Ratchetting of railhead material of insulated rail joints (IRJs) with reference to endpost thickness Nirmal Kumar Mandal ⇑ Central Queensland University, Centre for Railway Engineering, Rockhampton 4702, Queensland, Australia article info Article history: Received 17 February 2014 Received in revised form 5 July 2014 Accepted 6 July 2014 Available online 16 July 2014 Keywords: Ratchetting Insulated rail joint Modified Hertzian contact theory Metal plasticity Endpost abstract Insulated rail joints (IRJs) are the most important structural link in a railway track for elec- trical signal purposes. Because of the presence of the discontinuity in the rail material at IRJs, problems with maintaining rail/track geometric requirements and much increased dynamic wheel load effects on IRJs result. Material degradation and damage to the rail ends at the discontinuity therefore occur. A few studies have been carried out to address this issue globally. A local stress and damage analysis is essential to study the material behav- iour of the rail ends with an appropriate elasto-plastic material model. For cyclic loading, a kinematic hardening material model alone is not enough to predict ratchetting damage, plastic deformation and initiation of rolling contact fatigue (RCF) defects at the rail ends of IRJs. In this paper, a three-dimensional (3D) finite element analysis (FEA) is carried out to study the distribution of stresses and strains in the vicinity of the IRJs using modified Hertzian Contact Theory (HCT). A solid rail model with a 10 mm thick fibreglass insulating endpost filling the rail discontinuity is considered and two beam elements are connected to the solid rail model by equation constraints. A 5 mm fibreglass endpost is also considered for comparison purposes. A combination of nonlinear kinematic and isotropic hardening material models is considered in the simulation. A local stress analysis model, called sub-modelling, is incorporated to capture degradation of materials accurately and to obtain ratchetting damage of the endpost material of the IRJ. It also captures the decay of the ratchetting rate. The effects of cyclic wheel loads on the IRJ are also presented. The analysis indicates that material degradation occurs progressively due to the loading spectra. Simu- lation results also present the IRJs mechanical behaviour with response to endpost thick- nesses for enhancing better geometric design of IRJs. Ó 2014 Elsevier Ltd. All rights reserved. 1. Introduction A high dynamic wheel load is almost certain to develop at IRJs because of manufacturing tolerances in the alignment of the two joined lengths of rail and subsequent plastic deformations of the two adjacent rail ends. The effect is magnified because of the sudden variation in track stiffness due to change of bending and shear rigidity of the rails at IRJs. Severe plastic deformation at the rail ends and a reduction of specified endpost thickness (Fig. 1) are a safety issue for rail operations per- sonnel as there is potential for the insulation to fail and cause a failure of the signalling system. Because of loss of vertical http://dx.doi.org/10.1016/j.engfailanal.2014.07.003 1350-6307/Ó 2014 Elsevier Ltd. All rights reserved. ⇑ Tel.: +61 7 4923 2064; fax: +61 7 4930 6984. E-mail address: [email protected]Engineering Failure Analysis 45 (2014) 347–362 Contents lists available at ScienceDirect Engineering Failure Analysis journal homepage: www.elsevier.com/locate/engfailanal
Insulated rail joints (IRJs) are the most important structural link in a railway track for elec-trical signal purposes. Because of the presence of the discontinuity in the rail material atIRJs, problems with maintaining rail/track geometric requirements and much increaseddynamic wheel load effects on IRJs result. Material degradation and damage to the rail endsat the discontinuity therefore occur. A few studies have been carried out to address thisissue globally. A local stress and damage analysis is essential to study the material behav-iour of the rail ends with an appropriate elasto-plastic material model. For cyclic loading, akinematic hardening material model alone is not enough to predict ratchetting damage,plastic deformation and initiation of rolling contact fatigue (RCF) defects at the rail endsof IRJs.
In this paper, a three-dimensional (3D) finite element analysis (FEA) is carried out tostudy the distribution of stresses and strains in the vicinity of the IRJs using modifiedHertzian Contact Theory (HCT). A solid rail model with a 10 mm thick fibreglass insulatingendpost filling the rail discontinuity is considered and two beam elements are connected tothe solid rail model by equation constraints. A 5 mm fibreglass endpost is also consideredfor comparison purposes. A combination of nonlinear kinematic and isotropic hardeningmaterial models is considered in the simulation. A local stress analysis model, calledsub-modelling, is incorporated to capture degradation of materials accurately and to obtainratchetting damage of the endpost material of the IRJ. It also captures the decay of theratchetting rate. The effects of cyclic wheel loads on the IRJ are also presented. The analysisindicates that material degradation occurs progressively due to the loading spectra. Simu-lation results also present the IRJs mechanical behaviour with response to endpost thick-nesses for enhancing better geometric design of IRJs.
