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On the mechanism of squat formation on train rails – Part II: Growth
International Journal of Fatigue 47 (2013) 373–381
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On the mechanism of squat formation on train rails – Part II: Growth Michaël Steenbergen a,⇑, Rolf Dollevoet b a b
Delft University of Technology, Faculty of Civil Engineering and Geosciences, Railway Engineering Group, Stevinweg 1, 2628 CN Delft, The Netherlands ProRail Inframanagement, Rail Systems, Moreelsepark 3, 3511 EP, Utrecht, The Netherlands
a r t i c l e
i n f o
Article history: Received 21 November 2011 Received in revised form 12 April 2012 Accepted 18 April 2012 Available online 11 May 2012 Keywords: Squat Rolling Contact Fatigue (RCF) Rail crack White etching layer Shear stress
a b s t r a c t Longitudinal cross-sectioning of squats reveals characteristic features of internal crack front propagation. Leading crack planes propagate over longer lengths and greater depths as compared to more superficial trailing crack planes. A favourite depth of crack propagation occurs in the subsurface (2–3 mm), is related to the residual longitudinal stress profile, and may lead to an internal crack ‘terrace’. Especially during deeper crack propagation and branching oxidation processes are found to be metallurgical drivers of crack growth. Contact surface modification during squat growth can be distinguished between phases of transient local stress redistribution and of dynamic wheel–rail contact. If the hypothesized shearing wedge in the failure mechanism loses its load bearing capacity, this gives rise to a redistribution of normal stresses within the actual contact ellipse and the formation of a hardness envelope along the crack pattern. This may partially explain why maturing squats show decoloured and hardened surface areas bordering the surface-breaking cracks. A second effect occurs for contact patches not matching the failure ‘envelope’: due to the Poisson effect the surface overlying the crack planes settles slightly, experiences reduced contact, and corrosive products, ‘pumped’ from inside the cracks, may accumulate on the surface (as confirmed by SEM-EDX analysis). During progressive growth of the defect the harder and decoloured envelope as well as the original wedge is pressed into the deeper elastic material, accompanied by a gradual expansion of the contact band and a bilateral bridging of the defect. This may cause high-frequency impact, resulting into progressive internal crack growth affecting the global stress response and rail fracture. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Part I of this paper dealt with the physical nature of squat initiation on train rails (grade R260Mn), starting from a phenomenological analysis. The leading or single branch of the squat was shown to be a shear-induced fatigue crack, initiated by delamination or fracture of white etching surface material and following the anisotropic microstructure when growing into the railhead. The trailing crack of a branched squat was found to break through the material texture and was explained with the hypothesis of a transverse, wedge-shaped failure mechanism of the surface layer of the rail, either within the actual elliptical Hertzian contact patch or the envelope of possible contact patches in the influence area of the leading crack, and developing at the position of this shear fatigue crack under transverse shear loading towards the rail gauge face. This paper deals with the further growth stages of squats after initiation, again considering the grade R260Mn: the propagation of crack fronts into the deeper material, the modification of the ⇑ Corresponding author. Tel.: +31 15 2783385; fax: +31 15 2783443. E-mail addresses: [email protected] (M. Steenbergen), Rolf.Dol [email protected] (R. Dollevoet). 0142-1123/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijfatigue.2012.04.019
contact surface during squat formation and its interaction with the moving wheel–rail contact. The same approach is followed as in the first part: a mechanical–metallurgical interpretation is given, departing from a phenomenological analysis. 2. Crack front propagation into the railhead The present section deals with both spatial aspects and metallurgical aspects of propagation of crack fronts into the deeper material. 2.1. Spatial aspects Fig. 1 shows a longitudinal cross-section through a moderate, branched squat. The cross-section is taken approximately halfway the length of the leading crack at the surface, and because of the direction of propagation of both crack fronts, the time lag in the development of both branches and the resulting asymmetry, it does not intersect the trailing crack plane. The macrograph shows the presence of several crack planes, almost parallel to each other, developing in the running direction under a shallow angle with the surface, and one of which is dominant. The latter one has
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(a)
(b)
V
crack tip 5 mm
Fig. 1. Branched, moderate squat (a) and longitudinal cross-section over the leading branch (macro; different scale) (b).
propagated, at this transverse position, to a depth of 4 mm and over a length of 15 mm. The crack path is almost linear up to a depth of about 3 mm, where it starts to curve downward into the railhead. Fig. 2 shows a second example of a longitudinal cross-section, taken at a different lateral position: at a distance of a few millimetres from the branching point at the surface. Therefore, both crack planes do not intersect the surface. At this position, both subsurface ‘wings’ of the mechanism are clearly visible. The trailing branch has propagated almost symmetrically with respect to the origin, but is shorter and has developed with a time lag. The leading branch has propagated to a depth of approximately 2.5 mm. Cross-sectioning of moderate and advanced branched squats shows that the previous is valid in general; the leading crack dominates and propagates to larger depths and over greater lengths as compared to the more superficial trailing branch. As a rule of thumb, the depth and length dimensions of the trailing
(a)
V gauge face
(b)
V
crack can be estimated at about 50% of those of the leading one. This is fairly consistent with both the different nature of both crack planes, as it follows from the hypothesised failure mechanism, and the anisotropic microstructure of the subsurface. The path of the leading branch is ‘prepared’ by the texture and the grain and dislocation orientation, whereas the trailing crack front has to break through the deformed texture, and will therefore not easily grow to larger depths. Especially Fig. 2 also shows an effect which is more generally observed: the crack fronts have a ‘favourite’ depth for propagation, where they often deviate in a direction parallel to the surface. Sometimes this may lead to the development of a real, subsurface crack ‘terrace’ with length dimensions in the order of tens of millimetres. This favourite depth, which can also be found in the literature (see e.g. Magel et al. [1]), is about d = 2–4 mm, depending on the loading conditions and history. It is explained by the strong gradient of longitudinal, axial residual stresses rxx in the subsurface of the rail within the contact band. It develops in the railhead during train operation, which introduces high compressive stresses in longitudinal direction in the surface, whereas originally a tensile stress field is present in the railhead at the moment of installation, originating from the roller straightening process (see e.g. Schleinzer and Fischer [2] and Ringsberg and Lindbäck [3]). The global shape of the longitudinal residual stress profile at the moment of installation, as well as the change in the top of the railhead resulting from train operation are shown in Fig. 3. According to both investigations referred to above, the order of magnitude of the peak tensile stress at the railhead is 150–200 MPa after roller straightening. The change in residual stress profile due to train operation is confirmed by Magiera et al. [4], who presented measurement results for railheads at the end of their service life. The exact quantitative residual stress profile and the depth of the extreme gradient of the stress profile in the pearlitic subsurface (therefore ignoring transitions between the pearlitic base material and a WEL, which occurs at depths of less than 0.1 mm) depends on the axle load, its history, the distribution of driven and non-driven wheels and the friction coefficient; typically it is however in the range 2–4 mm for conventional operating conditions. This value is in the same order of magnitude as the dimension of the semi-axes of the contact ellipse (in the order of 3 mm), which is the local influence depth of the contact load. In order to understand why the strong vertical gradient in rxx in the subsurface causes a favourite crack depth it must be realised that it is coupled to a local extreme value of the shear stress field szx over the height. The high value of the shear stress szx functions as a kind of protective shield for the deeper material, located at the bottom of the hardened running band ‘strip’ embedded in the railhead, as discussed in Part I. Apparently not only the surface-breaking cracks deviate at the border of the strip, but also the inward cracks are forced to deviate when they reach the boundary of this strip. Illustrating in this context is a recent study by Rossmanith and Fischmeister [5] into subway rail surface cracking: they find cracks that grow almost vertically into the rail surface to suddenly deviate under almost 90° at the depth of the extreme value of the residual shear stress in the subsurface, which was between 0.5 and 1 mm for this light rail case. The ‘crack-guiding’ effect, due to accumulation of longitudinal shear stresses, of the borders of the embedded strip is illustrated in Fig. 4 for an advanced squat. 2.2. Metallurgical aspects
Fig. 2. Top view of a V-shaped squat (a) and longitudinal cross-section along the front of the squat, at a few mm distance from the branching point (b).
