Tribology International 94 (2016) 118–125
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Effect of wear on rolling contact fatigue crack growth in rails Reza Masoudi Nejad, Mahmoud Shariati n, Khalil Farhangdoost Faculty of Engineering, Department of Mechanical Engineering, Ferdowsi University of Mashhad, Mashhad, Iran
art ic l e i nf o
a b s t r a c t
Article history: Received 25 April 2015 Received in revised form 29 July 2015 Accepted 19 August 2015 Available online 28 August 2015
The purpose of this paper is to analyze the influence of the load direction and the phenomenon of wear on rolling contact fatigue crack growth. For this purpose, a UIC60 rail with accurate geometry using FEM is studied. In this regard, a three-dimensional finite element model is provided. The maximum stress caused by wheel/rail contact for a new/worn wheel profiles was obtained using such model. Then, using Franc 3D software, during stress analysis for different situations of wheel, different values of stress intensity factors are obtained. The behavior of crack under fatigue loading was studied using a threedimensional modeling. & 2015 Elsevier Ltd. All rights reserved.
Keywords: Fatigue crack growth Rail FEM Stress intensity factor
1. Introduction In recent decades, the advent of numerical method, NonDestructive Tests (NDTs) and finite element softwares has caused numerous investigations on fatigue crack growth that is the most important reason for fracture in mechanical components [1]. In railway engineering, many studies are performed on calculating residual stress field and fatigue life in wheel and rail by considering the effect of different parameters [2,3]. The railroad wheel has the initial residual stress created by the manufacturing process, and this residual stress changes due to the mechanical stress caused by service conditions. The residual stresses of railroad wheels are influenced by the heat treatment during manufacture processing [2]. Masoudi Nejad et al. [4,5] developed a three dimensional elastic– plastic finite element model to estimate residual stresses which are cause due to manufacturing process in the wheel structure for Iran’s railways. Masoudi Nejad [6] investigated the stress field due to press fitting process of a bandage wheel and the stress field due to wheel/ rail contact. Farrahi et al. [7] carried out an investigation on fatigue life and crack growth prediction in a bandage wheel due to the stress field which is caused during mechanical loading and press fitting process of bandage wheel. The effect of several parameters, vertical loads, initial crack length and friction coefficient between rim and hub/wheel, on the fatigue life in railway wheels is investigated. Failure in rail structures happens because of many reasons and the fracture that is caused by fatigue may have more effect and be more intense in compared to other causes of failure in such n
Corresponding author. Tel.: þ 98 939 993 5405. E-mail addresses:
[email protected] (R. Masoudi Nejad),
[email protected] (M. Shariati),
[email protected] (K. Farhangdoost). http://dx.doi.org/10.1016/j.triboint.2015.08.035 0301-679X/& 2015 Elsevier Ltd. All rights reserved.
structures. So, the accurate prediction of crack growth in rail using finite element software decreases maintenance costs. The rolling contact fatigue (RCF) in rail is caused by the rail/wheel contact and leads initiation of surface and subsurface cracks. The fatigue performance of the rails is a function of many factors, including service conditions, loading, material properties, environmental factors, and manufacturing processes. In continue, Wong et al. [8] concluded that shallow (surface) angled cracks cause pitting or transverse cracks under special conditions (circumstances). They also studied the effect of different parameters such as initial crack angle and loading condition in the pitting and transverse crack initiation. Kabo [9] studied the fatigue impact of material defects under rolling contact loading condition and investigated the response to overloads and the effect of clusters of defects. He also calculated the fatigue impact using multiaxial fatigue criteria and used finite element simulations to analyze stressess and strains in the vicinity of defects. Beretta et al. [10] presented that the crack initially propagates parallel to the rail surface and then it is willing to propagate through the depth of the rail. They studied crack growth mechanisms and its path in rail web which are the main factors for determining the rail inspection time intervals. At first, they shown mode II by conducting a fractographic analysis and deduced that mode I occurs after the final crack deviation. At the end, their results declare that the initial crack tend to propagate in a path in which mode II stress intensity factor is close to its maximum value and mode I stress intensity factor is willing to maximize mode I crack growth after kinking. Skyttebol et al. [11] presented a finite element analysis to study the effect of welding residual stresses on fatigue crack propagation in rail welds. They simulated the rail/wheel contact by considering residual stress field using SACC finite element software and also studied the effect of axle load, crack location, crack size and rail
