An Engineering Analysis of Insulated
Rail Joints: A General Perspective
Nirmal Kumar Mandal and Brendan Peach
Centre for Railway Engineering Faculty of Sciences, Engineering and Health
CQUniversity, Rockhampton Queensland 4702
Australia
Abstract
The insulated rail joint (IRJ) is considered as a necessary evil by the rail transportation and maintenance industry. For automated block signalling it is required to have sections of track electrically insulated from each other, disallowing the rail to be continuously welded as is done where possible. The IRJ is however substantially weaker than the rail and so is subjected to large stresses, causing failure. This paper investigates an engineering analysis of different designs and failure modes of the IRJ and a 3D finite element model for analysing the stresses experienced by three different joint bar sizes, one of 30mm width, one of 34mm width and one of 40mm width. The paper is part of a greater study into the IRJ and searching for ways to improve the performance of the assembly.
Key Words: Insulated rail joints, engineering analysis, damage of rail joints, sensitivity analysis
1. Introduction
1.1 Basic requirement of IRJ
Two main types of rail joints are employed in modern railway track: continuous welded rails (CWRs) and insulated rail joints (IRJs). There are two critical requirements; one is geometric and other one is mechanical in nature. One of the most basic geometric requirements for railway tracks is the need for a smooth running track by lining up the rail ends horizontally and vertically. Prior to about 1970, rails were bolted together by using two joint bars, one on each side of the web with 4 or 6 bolts through the rail track as a geometric requirement. Today though, most rail sections are welded together except in tight curves and other places that require the easy regular rail replacement facilitated by joint bars. In terms of mechanical performance, these joint bars have a lower vertical bending stiffness than the rail track itself [1, 2]. As a result, large deflections in the joint region are generated while wheels pass through. The large deflections can accelerate track deterioration. This in turn yields larger wheel forces caused by the dynamics of the passing wheels and damaged tracks. Accumulation of continuous damage and defects on IRJs can be illustrated as a vicious cycle shown in figure 1.
The lower vertical bending stiffness, coupled with the rising tonnage rates and axle loads experienced in the last 10 years from numerous industries means sections of track that feature joint bars suffer a very short service life [2, 3]. With such short service lives, the economics of developing IRJs with longer service lives are compelling.
Figure 1: A vicious cycle of track and IRJ degradation due to high dynamic wheel loads.
The purpose of IRJs is to allow a railway signalling system to locate trains by maintaining a shorting circuit system. The wheel sets act as conductors between the two running rails; one rail has a low voltage current (signalling rail) and the other rail acts a ground. The IRJs section the signalling rails into isolation blocks. The train locations are determined by identifying which rail section is being short-circuited. When a train passes a joint and enters a section, it triggers a signal indicating that no other trains can enter into that section.
Figure 2: Delamination and damage of rail end and endpost [4]
It is necessary for researchers to improve IRJ’s for longer track service life, reliability and efficiency. The service life of the joints is as short as 200 million gross tonnages (GMTs) and they may be replaced in the track in as little as 12- 18 months on a high tonnage route [3, 5]. In Australia, the associated annual cost for maintenance and replacement of IRJ’s is estimated to be $5.4 million direct and $ 1.1 million indirect costs annually [6]. Therefore there is a pressing need to closely examining the failure mechanism of the existing IRJ designs with a view to improving their reliability, service life and efficiency. Part of this paper is published in a conference [7].
1.2 Different IRJ designs
Many IRJ designs are reported in the literature. They are based on various supporting systems, alignment of end post, end post materials, joint bar and insulation. A typical configuration of the current IRJ is illustrated in figure 3.
Small IRJ defects
Wheel impact
Track degradation
Figure 3: A typical IRJ showing rail, end post, insulation, joint bar and bolts.
Figure 3 illustrates that adjacent ends of the rails are secured at the same level by bolts through joint bars, and insulated end post material is placed in between the rail ends for electrical isolation. Bolts and joint bars are also isolated from the web of the rail by insulated material. There are several designs of IRJ in the literature and their design is based on alignment of end post, joint bar length and supporting system. Pang [8] presented several IRJ designs in his ME thesis. Design of IRJ’s can be classified as either suspended or supported joints and supported joints may be further classified as continuous or discretely supported. This classification is based on the position of IRJ in relation to the sleepers of the rail bed. Figure 4 shows a symmetrically suspended joint in between the sleepers as opposed to the IRJ in figure 5 which is an unsymmetrically supported one. In relation to supported joints, a discretely supported IRJ can be seen on a concrete sleeper (figure 6) and on a single timber sleeper (figure 7) and on double timber sleeper (figure 8). In addition, a continuously supported joint is also described in the literature (figure 9). In this design, joint bars (fishplates) are reshaped to a new form that can be supported over the sleepers. In practice, 4-bolt joint bars (figure 4) and 6-bolt joint bars (figure 6) are most popular. Because of higher number of bolts, the length of joint bar is also different. As per the Australian Standard [9], lengths of 4-bolt joint bar and 6-4-bolt joint bar are 576 mm and 830 mm respectively.