In the preceding paragraph, attention was paid to spatial aspects of crack front propagation into the deeper railhead. This paragraph continues with driving mechanisms behind this propagation. The role of mechanical factors – notably the shear surface tractions – was discussed in Part I. Optical microscopy of
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Fig. 3. Qualitative residual stress profile of the rail in the centre-line, after roller straightening (as built into the track) and after train operation: the latter introduces a strong axial stress gradient in the subsurface over the depth.
‘crack guide’
Fig. 4. The border of the work-hardened strip, embedded in the railhead, serves as a crack-plane guide (in 3D) due to local shear stress accumulation.
cross-sections however reveals also a metallurgical driver of deeper crack front propagation, in the area where the microstructure is no longer heavily deformed. This is exemplified with a very typical example in Fig. 5, showing a crack root (for the example of Fig. 2, as indicated in this figure) at about 1.75 mm under the surface. The root is entirely filled with oxides, and in general cracks are found filled with oxides. As oxidation processes always result into a volumetric change (expansion) it follows that oxidation plays a significant role in the deeper crack growth and branching process. This process is therefore not entirely mechanically driven or driven exclusively by a mechanism like fluid entrapment, which is often mentioned in the literature as responsible for growth of RCF cracks such as head checks.
3. Surface modification and interaction with the wheel–rail contact The presence of a fatigue crack and an eventual failure mechanism in the running surface affects the local wheel–rail contact stress distribution and response field. This affecting can be distinguished into two phases. In a first phase there is no longitudinal surface irregularity yet, and therefore only a transient stress redistribution occurs over the contact surface. In a second phase there is a longitudinal surface irregularity inducing dynamic wheel–rail contact with eventual contact loss and impact loading. In order to explain the trailing crack of a squat and its characteristics, a transverse shear failure mechanism was hypothesised under the wheel load, concomitant to the leading fatigue crack. There are two possibilities for the basis of such a failure mechanism. The first one is a reversible elastic deformation, occurring under each contact loading: a lateral displacement or ‘shift’ of the wedge enclosed by the V-crack pattern towards the rail gauge face. This implies a shear strain field czy in the subsurface, enclosed by both crack planes and decreasing in downward z-direction. Because
Fig. 5. Etched micrograph of Fig. 2 showing typical oxide filling of crack roots.
elastic material at the gauge side of the running band spatially confines the wedge, this lateral shift is maximised by the crack-width of the surface-breaking crack pattern. The second possibility is a similar lateral shift, but then as an irreversible plastic deformation; the shear strain field czy has a plastic or partially plastic nature. To derive the further consequences for the contact behaviour, it is necessary to distinguish between the position and size of the mechanism with respect to the contact patch, as discussed in Part I (Fig. 14). There were again two possibilities: the mechanism develops within the actual contact patch (typically applicable to ‘baby squats’) or it develops within the envelope of contact patches at the leading crack position (typically applicable to larger, maturing squats). It is straightforward that in practice both possibilities will occur, as both the wheel and the rail profile are not unique and each successive contact is different in size and position, within a bandwidth. In the following, the first possibility will be considered first. 3.1. Failure mechanism within the actual contact patch It may be argued that the lateral shift of the wedge in the failure mechanism is microscopic and thus negligible. Still, it may not be ignored concerning its role in the wheel–rail contact. The railhead is a curved surface and any lateral shift of the wedge yields a simultaneous settlement. If this settlement, according to the second possibility, has a plastic nature it may therefore eliminate or substantially reduce the load bearing capacity of the wedge, if
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the instantaneous elastic deformation of the rail surface under wheel loading has a comparable order of magnitude. The fulfilment of the latter condition is however certain from the occurrence of the failure mechanism itself, which is excluded with a fully maintained bearing capacity. The occurrence of this type of modified contact has been verified in the field by applying Fuji Prescale HSS 350 pressure film on rails affected by squat formation, under train operation. An example is shown in Fig. 6, for a branched squat and a passenger train with relatively freshly reprofiled wheels. The wedge ‘cut’ from the contact is clearly visible (as the registration is an overlap, this occurs for all passing wheels), as well as the stress concentration on the gauge shoulder, which is at the basis of the failure mechanism. The question now arises what happens to the wheel–rail contact after occurrence of the failure mechanism. To derive this, again the idealised and elementary case of Part I, Fig. 14a is considered. According to the Hertzian theory, normal and transverse contact stresses resulting from the vertical wheel load form a semi-ellipsoid. At the moment that the convective elliptical stress field coincides with the ellipse enveloping the mechanism, a redistribution of stresses is unavoidable; the wheelload must be borne at each position along the rail. Due to the transverse curvature of the railhead, the contact area can moreover not increase instantaneously. Normal stresses therefore redistribute within the original contact ellipse, and the material along both sharp edges of the wedge exhibits significant strain hardening. This process is illustrated in Figs. 7 and 8 in all three dimensions. It causes the wedge to get enveloped by a hardness ‘wall’. In the field, the formation of a dark-coloured, almost black zone can be observed as soon as a surface-breaking crack pattern initiates. It envelops the crack pattern in the form of two lobes (Fig. 9). As has been discussed in Part I, this process (in its idealised form) only occurs for branched ‘baby’ squats that have just initiated (the surface pattern can be enveloped by an actual contact patch), where crack fronts are penetrating the top layer and large internal crack planes have not formed yet (examples are visible in Fig. 14 at the right). Hardness measurements along both decoloured edges show values in the order of 500 HV on normal 260 HV rail, compared to values between 300 and 350 HV in the directly adjacent and blank material in the running band. It is interesting to note that the shearing or sheared wedge itself exhibits hardness values between 300 and 350 HV, similar to the original running band, which may indirectly confirm a break-down of the bearing function after occurrence of the mechanism. There is however a second
gauge face
Fig. 6. Contact pressure registration along a rail with a moderate branched squat and reduced contact at the shearing wedge.
explanation of the formation of the decoloured lobes at the surface, as will be argued in Section 3.2. As has been discussed, redistribution of stresses after partial failure of the surface in the load-bearing path is unavoidable: due to the transverse curvature of the railhead an immediate use of the rail material outside the running band is not possible. On a longer term, a secondary surface effect can be observed in the field for severely advancing squats: the decoloured envelope is pressed into the deeper elastic material and a gradual lateral expansion of the contact patch occurs as a function of the rail surface deformation in normal direction. Because of the increasing transverse curvature of the wheel profile towards the flange root, the ‘bridging’ of the defect is bilateral and not only at the field face, which is the face that would follow from the mechanism. 3.2. Failure mechanism within the envelope of potential contact patches The attention will be turned now to the second possibility: the wedge is not enclosed by the actual contact patch, which either covers the wedge only partially or is smaller than the portion enclosed by the surface-breaking cracks. The first case is not an elementary one and has no need to be considered individually. In the second case (as depicted in Part I, Fig. 14b) however, the consequences for the wheel–rail contact are entirely different. There is no redistribution of stresses in the central position. There is no difference between an elastic or a plastic nature of the lateral displacement of the wedge. As the contact patch moves over the subsurface crack planes before and after the wedge (respectively the trailing and the leading wing), it passes over an area, a thin slice of material, which is spatially unconfined, as illustrated in Fig. 10. Due to the Poisson effect the area overlying the cracks will settle slightly. As a result this area will experience reduced contact in cases when the contact patch covers the affected area only partially. Also the occurrence of this type of modified contact has been verified in the field. Fig. 11 shows an example, again obtained by applying pressure film on rails affected by squat formation under train operation. The passing train is a passenger train with a moderate wheel quality, and the squat is moderate. In clear contrast to Fig. 6, there is no contact at both lobes of the defect. As the area overlying the cracks settles slightly, corrosive products may accumulate on the surface, especially because the area is adjacent to the cracks. The void area enclosed by the cracks ‘traps’ water as a result of capillarity. Fluids from inside these cracks and containing oxides are continuously being ‘pumped’ out under passing wheels and pressed into the adjacent surface. The presence of these corrosive elements (especially oxides) on the decoloured and dark area overlying the crack planes has been confirmed from scanning electron microscopy and energy-dispersive X-ray spectroscopy (SEM/EDX) (Steenbergen [6]); EDX spectra are shown for blank reference surface and the decoloured surface in Fig. 12. Once the area overlying the crack planes in the running band has settled, a local contact band widening may occur, in a perfectly similar way as pointed out in the previous section. The bilateral widening of the running band is shown in Fig. 13. This figure also exemplifies the general observation that for severely developed squats the whole area of the wedge and its decoloured envelope has settled and the load-bearing capacity is completely taken over by both ‘cheeks’ of the railhead. Because of the lower position of both edges with respect to the original running band, the latter involves necessarily a dynamic component of the contact load, which may result into the formation of a decaying wavy corrugation pattern after the squat (as also reported by Li [7]), and for critical combinations of geometry and speed into contact loss and impact. This repetitive impact with high-frequency stress components may very rapidly lead to critical growth of the leading crack and – if
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where there is no (or not yet a) contact failure mechanism and inherent necessity of stress redistribution (Part I, Fig. 1). 4. The presence of squat-like defects on rail welds
Fig. 7. Original Hertzian contact load distribution (semi-ellipsoid, top); wedgeshaped transverse failure mechanism with stress redistribution and the resulting hardening pattern on the rail surface (longitudinal cross-section, bottom).