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temperature. The results of their survey shown that thermal stress has the most important effect among all other parameters. Farhangdoost et al. [12] investigated on the effect of slippery fluid on rolling contact fatigue crack growth. In this study, they studied the effect of fluid inside the crack on fatigue crack growth by developing a two dimensional finite element model using FRANC-2D software. Besides that, they also performed an analysis to show the effect of friction between faces of crack and pressure ratio on rolling fatigue crack propagation. The interaction between wear and fatigue in rails causes the initiation of rolling contact fatigue defects. Scientist has performed many investigations on the interaction between wear and crack growth. Ringsberg et al. [13] presented an elastic–plastic finite element modeling and analysis for short crack growth in rails under rolling contact fatigue loading by considering the effect of wear. In continue, Donzella et al. [14] proposed a model for estimating the effect of wear on rolling contact fatigue crack growth. They also studied the effect of fluid, shakedown level, the crack growth behavior and the wear rate. Stock et al. [15] studied wear and rolling contact fatigue behavior of different rail materials. Franklin et al. [16] and Kapoor et al. [17] also investigated on the interaction between wear and rolling contact. Most of the previous studies which have been conducted in the field of fatigue and fracture in railway wheels and rails relate to the prediction of crack initiation and some other studies correspond to the crack propagation behavior in railway wheel with no load history consideration. But three dimensional analysis of crack growth in rail structures has not been under sufficient attention in Iran railways. In this paper, a three dimensional finite element analysis and simulation is performed to specify the location of maximum stress field due to wheel/rail contact by considering all possible parameters in Iran railway system. In continue, such stress fields are applied to estimate crack propagation and fatigue life using Franc-3D software for three worn wheel profiles and a new wheel that contain two cracks. One of these cracks are considered to be along wheel rotation direction and the other one is placed in the opposite direction to wheel rotation.
2. Finite element modeling and contact analysis Studying fatigue and fracture of railway structure in the present investigation requires to find the crack initiation location by modeling wheel/rail contact in finite element softwares. For this purpose, the stress analysis of wheel/rail contact is performed using ANSYS finite element software. In order to geometric modeling of wheel and rail, the prominent profiles in Iran railways named as S1002 and UIC60 are used, respectively. Fig. 1 shows new S1002 (for wheel) and UIC60 (for rail) profiles and three types of the worn wheel are shown in Fig. 2 [19]. The first, second and third worn profiles are measured at 200,000, 300,000 and 500,000 km, respectively [19]. Fig. 3 shown wheel/rail contact for straight and curvilinear paths and the finite element modeling in Ansys software is also shown in Fig. 4. The mechanical properties of wheel and rail are presented in Table 1. Dynamic load on each wheel is 98 KN. The wheel degree of freedom (DOF) is free along the loading direction and it is fully constrained in two other directions. The boundary conditions in two sides of the rail are considered as clamped conditions. The rail slope that is applied to underside of the rail and towards the center of two rails is very important during mounting of the rail. This slope is usually applied as 1:20 and 1:40 degrees and 1:20 degree is selected as slope angle in this study. Wheel surface is chosen as main surface due to its finer elements and rail surface is selected as subsidiary surface. One of the mentioned surfaces should be selected as target and the order one as contact surface. For this reason, wheel and rail surfaces are
Fig. 1. Prominent profiles for modeling (a) cross section of new wheel, (b) cross section of UIC60 rail [18].
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chosen as contact and target surfaces, respectively. The friction coefficient is defined as 0.29 for wheel/rail contact and it is constant in all directions [3]. The model mesh has Eight-noded three-dimensional elements of type solid 45. Besides that, contact elements for wheel and rail are defined as contact 173 and target 170, respectively. Table 2 shows the finite element solution according to number of elements and maximum Von-Mises stress for new wheel and rail profiles are also presented. So, the proper number of elements for wheel and rail is according to Table 2. According to the results of finite element solution for wheel/rail contact, the maximum Von-Mises stress due to the contact of rail and new S1002 wheel is 518 MPa. The maximum value of VonMises stress for the contact of rail and the first, second and third types of worn wheel are also computed as 518 MPa, 539 MPa, 569 MPa and 591 MPa, respectively (Fig. 5). These maximum values of stress are higher than the yield strength of steel and this comparison shows that the plastic zone occurs at the contact surface between wheel and rail.