� 2014 Elsevier Ltd. All rights reserved.
1. Introduction
A high dynamic wheel load is almost certain to develop at IRJs because of manufacturing tolerances in the alignment ofthe two joined lengths of rail and subsequent plastic deformations of the two adjacent rail ends. The effect is magnifiedbecause of the sudden variation in track stiffness due to change of bending and shear rigidity of the rails at IRJs. Severe plasticdeformation at the rail ends and a reduction of specified endpost thickness (Fig. 1) are a safety issue for rail operations per-sonnel as there is potential for the insulation to fail and cause a failure of the signalling system. Because of loss of vertical
stiffness and the resulting high dynamic wheel-rail contact force at IRJs, they are recognised as weak links in the track struc-ture. In a study, Davis and Akthar [6] indicated that IRJs have a lower service life compared to all other running surface com-ponents, including switch points and turnout frogs. The Australian rail industry faces a significant amount of maintenanceand replacement costs conservatively estimated to be $5.4 million annually in direct costs and $1.10 million in indirect costs[15].
The endpost thickness at IRJs influences the dynamic impact forces at the discontinuity. Wen et al. [18] considered awider rail end gap (endpost thickness) of 15 mm. Other gap ranges reported in the literature varied from 4 mm to 8 mm[8,17]. A wide range of endpost thickness of rail joints from 4 mm to 15 mm was found in the literature in studies of IRJsmechanical behaviour. This paper considers two cases: 10 mm and 5 mm. The reason for this selection of endpost thicknessis that an 8 mm endpost thickness was previously used in heavy haul lines of Queensland, Australia. Currently, an endpostthickness of 6 mm thick is being used. Relating to endpost materials, popular IRJ endpost insulation materials are mainlythermoplastic polymer or fibreglass. Two polymers commonly used are polytetrafluoroethylene and polyhexamethylene adi-pamide (Nylon 66). It was observed that a thicker endpost produced higher dynamic impact forces. This dictated the selec-tion of the two cases as mentioned above to investigate the difference in mechanical behaviour.
2. Literature review
The literature review section focuses on the stress analysis of IRJs. It is based on finite element analysis (FEA), and labo-ratory and field measurements of stress and strain signatures. Dynamics analysis of IRJs targeting impact forces [11] due torail joints is not presented here.
2.1. Finite element analysis
Plaut et al. [14] investigated a tapered bonded joint using a finite element analysis for finding deflections, bendingmoments and stresses. The simulation was based on a 9.5 mm thickness fibreglass endpost angled across the web of the railcross-section at a 6.4� inclination to the longitudinal axis of the rail at the IRJ. A static analysis with a single wheel load waspresented. Based on this analysis, the inclined joints were shown to provide some benefit over square joints such as lowerdeflections, bending moments and shear stresses in the adhesive.
A dynamic elastic–plastic finite element stress analysis considering a height difference of the rail ends at a rail joint wasperformed by Cai et al. [3]. Both implicit code (ANSYS) and explicit code (LS-DYNA) were considered to simulate the contactand impact of a wheel on the rail joint with a narrow gap between the two rail ends. Contact forces, stresses and strains atthe railhead were investigated considering rail height mismatch, axle load and train speed. The results show that the heightdifference of rail ends has a significant effect on wheel-rail contact forces, stresses and strains at the railhead provided thatthe rail gap (thickness of endpost) is not large. For wider gaps without height mismatch, the wheel-rail dynamic force is rel-atively insensitive to wheel speed. The stress, strain and dynamic force are found to be sensitive to static wheel load.
Pang [13] presented a contact impact at the wheel-rail interface using a 3D dynamic model. An elasto-plastic FEA basedon an explicit algorithm was employed to investigate contact impact force spectra and contact pressure distribution in thevicinity of IRJs. Endpost rail end gaps considered in the simulation were 5 mm and 10 mm. The results showed that the con-tact pressure distribution near an IRJ was very different from that at a zone away from the IRJ. Material damage of endpostand railhead in the vicinity of IRJs were not considered.
