On the use of XFEM for frictional crack face contact. Application to rolling contact crack growth in rails

Abstract

In this study, an existing numerical framework in 3D for predicting stationary rolling contact fatigue crack growth direction and rate in rails using the eXtended Finite Element Method (XFEM) is extended to account for the influence of crack face friction. To enable this extension, as the first part of the study, the accuracy and robustness of XFEM for stationary frictional cracks in 3D simulations, together with its practical implementation in the commercial FE software ABAQUS, are evaluated through a set of numerical tests. A rectangular block model with a predefined crack geometry is here considered, and the XFEM results in terms of resolved contact shear stresses are compared with the explicitly meshed fracture surface. Crack face friction is implemented using Coulomb’s model with varying friction coefficients, and the comparisons are conducted for pure shear load and combined shear–compression load. To account for crack face friction in a stationary setting using XFEM in ABAQUS, crack propagation is suppressed by assigning high critical values for damage initiation and evolution. The trends for the computed shear stresses aligned well those obtained using explicit crack modeling, despite some deviations in absolute values, thereby indicating that the method is sufficiently robust for the qualitative purposes of this study. As the second part of the study, crack face friction is implemented for pre-existing head check cracks in rails. Crack growth rates and directions are evaluated by employing Paris-type equations and an accumulative vector crack tip displacement criterion, respectively, using stress intensity factors extracted directly from ABAQUS. The results are evaluated for a semi-circular crack plane with two crack radii under a wheel–rail contact load and a combined contact and bending load at three points along the crack front. It was found that crack face friction had a significant impact on growth rates for all points, crack radii and load cases, where a higher coefficient of friction resulted in a lower rate of crack growth. These reductions were found to correspond to large increases in traffic capacity before reaching a certain crack radius. More specifically, the highest investigated friction coefficient was found to reduce growth rates by up to 49% for the case of combined contact and bending loads, which in turn resulted in up to 72% traffic increase for reaching the same crack size, compared to the frictionless case. This highlights the importance of accounting for crack face friction to obtain more realistic predictions and to support efficient maintenance planning of rails. The influence of crack face friction on growth direction was found to be limited, with no clear observed trends due to a limited number of studied cases, under either pure contact or combined contact and bending loads.