proposed and implemented on criteria based on CFs and CTDs. The predicted directions are compared towards mixed-mode fatigue crack growth experiments from the literature. Of the evaluated criteria, the ones based on CFs and CTDs accurately predict the tensile-mode growth. Classical SIF-based criteria seem to handle tensile-mode growth under moderate shear-mode loading. Moreover, the criterion based on CTDs captures the shear-mode growth and the tensile-mode growth as well as the transition between them. The latter growth schemes essentially resemble the RCF crack growth. In an investigation of the influence of various railway operational parameters on predicted RCF crack growth directions, the coefficient of friction at the wheel–rail interface was found the most influential as compared to the wheel tonnage and crack-face friction. The latter had no effect on predicted directions, due to crack-tip opening at the instances of maximum shear CTDs.