Fig. 8. Hardness pattern on the rail surface after redistribution of normal contact stresses.
the global stress response is severely affected by this growth – to fracture of the rail. An example of a decaying corrugation pattern after the squat is shown in Fig. 14. It is very typical in the sense that squats, in very different growth stages, appear on the gauge shoulder within the running band (relatively high effective conicity with maximum tangential stresses towards the gauge face), whereas the wavy pattern is formed towards the field face, in line with the slightly settled area overlying the cracks. The mechanism explained in the beginning of this section can also be considered as responsible for surface darkening (‘lobe formation’) in the presence of a single crack without trailing crack,
Field observations show that on welds different examples of surface defects may arise that seem at first sight similar to squats on plain rail. They are therefore often classified as ‘squats’ (see also the field survey presented by Li et al. [8] and Li [7]). These defects however have two characteristics that are distinct to those of squats. Firstly, they do not develop the typical two lobes accompanying an in principle symmetric and V-shaped surface-breaking crack pattern, but in general just one or two isolated lobs. Secondly, they are not necessarily accompanied by surface-breaking cracks. The nature of these weld surface defects is discussed in this section in more detail. The most common types of rail welds are the aluminothermic weld and the flash butt weld. Both types of welds exhibit essentially different hardness profiles along the running surface. The aluminothermic weld, which has a much greater ‘affected’ length as compared to the flash butt weld, is characterised by a double and pronounced hardness dip at both sides of the welding material, the transitions from the heat-affected zone to the parent material. The flash butt weld is characterised by a hardness peak in the centre of the weld. Hardness profiles for both weld types are discussed by Mutton [9] and Steenbergen et al. [10]; a typical example, for worn rails, is shown in Fig. 15. These pronounced hardness transitions along the running band establish the common factor between matured squats with increased ‘hardness banks’ crossing the running band, as described in this paper, and rail welds. In the case of squats, if two hardness peaks are present, they are coupled according to the two branches of the V-shaped surface crack pattern. In the case of aluminothermic welds, there are two individual hardness dips. Flash butt welds have a single hardness peak. These localised hardness changes along the contact band serve as ‘triggers’ for the subsequent surface deterioration in the form of non-uniform shakedown, induced by the moving contact stress field and the iterating load. The above described properties match with the appearance of the surface defects that can be observed on rail welds: aluminothermic welds can show a set of two isolated decoloured lobes at both sides of the welding material, whereas flash butt welds show a single lobe at or very close to the centre of the joint, which may be accompanied by cracking and material crumbling if the material hardening capacity is locally exceeded. Corresponding examples are shown in Fig. 16. The previous does not imply that real squats cannot occur on welds. Fig. 17 shows a rare example on a flash butt weld, with a branched surface-breaking crack pattern. V-shaped cracks have developed to both rail faces, which may at first view seem incompatible with the theory presented in this study. The large width of the running band and the fact that the example has been found on a track with rather intensive freight traffic, however suggests that this exception might be caused by hollow wear of wheel bands of passing freight trains, giving transverse shear components to both sides of the rail. 5. General field observations and discussion Field observations on squats show a number of facts that are helpful to further validate the theory presented in Parts I and II of this study. Observations regarding the 3D geometry and characteristics of the defect itself were already extensively discussed. What remains are more general field observations; they are discussed point by point in this section.
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Fig. 9. Examples of V-shaped surface-breaking crack patterns enveloped by a dark-coloured zone (typically forming two lobes).
x
rail with an important contribution of shear tractions (and/or microslip) to the rail loading. This means that at some borne tonnage the rail becomes ‘ripe’ for squat formation.
subsurface crack planes leading wing
y trailing wing actual contact patch
gauge rail face
running band
Fig. 10. Potential contact patches passing over subsurface crack planes within the local contact patch envelope, ‘confining’ the mechanism.
V
gauge face
Fig. 11. Contact pressure registration for a squat with reduced contact at both lobes.
(a) Squats are often found in clusters. This observation is consistent with the established role of the WEL in fatigue crack initiation. A WEL (except for cases of localised wheel spin or slip) never develops at an isolated cross-section, but over a certain length of
(b) According to the statistical evaluation of the field survey by Li et al. [8,7], 74% of squats are found above the sleeper. This is consistent with the fact that the contact is stiffer on the rail supports relative to the field. As a consequence, contact loads vary within a bandwidth over time and space and reach an amplitude on top of the sleepers, increasing also the bi-directional shear contribution at these positions. The increasing dynamic contact stresses within the sleeper bay were confirmed by Böhmer and Klimpel [11]. (c) In the study by Kerr et al. [12] squats on high rails in curves are reported to be nearly twice as probable as compared to low rails – though curved track overall has similar rates as tangent track. This is consistent with both the fact that wheel slip on high rails leads to increased growth of a WEL and the fact that the transverse shear stresses on the rail, directed towards the gauge face and crucial in the development of the defect, increase in the high leg of a curve whereas they decrease in the low leg. (d) A generally reported observation, confirmed by the Dutch experience, is that squats do not – or much less – occur in tunnels (see e.g. Marich [13] and Grassie et al. [14]). It may be explained by a double reason. Firstly, white etching layers are less likely to develop in tunnels, though the latter assertion should be verified by experimental research. This reduced probability is partly due to the fact that stations and signalling posts, associated to zones of high braking and traction and thus shear tractions, are rarely positioned in tunnels, thereby reducing the occurrence of macroslip between wheels and rails. The most important distinction between the loading regime conditions in tunnels and in open air is however the absence of precipitation in tunnels. Especially the transitions between whether circumstances can be considered as critical: when the contact suddenly changes from ‘dry’ to ‘wet’, for example at the beginning of a rain shower with suddenly emerging isolated wet positions on the rail, this has a significant influence on the adhesion, which may suddenly drop with a percentage up to 50% (see Arias-Cuevas et al. [15]), and therefore lead to locally increased slip and strong slip variations. When this process is cyclic, a WEL may develop rather easily, creating the prerequisite for the squat formation mechanism. A second reason, inherent to the found role of oxidation in crack expansion, is that the absence of precipitation in tunnels reduces eventual crack growth. (e) Squats tend to reappear at their original location after rail grinding, even if all visible effects at the surface have been removed, as also remarked by Kerr et al. [12]. Rail grinding generally removes a layer with a thickness in the order of tenths
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Fig. 12. EDX spectrum of blank surface (top) and the decoloured area bordering the surface-breaking crack pattern (bottom); a prominent presence of corrosive elements.
gauge face
Hardness [HV] 350 flash butt
325
V
300
aluminothermic
275
250 Fig. 13. Severely developed squats and contact registration; both the ‘wedge’ and the hardness envelope have settled, along with progressive bilateral contact zone expansion.
