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Study on the Growth Rates of Rolling Contact Fatigue Crack in Wheel/Rail Steel

Makoto AKAMA

Railway Technical Research Institute, Tokyo, Japan

Abstract

Rolling contact fatigue (RCF) is still an important problem in various phenomena in railway fields such as wheel shelling or squats of rail. Therefore, a method was developed and prepared to observe the fatigue crack propagation under mixed loading of tensile and in-plane shear modes that can simulate rolling contact conditions by an in-plane biaxial fatigue machine. In the experiments, simplified cycles were applied to the analysis of RCF cracks including the effect of fluid trapped inside the cracks. Growth rate laws for wheel and rail steel were obtained by means of least square regression analysis in terms of the effective stress intensity factor range. The fracture surfaces near the crack tip region of tested specimens were observed by SEM and discussed to relate the superiority of pearlite structure in detail.

1. Introduction

Wheel shelling and squats of rail cause loss of large pieces of metal from wheel treads and rail head as a result of wheel-rail rolling contact fatigue (RCF) . This kind of crack develops easily inside these parts when fluid exists. The subject is related to both safety and costly problems for the railway industry. If the rate of growth of these cracks can be calculated accurately, an appropriate action will be taken to maintain the integrity of wheel and rail, and save considerable amounts of cost.

Some researchers have investigated the behavior of cracks under the RCF condition. Bold [1] performed tests where cyclic tensile mode (mode I) and in-plane shear mode (mode II) cycles were applied sequentially to cruciform specimens made of rail steel. In his loading cycles, the mode I loading is applied and removed before the fully reversed mode II cycle is applied. The loading cycles produced co-planar crack growth when the ratio of the nominal value of ∆KII to ∆KI, ∆KIInom/∆KInom was smaller than or equal to approximately 2.0, otherwise mode I crack growth was found after crack branching. Wang et al. [2] have investigated the effective values of the stress intensities and the effect of overlapping the mode I and mode II loading cycles. Cruciform specimens made of rail steel were chosen to perform the tests under dry conditions. Different ratios of ∆KIInom/∆KInom and various degrees of overlap were studied. Experimental results show that a long co-planar crack is producible under certain circumstances and that the crack closure ratio and the crack locking ratio are not constant. Co-planar cracks branch under certain loading conditions. It is shown that the effective mode I stress intensity range is a control parameter that determines the crack growth direction. Increasing the degree of overlap between the mode I and mode II loading cycles raises the critical value of the effective mode I stress intensity range ∆KIeff. This critical level must be exceeded in the mode I cycle if stable co-planar cracking is to be maintained. For the rail steel that they used, an empirical branch criterion was expressed by the inequality. This relationship may depend on the type of steel.

As mentioned above, the research work on the fatigue experiments under the mixed loading of mode I and mode II cycles seems to be concentrated on the rail steel. However, wheel shelling is also important in view of safety and economy. Furthermore, it is certain that the fracture surfaces of specimens can provide more information concerning the crack growth mechanism, and it seems rare to investigate them in detail in the past researches. Therefore, the fatigue tests are performed to obtain the fatigue crack growth rate under the mixed loading of mode I and mode II cycles that can simulate RCF conditions by an in-plane biaxial fatigue machine using wheel and rail steel. In these tests, simplified cycles are applied to the analysis of RCF cracks including the effect of fluid trapped inside the cracks. The fracture surfaces near the crack tip region of tested specimen will be observed in detail with a scan electron microscope (SEM). 2. Experimental procedure 2.1 Biaxial fatigue machine

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Fig.1: Schematic view of biaxial testing machine.