Figure 5: Unsymmetrically suspended IRJ
Figure 6: Discrete concrete sleeper supported IRJ [11]
Figure 7: Discretly supported IRJ on a timber sleeper
Figure 8: Supported IRJ on two timber sleepers [12]
Figure 9: Continuously supported IRJ on sleepers [13]
Most popular end post materials are mainly thermoplastic polymer or fibre-glass used for insulation purposes in IRJ’s. Two polymers commonly used are polytetrafluoroethelene (PTFE) and polyhexamethylene adipamide (Nylon 66) [14]. Material properties of these insulation materials are shown in table 1 below [15].
Another aspect of the end post is the fitting of it in between the rail ends of IRJ. There are two designs of end post fitting: glued IRJ and non-glued (loose) IRJ. Non-glued end post is put firm in place by the action of bolt connections through rails and joint bars. The end post is working an insulation material between two rails for electric signal purposes. Insulation is further included between rail web and joint bars of IRJ. Epoxy as an adhesive material is used to ensure a full contact between rail web and insulation surfaces and between joint bars and insulation surfaces (figure 10).
Table 1: Material properties of popular insulation materials
Materials Young’s Modulus, E (MPa) Poisson’s ratio,
υ
Epoxy fibre-glass 4500 0.19
Nylon 66 1590 0.39
(a) (b)
Figure 10: Types of IRJ: square (figure a), inclined (figure b)
Similar to all other railroad structures, the IRJ’s are placed on a bed which contains several flexible layers: sleepers, pads and ballasted structures. The ballast structure possesses three layers called ballast, sub-ballast and subgrade. This is the most conventional track structure employed in Australia. The IRJ is placed on the top of the structure fastened on the sleeper. Figure 11 pictures a traditional types of bedding employed in Australia [8]. The performance and behaviour of an IRJ depend not only on the IRJ design but also on the stiffness and damping of the super rail structures.
Figure 11: Conventional ballasted Track [8]
Rail joints have been developed over a period of many years. The IRJ is the modern form of rail joint. In the initial design of rail joints, joint bars were not used. Instead, iron straps were employed to bolt the rail end together. Later, the angle bar (joint bar) was developed (figure 12). The bar fitted tightly between the head and base of the rail and the angle shape allowed a greater moment of inertia in both the vertical and horizontal planes. By fitting tightly between the head and base of the rail, the angle bar was able to pass bending moments from one rail to the next. The production process of the joint bar was any form of casting, forging or rolling. In older rail joint design, joint bar contact was with head of the rail or to a small radius head web fillet radius. Due to this small fillet radius, together with the joint bars that fit on the sloping underside of the head, yielded to stress concentration in the resign and caused head web separation at the end of the rail. This problem was eliminated by employing with a larger head web fillet radius. As such head contact and head web contact joint bars were present in that time.
Fastening
Sleeper pad
Sleeper
Ballast
Sub-ballast
Sub-grade
Figure 12: Angle joint bar rail joints: toeless (a) and with toe (b) [16]
As stated above, the insulated rail joint is an integral part of modern rail systems, allowing sections of track to be electrically insulated from each other to allow block signalling. Failure of the joint resulting in two sections of track to be uninsulated poses a significant safety risk to personnel and operational efficiency. Insulated Rail Joints are continuously subjected to varying dynamic loads generated by rolling stock, stresses due to thermal expansion and electrical potential. Therefore, a careful analysis is demanding. A typical diagram of an insulated rail joint is shown below in figure 13 [9].
Figure 13: IRJ Assembly of 6-Bolt.
2 Failure modes of IRJ
elsewhere along a continuous rail. Based on various worldwide designs of IRJ’s, the following are the failure modes of IRJ:
• Bond failure/delamination of end post • Broken joint bar and looseness of the bolt
• Crushed end post and metal flow/material fatigue on railhead.
The modes of failure of IRJ’s in Australia and in other countries differ. Metal flow or plastic deformation in the vicinity of IRJ’s is a major problem in Australia, whereas delamination, bond failure, broken joint bar, or looseness of the bolts are the various modes of failure in America and other countries.
By examining a sample of twenty IRJ’s from revenue service lines in America, Davis and Akthar [3] identified that most of the joints had more than one defect. The degradation modes analysis of these joints on a heavy haul coal route found that maximum failure occurred by virtue of bond failure (nearly 40%), followed by broken bolts (25%), broken bar (17%) and end post crushed/battered (5%). The bond failures (figures 14 and 15) are due to distressed IRJ sub-grade and ballast layer support in track and high level of shear stress under severe wheel loads. The weakened epoxy IRJ bond allowed moisture entry and larger deflection. A sign of rust is evident near the end post (figure 14).