A similar analysis [18] was also carried out using FEA code ANSYS/LS-DYNA to simulate contact impact behaviour at IRJsby coupling both implicit and explicit methods. A linear kinematic hardening material behaviour was considered. Stresses
and strains in the railhead were investigated for combinations of axle load and train speed, producing various contact forcesfor a wider gap joint of 15 mm endpost thickness as stated earlier.
A numerical study of deterioration of IRJs was carried out by Sandstrom and Ekberg [17] to investigate plastic deforma-tion and fatigue impact. A generalised neo-Hooke constitutive material model was considered for capturing plastic strainaccumulation. The range of endpost gap considered was 4–8 mm.
A combined numerical analysis of dynamic and plastic deformations at an IRJ was carried out by Kabo et al. [8]. Both lowand high frequency vehicle dynamics were investigated focussing on multi-body dynamics. The material degradation at therail joint was examined with a focus on rolling contact fatigue (RCF) and plastic deformation. A square insulated (glued) jointfor 50 kg/m rail with six bolts and a nylon endpost of 4 mm thickness were considered. A fixed boundary condition at thefoot of the rail was employed, and longitudinal and lateral displacements of the outer rail ends were restricted. Frictionbetween wheel and rail and between the rail ends and endpost was neglected. An elastic–plastic material model (non-linearkinematic and isotropic hardening) was considered in the simulation, and a plastic zone in the railhead was presented. Therailhead material deformed plastically up to 6 mm depth from the rail top surface. It is necessary to investigate the change ofplastic zone in the railhead due to various design parameters of IRJ.
Wen et al. [19] also studied dynamic vehicle track interaction and plastic deformation of rail welds using a 3D FEA sim-ulation. The solid rail model was 1340 mm long with a sleeper spacing of 600 mm. The length of the rail was long enough tostudy the local behaviour near the rail weld. The bottom surface of the rail was fixed. A linear kinematic hardening modelwas considered for the high mesh density wheel-rail contact area where material volume undergoes elastic–plastic defor-mation. Other parameters considered in this simulation were: Young’s modulus of 206 GPa, Poisson’s ratio of 0.3, yield stressof the rail material of 526 MPa, axle load of 15 tonnes, the rail cant 1/40, the track gauge of 1435 mm and surface irregularitywavelength of 0.1–0.5 m with depth from �0.5 to 0.5 mm.
2.2. Experimental studies
Nicoli et al. [12] performed laboratory tests on single lap joint and double cantilever beam configurations of various com-binations of adhesives, fibrous insulators and rail surface treatment to investigate the potential for these to prolong the ser-vice life of IRJs for rail operations. A comparison between a square and an inclined IRJ was recently performed by Dhanasekarand Bayissa [7] using field testing data from a heavy haul coal railway and it was argued that there were no significantadvantages of inclined IRJs over square IRJs.
2.3. Summary
In summary it can be stated that a wide range of IRJ gap (endpost thickness) from 4 mm to 15 mm was found to have beeninvestigated. The primary outputs of this research are contact stress and pressure distributions. An important question arises– what is the optimum endpost thickness of IRJs that gives lowest material degradation, damage and ratchetting mode offailure? This paper addresses this question considering two extremes of endpost thickness: 10 mm and 5 mm. As modifiedHertzian pressure distribution, variation of contact zone and influence of dynamic loads when a wheel approaches the end-post are important in understanding the performance of IRJs under cyclic wheel loading, they are incorporated in this paper.The current study includes material degradation of endpost materials to examine peak pressure load tolerance for a contactgeometry based on modified HCT. A FE model is used to determine the stress distribution on the railhead in the vicinity ofendpost. A local stress analysis is carried out by use of a sub-modelling strategy. Cumulative damage to railhead materials ofIRJs in the vicinity of the endpost is also presented.
3. Modelling
FEA global model and sub-model of IRJs have been previously presented [9]. These models are modified to accommodatechanges in IRJ design such as changes of endpost thickness. For completeness, both the global model (Section 3.1) and thesub-modelling process (Section 3.2) are presented briefly. Section 3.3 discusses elasto-plastic material properties used in thispaper.
