Introduction

Crack geometry and stresses in the railhead may be characterized by a stress intensity factor, K, and resistance to fracture is described by fracture toughness, K Ic. Fracture resistance under plane strain, mode I loading conditions may be denoted by K Ic. To obtain K Ic, it is assumed that the crack tip plastic zone is small compared with the crack length and the specimen dimensions. A method based on fracture mechanics fundamentals was used to evaluate the potential for unstable growth of cracks in head of Grade 900A-UIC60 rail steels. This method combines the effects of stress, crack length, and material fracture resistance to establish a failure criterion. The criterion for failure embodied in this approach is stress intensity factor, K, equaling or exceeding fracture toughness, K Ic. Application of this approach requires a means of determining an analytical expression for the stress intensity factor that could be applied to various cracks. Standard test techniques were used to measure fracture toughness, K Ic. Evaluation of the critical crack size under service conditions plays a central role in application of the theory. The growth of a fatigue crack must be analyzed to complete the determination of the behavior of the cracked structures. Fracture in rails is a relatively complicated problem that combines the effects of load, stress distribution, fracture properties, and crack growth characteristics [1].

Different conditions of variable and complex loadings, secondary stresses, seasonal changes in environment, and so forth must be taken into account to study fracture in rail steels. Rails are subjected to primary and secondary loading components. In primary loading, the wheel load is applied from rolling contact to the rail producing bending stresses, axial stresses, and Hertzian pressure [2]. Secondary loads, including thermal and residual stresses, are superimposed on the primary loads. Statistical analyses of rail failures have shown that temperature has a strong influence on the failure probability [3].

Cracks may initiate at or below the surface due to high traction forces that result from the motion of vehicles over the track. Subsurface cracks propagate toward the rail surface and behave like surface cracks after penetration [4]. Crack initiation and propagation may be described as follows. A dark spot develops at the rail surface, and subsequently a crack occurs at the surface or subsurface of the rail. The crack grows in an inclined angle below the surface, and then it branches into a horizontal and a transverse crack. The transverse crack extends down into the rail and finally causes rail fracture [5]. Among many distinct forms of cracks, the two progressive transverse defects of detail fracture and tache ovale defect are known to be more important from a fracture mechanics viewpoint. The first type usually originates from a longitudinal seam or streak near the running surface on the gage side of the railhead, while the second type originates from manufacturing defects, such as hydrogen flakes. The first type of the crack is the focus of the present study. Figure 1 shows the geometry of a transverse internal rail defect (such as a detail fracture) modeled as an elliptical flaw embedded in the railhead.

Fig. 1
figure 1

Modeling of internal defect in railhead [6]

Full size image

In general, a critical size crack is defined as the crack size that is expected to cause a failure under the next group of operational loads. The choice of a critical size will affect the frequency of periodic inspection required to find and remove crack before the rail fails [6].

Experimental

The material used in this study was Grade 900A rail steel with the mechanical properties as tabulated in Table 1 and the chemical composition as summarized in Table 2 [7].

Table 1 Mechanical properties of the rail Grade 900A, UIC60 [7]
Full size table
Table 2 Chemical composition of material(wt.%) [7]
Full size table

To obtain reliable plane strain fracture toughness, K Ic, 10 compact tension (CT) specimens were prepared from a Grade 900A, UIC60 railhead steel using electrical discharge machining (EDM). They were cut normal to the rail cross section (see Fig. 2 [8]), machined, and then notched to the standard dimensions. The specimen geometry including the notch configuration is given in Fig. 3 [9]. For the purpose that the fatigue crack initiates as quickly as possible, a chevron type notch was machined in the specimen. The chevron notch shape is illustrated in Fig. 4 [10].

Fig. 2
figure 2

The place where a sample was removed [8]

Full size image
Fig. 3
figure 3

The specimen geometry [9]

Full size image
Fig. 4
figure 4

The chevron notch [10]

Full size image

The tests that were performed in accordance with ASTM E 399 and BS 7448:

  • A test machine was used that applied a cyclic force to the specimen for a fatigue precrack at the tip of the machined notch. The size of this precrack and the amount of the applied oscillating force were calculated according to standards, and the fatigue precrack was made at room temperature.

  • After precracking, the machine applied an increasing force to the precracked specimen until it failed. According to the recommended procedure described in ORE D156, the tests were performed at −20 °C (±2 °C) to improve the possibility of measuring a valid fracture toughness [8]. It should be noted that, in general, fracture toughness decreases with decreasing temperature.

After fracture, the fracture surfaces were examined using a scanning electron microscope (SEM) at 20 kV, and typical micrographs revealing the fracture surface morphology were taken.

Results and Discussion

Plane Strain Fracture Toughness Test

A summary of K Ic test results at −20 °C is given in Table 3. In addition, a typical load displacement record obtained during one of those tests is shown in Fig. 5. All the values are valid according to the measures proposed by ORE D156 [8]. The criterion for minimum thickness in E 399 test, which is expressed as B min = (K Ic/σys)2, is based on the experimental work carried out by many authors [e.g., 9, 10] on steel and aluminum alloys. If the specimen thickness and/or the crack length are smaller than those proposed in the criterion, the resultant K Q will be larger than K Ic. Consideration of the data from the tests that are tabulated in Table 4 reveals that the criterion for the minimum thickness and crack length in the tests carried out in present study is about 8 mm. A comparison of this value with the specimen thickness and its fatigue crack length indicates that the mean K IC obtained from these tests are valid and reliable.