Figure 14: Failed glued bond in IRJ [5]
The wheel/rail contact impact and the associated longitudinal stress due to wheel loads and perhaps also to thermal effects contributed to bolt looseness. This effect along with the larger deflection due to soft end post material further worsen the structural integrity and produces higher impact forces at the IRJ. As a result, breaking of joint bar bolts (due to bending), battered end post (figure 15) and broken joint bar (figure 16) failures might occur.
Figure 15: End post crushed in IRJ due to pull-apart [5]
Figure 16: Shear failure of joint bar due to shear mode of failure [17]
Railhead surface defects due to metal plasticity (metal flow) in the vicinity of the IRJ is another type of failure mode. Initiation of this failure mode depends on the presence of running surface defects on the railhead (figure 17). It can progress to railhead metal failure such as squashing (figure 18) and chipping out (figure 19). Key factors associated with this type of failure include high impact factor due to rail end gap, rail end height mismatch and instantaneous dip angle formation and the associated loading rate dependent metal plasticity as the wheel load exceeds the material yield point at the point of contact.
Figure 17: Running surface defect of IRJ [5]
Figure 19: A typical IRJ failure (chipping out) in Australian heavy haul networks
3 Engineering analysis of IRJ
In the design of a new track and examination of existing tracks, it is necessary to understand the way the dynamic force at the wheel/rail interface varies with speed and axle load, especially at IRJs. High dynamic forces induce large stresses on track, fatigue cracks in rail, geometric deformation of ballast and sub-ballast. These high dynamic forces lead to track degradation.
Figure 20: Variation of vertical dynamic load due to wheel rail contact at dipped joint [24]
In a pioneer research on rail joint, Jenkins et al. [21] provided empirical relations for the evaluation of impact forces P1 and P2.
u t t u t t t u u u e e H
m
k
m
m
K
c
m
m
m
V
P
P
m
m
m
k
V
P
P
}
)
(
1
{
)
(
2
)
/
1
/(
2
2 / 1 0 0 2 0 0 1+
−
+
+
=
+
+
=
π
α
α
(1)where
P
0 is static wheel load, mu is unsprung mass, KH is linearised Hertzian wheel/rail contact stiffness, V0 is the vehicle speed,α
is joint angle, and me, mt, kt, ct are equivalent track system parameters defined in Jenkins et al. [21].The concept of dynamic impact forces P1 and P2 due to the presence of an IRJ is presented above. More
analysis and interpretation are demanded to understand fully its implication and its general modelling. This can be discussed in a separate article. The following section discusses finite element simulation relating to stress and strain measurement of different components of the IRJ, followed by a stress analysis considering rail as a beam on elastic foundation.
3.1 Stresses and strains estimation in IRJ
For railway track design, fatigue and fatigue life estimation of rail and IRJ’s, an accurate determination of stress and strain distributions are important. In this section a detailed study of stress analysis of rail joints is carried out.
Figure 21: A comparison of rail bending moments in the vicinity of rail joint [1].
Chen and Kuang [15] carried out a 3D finite element analysis on an insulated rail joint to investigate the effect of rail joint parameters on the contact pressure distribution and contact stress variation near wheel-rail contact zones at the joint. Three different linear elastic materials such as epoxy-fibreglass, polytetrafluoroethylene and nylon-66 were considered. The interaction between wheel and rail was simulated by contact element. The results of this analysis suggested that the influences of the joint on contact stress distributions were significant. They indicated that, due to nonlinearity, traditional Hertzian contact theory (HCT) was no longer sufficient to predict stress contours.
Chen [4] employed an elastic-plastic plain strain finite element method to investigate the effects of free rail end on contact stress distribution. The simulated results suggested that contact stress distributions around the rail end are sensitive to the contact distance from the free end. Von Mises stress shifted more towards the contact zone from the subsurface and the plastic zone and Von Mises stress increased gradually as contact point moved to rail end.
In an extension of Chen [4], Chen and Chen [25] studied the effects of an insulated joint on the wheel/rail contact stresses under the condition of partial slip. Both wheel-rail normal and tangential stress distribution were presented using 2D plane strain FE analysis considering effects of contact distance from GIJ and different end post materials. The friction coefficient
µ
between wheel and rail was considered as 0.3 for providing tangential tractions. It is most obvious that, when a wheel rolls across the joint, the joint causes a big impact on the rail end which causes a significant dynamic effect on the rail structure. A contact-impact analysis of the rail joint region using a dynamic finite element method was carried out by Wen et al. [2]. The implicit and explicit FE methods were coupled to simulate contact forces, the stresses and strains in the railhead. A linear kinematic hardening material model was considered depicting the influences of axle load and wheel speed. A wider rail end gap of 15 mm was considered. Other gap ranges studied vary from 4 mm to 8 mm [26, 27].Cai et al. [28] studied a dynamic elastic-plastic finite element stress analysis considering a height difference of the rail ends at a rail joint. Both implicit code (ANSYS) and explicit code (LS-DYNA) were considered to simulate the contact and impact of a wheel on the rail joint with a narrow gap. Contact forces, stresses and strains at railhead were investigated considering rail height mismatch, axle load and train speed. The results show that the height difference of rail ends of joint is more sensitive to wheel-rail contact forces, stresses and strains at railhead provided that rail gap (thickness of end-post) is not wide enough. The influences of rail end gap and height mismatch on different parameters are tabulated (table 2) in the following.