3.1. Global model and mesh
A 3D FEA was carried out to simulate railhead stress and strain distributions in the vicinity of the endpost of the IRJ. Onesolid rail incorporating the IRJ and two beam models at the ends of this solid rail are considered, making this global rail mod-el’s length a total of 12 m. The length of the solid rail model itself is 2.4 m. This length is enough to simulate stress distri-butions on the railhead near the endpost [19]. The profile of the solid rail part was modelled as per the directionsprovided in Australian Standard AS 1085.20 [1]. The actual cross-section of the IRJ (Fig. 2a), its simplified version for FEA(Fig. 2b) and the side view of the IRJ (Fig. 2c) are shown in the figure. This is an IRJ with six bolts and an endpost thicknessof 10 mm. The endpost is bonded to the ends of the rails using the tie constraint in ABAQUS. The bonding strategy using thetie constraint is popular in simulations [8]. The solid rail model with parts of the two beam models is shown in Fig. 3.
(a) (b)
(c)EndpostJoint bar Rail 2Rail 1
Fig. 2. Assembly and simplified model of IRJ: (a) cross-section of IRJ, (b) simplified FEA model, and (c) side view of IRJ.
Fig. 3. Global rail joint model with beam elements at both ends of the rail.
The material modelling of the top of the fine (high density) mesh part (Fig. 3) of the railhead is elastic–plastic, and the restis elastic. The elastic–plastic material modelling is considered in the wheel-rail contact zone because the high contact pres-sure load on the railhead there exceeds the yield stress of the rail steel material. Tables 1 and 2 present elastic and plasticproperties respectively of the materials used in the IRJ. Symbols of elastic–plastic material properties are discussed in con-stitutive model Section 3.3.
As the solid model and beam models were drawn in their own coordinate system, they were put into a global coordinatesystem (Fig. 4). Beam elements were connected to the solid rail model (Fig. 4) by equation constraints provided in ABAQUS.
Table 1Elastic properties of rail and endpost [4,9] and [10].
Parameters Young’s modulus (MPa) Poisson’s ratio
Rail 207,000 0.3Rail top 207,000 0.3Epoxy/fibreglass 4500 0.19
Table 2Elastic–plastic properties of railhead (Fig. 3 – railhead high density mesh part) [2,16].
ry (MPa) K1 (MPa) b c (MPa) c
780 152 3.97 393,000 8.3
Beam element
Connection point
Rail solid element
Fig. 4. Global rail joint model with beam elements at both ends of the rail.
All six degrees of freedom (dofs) of the solid rail model were connected to the beam element at both of the outer ends of thatrail. The 60 kg/m rail model was positioned with a 1/20 cant. The centre to centre sleeper spacing was set as 700 mm (Fig. 5),and the sleepers were 130 mm wide where they contacted the foot of the rail rigidly. The fixed support condition of rail footto sleeper is popular in simulation [8,19]. This is a suspended IRJ situation; the endpost is situated symmetrically in betweenthe sleepers. The other common type of IRJ arrangement is ‘‘supportive’’ where the endpost is located directly above the slee-per (not covered in this paper).
In the simulation load module, bolt load and wheel load were applied to the IRJ. A fixed sleeper boundary condition [8,19](Fig. 5) was activated in the initial step.
Analysis was carried out in two steps. Step 1 was used for the bolt load. The bolt load Pb was calculated from the bolttorque T, the bolt diameter D and a coefficient Kb (Kb = 0.19–0.25) as shown in Eq. (1). For the purpose of numerical compu-tation, T, D and Kb were selected as 1050 Nm, 24 mm and 0.22 respectively which provided a bolt load of 200 kN.
Pb ¼T
KbDð1Þ
In step 2, a cyclic dynamic wheel load (100 loading cycles) was applied over 0.2 s. Wheel-rail contact force obtained fromthe contact-impact analysis [13] was idealised and applied normal to the railhead surface in such a way that the maximumpressure occurred at the edge of the railhead symmetric to the rail cross section (Figs. 5 and 6). It should be noted that, at thetime of contact-impact, the contact pressure was distributed across the endpost on both railheads. A dynamic wheel load of174 kN incorporating a dynamic load factor of 1.16 [11] was considered. A contact patch in wheel-rail contact is usually ellip-tical and the corresponding contact pressure is ellipsoidal as defined by HCT or the modified HCT. As the wheel-rail contactpoint moves closer to the rail end, traditional HCT does not predict the contact pressure distribution and contact zone accu-rately [4]. Because of discontinuity of rail at the endpost and elastic–plastic deformation, the contact area is increased [5,4].When the wheels are directly over the endposts, the wheel load is supported mainly by the rail ends and two points of con-tact occur. Because of the edge effects of the rail end, peak pressure at the end of the rail is increased compared to the peakpressure obtained by HCT.
