Fatigue lifetime estimation of railway axles
Introduction
Train components especially railway axles are subjected to a large amount of load cycles (108–109 cycles) during operation period [1]. Therefore, risk of a railway axle fatigue failure with possible consequent derailment of a train is relatively high, however regular inspections and safe life design are demanded. According to the latest report of European Railway Agency from year 2014 [2], the number of all railway axle failures in European Union was 147 between years 2010 and 2012. It is decrease in the comparison with the previous years (329 railway axle failures were recorded [3], [4] during period from 2006 to 2009). However, accuracy of the railway axle lifetime prediction is still important topic, see comprehensive articles [1], [5], [6], [7]. Classical design based on Wöhler's approach and knowledge of fatigue strength of the axle is in the last decade very often supplemented by “Damage Tolerance Design” methodology. This methodology assumes existence of a small initial defect (e.g. fatigue crack) [5], [6], [7], [8], [9], [10], [11], because there is not 100% reliability that this crack is detected during maintenance interval. It is given by the fact that detection by non-destructive testing methods is of probabilistic character, see Fig. 1. For instance an existing crack with length about 2 mm is detected by magnetic powder inspection in approximately 95% cases. In other words, the crack of 2 mm length is not detected in 5% cases. According to this fact, the railway axle should be designed for the safe operation even though it can contain a crack of few millimetres in length. Then it is necessary to determine the residual fatigue lifetime (RFL) of the railway axle, which corresponds to fatigue crack growth from size of a small detectable defect to the critical crack length. Some methodology is being currently developed (see [5], [6], [7], [8], [9], [10], [11]) and several projects were dedicated to this issue e.g. WIDEM [12], MARAXIL [13] or EURAXLES [14]. Due to many important factors which can significantly influence fatigue lifetime of the railway axle the whole methodology is still in development, see e.g. papers from last 2 years [15], [16], [17], [18], [19], [20].
The aim of this paper is to present the procedure of determination of RFL of the railway axles developed in the cooperation with Bonatrans Group as one of the leading producers of railway wheelsets.
The methodology presented is based on Damage Tolerance concept. For safety reasons initial defect has to be detected by non-destructive testing method with high probability (1– 2 mm defects are considered). Using finite element analysis of the railway axle containing crack, stress intensity factors of growing crack are determined and the number of load blocks necessary for fatigue crack propagation from initial defect to critical crack length is evaluated. As an example the driving railway axle is considered in the following, see Fig. 2.
Section snippets
Determination of critical position of the initial crack
For the RFL estimation of the axle it is necessary to determine location, where potential crack causes the shortest RFL (the fastest propagation growth from initial crack size up to critical one). There is two main sources of loading in the critical area - bending and press-fit loading. Press-fit loading is a constant during whole service interval (for given location). Bending loading is changing due to dynamic forces (effect of ride to curved track, over switches, crossovers, etc.). The
Estimation of the fatigue crack front shape during crack propagation
According to relevant literature e.g. [24], [25], a crack front shape can be simplified as semi-elliptical. Nevertheless, the ratio between axes of the ellipse is continuously changing during crack propagation. It is necessary to estimate crack shape evolution numerically due to significant influence of the crack shape on the resulting stress intensity factor and consequently on the estimated RFL of the railway axle [23], [24], [25].
According to work of Sih, see e.g. [26], [27], the shape of
Results of K-calibration
As soon as the critical position for the shortest RFL is known it is important to estimate the stress intensity factor KI as a function of the crack length a. Using optimized crack front shapes obtained by the procedure described in the previous chapter a stress intensity factor was evaluated in the critical position 8 mm from the railway wheel seat (see Fig. 6) as a function of crack length a. The total stress intensity factor has to be separated into two kinds of loading; bending and loading
Influence of press-fits on the stress intensity factor values
The existence of press-fits significantly increases the magnitude of the stress of considered crack in the critical location. Therefore, the presence of the press-fits should be taken into account in procedures of RFL estimation. There exist several approaches how model press-fitted wheel on the railway axle. In FE analysis the press-fits can be modelled using nonlinear contact (with consideration of friction) between wheel and axle. Such procedure provides precise description of the stress and
Fatigue crack grow rate
The RFL of railway axle is considered as number of applied load blocks (load block considers all variable amplitudes of load spectrum) necessary for fatigue crack growth from initial (detectable) up to critical crack length. Fig. 15 shows typical fatigue crack length evolution in dependence on number of applied load blocks. It is obvious that fatigue crack propagation rate in early stages is quite slow, but in final stages of lifetime the fatigue crack grows quickly and fatigue failure occurs.
Lifetime prediction
The stress intensity factors in the numerical model are calculated for loading of railway axle corresponding to ride on straight track (dynamic forces are not present in this case). However, RFL is given by acting of all load levels from load spectrum, see Fig. 3. The total stress intensity factor KI,max is given by superposition of stress intensity factor caused by bending of the axle (this part is described by load spectrum) and load caused by press-fitted wheel, see Fig. 14a. Each load level
Influence of threshold value determination on RFL
This chapter shows impact of threshold value on calculated RFL of railway axle. The RFLs in Table 1 were determined for mean values of da/dN–K curve, see Fig. 17b. Fig. 19 shows histogram of da/dN–K curve data with propagation rate lower than 10− 9 m/cycle. These data corresponds to crack propagation near the threshold value. The histogram in Fig. 19 is fitted by normal distribution function and two conservative fits 90% and 99% of threshold value are marked there. For instance the conservative
RFL calculated for various probability fits of whole da/dN–K curve
Previous chapter was focused on sensitivity of determination of threshold value on calculated RFL of railway axle. This chapter shows difference in estimated RFLs determined for mean values of whole da/dN–K curve and two conservative fits of whole da/dN–K curve. The data in linear region are fitted by least square method (by line in log-log coordinates). The line creates so-called baseline (50% fit) for other two fits. Fig. 21 shows distances of da/dN–K data (in linear region) from baseline.
Effect of overload on residual fatigue lifetime estimations
Previous estimations did not take into account retardation effects which can occur during variable amplitude loading. The load cycles with importantly higher amplitudes (overloading cycles) enlarge plastic zone ahead of the crack tip. Compressive residual stresses ahead of the crack tip contribute to the decrease of fatigue crack propagation rate (retardation effect), see Fig. 23.
The generalized Willenborg model [47], [48] was chosen for modelling of the retardation effects due to overload
Conclusions
This paper presents methodology for the fatigue lifetime assessment of railway axles using fracture mechanics concepts. Based on the results obtained conclusions can be summarized as follows:
- a)
The evolution of fatigue crack front during crack propagation can be credibly numerically estimated by presented algorithm. The algorithm is based on the assumption of the constant stress intensity factor value along the crack front. This assumption follows from energy considerations of crack propagation.
- b)
It
Acknowledgement
The work was supported through the specific academic research grant No. FSI-S-14-2311 provided to Brno University of Technology, Faculty of Mechanical Engineering and by research infrastructures IPMINFRA (supported by the Ministry of Education, Youth and Sports of the Czech Republic trough project No. LM2015069) and CEITEC – Central European Institute of Technology supported by the project CZ.1.05/1.1.00/02.0068 financed from European Regional Development Fund.
The cooperation between the
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