Table 2: Sensitivity of load and stress parameters for a narrow rail gap and with height mismatch
Parameters/conditions Static wheel load, P0 (kN) Speed, V0 (km/h) Height mismatch, h mm
Dynamics wheel load Not Sensitive Moderately sensitive
Highly sensitive Von-Mises stress Not Sensitive Not Sensitive Highly sensitive Maximum shear stress Not Sensitive Not Sensitive Highly sensitive Equivalent plastic strain A little Sensitive Highly sensitive Highly sensitive
Talamini et al. [24] investigated the influence of physical track conditions in the vicinity of a rail joint on joint bar fatigue life. The dynamic load factor at a rail joint considering joint characteristics such as joint efficiency (looseness), rail end gap and track stiffness was approximated. Then a 3D finite element analysis of the rail joint was conducted to estimate the bending stresses at the joint due to a passing wheel load. The live bending stresses were then used to estimate the fatigue life of the joint bars using Miner’s linear rule. The effect of thermal expansion due to rail temperature below the rail neutral temperature was investigated. k A U M U o o
S
S
S
S
S
N
N
=
[
(
−
)
]
1/ (2)in which SM and SA are the mean and alternating stress respectively, and No, So, SU and k have fixed values
[22].
The combined effects of rail temperature above and below the rail neutral temperature and the wheel load are presented in table 3. When rail temperature is below the rail neutral temperature, the bottom part of the rail or rail joint is critical. The reverse is true when rail temperature is high compared to the rail neutral temperature.
Bolt joint looseness was investigated by Ding and Dhanasekar [29] considering a bonded bolted steel butt joint. A 3D finite element modelling subjected to two steps of loading such as pre-stressing to bolts followed by the application of in-plane bending load on railhead was considered. Loss of bolt tightness was modelled by adjusting the extensional displacement values; 0 mm for fully loose, 0.25 mm for partially loose and 0.5 mm for fully tight. The 0.5 mm extension corresponded to a stress level close to yield of the bolt.
Table 3: Combined effects of vertical wheel load and longitudinal thermal load
Different conditions Vertical wheel load Axial thermal load Expansion
trail<t neutral
Rail top compression tension
Rail foot tension tension
Joint bar top compression tension Joint bar foot tension tension Contraction
trail>t neutral
Rail top compression compression
Rail foot tension compression
Joint bar top compression compression Joint bar foot tension compression
To study the effects of joint bar looseness, rail height mismatch and train speed on crack driving force on a bolt hole crack was investigated by a finite element analysis [30]. The looseness of the bolts was modelled by varying gaps between rail and joint bar, and the height mismatch by imposing an impulse to the end of one rail. The results showed that the crack driving forces were sensitive to both joint looseness and height mismatch.
Failure of the adhesive layer between rail and joint bars was investigated by a finite element analysis [32]. A standard butt joint was considered. Both vertical wheel load and the tensile load due to temperature effect were employed. The vertical displacement of the rail and shear and peel stresses in the epoxy adhesive layer were determined. A sensitivity analysis of location of wheel, length and thickness of the joint bar and size of ties was performed.
Busquet et al. [33] undertook a 3-D elasto-plastic FE model to investigate the rail mechanical behaviours due to the action of a rolling wheel. In this study, plastic flows in the near-surface layer of the rail were investigated as a function of friction coefficient. It included the depth and distribution of plastically deformed layers. The plastic flow situations of this study were found to correlate well to the microstructural observations of plastic flow in real railheads and existing theoretical studies.
Abolbashari [34] carried out a finite element analysis to optimize the shape of the joint bars. The author considered different thickness of joint bar ranging from 35.73 mm to 52 mm with a view to obtaining a good shape and size of a joint bar that experienced less stresses on it from wheel loads. Using a simplified FE model with proper boundary conditions and loading, about 18% reduction of maximum von-Mises stress can be achieved.