A numerically approximated stepped idealised load patch is shown in Fig. 6. A contact area grid of 26 mm in the longi-tudinal and 20 mm in the lateral direction which is bigger that obtained by HCT, was considered. The peak pressure of
700mm
endpost
wheel load
130mm
Fig. 5. Position of sleepers with respect to the endpost.
Longitudinal direction of rail
44MPa
610MPa 2500MPa
Fig. 6. Applied pressure distribution on railhead surface (not to scale).
2500 MPa (Figs. 5 and 6) on the railhead causes a stress level exceeding the yield stress of the material (780 MPa – Table 2).Therefore, it can reasonably be expected that the elastic–plastic material model will play an important role. A combinedmaterial model incorporated in ABAQUS is considered in this simulation and the material parameters of the model (Table 2)are obtained from the literature [2,16].
With this peak pressure, the load factor P0/k is 5.5 where k is yield strength in shear. The value of k can be obtained byconsidering von-Mises criteria. The load factor P0/k of 5.5 puts the loading into the situation of exceeding the shakedownload limit and it results in sub-surface repeated plastic flow conditions [2]. Consequently, a ratchetting material behaviourevolves.
An eight-node fully integrated linear brick element (C3D8) was considered for all components in the solid modelling zonein the mesh module. This type of element was considered because, in elastic–plastic material deformation, it does not sufferfrom volumetric locking. Therefore, the incompressibility nature of rail steel in plastic deformation causes no problem. Highmesh density was introduced in the region close to the IRJ (Fig. 3). In the job module, the simulation was completed to obtainthe displacement dofs at the nodes of the global model, which were then used to run a sub-model of rail separately as dis-cussed in the following section.
3.2. Sub-model
It is necessary to model a critical region very close to the endpost with a very fine mesh for local damage analysis. It is notpractical to make a fine mesh apply to the whole global rail model. Instead, a small region, near to endpost, can be analysedwith higher mesh density – this is called sub-modelling. Using full integration within ABAQUS/Standard, it is possible toobtain accurate stress/strain behaviours. ABAQUS/Standard is utilised for the sub-model. A small section of railhead(61.25 mm long � 16 mm deep � 70 mm wide) adjacent to the endpost was considered for sub-modelling. Four differentmeshes for sub-modelling were investigated using convergence analysis. Fig. 7 depicts the fine mesh selected for the sub-modelling analysis.
The global model was run first, then the sub-model. The time dependent variables (driven variables) saved in the globalanalysis were transferred through the output database (.odb) file to the relevant boundary nodes of the sub-model. Throughconvergence analysis [9], a particular sub-model mesh was selected based on peak applied pressure and resulting verticalstress at the same location on the railhead material. The computation time and the error (%) between the normal surfacestress and the applied pressure as a function of the number of elements of the four meshes tested for sub-modelling werecalculated. The error from sub-modelling using the selected fine mesh based on the 2500 MPa applied peak pressure is about0.72%. Considering error and simulation time for all four meshes tested for the sub-modelling, the selected fine mesh (41,600elements and 46,166 nodes) was considered optimal for further studies.
To capture progressive material degradation of the rail end at the IRJ due to complex multi-axial loadings at the wheel-rail contact interface, an appropriate material model is necessary. Applying appropriate material models is important foranalysis in the elasto-plastic range. Accumulation of plastic strain over cycles, called ratchetting, is an important phenom-enon for damage analysis, especially in railhead material when the cyclic wheel pressure load exceeds the yield point of thematerial and the load factor P0/k exceeds a value of 4.68 [2]. It also enables the simulation of the decay in ratchetting rate dueto the cyclic ratchetting material response.
The yield surface of the material model is defined by a von-Mises yield surface, where the yield function u is defined as[16]:
where the operator ‘:’ defines the contraction x:y = xijyij.The non-linear hardening model used in this simulation includes both isotropic and kinematic hardening. This means that
the yield surface is free to move in stress space and free to change its shape or size. The isotropic hardening law can be statedas:
_K ¼ kb 1� KK1
� �ð3Þ
This law indicates decay in the ratchetting rate. In Eq. (3), k is the plastic multiplier, b governs the initial rate of isotropichardening, K is the drag stress and K1 is the saturated drag stress due to isotropic hardening. A non-linear kinematic hard-ening rule ensures the steady accumulation of plastic strain. The law can be expressed as in Eq. (4) where c and c are thematerial parameters and X is the back stress:
_X ¼ k c
ffiffiffi23
rndev � cX
!ð4Þ
where ndev ¼ sdevjsdev j
.
