The sections below first deal with the basics—what damage looks like, what causes it, and what mechanisms are at work. Furthermore, the foundation of the model used, its adaptations for the TDM, and further investigations are presented.
7.1. Damage, Forces, and Mechanisms
The following paragraphs outline the basics of damage, forces, and stresses, as well as the underlying damage mechanisms.
Rails can suffer from visible
damage, for example, surface cracks such as gauge corner cracking or head checking, as noted by Cannon et al. [
43]. Furthermore, material loss leads to a reduction in cross-section and changes in profile, as noted by Lewis et al. [
44]. This damage can compromise the structural integrity of the tracks and pose safety risks to train operations.
Head checks, gauge-corner cracks, and squats represent surface-initiated Rolling Contact Fatigue (RCF) defects resulting from high normal and tangential stresses between the wheel and rail. These stresses cause severe shearing of the rail’s surface layer, leading to fatigue or ductility exhaustion. Microscopic cracks propagate at a shallow angle through plastic-deformed surface layers until reaching a depth at which the steel retains its original properties. These cracks may lead to surface spalling, but in rare cases, they can turn down into the rail, posing a risk of rail breakage if undetected. The continuous formation of RCF cracks at a site increases this danger, as fractures at one crack increase the stress in the vicinity, escalating the risk of further breaks and rail disintegration. RCF initiation typically lacks a specific association with metallurgical, mechanical, or thermal faults; instead, it stems from the steel’s inability to withstand the operating conditions it faces. This issue is observed across a broad spectrum of rail-steel types commonly used today. In certain scenarios, the manifestation of this problem is evident in the formation of countless fine surface head checks on the high rail of curves, with some potentially giving rise to deep transverse head cracks. This underscores the widespread nature of RCF-related challenges in rail infrastructure. The squat defect represents another form of fatigue damage, occurring more unpredictably in very shallow curves and tangent tracks. These surface-initiated RCF issues, including head checks and squats, present particular challenges for inspection. In both cases, the development of a downward-turning fatigue crack ultimately results in rail failure. The issue can be mitigated by grinding the rail running surfaces to eliminate fatigue-damaged material.
In wheel–rail contact, both rolling and sliding occur in the contact area. On straight tracks, the wheel tread contacts the railhead, but in curves, the wheel flange may contact the gauge corner, leading to significant sliding motion. The contact area is segmented into regions of stick and others with slip occurring. Increasing the tangential load enlarges the slip region and reduces the stick region, resulting in a combined rolling and sliding contact. Once the tangential load becomes saturated, the stick region disappears, transitioning the entire contact area into a state of pure sliding. Curves, in particular, exhibit a significant sliding component, especially at the gauge corner of the railhead’s contact patch. The sliding in the wheel–rail contact, intensified by often non-existing lubrication, results in wear. This wear phenomenon exhibits a noteworthy characteristic: an escalation in the severity of loading, encompassing factors such as normal load, sliding velocity, or surface temperature, triggering a sudden change in the wear rate, marked by an abrupt increase in the volume loss per sliding distance. These jumps between the “wear regimes” are described below in the “Mechanisms” section.
Bolton et al. [
45] employed an alternative method for analysing wheel–rail wear data. This method entails graphing the wear rate in grams of mass loss per metre rolled per square millimetre of contact area against
, where T represents the tractive force, γ denotes the slip, and A signifies the contact area. Through the twin disc testing of rail materials, this approach revealed three discernible wear regimes: mild, severe, and catastrophic. This method is based on an approach to friction work similar to the Burstow model.
For railway engineering, it is crucial to consider the
forces that act on the rail and the resulting
stresses. Grassie et al. [
46] investigated the impact of traction and curving on the tangential forces between railway rails and wheels. Calculations for a two-axle bogie in curved tracks of varying radii revealed that traction significantly influences tangential forces, particularly on high rail wheels. The study observed that the ability of a bogie to steer diminishes with increased tractive effort, and low inter-axle yaw stiffness improves steering in non-powered bogies but worsens it under traction. Cant deficiency was identified as a factor that redistributes tangential loads among the four wheels, offering benefits in load distribution and reduction under various traction conditions.
According to Grassie [
47], it is important to examine the tangential forces on a rail that arise from the interplay of traction and curving. These forces play a substantial role in wear and shakedown processes, providing insights into the various types of damage occurring on both rails and wheels. The study explored the rail damage associated with curves, emphasising tangential forces from curving and traction, which can alter rail shapes. High rail gauge corners align with passing wheels, while plastic flow is common in low rails. Periodic wear and plastic deformation occur due to dynamic vehicle behaviour. Reprofiling offers a solution to reducing damage and flow, especially in high rails, which is well understood and documented.
Damage mechanisms explain what happens within the rail structure under different operational conditions and stresses.
Rolling contact fatigue (RCF)
According to Kapoor et al. [
48] RCF is a phenomenon that occurs in various mechanical components, such as railways, gears, and bearings, due to combined rolling and sliding contact. Cyclic loading induces crack-like flaws in the material, which can progress into larger cracks if subjected to continued loading. This can potentially result in fractures, such as rail breaks in railway systems.
In the contact patch between the wheel and rail, pressures of up to 1500 MPa and even higher can occur. Therefore, high resistance to these loads is crucial. Frequent cycles of wheel passage with high contact pressures can create crack-like flaws that subsequently evolve into small cracks. These small cracks typically grow at shallow angles, ranging between 0 and 40 degrees relative to the surface. This “crack initiation phase” is shown in
Figure 4a. These cracks advance with repeated loading and may merge, as shown in
Figure 4b. The branch crack can extend either upward to the rail surface or downward into the rail foot. During upward propagation, a portion of the rail surface may detach or spall, resulting in a rough surface along the rail, as shown in
Figure 4c. Conversely, if the branch crack extends downward, it poses the risk of a rail break (
Figure 4d), potentially leading to derailment or a severe accident.