Kabo et al. [26] performed a numerical analysis combining dynamic and plastic deformation and material deterioration of IRJ’s to investigate the influence of the rail joint on generation of wheel-rail impact load and subsequent material deterioration of the joint. It was argued that these joints form local irregularities and result in a local change of dynamic track stiffness. It was observed that not only the dynamic characteristics of the track by virtue of the presence of the IRJ were altered, but also the surface irregularities caused a high increase in contact load. Consequently, a high stress concentration and a corresponding plastic deformation occurred at the joint.
Sandstrom [27] considered a 3D FE model to study plastic deformation and fatigue impact of an insulated joint. A sophisticated constitutive material model capable of capturing ratchetting under multi-axial loading conditions was employed. Illustrating low cycle fatigue parameters, plastic zone sizes and effective strain magnitudes, the study indicated that the main damage mechanism at the joint is ratchetting and not low cycle fatigue.
Dhanasekar et. al. [35, 36] presented field testing of dynamic impacts occurring at the IRJ due to wheel passages. Strain gauges were used in the throat and foot of the rail in square and inclined joints. Vertical, longitudinal and shear strains are reported in the study. An automated computer system powered by a solar system was used to collect strain data.
Although numerical simulation by finite element analysis is important for stress analysis in railway joints, it also important to calculate top and bottom bending stresses of rail and joint bar considering beam on elastic foundation theory. The following section discusses briefly the general concept and procedures to calculate longitudinal stresses of the IRJ.
3.2 Stress analysis using beam on elastic foundation
This section details a complete analysis of rail bending due to vertical wheel load based on beam on elastic foundation theory (figure 22). It was initially proposed by Winkler [37].
If EIr be the flexural rigidity of the rail, the deflection curve of the rail is given by equation (3) where k is
the foundation modulus, which is load per unit length of the rail to produce a foundation deflection of unity.
4
4 r
d y
EI
ky
Figure 22: Rail on elastic foundation model with a vertical wheel load P.
For an infinite long rail (figure 22), the deflection of the rail in the simple case of load P acting in the vertical plane of symmetry is as set out in equation (4):
(cos
sin
)
2
xP
y
e
x
x
k
λ
λ
−λ
λ
=
+
(4)where the factor
λ
can be defined as44
rk
EI
.According to Talamini et al., [24], the longitudinal bending moment distribution Mr(x) of the rail is given
by equation (5):
( )
(cos
sin )
4
x rP
M x
e
λλ
λ
λ
−=
−
(5)As per the beam theory, the maximum bending moment occurs at the location of applied load. It is denoted by Mr (x=0) or Mr (0). Therefore, maximum bending moment for continuous rail (equation (6))
and for jointed rail caused by P2 forces defined as before (equation (7)) are:
(0)
4
rP
M
λ
=
(6)2
(0)
4
rP
M
λ
=
(7)Using the bending moment relation, the stresses in rail and joint bar can be calculated. Just like rail, joint bars are assumed to behave as a beam in bending and are assumed to carry a fraction of the bending moment produced by a continuous rail. The fraction is denoted by
ψ
and it has a numerical value about 0.6-0.8 [21] for a good condition new joint. The factor is called joint efficiency factor. The maximum value of the factor can be expressed by the bending moments of joint bars and rail as in equation (8):4 max max j j r r
M
I
M
I
ψ
=
=
(8)The suffix j stands for joint bar and r for rail, with I being the moment of inertia. Taking the moment of inertia of rail and joint bar for 60kg/m rail [9], the fraction is about 0.58 and it is close to the range. The bending moment of joint bar, Mj can then be related to Mr using the factor,
ψ
as in equation (9):2
(0)
4
j r
P
M
ψ
M
ψ
λ
=
=
(9)The moment relations for rail and joint bar can thus be used to calculate longitudinal stresses of rail and joint bars using the section modulus of rail (Sr) and joint bar (Sj). Equation (10) is for rail and equation
(11) for joint bar.
(0) (0)
r r r
r
r r
M C M
I S
σ
= = (10)x
j j j j
j j
M C M
I S
σ = = (11)
It has been established that the stress equations for rail and joint bar are dependent on the factor,
λ
which is very much dependent on vertical foundation modulus, k. The vertical stiffness value is the mean value of all the stiffness values of ballast, sub-ballast and sub-grade. It is also possible to calculate k values from the stiffness value of ballast [21]. If ks is the ballast stiffness per sleeper end (N/m), k can becalculated as [21]:
s
k
k
l
=
(12)where l is the sleeper spacing (m).