The material constants are presented in Table 2.
4. Simulation results and discussions
This section details stress, strain and deformation distributions of IRJ materials in the vicinity of the rail discontinuity.
4.1. Deformation of rail end material
Figs. 8 and 9 present residual deformation in the longitudinal and vertical directions respectively at the IRJ after 100 loadcycles; these are obtained from simulation using the global rail model. From Fig. 8, it is evident that the endpost material iscompressed because of the permanent deformation of railhead end material towards the endpost. Fig. 9, on the other hand,depicts vertical permanent deformation of the endpost and railhead end materials. Fig. 10 shows a permanent deformation
Fig. 8. Longitudinal residual deformation of railhead material after 100 load cycles for 10 mm endpost IRJ.
Fig. 9. Residual dipping of endpost and railhead material in the vicinity of the IRJ after 100 load cycles for 10 mm endpost IRJ.
-0.03
-0.02
-0.01
0
0.01
0.02
0.03
0.04
0.05
0.06
0 10 20 30 40 50 60
U3
(mm
)
Distance across the rail joint (mm)
U3 loading
U3 unloading
endpost
Metal flow
Fig. 10. Longitudinal deformation of railhead materials across the IRJ after 100 load cycles for 10 mm endpost IRJ.
(metal flow) of railhead material in the longitudinal direction of about 0.017 mm, nearly 1.065 times greater than that of the5 mm gap IRJ (Table 3). Fig. 11 shows railhead material dipping in the vertical direction across the IRJ of about 0.058 mm,which is nearly 1.09 times greater than that of the 5 mm gap IRJ (Table 3).
4.2. Strain distributions
Plastic strain (PE) and equivalent plastic strain (PEEQ) are important indicators of material degradation and damage to thestructure of the material. Plastic strain details plastic deformation for one cycle, whereas PEEQ presents plastic deformationand damage over multiple cycles.
Fig. 12 illustrates a comparison of equivalent plastic strain over 100 loading cycles in 0.2 s and Fig. 13 shows longitudinalplastic strain variation of top rail end material with decay of ratchetting rate (Fig. 14) for both 5 mm and 10 mm endpostthicknesses. It is evident from Fig. 12 that progressive damage and degradation of the IRJ is critical for a thicker endpostIRJ. Accumulation of plastic strain of the 10 mm thick endpost at the end of 100 cycles (top curve of Fig. 12) is nearly fourtimes greater than that of the 5 mm thick endpost. However, the decay in ratchetting rate of plastic strain for the 10 mmendpost is also higher (Fig. 14). As a result, constitutive material behaviour moves towards a steady state condition, suggest-ing a shift from ratchetting to a uniform ratchetting or low cycle fatigue (LCF) for both IRJs of different endpost thicknesses.
Table 3Permanent deformation of endpost material of IRJs after 100 load cycles.
The thicker the endpost the quicker to achieve the uniform ratchetting state (Fig. 14) because of decay in ratchetting rate.This supports the established ratchetting rate pattern published in the literature [16]. Similarly, ratchetting material behav-iour in relation to vertical plastic strain (PE22) is observed (Figs. 15 and 16). It is evident that progressive damage (ratchett-ing) in vertical plastic strain (Fig. 15) over 100 cycles is gradually increasing with decay in ratchetting rate (Fig. 16). Thecomparison suggests that a narrow endpost IRJ (5 mm thickness) performs better in relation to damage and degradationof the endpost material. It was established in the literature [13] that a 5 mm endpost IRJ experienced less dynamic wheelload at the IRJ compared to that of a 10 mm endpost IRJ.
Using path analysis on the face of rail end through to a depth of 16 mm (Fig. 7) from the rail top surface, the plastic zoneresulting from 100 loading cycles can be presented for a better understanding of sub-surface material behaviour. The resid-ual plastic strains in the sub-surface direction on the face of rail end after 100 loading cycles are presented in Figs. 17–19,with Fig. 17 for residual longitudinal plastic strain, Fig. 18 for residual vertical plastic strain and Fig. 19 for residual shearstrain. Fig. 17 shows a higher residual plastic strain (PE33) at the railhead surface for a 10 mm endpost IRJ compared to that
0
0.000005
0.00001
0.000015
0.00002
0.000025
0.00003
0.000035
0.00004
0 20 40 60 80 100
Rat
chet
tig
n r
ate
- P
E33
No. of cycles
10mm endpost5mm endpost
Fig. 14. A comparison of ratchetting rate for two IRJs of different endpost thickness.