Position from the weld centre [mm] -60
-40
-20
0
20
40
60
Fig. 15. Typical hardness profiles along different weld types in rail.
of millimetres. At the stage that squats appear at the surface – which is well beyond the stage the formation of white etching surface material, crack fronts have already penetrated the top layer, and deeper material is subject to plastic strain accumulation and ratcheting under transverse shear stress at critical positions. It is therefore rather probable that the same defect appears at the same spot, as it remains basically unaffected by the grinding process.
(f) Squats on crane rails have not been reported so far, despite the very high axle loading along with strong work hardening of the rail surface. On the contrary, excessive wear and also surface damage at welds due to hardness transitions are well-known problems for crane rails. The non-conical wheel–rail profile however
Fig. 14. Squat followed by a decaying corrugation; trains run to the right and the gauge face is at the bottom.
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Fig. 16. Surface defects on aluminothermic (a) and flash butt (b) welds, resembling squats.
very vulnerable to squat formation, as well as track parts with a reduced gauge width and curves. Periodic maintenance of geometric wheel quality on the one hand and frequent, cyclic grinding programmes on the other hand, as well as the use of anti-headcheck profiles in curves do reduce spin creep, both also lead to a trend of narrowing contact bands at a unique position of single-point contact on the rail crown. This mono-culture makes an effective use of material along the whole rail crown difficult. Models like the one presented by Magel and Kalousek [16] (see also Magel et al. [1]) may alleviate this problem by adjusting grinding profiles, when also the sensitivity to squat formation is implemented. Fig. 17. ‘Double’ squat on a flash butt weld, with a V-shaped crack to both sides.
6. Conclusions excludes transverse shear components; moreover longitudinal shear forces by driven wheels do not occur. Fatigue and failure due to tangential contact stresses is therefore not a problem. (g) A general feeling (to be further verified statistically) is that squats develop faster on conventional passenger lines, high-speed lines and also mixed lines in comparison to dedicated freight lines. An explanation in line with the presented theory may be looked for in the following. Well-maintained wheelbands tend to concentrate stresses on the rail crown/rail shoulder; as a result of the small contact zone stresses are relatively high. This has a double consequence. Firstly, only a narrow region across the railhead is subject to work hardening, with consequences as discussed in Section 2.1, but now much more intensified. Consequently, a smaller value of szy is now sufficient to produce transverse material failure in this zone. Secondly and from the loading side, newly profiled wheels exert higher transverse shear stresses on the railhead. This combination of higher loads and weakened material leads to early failure. This also means that dedicated freight lines with their wider contact bands are less sensitive to squat formation, even if white etching layers develop rather easily on freight lines. The latter might be related to the increased spin creep and microslip in larger wheel– rail contact patches. It finally remarked that the presented theory and evidence provide no basis to suppose that squats could grow directly from preexisting surface defects such as indentations, pits or casting skin non-uniformities. Depending on their position on the railhead and their size in relation to the wheel–rail contact patch, they may trigger a contact stress variation or dynamic wheel–rail excitation, which may facilitate the discussed mechanisms that play a role in the squat formation process. It is however not a direct consequence. This conclusion is important in the context of track maintenance such as rail grinding. On the other hand, it is straightforward that the effective conicity is a crucial control parameter regarding tangential stresses and therefore the sensitivity to squat formation. Specific switch parts may in this sense be considered as
Macroscopic and microscopic analyses of cross-sections over squat defects revealed metallurgical mechanisms governing internal crack front propagation. The leading crack plane of branched squats was found to propagate over longer lengths (order tens of millimetres) and greater depths (order millimetres) before bending downward as compared to the more superficial trailing crack plane. The leading crack is therefore always critical. A favourite depth of crack propagation occurs at 2–3 mm, which is related to the residual longitudinal stress profile exhibiting a strong gradient at that depth. This may lead to the formation of an internal crack ‘terrace’. Oxidation processes along with branching were found to play a vital role in crack growth, especially when the crack front reaches the undeformed pearlitic microstructure. Surface modification during squat growth is important as it modifies the wheel–rail contact and therefore the rail loading. Maturing squats on grade R260Mn show decoloured and hardened surface areas bordering the surface-breaking cracks, and overlying the internal crack planes. If, in line with the hypothesized, shearinduced transverse failure mechanism, the V-shaped wedge loses its load bearing capacity, a redistribution of normal stresses within the contact ellipse occurs with hardening along the surface-braking crack pattern. This however only occurs if the actual contact patch for a passing wheel matches the ‘failure envelope’. If this is not the case, the surface overlying the crack planes may settle slightly due to the Poisson effect, giving rise to reduced contact. As a result, corrosive products, ‘pumped’ from inside the cracks often filled with fluid, may accumulate on the surface (as was confirmed by SEM-EDX analysis). This is a second reason for the surface decolouration along the surface-breaking cracks and lobe formation. The occurrence of both mentioned and essentially different types of contact – with reduced contact at the wedge portion and with reduced contact at both wings or lobes, has been verified in the field. During progressive squat growth the hardened and decoloured envelope and the wedge-shaped portion are pressed into the
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deeper elastic material, accompanied by a gradual expansion of the contact band and a bilateral bridging of the defect. The resulting settlement of the wheel trajectory triggers a dynamic wheel–rail interaction with high-frequency impact, which causes rapid internal crack growth which may result into rail fracture if the global stress response under passing axle loads is affected. Surface defects on rail welds resembling squats were discussed; they occur due to pronounced hardness transitions at the surface. The presented material provided no basis to support the position that squats could grow directly from pre-existing surface defects such as indentations, pits or casting skin non-uniformities, which is important in the context of maintenance. However, the effective conicity is a crucial control parameter in this context; high values may explain squat formation on specific switch parts, in curves and in narrow-gauge tracks. The study concluded with a series of more general field observations concerning squats, which were discussed in line with the presented theory and evidence. Acknowledgments The present study of squat defects was enabled by financial support of the Dutch rail infra manager ProRail (Rolf Dollevoet). This support is gratefully acknowledged. The help of Ruud van Bezooijen with field testing, observation and monitoring is kindly acknowledged. We would finally like to thank those international rail experts who provided feedback and constructive criticism on several aspects during the time period that the presented research was started and conducted; of them Stuart Grassie is mentioned in particular. References [1] Magel E, Roney M, Kalousek J, Sroba P. The blending of theory and practice in modern rail grinding. Fatigue Fract Eng Mater Struct 2003;26:921–9.
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[2] Schleinzer G, Fischer FD. Residual stresses in new rails. Mater Sci Eng 2000;A228:280–3. [3] Ringsberg JW, Lindbäck T. Rolling contact fatigue analysis of rails including numerical simulations of the rail manufacturing process and repeated wheel– rail contact loads. Int J Fatigue 2003;25:547–58. [4] Magiera J, Orkisz J, Karmowski W. Reconstruction of residual stresses in railroad rails from measurements made on vertical and oblique slices. Wear 1996;191:78–89. [5] Rossmanith HP, Fischmeister E. Surface damage and fracture of subway rails. In: Proc 13th int conf on civil, structural and environmental eng computing, Chania, Greece; 6–9 September, 2011. [6] Steenbergen MJMM. Squats – fundamentele aspecten voor vervolgonderzoek. Internal report 7-11-220-14. Delft University of Technology; 2011 [in Dutch]. [7] Li Z. Squats on railway rails. In: Lewis R, Olofsson U, editors. Wheel-rail interface handbook. Cambridge: Woodhead Publishing; 2009. p. 409–36. [8] Li Z, Zhao X, Esveld C, Dollevoet R, Molodova M. An investigation into the causes of squats – correlation analysis and numerical modeling. Wear 2008;265:1349–55. [9] Mutton PJ. Material aspects of weld behaviour in wheel–rail contact. In: Proc 5th int conf contact mechanics and wear of rail/wheel systems, Tokyo, Japan; 25–27 July, 2000. [10] Steenbergen MJMM, van Bezooijen GW. Rail welds. In: Lewis R, Olofsson U, editors. Wheel-rail interface handbook. Cambridge: Woodhead Publishing; 2009. p. 377–408. [11] Böhmer A, Klimpel T. Plastic deformation of corrugated rails – a numerical approach using material data of rail steel. Wear 2002;253:150–61. [12] Kerr M, Wilson A, Marich S. The epidemiology of squats and related rail defects. In: Proc conference on railway engineering, Perth, Australia; 7–10 September, 2008. [13] Marich S. Practical/realistic implementation of wheel/rail contact technologies – the Australian experience. In: Proc 7th int conf contact mechanics and wear of rail/wheel systems, Brisbane, Australia; 2006. [14] Grassie SL. ‘Squats’ and ‘Studs’ in rails: similarities and differences. In: Proc int heavy haul conf 2011, Calgary, Canada; 19–22 June, 2011. [15] Arias-Cuevas O, Li Z, Lewis R, Gallardo-Hernandez EA. Rolling-sliding laboratory tests of friction modifiers in dry and wet wheel–rail contacts. Wear 2010;268:543–51. [16] Magel EE, Kalousek J. The application of contact mechanics to rail profile design and rail grinding. Wear 2002;253:308–16.