The values of k and
λ
available in the literature are tabulated in table 4. Values specified in the American system of units have been changed into SI units.Table 4: Values of vertical foundation modulus, k Sources Timoshenko
[37]
Talamini [24]
Jeong [38]
Sun [39] Sun [39] Wen [2] Cai [28]
ks (MN/m) - - - 28.80 31.60 30.00 30.90
k (MN/m2) 10.42 20.84 13.89 42.04 46.13 43.79 45.11 The k values in table 4 can be used to calculate the corresponding
λ
values showing in table 5:Table 5: Calculated values of
λ
using its definition (λ
=44
rk
EI
)Sources Timoshenko [37]
Talamini [24]
Jeong [38] Sun [39] Sun [39] Wen [2] Cai [28]
λ
(1/m) 0.787 and 0.8 0.96 0.869 1.14 1.17 1.16 1.166Moment distributions on rail and joint bar can be calculated using equations (6, 7 and 9) incorporating the values of
λ
from table 5. If static wheel load, Po is about 150 kN and P2 force is 182 kN with dynamicimpact factor of 1.2, the moment distribution is estimated using the joint efficiency factor,
ψ
and it is put forth in table 6. A load factor of about 1.12 for example can be considered to calculate the bending distribution in continuous rail incorporating velocity effect. Different values ofψ
can be considered in the calculation. However, a value of 0.58 is used as it is obtained by equation (8) and the value is closed to the range defined by Jenkins et al. [21].Table 6: Maximum Moment
λ
(1/m) For continuous rail(1.12Po/4
λ
) in NmFor jointed rail (P2/4
λ
) in NmFor joint bar, (
ψ
P2/4λ
)in Nm where
ψ
=0.580.8 52500.00 56475.00 32987.50
0.787 53367.22 57184.50 33532.40
0.96 41998.92 47395.80 27489.60
0.869 48331.36 52359.00 30368.20
1.14 36842.10 39192.00 23149.00
1.17 35897.43 38888.89 22555.50
1.16 36206.90 39224.14 22750.00
Calculations of longitudinal stresses in rail and joint bars are fairly straight forward. The section modulus, S for rail and joint bar at head and foot are given in Australian Standard [9]. The values are presented in table 7 for 60 kg/m rail size.
Table 7: Geometric properties (section modulus, S) of rail and joint bar [9]
Types For Rail For Joint Bar
Head Foot Head Foot
S (mm3) 323.2x103 371.4x103 64.72x103 57.33x103
Using the section modulus values of rail and joint bar, the equations (10) and (11) yield the necessary longitudinal stresses in rail and joint bar as presented in table 8. There are two joint bars. Therefore a factor of 2 is incorporated in the joint bar column in stress calculations.
Table 8: Longitudinal stresses at rail and joint bar (MPa)
λ
(1/m) Continuous rail(1.12Po/4
λ
)/SJointed rail (P2/4
λ
)/SJoint bar (
ψ
P2/4λ
)/2Shead foot head foot head foot
0.8 162.44 141.35 174.73 152.05 254.84 287.69
0.787 165.12 143.69 176.93 153.97 259.05 292.45
0.96 129.94 113.08 146.64 127.61 212.37 239.75
0.869 149.54 130.13 162.00 140.97 234.61 264.85
1.14 113.99 099.19 121.26 105.52 178.84 201.89
1.17 110.88 096.66 120.32 104.70 174.25 196.71
1.16 112.03 097.49 121.36 105.61 175.75 198.41
1.166 111.45 096.98 120.73 105.06 174.85 197.39
The unit of calculated stresses on rail and joint bar are in MPa. The magnitudes are comparable with the calculation provided by Talamini et al. [24]. Table 8 gives stress calculations for the wide range of foundation modulus available in the literature. In the following section, a finite element analysis is carried out to see the effects of railhead stress pattern due to different joint bar thicknesses.
4. SPECIFICATIONS AND FINITE ELEMENT MODELLING OF IRJ
The Abaqus FEA product suite consists of three core products: Abaqus / Standard, Abaqus / Explicit and Abaqus / CAE. This study used the Abaqus / CAE product as it is suited for modelling and can output visual data and graphs. Abaqus is divided into modules whereby the complete model is built module by module, adding data and information at every step. First the geometry of the model is drawn, and then the material properties of each part are assigned and assembled. After that the interactions between the parts are created. Then loads and boundary conditions are established before which the model is seeded and meshed into finite elements. When the job is being run Abaqus applies loads to the meshed elements in time increments, starting off small and increasing. When the calculations are finished the results may be obtained.
Figure 23: sectional view of IRJ.
Figure 24: Dimensions of the bolt used in IRJ (dimensions in mm)
Geometric modellings of rail, joint bar and bolts are undertaken by Auto-cad and then they are imported to Abaqus to do further modelling and analysis. The dimensions and specifications of each part are based on the relevant standard [9]. The following figures show detailed specifications: figure 25 for rail cross-section, figure 26 for railhead, figure 27 for rail web hole spacing, figure 28 for joint bar profile and figure 29 for joint bar hole spacing. A joint bar thickness of about 34 mm is used in practice. Therefore three different thicknesses of 30 mm, 34 mm and 40 mm are employed in this analysis to investigate the IRJ behaviour in terms of stress and strain distributions on railhead due to wheel load. An end post thickness of 10 mm is also considered.