An in-plain biaxial testing system was prepared to investigate the crack propagation under mixed mode conditions. This biaxial testing machine consists of four hydraulic actuators of a 200kN (tension/compression) capacity each for static and fatigue loads. These four actuator assemblies make two pairs of X and Y axis, and are rigidly mounted in an octagonal box-shaped frame diagonally as shown in Fig.1. The frame is of heavy-duty welded construction, and placed horizontally. A load cell and a linear variable differential transformer are installed in each actuator assembly. The components include four hydraulic actuator assemblies, manifolds, a control console and a hydraulic pump unit. To obtain and keep the designated stress ratios during fatigue tests, an improved control system was developed and introduced into this work. Two pairs of actuators were controlled by feedback signals of not only load signals but also the positioning ones. 2.2 Specimen and Applied Loading The study by Wong et al. [2] is referred to for the specimen and applied loading. A cruciform specimen as shown in Fig.2 with a 45° starter notch made by spark erosion is used. The half notch length is 2mm. It has a uniformly stressed square working section, 72mm by 72mm, 4mm in thickness, to observe propagation behaviors. A tensile load is applied through pins and a compressive load is applied at the edge of the specimen, with the backlash removed by wedge tightening mechanism as shown in Fig.3. Three kinds of steel are used as the specimen, actual wheel steel (WT) and rail steel materials (RP and RF). The difference between RP and RF material is that a microstructure of RP is a coarse pearlite whereas that of RF is a fine pearlite. Chemical compositions are shown in Table 1. Heat treatment of WT is as follows. The specimen is heated to 860°C, held for 2 hours, oil quenched, tempered at 490°C and held for 7 hours. The ultimate tensile strength, 0.2% proof stress and microstructure are shown in Table 2. The starter notch is initially pre-cracked by using equibiaxial mode I loading with the stress ratio (R) of zero.

The loading history is similar to that experienced by RCF cracks obtained from the theoretical models developed by various researchers [3 - 5] and is shown in Fig.4. It is simulated by actuating both axes of the biaxial machine to apply the required mode I and II load sequence to the crack. Figure 5 shows the examples of loading of X and Y axis to produce the loading for 45° crack. The tests are performed under dry conditions with a testing frequency of less than 1.0Hz. Table 3 shows the ratios of nominal mode II stress intensity factor (∆KIInom) to nominal mode I stress intensity factor (∆KInom), the degree of an overlap between the mode I and the mode II loading cycles examined. The shapes of the load waveforms are checked on a 2-channel storage oscilloscope. The crack length is measured by a traveling microscope at the resolution of 0.001 mm crack growth.

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Fig.2: Shape of cruciform specimen. Fig.3: Arrangement of specimen, grips, pin and wedges.

Table 1: Chemical composition (wt%).

Material C Si Mn P SWT 0.65 0.26 0.73 0.016 0.01RP 0.68 0.26 0.93 0.016 0.01RF 0.79 0.17 0.82 0.019 0.01

Table 2: Mechanical properties and microstructures.

Material Ultimate tensile strength (MPa) Proof stress (MPa) Microstructure

WT from 981to 1030 from 618 to 657 Tempered martensiteRP 934 511 PearliteRF 998 599 Fine pearlite

Fig.4: Applied loading cycles.

The effective stress intensity ranges experienced by the crack tip (∆KIeff and ∆KIIeff) are measured in each experiment. They are defined as follows:

aFUKUK IInomIIeff πσ∆∆∆ == (1)

aFUKUK IIIInomIIIIeff πτ∆∆∆ == (2)

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Fig.5: Applied sequential loading cycle of X and Y axes. (The vertical axis represents the relative value of X and Y axis load with the maximum X axis load taken as unity).

Table 3: Testing conditions.

Exp. No. ᤠ¢KIInom/ᤠ¢KInom Degree of overlap (Degree)WT1 1.0 0, 10, 20, 30, 40, 50, 60, 70, 80, 90, 120WT2 1.0 30, 60, 90, 120WT3 1.25 10, 20, 30, 40, 50, 60, 70, 80, 90, 120WT4 1.0, 1.375, 1.5, 1.9, 2.0 10, 30, 60RP1 1.0 0, 10, 20, 30, 40, 50, 60, 70, 80, 90RP2 1.5 0, 10, 20, 30, 40, 50, 60, 70, 80, 90RP3 1.0 30, 60, 90, 120, 150RP4 1.5 30, 60, 90, 120RP5 2.0 0RP6 2.5 0RP7 1.6, 1.7, 1.8, 2.0 10, 30, 60RF1 1.0, 1.375, 1.5 30

where ∆σ and ∆τ are normal and shear stress ranges, respectively; a is a half crack length; F is a non-dimensional parameter that depends on the geometry of specimen and crack that is represented as

( )W/asecF 2π= ; W is a half diagonal of the working section of the specimen; and UI and UII are the closure ratio and locking ratio represented by the following equations, respectively;

minthmaxth

minamaxaI vv

vvU

−−

= (3)