Contents lists available at SciVerse ScienceDirect
International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
On the mechanism of squat formation on train rails – Part II: Growth Michaël Steenbergen a,⇑, Rolf Dollevoet b a b
Delft University of Technology, Faculty of Civil Engineering and Geosciences, Railway Engineering Group, Stevinweg 1, 2628 CN Delft, The Netherlands ProRail Inframanagement, Rail Systems, Moreelsepark 3, 3511 EP, Utrecht, The Netherlands
a r t i c l e
i n f o
Article history: Received 21 November 2011 Received in revised form 12 April 2012 Accepted 18 April 2012 Available online 11 May 2012 Keywords: Squat Rolling Contact Fatigue (RCF) Rail crack White etching layer Shear stress
a b s t r a c t Longitudinal cross-sectioning of squats reveals characteristic features of internal crack front propagation. Leading crack planes propagate over longer lengths and greater depths as compared to more superficial trailing crack planes. A favourite depth of crack propagation occurs in the subsurface (2–3 mm), is related to the residual longitudinal stress profile, and may lead to an internal crack ‘terrace’. Especially during deeper crack propagation and branching oxidation processes are found to be metallurgical drivers of crack growth. Contact surface modification during squat growth can be distinguished between phases of transient local stress redistribution and of dynamic wheel–rail contact. If the hypothesized shearing wedge in the failure mechanism loses its load bearing capacity, this gives rise to a redistribution of normal stresses within the actual contact ellipse and the formation of a hardness envelope along the crack pattern. This may partially explain why maturing squats show decoloured and hardened surface areas bordering the surface-breaking cracks. A second effect occurs for contact patches not matching the failure ‘envelope’: due to the Poisson effect the surface overlying the crack planes settles slightly, experiences reduced contact, and corrosive products, ‘pumped’ from inside the cracks, may accumulate on the surface (as confirmed by SEM-EDX analysis). During progressive growth of the defect the harder and decoloured envelope as well as the original wedge is pressed into the deeper elastic material, accompanied by a gradual expansion of the contact band and a bilateral bridging of the defect. This may cause high-frequency impact, resulting into progressive internal crack growth affecting the global stress response and rail fracture. Ó 2012 Elsevier Ltd. All rights reserved.
1. Introduction Part I of this paper dealt with the physical nature of squat initiation on train rails (grade R260Mn), starting from a phenomenological analysis. The leading or single branch of the squat was shown to be a shear-induced fatigue crack, initiated by delamination or fracture of white etching surface material and following the anisotropic microstructure when growing into the railhead. The trailing crack of a branched squat was found to break through the material texture and was explained with the hypothesis of a transverse, wedge-shaped failure mechanism of the surface layer of the rail, either within the actual elliptical Hertzian contact patch or the envelope of possible contact patches in the influence area of the leading crack, and developing at the position of this shear fatigue crack under transverse shear loading towards the rail gauge face. This paper deals with the further growth stages of squats after initiation, again considering the grade R260Mn: the propagation of crack fronts into the deeper material, the modification of the ⇑ Corresponding author. Tel.: +31 15 2783385; fax: +31 15 2783443. E-mail addresses: [email protected] (M. Steenbergen), Rolf.Dol [email protected] (R. Dollevoet). 0142-1123/$ - see front matter Ó 2012 Elsevier Ltd. All rights reserved. http://dx.doi.org/10.1016/j.ijfatigue.2012.04.019
contact surface during squat formation and its interaction with the moving wheel–rail contact. The same approach is followed as in the first part: a mechanical–metallurgical interpretation is given, departing from a phenomenological analysis. 2. Crack front propagation into the railhead The present section deals with both spatial aspects and metallurgical aspects of propagation of crack fronts into the deeper material. 2.1. Spatial aspects Fig. 1 shows a longitudinal cross-section through a moderate, branched squat. The cross-section is taken approximately halfway the length of the leading crack at the surface, and because of the direction of propagation of both crack fronts, the time lag in the development of both branches and the resulting asymmetry, it does not intersect the trailing crack plane. The macrograph shows the presence of several crack planes, almost parallel to each other, developing in the running direction under a shallow angle with the surface, and one of which is dominant. The latter one has
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(a)
(b)
V
crack tip 5 mm
Fig. 1. Branched, moderate squat (a) and longitudinal cross-section over the leading branch (macro; different scale) (b).
propagated, at this transverse position, to a depth of 4 mm and over a length of 15 mm. The crack path is almost linear up to a depth of about 3 mm, where it starts to curve downward into the railhead. Fig. 2 shows a second example of a longitudinal cross-section, taken at a different lateral position: at a distance of a few millimetres from the branching point at the surface. Therefore, both crack planes do not intersect the surface. At this position, both subsurface ‘wings’ of the mechanism are clearly visible. The trailing branch has propagated almost symmetrically with respect to the origin, but is shorter and has developed with a time lag. The leading branch has propagated to a depth of approximately 2.5 mm. Cross-sectioning of moderate and advanced branched squats shows that the previous is valid in general; the leading crack dominates and propagates to larger depths and over greater lengths as compared to the more superficial trailing branch. As a rule of thumb, the depth and length dimensions of the trailing
(a)
V gauge face
(b)
V
crack can be estimated at about 50% of those of the leading one. This is fairly consistent with both the different nature of both crack planes, as it follows from the hypothesised failure mechanism, and the anisotropic microstructure of the subsurface. The path of the leading branch is ‘prepared’ by the texture and the grain and dislocation orientation, whereas the trailing crack front has to break through the deformed texture, and will therefore not easily grow to larger depths. Especially Fig. 2 also shows an effect which is more generally observed: the crack fronts have a ‘favourite’ depth for propagation, where they often deviate in a direction parallel to the surface. Sometimes this may lead to the development of a real, subsurface crack ‘terrace’ with length dimensions in the order of tens of millimetres. This favourite depth, which can also be found in the literature (see e.g. Magel et al. [1]), is about d = 2–4 mm, depending on the loading conditions and history. It is explained by the strong gradient of longitudinal, axial residual stresses rxx in the subsurface of the rail within the contact band. It develops in the railhead during train operation, which introduces high compressive stresses in longitudinal direction in the surface, whereas originally a tensile stress field is present in the railhead at the moment of installation, originating from the roller straightening process (see e.g. Schleinzer and Fischer [2] and Ringsberg and Lindbäck [3]). The global shape of the longitudinal residual stress profile at the moment of installation, as well as the change in the top of the railhead resulting from train operation are shown in Fig. 3. According to both investigations referred to above, the order of magnitude of the peak tensile stress at the railhead is 150–200 MPa after roller straightening. The change in residual stress profile due to train operation is confirmed by Magiera et al. [4], who presented measurement results for railheads at the end of their service life. The exact quantitative residual stress profile and the depth of the extreme gradient of the stress profile in the pearlitic subsurface (therefore ignoring transitions between the pearlitic base material and a WEL, which occurs at depths of less than 0.1 mm) depends on the axle load, its history, the distribution of driven and non-driven wheels and the friction coefficient; typically it is however in the range 2–4 mm for conventional operating conditions. This value is in the same order of magnitude as the dimension of the semi-axes of the contact ellipse (in the order of 3 mm), which is the local influence depth of the contact load. In order to understand why the strong vertical gradient in rxx in the subsurface causes a favourite crack depth it must be realised that it is coupled to a local extreme value of the shear stress field szx over the height. The high value of the shear stress szx functions as a kind of protective shield for the deeper material, located at the bottom of the hardened running band ‘strip’ embedded in the railhead, as discussed in Part I. Apparently not only the surface-breaking cracks deviate at the border of the strip, but also the inward cracks are forced to deviate when they reach the boundary of this strip. Illustrating in this context is a recent study by Rossmanith and Fischmeister [5] into subway rail surface cracking: they find cracks that grow almost vertically into the rail surface to suddenly deviate under almost 90° at the depth of the extreme value of the residual shear stress in the subsurface, which was between 0.5 and 1 mm for this light rail case. The ‘crack-guiding’ effect, due to accumulation of longitudinal shear stresses, of the borders of the embedded strip is illustrated in Fig. 4 for an advanced squat. 2.2. Metallurgical aspects
Fig. 2. Top view of a V-shaped squat (a) and longitudinal cross-section along the front of the squat, at a few mm distance from the branching point (b).