-0.0075
-0.007
-0.0065
-0.006
-0.0055
-0.005
-0.0045
-0.004
-0.0035
-0.003
0 0.02 0.04 0.06 0.08 0.1 0.12 0.14 0.16 0.18 0.2
PE
22 s
trai
n
Time (s)
PE22 - 5mm
PE22 - 10mm
Fig. 15. Cyclic variation of vertical plastic strain over 100 load cycles.
0
0.000005
0.00001
0.000015
0.00002
0.000025
0.00003
0.000035
0.00004
10 20 30 40 50 60 70 80 90 100
Ratc
he�
ng r
ate
PE22
No. of cycles
Ratche�ng rate 10mm
Ratche�ng rate 5mm
Fig. 16. Residual vertical plastic strain rate of the railhead material at IRJ for 100 load cycles.
of a 5 mm endpost IRJ. However, variation of residual PE33 in the sub-surface is similar for both cases. This pattern is alsotrue for residual PE22 (Fig. 18), although the 10 mm endpost IRJ yields more sub-surface residual PE22 strain compared tothat of the 5 mm endpost IRJ. It is evident that, at 2–3 mm sub-surface depth, crack initiation is more likely. Residual shearplastic PE 23 strain (Fig. 19) for the 10 mm endpost IRJ is much more than that of the 5 mm endpost IRJ. The depth of theplastic zone in the sub-surface is similar at about 10–12 mm (Figs. 17–19). More information in relation to this point canbe seen in sub-surface stress distributions (Section 4.3)
0
2
4
6
8
10
12
14
16
0 0.001 0.002 0.003 0.004 0.005 0.006
Dep
th m
m
Residual PE33 strain
PE33 10mm
PE33 5mm
Fig. 17. Residual longitudinal plastic strain in the sub-surface on the face of the rail end after 100 load cycles.
Indicative contour plots of stress distributions from sub-modelling are presented in Figs. 20–22 for the 10 mm endpostthickness IRJ, with Fig. 20 for residual vertical stress, Fig. 21 for residual longitudinal stress and Fig. 22 for residual von-Misesstress. A sub-surface vertical residual stress of about 334 MPa is developed after 100 load cycles which is below the yieldstress of the rail steel (780 MPa) considered in this study. Other residual stress components in the railhead at the IRJ are verylarge, being about 933.5 MPa for longitudinal stress (Fig. 21) and about 980.0 MPa for von-Mises stress (Fig. 22). Longitudinaland von-Mises residual stresses are very sensitive to surface and sub-surface crack initiation and degradation of rail endmaterials. Fig. 23 shows a comparison of residual longitudinal stress of top rail end surface material over 100 loading cyclesfor 5 mm and 10 mm endposts. Disregarding some initial variation, ratchetting damage after 20 cycles is similar for both.
Fig. 20. Residual vertical stress distribution at the end of the rail after 100 loading cycles.
Fig. 21. Residual longitudinal stress distribution at the end of the rail after 100 loading cycles.
Residual stress distributions in the sub-surface of the rail end face are presented. Figs. 24 and 25 present sub-surfacestress variation on the face of the rail end after 100 cycles of wheel load. A similar trend of stress variation in the sub-surfaceof the rail end is observed. The depth of the plastic zone is the same. However, residual vertical stress (Fig. 25) for the 10 mmendpost IRJ is higher than that for the 5 mm endpost IRJ.
Figs. 26 and 27 present cyclic variation of longitudinal and von-Mises stress components of railhead material at the end ofthe rail adjacent to the 10 mm IRJ discontinuity for 100 load cycles. Both figures show a gradual increase of residual com-ponent of stress at a decaying rate; residual longitudinal stress increases up to 933.45 MPa (Fig. 26) and residual von-Misesstress reaches 980 MPa (Fig. 27).
5. Validations
Any new results and simulated data need to be validated to prove their relevance. This can be carried out by laboratorymeasurements, field testing and comparison with similar data established in the literature, co-relating input and output dataetc.