5

minthmaxth

minamaxaII uu

uuU

−−

= (4)

where vamax, vamin, vthmax and vthmin are measured maximum, measured minimum, theoretical maximum and theoretical minimum opening displacement; uamax, uamin, uthmax and uthmin are those of sliding displacement, respectively. To measure the crack closure or crack locking, the surface replica technique [6] is used. This procedure is not based on the assumption that the factional force is constant when the crack is sliding. Instead, it compares real sliding displacement ranges with theoretical ones. 3. Experimental results Experiments are performed by using four specimens made of WT, seven specimens made of RP and one specimen made of RF that are referred to as WT1,…, WT4, RP1,…, RP7, and RF1 respectively. The experiments WT1 to WT3, RP1 to RP4 and RF1 mainly produced co-planar crack growth rate data, whereas the experiments RP5 and RP6 produced branch crack growth rate data. The experiments WT4 and RP7 investigated the branch criterion.

The co-planar crack grew almost straight for all degrees of overlap in the experiments WT1, WT2, WT3, RP1, RP2, RP3 and RF1. After the crack length on each side has extended to approximately 3mm, the degree of overlap between the mode II and the mode I loading cycles was increased in 10° steps or 30° steps except RF1 in which the degree of overlap kept constant at 30°. The values of ∆KIInom and ∆KInom were returned to approximately the same values for each step of loading by decreasing loads. The crack growth rates at both ends of the central crack were similar and the crack remained co-planar, even for the 90° overlap. In the experiment RP4, the co-planar crack branched at 120° of overlap. It is difficult to estimate the mode I crack closure ratio and mode II crack locking ratio at the crack tip when the crack was short. However, some measurements of crack closure and crack locking displacements were made near crack tip, and these two ratios were estimated by extrapolating back to the crack tip. Figure 6 shows an example of the results of crack closure ratio and crack locking ratio derived from the experiments of specimen made of rail steel. This indicates that neither the crack closure nor the locking ratios is constant. It is seen that the increase of overlap may increase the residual crack opening, and lead to increases in both ratios above unity.

Fig.6: Crack closure ratio and crack locking ratio at different degrees of overlap. 3.1 Co-planar fatigue crack growth rates The crack growth rates were plotted against the nominal stress intensity range and the effective stress intensity range, for the mode I and mode II parts of the sequential cycles, respectively. However, none of the graphs give a good correlation of the growth rates when these single parameters were used. Thus the crack growth rates appear to depend both on applied stress intensities in the composite cycle, and on the degree of overlap.

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Fig.7: Co-planar crack growth rate data for WT. Fig.8: Co-planar crack growth rate data for RP.

Fig.9: Co-planar crack growth rate data for WT, RP and RF. Fig.10: Branch crack growth rate data.

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Different approaches were tried to find a satisfactory model for the crack growth rates under this

mixed mode loading. The first approach was to assume that the crack growth rates were controlled by either mode I or mode II mechanism. Under mixed mode loading, the mode I effective stress intensity range may be modified by a contribution from the mode II effective stress intensity range, and vice versa. Figures.7 and 8 show that a better correlation is found when the crack growth rates are plotted with a modified mode I effective stress intensity range, or a modified mode II effective stress intensity range for WT and RP materials. The two models are expressed as follows.

32281

11 110444

..

IIeff

IeffIIeff K

KK.

dNda

+××= −

∆

∆∆ (5)

for WT material, and 17221

11 110473

..

Ieff

IIeffIeff K

KK.

dNda

+××= −

∆

∆∆ (6)

for RP material. The exponents 1.8 and 1.2 were chosen by trial and error to give a reasonable correlation between the measurements. The remaining coefficients in equations (6) and (7) were obtained by means of least square regression analysis from fitted lines in Figs.7 and 8, respectively.

Next, based on the crack tip opening and sliding displacements, the growth rates might be plotted against the equivalent effective stress intensity range at the crack tip shown in Fig. 9 for all materials. This graph gives a satisfactory correlation. The model is expressed like the Paris-type law as:

m

IIeffIeff KKCdNda

+= 22 ∆∆ (5)

where 222and10788 11 .m.C =×= − for RP material, 572and10489 11 .m.C =×= − for WT material and