In the preceding paragraph, attention was paid to spatial aspects of crack front propagation into the deeper railhead. This paragraph continues with driving mechanisms behind this propagation. The role of mechanical factors – notably the shear surface tractions – was discussed in Part I. Optical microscopy of
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Fig. 3. Qualitative residual stress profile of the rail in the centre-line, after roller straightening (as built into the track) and after train operation: the latter introduces a strong axial stress gradient in the subsurface over the depth.
‘crack guide’
Fig. 4. The border of the work-hardened strip, embedded in the railhead, serves as a crack-plane guide (in 3D) due to local shear stress accumulation.
cross-sections however reveals also a metallurgical driver of deeper crack front propagation, in the area where the microstructure is no longer heavily deformed. This is exemplified with a very typical example in Fig. 5, showing a crack root (for the example of Fig. 2, as indicated in this figure) at about 1.75 mm under the surface. The root is entirely filled with oxides, and in general cracks are found filled with oxides. As oxidation processes always result into a volumetric change (expansion) it follows that oxidation plays a significant role in the deeper crack growth and branching process. This process is therefore not entirely mechanically driven or driven exclusively by a mechanism like fluid entrapment, which is often mentioned in the literature as responsible for growth of RCF cracks such as head checks.
3. Surface modification and interaction with the wheel–rail contact The presence of a fatigue crack and an eventual failure mechanism in the running surface affects the local wheel–rail contact stress distribution and response field. This affecting can be distinguished into two phases. In a first phase there is no longitudinal surface irregularity yet, and therefore only a transient stress redistribution occurs over the contact surface. In a second phase there is a longitudinal surface irregularity inducing dynamic wheel–rail contact with eventual contact loss and impact loading. In order to explain the trailing crack of a squat and its characteristics, a transverse shear failure mechanism was hypothesised under the wheel load, concomitant to the leading fatigue crack. There are two possibilities for the basis of such a failure mechanism. The first one is a reversible elastic deformation, occurring under each contact loading: a lateral displacement or ‘shift’ of the wedge enclosed by the V-crack pattern towards the rail gauge face. This implies a shear strain field czy in the subsurface, enclosed by both crack planes and decreasing in downward z-direction. Because
Fig. 5. Etched micrograph of Fig. 2 showing typical oxide filling of crack roots.
elastic material at the gauge side of the running band spatially confines the wedge, this lateral shift is maximised by the crack-width of the surface-breaking crack pattern. The second possibility is a similar lateral shift, but then as an irreversible plastic deformation; the shear strain field czy has a plastic or partially plastic nature. To derive the further consequences for the contact behaviour, it is necessary to distinguish between the position and size of the mechanism with respect to the contact patch, as discussed in Part I (Fig. 14). There were again two possibilities: the mechanism develops within the actual contact patch (typically applicable to ‘baby squats’) or it develops within the envelope of contact patches at the leading crack position (typically applicable to larger, maturing squats). It is straightforward that in practice both possibilities will occur, as both the wheel and the rail profile are not unique and each successive contact is different in size and position, within a bandwidth. In the following, the first possibility will be considered first. 3.1. Failure mechanism within the actual contact patch It may be argued that the lateral shift of the wedge in the failure mechanism is microscopic and thus negligible. Still, it may not be ignored concerning its role in the wheel–rail contact. The railhead is a curved surface and any lateral shift of the wedge yields a simultaneous settlement. If this settlement, according to the second possibility, has a plastic nature it may therefore eliminate or substantially reduce the load bearing capacity of the wedge, if
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the instantaneous elastic deformation of the rail surface under wheel loading has a comparable order of magnitude. The fulfilment of the latter condition is however certain from the occurrence of the failure mechanism itself, which is excluded with a fully maintained bearing capacity. The occurrence of this type of modified contact has been verified in the field by applying Fuji Prescale HSS 350 pressure film on rails affected by squat formation, under train operation. An example is shown in Fig. 6, for a branched squat and a passenger train with relatively freshly reprofiled wheels. The wedge ‘cut’ from the contact is clearly visible (as the registration is an overlap, this occurs for all passing wheels), as well as the stress concentration on the gauge shoulder, which is at the basis of the failure mechanism. The question now arises what happens to the wheel–rail contact after occurrence of the failure mechanism. To derive this, again the idealised and elementary case of Part I, Fig. 14a is considered. According to the Hertzian theory, normal and transverse contact stresses resulting from the vertical wheel load form a semi-ellipsoid. At the moment that the convective elliptical stress field coincides with the ellipse enveloping the mechanism, a redistribution of stresses is unavoidable; the wheelload must be borne at each position along the rail. Due to the transverse curvature of the railhead, the contact area can moreover not increase instantaneously. Normal stresses therefore redistribute within the original contact ellipse, and the material along both sharp edges of the wedge exhibits significant strain hardening. This process is illustrated in Figs. 7 and 8 in all three dimensions. It causes the wedge to get enveloped by a hardness ‘wall’. In the field, the formation of a dark-coloured, almost black zone can be observed as soon as a surface-breaking crack pattern initiates. It envelops the crack pattern in the form of two lobes (Fig. 9). As has been discussed in Part I, this process (in its idealised form) only occurs for branched ‘baby’ squats that have just initiated (the surface pattern can be enveloped by an actual contact patch), where crack fronts are penetrating the top layer and large internal crack planes have not formed yet (examples are visible in Fig. 14 at the right). Hardness measurements along both decoloured edges show values in the order of 500 HV on normal 260 HV rail, compared to values between 300 and 350 HV in the directly adjacent and blank material in the running band. It is interesting to note that the shearing or sheared wedge itself exhibits hardness values between 300 and 350 HV, similar to the original running band, which may indirectly confirm a break-down of the bearing function after occurrence of the mechanism. There is however a second
gauge face
Fig. 6. Contact pressure registration along a rail with a moderate branched squat and reduced contact at the shearing wedge.