In the FEA process, the convergence study of mesh discussed in Section 3.2 indicated that the simulated results convergednicely, and sub-modelling using the selected fine mesh was undertaken for further analysis as it gave insignificant error.Fig. 28 is the contour plot of vertical stress at the end of the rail for the 10 mm endpost IRJ. Compressible stress at the samesurface, where the pressure load was applied, was about 2547 MPa. As peak pressure load was 2500 MPa, the simulation
Fig. 22. Residual von-Mises stress distribution at the end of the rail after 100 loading cycles.
-1000
-900
-800
-700
-600
-500
-400
-300
-200
-100
0
0 10 20 30 40 50 60 70 80 90 100
Res
idu
al S
33 s
tres
s (M
Pa)
Loading cycles
S33n3- 5mm
S33n3 -10mm
Fig. 23. Cyclic variation of residual longitudinal stress on the top railhead surface over 100 loading cycles.
error was estimated to be less than 2%. Fig. 29 shows a contour plot of pressure distribution at the rail end for a 5 mm end-post IRJ from sub-modelling analysis. Resulting peak pressure at the rail crown surface where pressure was applied is2412 MPa with 3.5% error.
0
2
4
6
8
10
12
14
16
-150 -100 -50 0 50 100 150 200 250 300 350
Dep
th m
m
Residual S22 stress (MPa)
S22 10mm
S22 5mm
Fig. 25. Residual vertical stress in the sub-surface on the face of the rail end after 100 load cycles.
-1200
-1100
-1000
-900
-800
-700
-600
0 0.05 0.1 0.15 0.2
S33
(M
Pa)
Time (s)
Fig. 26. Cyclic variation of longitudinal stress of end of the railhead material at IRJ for 10 mm endpost IRJ.
0
200
400
600
800
1000
1200
1400
0 0.05 0.1 0.15 0.2
von
Mis
es (
MP
a)
Time (s)
Fig. 27. Cyclic variation of von-Mises stress of end of the railhead material at IRJ for 10 mm endpost IRJ.
Field testing was performed to validate the simulation results and details were presented in a paper by Mandal andDhanasekar [9]. Two digital image processing tools, Image tool (IT) and Screen Callipers (SC) were used to measure thethickness of the endpost of a squared IRJ in the heavy haul coal line near Rockhampton. Both digital image processing toolswere calibrated before using them to measure thickness of the endpost. The thickness measured by IT and SC was nearly thesame. The ratio of deformed endpost thickness to the original endpost thickness in field tests and simulations was comparedand found to be only 3.5% error.
Thorough laboratory testing was performed to verify the simulation results. The testing involved measurement of strainfields in the railhead and on the rail foot. Fig. 30 shows the testing set up and Fig. 31 shows a comparison of longitudinalstrain fields from the foot of the rail 10 mm away from the endpost. Both test and simulation results correlate well.
Through the mesh convergence study, comparison of surface vertical stress with applied pressure load on that surface,laboratory testing and the field testing, it is believed that the FEA results of the current study can be trusted.
Fig. 28. Vertical stress distributions at the end of the rail for loading conditions.
Fig. 31. Longitudinal strain on the bottom surface of the rail at a distance of 10 mm away from the endpost (‘L’ for loading and ‘UL’ unloading conditions).
A global model and a sub-model of an IRJ are presented. The load ratio, P0/k, was kept above the shakedown limit. Some ofthe results of the FE model were validated using a field experiment. Based on the observations and analysis, the followingconclusions are made:
� A thicker endpost joint is more prone to progressive IRJ railhead material damage. In the sub-surface, the effect of endpostthickness on plastic deformation is not significant.� A 5 mm thick endpost can improve fatigue behaviour of railhead material as compared to a 10 mm thick endpost.� Maximum residual stresses are at the subsurface about 2–3 mm depth on the railhead end face. However, maximum lon-
gitudinal residual stress is at the surface of the railhead.� The most influential stress components for surface damage are longitudinal stress and von-Mises stress, and for subsur-
face damage, both von-Mises and vertical stresses are important.� The ratchetting rate follows a logical decay pattern.
Acknowledgements
The Rail CRC provided funding to Project #75 – Novel Rail Joint Project. Thanks go to Prof. M. Dhanasekar for his properguidance to finish this research. Tim McSweeney, formerly fixed infrastructure manager, QR and currently Adjunct ResearchFellow, CRE is thankfully acknowledged for his advice at many stages of this ongoing project.
References
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