112and10051 10 .m.C =×= − for RF material. It is seen from this Figure that the crack growth rate for pearlite steel is lower than that for tempered martensite steel when the ratio ∆KIInom/∆KInom is the same. On the other hand, generally speaking, as ∆KIInom/∆KInom increases, the crack growth rates becomes lower in the same steel. 3.2 Branch crack growth rates Branch cracks occurred and propagated where the ratios of ∆KIInom to ∆KInom were greater than 2.0 for the case of RP material. The experiment RP5 was for the case where ∆KIInom/∆KInom = 2.0 and the experiment RP6 for ∆KIInom/∆KInom = 2.5. For this specimen geometry, the branch crack growth corresponds to the ordinary mode I growth and undergoes a stress intensity cycle consisting of a large fully-reversed mode I cycle from the mode II loading, followed by a smaller mode I cycle at R = 0 from the mode I loading. It was considered that the growth rate from smaller cycles would be much lower than that of larger cycles under constant amplitude loading, and that it would be further reduced by the residual plastic zones and the residual stresses of the larger cycle. Therefore, the growth rates were plotted against the ∆KInom from the mode II loading cycles only. The calculations of ∆KInom were performed using the procedure proposed by Gao et al. [7] in which the stresses acting normal to the crack plane were considered. The results are shown in Fig.10. 3.3 Fracture surface observation by scanning electron microscope (SEM) The fracture surface of the tested specimen can give information to explain the crack growth mechanism. Therefore, the fracture surfaces near the crack tip region of tested specimen were observed by scanning electron microscope (SEM). Figure 11, 12 and 13 shows the fracture surface near the crack tip region at ∆KIInom/∆KInom =1.25 for WT specimen, at ∆KIInom/∆KInom = 1.5 for RP and RF specimen, respectively. The

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crack surfaces contained much oxide fretting debris, especially in RP and RF specimens that were tested at high ∆KIInom/∆KInom and observations were carried out after the debris was removed. In case of WT3 and RP2 specimens, indistinct striation patterns were found, whereas heavily deformed ridges and valleys that were rubbed out in the direction of the mode II sliding were seen in all kinds of specimens. It is thought, therefore, that the damage near the crack tip is likely to be caused by the mode II loading mainly.

Fractographic features in the lamellar of pearlite are complex and tend to vary from grain to grain depending on their orientation to the crack plane. Fracture surfaces are relatively rough due to the laminated structure within each grain. Small step-like features, slip or micro-cleavages, are observed on platelet surfaces at high magnifications. During fatigue growth, cracks were found to be arrested at laminate colonies oriented normal to the crack growth direction and deflect along the micro-laminar interface.

Fig.11: Fracture surface near the crack tip of WT3 specimen. (Arrow indicates the direction of crack propagation).

Fig.12: Fracture surface near the crack tip of RP2 specimen. (Arrow indicates the direction of crack propagation).

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Fig.13: Fracture surface near the crack tip of RF1 specimen. (Arrow indicates the direction of crack propagation). 4. Discussion The effective stress intensity ranges have been measured in all tests and they are recognized as more fundamental parameters to characterize the crack tip condition. Researchers have studied the effect of ∆KIeff and ∆KIIeff under uniaxial loading individually. However, no publications are available on the relationship between ∆KIeff and ∆KIIeff under biaxial non-proportional loading. It is expected that complex stress/strain relationships will be generated at the crack tip under non-proportional mixed mode loading. Figure 6 shows that either the experimental mode I crack closure ratios or the mode II crack locking ratios is not constant. The detailed mechanisms for the underlying changes in the crack closure and locking ratios are not yet clear. However, it appears that the increase of overlap may increase the residual crack opening, as both ratios increase to unity with a high degree of overlap. A possible explanation of these two figures suggests that the plastic flow near the crack tip becomes easier at a higher degree of overlap under the same nominal stress intensity ranges because of the combined tensile and shear stresses acting at the crack tip.

It has been well known that the main feature observed on fracture surface under mode I loading is the striation. However, no clear striation patterns were found but fretting products and severe rubbing between the crack surfaces were observed. It has been reported that such surface damage can only take place if there is interference between the crack flanks in specimens under mode II loading [8]. Therefore, the main crack growth mechanism is considered to be the mode II growth. When ∆KIInom/∆KInom is small, the mode I loading is superior and the interaction between crack faces is insignificant. Furthermore, larger mode I load can leave a large residual opening displacement at the crack tip, therefore, unlock the crack and increase the growth rate. However, as ∆KIInom/∆KInom increases, both the ∆KInom and ∆KIInom are attenuated whenever crack faces are in contact, and consequently the fatigue crack growth rates are considered to become lower.