explanation of the formation of the decoloured lobes at the surface, as will be argued in Section 3.2. As has been discussed, redistribution of stresses after partial failure of the surface in the load-bearing path is unavoidable: due to the transverse curvature of the railhead an immediate use of the rail material outside the running band is not possible. On a longer term, a secondary surface effect can be observed in the field for severely advancing squats: the decoloured envelope is pressed into the deeper elastic material and a gradual lateral expansion of the contact patch occurs as a function of the rail surface deformation in normal direction. Because of the increasing transverse curvature of the wheel profile towards the flange root, the ‘bridging’ of the defect is bilateral and not only at the field face, which is the face that would follow from the mechanism. 3.2. Failure mechanism within the envelope of potential contact patches The attention will be turned now to the second possibility: the wedge is not enclosed by the actual contact patch, which either covers the wedge only partially or is smaller than the portion enclosed by the surface-breaking cracks. The first case is not an elementary one and has no need to be considered individually. In the second case (as depicted in Part I, Fig. 14b) however, the consequences for the wheel–rail contact are entirely different. There is no redistribution of stresses in the central position. There is no difference between an elastic or a plastic nature of the lateral displacement of the wedge. As the contact patch moves over the subsurface crack planes before and after the wedge (respectively the trailing and the leading wing), it passes over an area, a thin slice of material, which is spatially unconfined, as illustrated in Fig. 10. Due to the Poisson effect the area overlying the cracks will settle slightly. As a result this area will experience reduced contact in cases when the contact patch covers the affected area only partially. Also the occurrence of this type of modified contact has been verified in the field. Fig. 11 shows an example, again obtained by applying pressure film on rails affected by squat formation under train operation. The passing train is a passenger train with a moderate wheel quality, and the squat is moderate. In clear contrast to Fig. 6, there is no contact at both lobes of the defect. As the area overlying the cracks settles slightly, corrosive products may accumulate on the surface, especially because the area is adjacent to the cracks. The void area enclosed by the cracks ‘traps’ water as a result of capillarity. Fluids from inside these cracks and containing oxides are continuously being ‘pumped’ out under passing wheels and pressed into the adjacent surface. The presence of these corrosive elements (especially oxides) on the decoloured and dark area overlying the crack planes has been confirmed from scanning electron microscopy and energy-dispersive X-ray spectroscopy (SEM/EDX) (Steenbergen [6]); EDX spectra are shown for blank reference surface and the decoloured surface in Fig. 12. Once the area overlying the crack planes in the running band has settled, a local contact band widening may occur, in a perfectly similar way as pointed out in the previous section. The bilateral widening of the running band is shown in Fig. 13. This figure also exemplifies the general observation that for severely developed squats the whole area of the wedge and its decoloured envelope has settled and the load-bearing capacity is completely taken over by both ‘cheeks’ of the railhead. Because of the lower position of both edges with respect to the original running band, the latter involves necessarily a dynamic component of the contact load, which may result into the formation of a decaying wavy corrugation pattern after the squat (as also reported by Li [7]), and for critical combinations of geometry and speed into contact loss and impact. This repetitive impact with high-frequency stress components may very rapidly lead to critical growth of the leading crack and – if
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where there is no (or not yet a) contact failure mechanism and inherent necessity of stress redistribution (Part I, Fig. 1). 4. The presence of squat-like defects on rail welds
Fig. 7. Original Hertzian contact load distribution (semi-ellipsoid, top); wedgeshaped transverse failure mechanism with stress redistribution and the resulting hardening pattern on the rail surface (longitudinal cross-section, bottom).
Fig. 8. Hardness pattern on the rail surface after redistribution of normal contact stresses.
the global stress response is severely affected by this growth – to fracture of the rail. An example of a decaying corrugation pattern after the squat is shown in Fig. 14. It is very typical in the sense that squats, in very different growth stages, appear on the gauge shoulder within the running band (relatively high effective conicity with maximum tangential stresses towards the gauge face), whereas the wavy pattern is formed towards the field face, in line with the slightly settled area overlying the cracks. The mechanism explained in the beginning of this section can also be considered as responsible for surface darkening (‘lobe formation’) in the presence of a single crack without trailing crack,
Field observations show that on welds different examples of surface defects may arise that seem at first sight similar to squats on plain rail. They are therefore often classified as ‘squats’ (see also the field survey presented by Li et al. [8] and Li [7]). These defects however have two characteristics that are distinct to those of squats. Firstly, they do not develop the typical two lobes accompanying an in principle symmetric and V-shaped surface-breaking crack pattern, but in general just one or two isolated lobs. Secondly, they are not necessarily accompanied by surface-breaking cracks. The nature of these weld surface defects is discussed in this section in more detail. The most common types of rail welds are the aluminothermic weld and the flash butt weld. Both types of welds exhibit essentially different hardness profiles along the running surface. The aluminothermic weld, which has a much greater ‘affected’ length as compared to the flash butt weld, is characterised by a double and pronounced hardness dip at both sides of the welding material, the transitions from the heat-affected zone to the parent material. The flash butt weld is characterised by a hardness peak in the centre of the weld. Hardness profiles for both weld types are discussed by Mutton [9] and Steenbergen et al. [10]; a typical example, for worn rails, is shown in Fig. 15. These pronounced hardness transitions along the running band establish the common factor between matured squats with increased ‘hardness banks’ crossing the running band, as described in this paper, and rail welds. In the case of squats, if two hardness peaks are present, they are coupled according to the two branches of the V-shaped surface crack pattern. In the case of aluminothermic welds, there are two individual hardness dips. Flash butt welds have a single hardness peak. These localised hardness changes along the contact band serve as ‘triggers’ for the subsequent surface deterioration in the form of non-uniform shakedown, induced by the moving contact stress field and the iterating load. The above described properties match with the appearance of the surface defects that can be observed on rail welds: aluminothermic welds can show a set of two isolated decoloured lobes at both sides of the welding material, whereas flash butt welds show a single lobe at or very close to the centre of the joint, which may be accompanied by cracking and material crumbling if the material hardening capacity is locally exceeded. Corresponding examples are shown in Fig. 16. The previous does not imply that real squats cannot occur on welds. Fig. 17 shows a rare example on a flash butt weld, with a branched surface-breaking crack pattern. V-shaped cracks have developed to both rail faces, which may at first view seem incompatible with the theory presented in this study. The large width of the running band and the fact that the example has been found on a track with rather intensive freight traffic, however suggests that this exception might be caused by hollow wear of wheel bands of passing freight trains, giving transverse shear components to both sides of the rail. 5. General field observations and discussion Field observations on squats show a number of facts that are helpful to further validate the theory presented in Parts I and II of this study. Observations regarding the 3D geometry and characteristics of the defect itself were already extensively discussed. What remains are more general field observations; they are discussed point by point in this section.
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Fig. 9. Examples of V-shaped surface-breaking crack patterns enveloped by a dark-coloured zone (typically forming two lobes).
x
rail with an important contribution of shear tractions (and/or microslip) to the rail loading. This means that at some borne tonnage the rail becomes ‘ripe’ for squat formation.
subsurface crack planes leading wing
y trailing wing actual contact patch
gauge rail face
running band
Fig. 10. Potential contact patches passing over subsurface crack planes within the local contact patch envelope, ‘confining’ the mechanism.
V
gauge face
Fig. 11. Contact pressure registration for a squat with reduced contact at both lobes.
