PSI - Issue 37

R. Baptista et al. / Procedia Structural Integrity 37 (2022) 57–64 Author name / Structural Integrity Procedia 00 (2019) 000 – 000

58

2

Nomenclature θ

crack propagation direction

tangential stress

σ θθ τ rθ K I K II

radial stress

mode I stress intensity factor mode II stress intensity factor radial distance to crack front

r

1. Introduction Throughout history, several accidents have occurred as a result of component fatigue failure. Fatigue failures can result from numerous causes such as poor component design, maintenance, component or set of components assembly, or result from external influences, such as environmental phenomena. Often fatigue failure turns out to be the result of the accumulation of several external factors to the applied fatigue loading, causing the component to fail early and unexpectedly. An example of this situation was the railway accident that occurred in 1998 in Germany (https://newstopaktuell.wordpress.com/category/die-ice-katastrophe-von-eschede). It was concluded that fatigue fracture damage on one of the wheels of the first carriage, was the main cause for the accident. Mechanical components may be subjected to complex loadings without a clear pattern. These loadings can have variable stress amplitudes and be applied in more than one direction. Due to the multiaxiality and the amplitude variation in these loadings, the material’s response will differ from the one veri fied in constant amplitude loadings. In the design phase of a component, it is necessary to have a method to correctly quantify the damage done to the component and estimate its fatigue life. A few studies were carried out and published about the evaluation of crack growth under multiaxial fatigue loadings using experimental and numerical analysis. Floros et al. (2019) investigated the evaluation of crack growth direction criteria based on stress intensity factors, energetic measures and kinematic measures using numerical simulations. In this study the authors concluded that the evaluated criteria based on energetic and displacement measures are able to correctly capture the tensile-mode fatigue crack growth direction. Moreover, the displacement-based criterion is capable to obtain the direction of shear-mode crack growth as well as the transition from shear- to tensile-mode growth and the subsequent tensile-mode growth. Ayatollahi et al. (2015) deals with a study of crack growth retardation and the location of fatigue crack initiation from stop-hole edge under different mode mixities using a developed fatigue code. The numerical results show that for mode-II loading conditions a larger reduction in the stress concentration due to stop holes is observed. The authors also concluded that the fatigue life extension of repaired specimens can be well predicted by the numerical model. Miao et al. (2018) performed a comparison between experimental and numerical results obtained to predict the fracture behavior of CTS specimen under I-II mixed mode loading. One of the main conclusions was the crack growth path and loading capability of CTS specimen are dependent on both loading angle and crack length. Desimore et al. (2006) analyzed the fatigue crack propagation of longitudinal flaws starting in butt-welded joints of rails. The authors performed several finite element simulations to determine the stress intensity factors promote by the passage of the wheel over the rail. Simulations show that fatigue crack growth is dominated by an out-of-phase Mode I – Mode II mechanism with an overlapping of about 180 degrees and the shear influence the crack growth propagation. This paper aims to explore the differences between two crack propagation models. Using an automatic fatigue crack growth algorithm and the finite element method, crack propagation on CTS and four-point bending specimens was simulated. Both specimens allow for pure mode I, mixed mode and pure mode II loading conditions. 2. Numerical Analysis Fatigue crack growth (FCG) was simulated in this paper using a previously developed automatic algorithm by Baptista et al. (2019). Two simple geometries were considered for FCG analysis. Both compact tension shear (CTS) and four-point bending (FPB) specimens allow for pure mode I, mixed mode and pure mode II loading conditions. Several loading conditions were compared against two different crack propagation criteria. Finally, a rail track section,