Table 3 Summary of K Ic test results
Full size table
Fig. 5
figure 5

A typical load-displacement record obtained during K Ic testing

Full size image
Table 4 Results of K Ic test
Full size table

Study of Fracture Surfaces

Macroscopic observations of fracture surfaces of the specimens clearly showed two discrete zones. These two distinct zones are shown in the optical micrograph of Fig. 6. The boundary of these zones is well distinguished. One zone with a shiny appearance is indicative of gradual crack propagation due to fatigue, while the other with an opaque dark look shows crack propagation after the fatigue crack length load combination reached a critical size in noncyclic loading. The fatigue fracture surface appears to be smooth and shiny. The fracture surface of the critical region looks also smooth without any “shear lip” (which is associated with ductile fracture), indicating that plane strain conditions were achieved.

Fig. 6
figure 6

Optical micrograph of fracture surface of a specimen

Full size image

SEM fractographs (Fig. 7) show entirely different morphologies for the two zones of fatigue fracture and final fracture. Figures 7a and b clearly reveal the presence of many small parallel lines, referred to as fatigue striations, which may appear on fatigue fracture surface in many materials and are oriented parallel to the advancing crack front.

Fig. 7
figure 7

Fracture surface morphologies. (a) and (b) Fatigue fracture surface showing the presence of striations. (c) Final brittle fracture surface due to plane strain conditions

Full size image

Forsyth and Ryder [11] provided critical evidence that each striation represents the incremental advance of the crack front as a result of one loading cycle and that extent of this advance varies with the stress range. This is shown clearly in Fig. 7a, which shows striations of differing width that results from a random loading pattern. Indeed, striations are most clearly observed on flat surfaces associated with plane strain conditions. The final fracture zone is illustrated in Fig. 7c, in which the coarse steps and deep river patterns are associated with the plane strain conditions and brittle fracture in low temperatures.

Critical Crack Size and Crack Growth Characterization

The mode I crack driving force was found to be sensitive to the volume of the fluid trapped in the crack. While the fluid entrapment mechanism promotes mixed-mode shear by reducing the crack face friction under certain circumstances, that is, by an optimum combination of factors such as residual stresses, crack inclination, and others, the crack will branch downward and continue to grow mainly in mode I. Note that high levels of K I will also be promoted by the fluid entrapment mechanism [2].

Critical crack size for detail fracture was calculated from the formula [6]:

$$ K_{{{\text{Ic}}}} = \frac{2} {\pi }M_{{\text{S}}} M_{1} \sigma {\sqrt {\pi \,a_{{\text{C}}} } }\, $$
(1)

where a c is the semimajor axis critical length of the elliptical crack, M S is an empirical factor to account for the elliptical shape of defect, M 1 is an empirical factor to account for the finite dimensions of the rail cross section, and σ is the longitudinal stress. The total longitudinal stress in the rail that is used in calculations of defect growth is the superposition of bending, thermal, and residual stresses. Dynamic motions of vehicles (pitch, bounce, and rocking) cause fluctuations in the magnitude of vertical wheel loads on the rail as trains travel over the track. Thermal stresses develop in continuous welded rail (CWR) through the difference between the rail neutral temperature and the rail service temperature. The distribution of residual stresses in the rail head is complex and varies from one rail to another [6]. A summary of critical crack size calculation results is given in Table 5. As seen, critical crack size depends only on the value of a.

Table 5 Critical crack size
Full size table

The number of cycles, N, to grow a crack from an initial size, a i, to a larger size, a f, can be calculated from [12]:

$$ N = \frac{1} {C}{\int\limits_{a_{{\text{i}}} }^{a_{{\text{f}}} } {\frac{{{\left( {1 - R{\text{(}}a{\text{)}}} \right)}^{q} }} {{{\left( {G{\text{(}}a{\text{)}}\Updelta \sigma {\text{(}}a{\text{)}}{\sqrt {\pi \,a} }} \right)}^{p} }}} } $$
(2)

where a is characteristic defect size, R is the minimum to maximum stress ratio, G(a) refers to a geometry function that depends on the type of defect that appears as G(a) = 2M S M 1(a)/π for the detail fracture, Δσ is the stress range, and the material constants C, p, and q have experimentally been determined elsewhere [13]. Equation 2 was derived from the Paris equation:

$$ \frac{{da}} {{dN}} = C\frac{{\Updelta K^{p} }} {{{\text{(}}1 - R{\text{)}}^{q} }} $$
(3)

by treating it as a separable ordinary differential equation. In this equation, ΔK is stress intensity factor range. In general, the stress range Δσ, the stress ratio R, and the geometry function G(a) depend on the crack size [12].

The crack growth from an initial size of a i to a service limit size of a f (critical crack size) is simulated by determination of relevant load cycles, N [14]. Residual cycles of rail life versus initial crack size are shown in Fig. 8. The figure indicates that growth rate of rail defects is relatively slow at first, but it increases as the flaw becomes larger.

Fig. 8
figure 8

Residual cycles of rail life versus initial crack size

Full size image

Displayed graphically in Fig. 9 are the allowable crack size ā versus the nondestructive testing (NDT) intervals for transverse cracks for different traffic conditions. As is to be expected, allowable crack size decreases with increasing the intervals between the nondestructive tests. The service limit of the transverse crack on the railhead is about 5 mm.

Fig. 9
figure 9

Allowable crack size of transverse cracks depending on nondestructive testing cycles for different traffic conditions

Full size image

Conclusions

This commentary shows that fracture mechanics can be applied to fairly complicated situations such as fracture of railroad rails. The task is to define the allowable crack size, and fatigue behavior in the railhead was studied. For this purpose, K Ic testing was performed on the rail steel to obtain K Ic value. By applying the fracture mechanics relationships, the following results were obtained:

  • The critical size of transverse cracks in the railhead is approximately 10 mm at −20 °C.

  • Transverse crack growth in the railhead initially occurs slowly, but it accelerates with increasing crack size.

  • The allowable crack size for continued service depends on the NDT intervals; it decreases as the NDT intervals increase.