Head checks are small surface defects that resemble hairline cracks and appear on the railhead (described and depicted in detail, for example, by Kapoor et al. [
48]). These defects are typically located at the wheel–rail contact points and occur at the top of the railhead on straight tracks and in curves with gentle curvature. In sharper curves, head checks develop at the gauge corner. Gauge-corner cracking refers to the development of cracks at the corner of the rail, which are open to the surface. Transverse cracks in the rail direction have the potential to cause a rail break.
There are various models for describing the damage mechanism of RCF on the rail surface. These have different approaches and, therefore, require a different depth of the boundary conditions and input parameters, but also lead to different results. The Burstow approach (
model) was chosen for the application of the TDM, as it allows for the entire life cycle to be modelled (refer to
Figure 5).
On the one hand, it is possible to use highly sophisticated models like the Finite Element Method (FEM) to calculate the load and damage within a single wheel–rail contact. Therefore, detailed knowledge of the boundary conditions and parameters for simulation is required. On the other hand, there is the “Whole Life Rail Model” (Burstow’s model) for modelling rail damage across the whole life cycle of the rail. The latter is used in the TDM by TUG.
Wear
Archard’s Simple Theory of Mechanical Wear [
50] and Rabinowicz’ Theory of Adhesive Wear [
51,
52,
53,
54] are two fundamental theories that provide a quantitative understanding of wear in sliding or rolling contacts.
According to Archard [
50], wear is directly proportional to the product of the normal load and sliding distance, known as the Archard wear equation. This theory assumes that wear occurs due to the removal of asperities (small irregularities) from the contacting surfaces. Archard’s approach considers wear as a result of plastic deformation and material removal. The wear rate is proportional to the hardness of the softer material and inversely proportional to its elastic modulus. Archard’s model is a widely used simplification for estimating the wear in various mechanical systems. It offers a practical and accessible framework for wear analysis.
Rabinowicz’ Theory of Adhesive Wear [
51,
52,
53,
54] focuses on situations where surfaces experience adhesion due to attractive forces between atoms or molecules. Adhesive wear occurs when micro-welding and material transfer take place between the contacting surfaces. Rabinowicz proposed a critical load for adhesion, beyond which, permanent bonding occurs, leading to increased wear. This theory emphasises the role of temperature in adhesive wear and highlights the importance of effective lubrication in reducing direct metal-to-metal contact.
Both theories described above are valid for pure sliding motion. The effects of combined rolling/sliding motion on the wheel–rail contact are more complex.
The wheel–rail system is one of the most commonly used rolling pairs in rail-based transportation systems, as Sommer et al. [
55] state. It is typically used without lubrication, with a few exceptions such as flange and switch lubrication. This pairing utilises the conical profile of the tread surfaces of railway wheels, which includes the transition radii to the flange, and the curved profile of railheads. These contact areas can range from being initially point-like to 100 to 200 mm², varying in size and not always maintaining an elliptical shape. The stress factors that are crucial in the context of a wheel–rail system include Hertzian pressure, tangential forces, and lateral guiding forces. The wear in this system is determined by frictional slip behaviour, which is influenced by the relative movements of the wheelset. The contact area experiences various types of friction, including adhesive, sliding, and rolling friction, which emphasise force closure.
Three wear mechanisms occur in the wheel–rail system: surface fretting, continuous wear due to slip processes, and wear influenced by adhesion and tribology. These mechanisms result in different types of wear, with rolling wear being predominant on tread surfaces and sliding wear prevailing in the flange area and corresponding rail flanks.
Jendel’s [
56] wear regime models classify wear into different categories or stages, each associated with specific operating conditions and wear mechanisms. These categories may include adhesive wear, abrasive wear, fatigue wear, and others, depending on the nature of the contact and the relative motion between surfaces. As demonstrated in
Figure 6, the wear coefficient experiences a sudden increase with small increments in load, whether caused by the contact load
or slip
.
Krause et al. [
57] exposed similar findings by showing the results as wear rates of twin-disc tests at a constant slip over area-specific friction power. It is evident that wear increases significantly when the friction power surpasses a threshold value.
Due to this wear behaviour, it is essential to be able to draw conclusions about the acting wear regime when evaluating the wear. The erratic, non-linear behaviour of the relationship between the contact load and wear rate requires comprehensive knowledge of the effective wear mechanism.
Interaction of rolling contact fatigue and wear
The wear of a rail surface can be beneficial in managing cracks by removing small cracks and slowing the advancement of larger ones [
58]. In
Figure 7, the crack extending into a railhead is depicted. The rate of crack growth at the tip, labelled
, is countered by a wear-induced reduction in the crack length at the crack mouth, labelled
, during the passage of a wheel. The net crack growth, represented as
, reflects the combined effect of crack advancement and wear-induced reduction. The reduction in crack length due to wear depends on the angle of the crack beneath the rail surface. Cracks at shallower angles experience amplified wear rates, especially below 30°, resulting in significant reductions in crack length with each wheel passage.
When the wear rate reaches a certain level, it can decrease the net crack growth rate to zero, halting the advancement of existing cracks, or even make it negative, signifying the erosion of existing cracks. Burstow’s model demonstrates this effect as well.
Figure 8 displays the individual damage functions (RCF and wear) as a function of the wear number
. In the damage model (refer to
Figure 9), these two functions are superimposed, with wear mitigating or even reversing the damage caused by RCF [
59].