(a) Squats are often found in clusters. This observation is consistent with the established role of the WEL in fatigue crack initiation. A WEL (except for cases of localised wheel spin or slip) never develops at an isolated cross-section, but over a certain length of
(b) According to the statistical evaluation of the field survey by Li et al. [8,7], 74% of squats are found above the sleeper. This is consistent with the fact that the contact is stiffer on the rail supports relative to the field. As a consequence, contact loads vary within a bandwidth over time and space and reach an amplitude on top of the sleepers, increasing also the bi-directional shear contribution at these positions. The increasing dynamic contact stresses within the sleeper bay were confirmed by Böhmer and Klimpel [11]. (c) In the study by Kerr et al. [12] squats on high rails in curves are reported to be nearly twice as probable as compared to low rails – though curved track overall has similar rates as tangent track. This is consistent with both the fact that wheel slip on high rails leads to increased growth of a WEL and the fact that the transverse shear stresses on the rail, directed towards the gauge face and crucial in the development of the defect, increase in the high leg of a curve whereas they decrease in the low leg. (d) A generally reported observation, confirmed by the Dutch experience, is that squats do not – or much less – occur in tunnels (see e.g. Marich [13] and Grassie et al. [14]). It may be explained by a double reason. Firstly, white etching layers are less likely to develop in tunnels, though the latter assertion should be verified by experimental research. This reduced probability is partly due to the fact that stations and signalling posts, associated to zones of high braking and traction and thus shear tractions, are rarely positioned in tunnels, thereby reducing the occurrence of macroslip between wheels and rails. The most important distinction between the loading regime conditions in tunnels and in open air is however the absence of precipitation in tunnels. Especially the transitions between whether circumstances can be considered as critical: when the contact suddenly changes from ‘dry’ to ‘wet’, for example at the beginning of a rain shower with suddenly emerging isolated wet positions on the rail, this has a significant influence on the adhesion, which may suddenly drop with a percentage up to 50% (see Arias-Cuevas et al. [15]), and therefore lead to locally increased slip and strong slip variations. When this process is cyclic, a WEL may develop rather easily, creating the prerequisite for the squat formation mechanism. A second reason, inherent to the found role of oxidation in crack expansion, is that the absence of precipitation in tunnels reduces eventual crack growth. (e) Squats tend to reappear at their original location after rail grinding, even if all visible effects at the surface have been removed, as also remarked by Kerr et al. [12]. Rail grinding generally removes a layer with a thickness in the order of tenths
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Fig. 12. EDX spectrum of blank surface (top) and the decoloured area bordering the surface-breaking crack pattern (bottom); a prominent presence of corrosive elements.
gauge face
Hardness [HV] 350 flash butt
325
V
300
aluminothermic
275
250 Fig. 13. Severely developed squats and contact registration; both the ‘wedge’ and the hardness envelope have settled, along with progressive bilateral contact zone expansion.
Position from the weld centre [mm] -60
-40
-20
0
20
40
60
Fig. 15. Typical hardness profiles along different weld types in rail.
of millimetres. At the stage that squats appear at the surface – which is well beyond the stage the formation of white etching surface material, crack fronts have already penetrated the top layer, and deeper material is subject to plastic strain accumulation and ratcheting under transverse shear stress at critical positions. It is therefore rather probable that the same defect appears at the same spot, as it remains basically unaffected by the grinding process.
(f) Squats on crane rails have not been reported so far, despite the very high axle loading along with strong work hardening of the rail surface. On the contrary, excessive wear and also surface damage at welds due to hardness transitions are well-known problems for crane rails. The non-conical wheel–rail profile however
Fig. 14. Squat followed by a decaying corrugation; trains run to the right and the gauge face is at the bottom.
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Fig. 16. Surface defects on aluminothermic (a) and flash butt (b) welds, resembling squats.
very vulnerable to squat formation, as well as track parts with a reduced gauge width and curves. Periodic maintenance of geometric wheel quality on the one hand and frequent, cyclic grinding programmes on the other hand, as well as the use of anti-headcheck profiles in curves do reduce spin creep, both also lead to a trend of narrowing contact bands at a unique position of single-point contact on the rail crown. This mono-culture makes an effective use of material along the whole rail crown difficult. Models like the one presented by Magel and Kalousek [16] (see also Magel et al. [1]) may alleviate this problem by adjusting grinding profiles, when also the sensitivity to squat formation is implemented. Fig. 17. ‘Double’ squat on a flash butt weld, with a V-shaped crack to both sides.
6. Conclusions excludes transverse shear components; moreover longitudinal shear forces by driven wheels do not occur. Fatigue and failure due to tangential contact stresses is therefore not a problem. (g) A general feeling (to be further verified statistically) is that squats develop faster on conventional passenger lines, high-speed lines and also mixed lines in comparison to dedicated freight lines. An explanation in line with the presented theory may be looked for in the following. Well-maintained wheelbands tend to concentrate stresses on the rail crown/rail shoulder; as a result of the small contact zone stresses are relatively high. This has a double consequence. Firstly, only a narrow region across the railhead is subject to work hardening, with consequences as discussed in Section 2.1, but now much more intensified. Consequently, a smaller value of szy is now sufficient to produce transverse material failure in this zone. Secondly and from the loading side, newly profiled wheels exert higher transverse shear stresses on the railhead. This combination of higher loads and weakened material leads to early failure. This also means that dedicated freight lines with their wider contact bands are less sensitive to squat formation, even if white etching layers develop rather easily on freight lines. The latter might be related to the increased spin creep and microslip in larger wheel– rail contact patches. It finally remarked that the presented theory and evidence provide no basis to suppose that squats could grow directly from preexisting surface defects such as indentations, pits or casting skin non-uniformities. Depending on their position on the railhead and their size in relation to the wheel–rail contact patch, they may trigger a contact stress variation or dynamic wheel–rail excitation, which may facilitate the discussed mechanisms that play a role in the squat formation process. It is however not a direct consequence. This conclusion is important in the context of track maintenance such as rail grinding. On the other hand, it is straightforward that the effective conicity is a crucial control parameter regarding tangential stresses and therefore the sensitivity to squat formation. Specific switch parts may in this sense be considered as
Macroscopic and microscopic analyses of cross-sections over squat defects revealed metallurgical mechanisms governing internal crack front propagation. The leading crack plane of branched squats was found to propagate over longer lengths (order tens of millimetres) and greater depths (order millimetres) before bending downward as compared to the more superficial trailing crack plane. The leading crack is therefore always critical. A favourite depth of crack propagation occurs at 2–3 mm, which is related to the residual longitudinal stress profile exhibiting a strong gradient at that depth. This may lead to the formation of an internal crack ‘terrace’. Oxidation processes along with branching were found to play a vital role in crack growth, especially when the crack front reaches the undeformed pearlitic microstructure. Surface modification during squat growth is important as it modifies the wheel–rail contact and therefore the rail loading. Maturing squats on grade R260Mn show decoloured and hardened surface areas bordering the surface-breaking cracks, and overlying the internal crack planes. If, in line with the hypothesized, shearinduced transverse failure mechanism, the V-shaped wedge loses its load bearing capacity, a redistribution of normal stresses within the contact ellipse occurs with hardening along the surface-braking crack pattern. This however only occurs if the actual contact patch for a passing wheel matches the ‘failure envelope’. If this is not the case, the surface overlying the crack planes may settle slightly due to the Poisson effect, giving rise to reduced contact. As a result, corrosive products, ‘pumped’ from inside the cracks often filled with fluid, may accumulate on the surface (as was confirmed by SEM-EDX analysis). This is a second reason for the surface decolouration along the surface-breaking cracks and lobe formation. The occurrence of both mentioned and essentially different types of contact – with reduced contact at the wedge portion and with reduced contact at both wings or lobes, has been verified in the field. During progressive squat growth the hardened and decoloured envelope and the wedge-shaped portion are pressed into the
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deeper elastic material, accompanied by a gradual expansion of the contact band and a bilateral bridging of the defect. The resulting settlement of the wheel trajectory triggers a dynamic wheel–rail interaction with high-frequency impact, which causes rapid internal crack growth which may result into rail fracture if the global stress response under passing axle loads is affected. Surface defects on rail welds resembling squats were discussed; they occur due to pronounced hardness transitions at the surface. The presented material provided no basis to support the position that squats could grow directly from pre-existing surface defects such as indentations, pits or casting skin non-uniformities, which is important in the context of maintenance. However, the effective conicity is a crucial control parameter in this context; high values may explain squat formation on specific switch parts, in curves and in narrow-gauge tracks. The study concluded with a series of more general field observations concerning squats, which were discussed in line with the presented theory and evidence. Acknowledgments The present study of squat defects was enabled by financial support of the Dutch rail infra manager ProRail (Rolf Dollevoet). This support is gratefully acknowledged. The help of Ruud van Bezooijen with field testing, observation and monitoring is kindly acknowledged. We would finally like to thank those international rail experts who provided feedback and constructive criticism on several aspects during the time period that the presented research was started and conducted; of them Stuart Grassie is mentioned in particular. References [1] Magel E, Roney M, Kalousek J, Sroba P. The blending of theory and practice in modern rail grinding. Fatigue Fract Eng Mater Struct 2003;26:921–9.
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