Figure 25: 60kg Rail Profile Figure 26: 60kg Rail Head Close Up 46
40
Figure 27: 60kg Rail web hole spacing.
Figure 28: 30mm Joint Bar Profile Figure 29: Joint Bar Hole Spacing
The joint bars in the assembly, for this study, fit flush on the rail web whereas in reality the joint bar would be slightly smaller to allow for insulation material.
Modelling the IRJ assembly isn’t an extremely hard task, but providing Abaqus with enough information to accurately simulate a real life assembly is quite difficult. Some assumptions have to be made while building the model to minimise computation time and to simplify the model as much as possible without affecting accuracy. Some assumptions that were made are listed below.
attempting to analyse the failure methods of the joint bar but to investigate the possibility of increasing the bar width. The sleepers were modelled by partitioning the bottom faces of the rail as shown below (figure 30) and applying fixed boundary conditions in all degrees of freedom as though the rail were tied to the sleepers.
Figure 30: Sleeper Boundary Conditions
Another assumption that was made was to model the bolts (figure 31) as analytical rigid bodies that are not deformable and just act as anchors between the rail and joint bar. This is one of the methods of performing the calculations on the bolt load in a step. It is sometimes difficult to interpret the errors generated, but it is thought that the joint bars were effectively getting pressed into the bolts, creating overclosures that cause the analysis to end. The only solution in the short term to rectify the problem was modelling the system with rigid body bolts. Other form of load considered on IRJ is wheel load. This is the load from wagon through axle.
Axle load varies from 15 to 30 tonnes in some applications. For a 30 ton axle load, the static wheel load amounts to 150kN. To allow for other loads and safety, a loading factor of 1.2 was introduced. This equates to a load of 180kN applied to the railhead. An area was partitioned on the railhead of the IRJ to distribute uniformly the wheel load, and an area of 140mm2 was chosen. Thus the uniform pressure applied to the railhead was calculated to be 1285 MPa.
Figure 31: Rail Face Mesh
An eight node linear hexahedral solid (brick) element with full integration (C3D8) is considered. The face of the rail had to be seeded more carefully to minimise distorted elements which are highly unfavourable. By partitioning and seeding the rail face, the following mesh was achieved (figure 31). A rail of 1332.5mm long was considered and was partitioned 430mm from the rail end. The rail between the end post and the partition section was seeded at approximately 10mm. From the partition to the end of the rail the seed density was approximately 20mm. This type of different seeding was considered to provide fine mesh in the vicinity of the IRJ. Each rail has around 17500 elements.
The joint bar is seeded throughout each instance at 10mm and has around 2500 elements. The different joint bar sizes have differing numbers of elements. The end post, on the other hand, is seeded at 5mm and has 232 elements.
5. Results and discussions
Figure 1 details the degradation cycle of the IRJ due to vertical wheel loads applied on it. However, for signalling purposes IRJ’s are an important part of modern railway track.
Various analyses of IRJ’s are carried out in this study through a discussion of different joint designs, dynamic load factor and various damage modes at the joint. It was shown that the joint bars are carrying about 1/3 of the bending moment a rail can carry. Being a weak link in railway track due to the rail discontinuity, IRJ’s create a few damage patterns ranging from mechanical defects to cumulative plastic flow across the end post. This latter problem is the local elasto-plastic material behaviour because of high dynamic wheel load on a small area of contact zone. Other than this contact zone, the remainder of the rail behaves elastically.
Rail joints are removed from the track when they are about to fail mechanically. Several types of inspections of appropriate frequency leading to remaining service life estimation trends of the joints are essential to determine the optimum time to take the joints out of service. Before they fail mechanically from defects such as joint bar failure (bolt hole cracks), rail end break etc., rail end battering due to metal flow is treated by grinding. Plastic flow of rail materials across the end post may cause the failure of the electrical signalling system. Therefore railway track maintainers or signalling people grind or cut the flow off with an angle grinder or a disc saw. When bolts break or bend, they are replaced rather than change the whole joint as a complete unit. Epoxy failure is another mode of failure relating to the rail signalling system integrity. Whatever may be the case of failure, an accurate determination of the remaining life of the joint is necessary to take the joint out the track before any catastrophic failures. Static and dynamic analysis using elasto-plastic material modelling and fracture mechanics give an indication of a life span and a standard can be defined to set a remaining service life that can be used to schedule the joint removal from the track.
This paper presents a sensitivity analysis of different joint bar thicknesses (30mm, 34mm, and 40mm) to compare stress and strain distributions on the railhead. A 3D FE model of IRJ’s was carried out with C3D8 elements. The selection of element type and mesh density is very important for accuracy of simulation. The characteristics of each element depend on its family, degree of freedom (dof), number of nodes, type of formulation and integration. Full integration is better to achieve a good level of accuracy as it possesses many Gauss points compared to reduced integration in relation to interpolation of dof. The following section presents results of a parametric comparison of different joint bar thicknesses.