3. Fatigue crack growth and life estimation of rail Superficial (surface) cracks are placed on the surface of the rail and they may change to transverse cracks after propagation because of many factor such as loading, friction and initial angle of crack. It should also be noted that transverse cracks are the most dangerous cracks in rails. Simulation of crack propagation is performed using Franc-3D finite element software which is programmed by Cornell university
Fig. 4. Finite element modeling of wheel/rail contact.
Table 1 The mechanical properties of railway wheel and UIC60 rail steels [3]. Component
Elastic module (GPa)
Poisson’s ratio
Yield stress (MPa)
Wheel Rail
205 206.9
0.3 0.295
527 483
Fig. 2. Geometry of new and worn wheel profile [19].
Fig. 3. Wheel/rail contact, (a) straight path, (b) curvilinear path [19].
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scientists [20,21]. A length of the rail is considered for modeling and only half of the rail length is modeled because of longitudinal symmetry. First, the meshed model is simulated in Ansys software with no crack (crack is defined using Franc-3D software). Then, the results are used as input data in Franc-3D software. Fig. 6 shows finite element model with crack and the number of elements in the
Table 2 Finite element results for different number of element for wheel and rail. Step Number of rail elements
Number of wheel elements
Maximum Von-Mises stress (MPa)
1 2 3 4 5 6 7 8 9 10 11
10,459 17,801 23,986 30,561 36,915 41,763 48,619 52,683 59,427 61,071 65,306
317 365 408 439 451 479 491 509 518 518 519
5809 6135 8769 10,248 13,267 18,420 24,098 27,651 29,134 32,456 34,519
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vicinity of crack and the contact load location are increased in order to achieve better results. Semi elliptical cracks are the most popular cracks in railway structures and many field observations has shown the presence of such cracks as dominant defect in these structures. In this study, a semi-elliptical crack is considered for modeling and analysis and the crack location is selected as discussed in previous section. The length of initial crack is considered as 3 mm and its depth is defined as 1 mm. besides that, two directions are considered for crack, the first one is in along loading condition and the other one is in the opposite direction to loading (Fig. 7). Two types of loading are considered in this study, the first load is associated with train weight that is applied perpendicular to rail section and the second one is related to rolling resistance force that is induced due to wheel/rail contact. The second force is also known as rolling friction force and is applied to crack planes and cause them to slip over each other. In continue, elements are defined and the model is meshed and stress analysis is carried out using Boundary Element System (BES) software. Then the stress intensity factors (SIFs) for three fracture modes are computed. The direction in which the crack propagates is specified using stress intensity factors. Two types of crack growth behavior are
Fig. 5. Stress distribution for the wheel/rail contact, (a) new wheel profile, (b) first type of worn wheel, (c) second type of worn wheel, (d) third type of worn wheel.
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Fig. 8. A sample of pitting defects in rail, (a) crack propagation in Franc-3D software, (b) experimental sample [27].
Fig. 6. Finite element modeling in Franc-3D software, (a) elements of the rail geometry, (b) initial geometry of crack.
the numerical prediction of the crack shape agrees very well with the field observation. Fatigue life estimation of wheel is conducted by obtaining stress intensity factors and using equations used in Refs. [22–24]. Modified Paris model also predicts crack growth and considers the effect of fatigue crack closure. The growth rate is defined by the equation as follows [25]:
da n =C ( ∆Keff ) =C (Kmax − Kop )n dN
(1)
where ΔKeff is the effective stress intensity factor is defined as the difference between the maximum stress intensity factor in mode I ( KI , max ) and stress level where the crack tip first opens ( Kop ). C and n are material constants that are considered as 3.14 and 4.25 × 10−9 m/Cycle, respectively. Crack opening stress function, f, is defined for plastic crack closure as follows (Eq. (3)) [26]: Fig. 7. Definition of different surface cracks.
possible in Franc-3D software: manual and automatic propagation. The crack propagation in manual one is optional, but it should be noted that the crack growth is not allowed to be more than 30% of the summation of all previous crack lengths. The crack growth path is determined using the maximum shear stress criterion and the crack may be propagated for one step right after determining the growth direction. The element are redefined after the first step in crack propagation and gets ready for resolving. This procedure repeats for every steps of crack propagation and continue to 19 steps until the crack length reach to 41 mm. It is seen in Fig. 8 that
f=
Kop Kmax
⎧ 2 3 ⎪ max R , A 0 + A1R + A2 R + A3 R =⎨ ⎪ A 0 + A1R ⎩
(
)
R≥0 −2≤R