The analyses were carried out with Abaqus and took a significant amount of time on both personal computers and Centre for Railway Engineering (CRE) computers. The results were generated in Abaqus according to the field outputs requested in the Step module. Figure 32 shows the difference in mesh density of the rail closer to the end post. Fine mesh is employed in the region of the IRJ. As the thickness of the joint bar increases, the number of elements also increases to maintain similar mesh density. Table 9 shows the number of element for the three different joint bars.
End post
Figure 32: Meshed model with 30mm Joint Bar Figure 33: von Mises stress distribution in joint Bars
Table 9: Number of elements of joint bars
Model No. of elements
30mm Joint Bar 40130
34mm Joint Bar 42394
40mm Joint Bar 44606
Figure 33 shows a comparison of von Mises stress distribution among the three joint bars for the different models, the 30mm bar being at the top and the 40mm bar at the bottom. The meshes aren’t exactly the same for each model and therefore the load doesn’t act in exactly the same way, so there is an element of inaccuracy in Figure 33 but it is suitable for a visual comparison. Note the areas of high stress at the bottom away from the middle of the joint bar. The 30mm bar has a visibly larger area of high stress as is expected.
It is necessary to compare the simulated results with those obtained by experiments or obtained from similar work published in the literature. It is also possible to compare the applied pressure and simulated vertical stress from the same nodes or surface of the element. This is achieved by creating a path through the middle on the top of the railhead across the joint. Such data from the path is transferred to MS Excel for a plot (figure 34).
Figure 34: Vertical stress across railhead
subject to 1285MPa of stress, therefore the vertical stress should equal the same if the model is reacting as expected. This means there is an error of 2.78%. This leads to a preliminary indication that the simulation results can be trusted.
Figure 35 shows the von Mises stresses for the three joint bar widths forming a path on the railhead. Again, whilst hard to discern from the graph, it should be noted that the maximum stress seen by the 40mm joint bar assembly is less than that of the 34mm joint bar assembly which in turn is less than that of the 30mm joint bar assembly. These results convey the expected trend in bending stress, i.e. a thicker joint bar reduces the stress in the rail. This result is consistent with the results reported by Abolbashari (2007). Figure 36 shows the vertical displacement of the rail head. As above, it can be seen again that the results convey the expected trend. The assembly with the 30mm joint bar experiences a greater displacement than the 40mm bar.
Figure 35: Von Mises Stress
Figure 37: Plane Shear Stress
Figure 37 shows the shear stress in the Y-Z plane, or 2-3 plane in the Abaqus model. It shows that the shear stress increases with increasing joint bar thickness. This is consistent with the work of Himebaugh [40, 41].
Another aspect of calculating the longitudinal stresses of IRJ’s is carried out considering beam on elastic foundation. A single point load was employed for simplicity. Vertical foundation modulus, k is an important parameter for stress calculation. A through literature search was carried out to find out the values of k used in different analyses. Based on these values, bending stresses of rail and joint bar are calculated. The magnitude of calculated stress for particular values of k is comparable with the values given by Talamini et al.[24]. However, the analytical stresses are not compared to that obtained by simulation. The analytical analysis does not consider the actual shape and size of the rail, thereby ignoring discontinuity and stress concentration. As a result, simulated bending stresses are larger in value than those which are supported by Talamini et al. [24].
6. Conclusions
Limited measurements, analysis and simulations were carried out to address both mechanical failure such as failure of the joint bar (bolt hole crack), joint looseness and height mismatch of IRJ’s. This is also true for metal flow and insulation damage problems. More research, field testing and calibration are necessary to predict accurately the IRJ damage, the total service life and remaining life of IRJ’s.
From the results, the following conclusions can be made:
The maximum displacement in the rail decreases from approximately 0.1125mm to 0.1064 to 0.1050mm for the 30mm, 34mm and 40mm wide joint bars respectively. The 40mm joint bar therefore has an approximate reduction in vertical displacement of about 6.7% and in von Mises stress of about 7.3%. The shear stress in the Y-Z plane is found to increase with increasing joint bar width. This is consistent with the study established in literature.
In conclusion, there is a small reduction in the stresses encountered by the rail when joined with a pair of joint bars of increased moment of inertia considering the thickness range considered. It suggests that increasing bending stiffness by increasing the thickness of the joint bar is not a good way to reduce stresses and displacements of the rail joint. An important way of increasing bending stiffness of the bar is to increase its height. The increase of stiffness of the bar by increasing height is more dominant compared to that of thickness. However, the reduction of stresses due to rise of joint bar thickness is consistence to the results available in literature.
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