The branch crack growth rates could not be represented by a single line as shown in Fig.10. All the cruciform specimen tests were performed under biaxial stress conditions where co-planar crack growth was produced under non-proportional mixed mode I and II loading. The non-singular stress [7], or the T-stress is acting at the crack tip under the biaxial loading. The T-stress is a function of the crack geometry and the loading on both axes. For the co-planar growth, the direction of crack growth α was 45°, so the T-stress was zero. Therefore, the effect of T-stress on the crack growth rates does not need to be considered in this case. When the angle α is not 45°, which is the case of branch cracks, T-stress does affect the crack tip plasticity and the plastic zone size increases as the shear part of the loading increases. Since larger plastic zone give higher growth rates, a separation of the data for ∆KIInom /∆KInom = 2.5 and ∆KIInom /∆KInom = 2.0 is observed in Fig.10 with the higher rate of shear loading (∆KIInom /∆KInom = 2.5) giving the higher growth rates.

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From the fracture surface observation by SEM, the reason why pearlite has much better fatigue crack growth resistance than tempered martensite may be explained as follows. The difference is likely to be related with original microstructures. In case of tempered martensite, cementites which precipitate along martensite laths come to be spherodized and are surrounded by soft ferrite. Therefore, it is assumable that the crack is apt to grow larger through the ferrite. On the other hand, in case of pearlite, the microstructure is lamella of ferrites and cementites with quite small interlamellar spaces. It is conceivable that fatigue cracks will be preventable from propagating on account of this solid structure and will hardly develop further. This effect is considered to be more remarkable when the spacing of the lamellar becomes finer. 5. Conclusions Fatigue tests were performed to obtain the fatigue crack growth rate under the mixed loading of mode I and mode II cycles which can simulate rolling contact conditions by an in-plane biaxial fatigue machine using wheel and rail steel. In these tests, simplified cycles were applied to the analysis of RCF cracks including the effect of fluid trapped inside the cracks. The results are summarized as follows. (1) Experiments showed that a long co-planar crack would be producible under a certain circumstances and that either the crack closure ratio or the crack locking ratio was not constant. (2) Three crack growth models were presented in the effective stress intensity range form. The contribution of mode I loading to the mode II loading cycle, and vice versa, has a significant effect on the co-planar crack growth rate. The two models were based on the concept that the co-planar cracks propagate principally, either by the mode I or the mode II mechanism when the crack tip was subjected to mixed mode loading cycles. The crack growth rate could therefore be correlated with the modified effective stress intensity range. In addition, one model used the principle of crack tip opening and sliding displacements, which provided a suitable control parameter to correlate the crack growth rate under mixed mode loading cycles. (3) It was seen that the crack growth rate for pearlite steel was lower than that for tempered martensite steel when the ratio ∆KIInom/∆KInom was the same. It was conceivable that improved properties of lamellar structure of pearlite steel were attributed principally to extrinsic shielding effects from crack paths resulting from the micro-laminated features.

References

[1] P. E. Bold et al.. “Shear Mode Crack Growth and Rolling Contact Fatigue,” Wear, Vol.144, pp.307-317, (1991). [2] S. L. Wong et al.. “A Branch Criterion for Shallow Angled Rolling Contact Fatigue Cracks in Rails,” Wear, Vol.191, pp.45-53, (1996). [3] L. M. Keer, M. D. Bryant. “A Pitting Model for Rolling Contact Fatigue,” ASME Journal of Lubrication Technology, Vol.105, pp.198-205, (1983). [4] M. Kaneta, Y. Murakami. “Propagation of Semi-Elliptical Surface Cracks in Lubricated Rolling/Sliding Elliptical Contact,” ASME Journal of Tribology, Vol.113, pp.270-275, (1991). [5] A. F. Bower. “The Influence of Crack Face Friction and Trapped Fluid on Surface Initiated Rolling Contact Fatigue Cracks,” ASME Journal of Tribology,, Vol.110, pp.704-711, (1988). [6] M. C. Smith, R. A. Smith. “Towards an Understanding of Mode II Fatigue Crack Growth,” Basic Questions in Fatigue : Vol. 1, ASTM STP 924, Fong, J.T. and Fields, R.J. Eds, pp.260-280, (1988). [7] H. Gao et al.. “Growth of Fatigue Cracks under Combined Mode I and Mode II Loading,” Multiaxial Fatigue, ASTM STP 853. K.J.Miller and M.W.Brown Eds., American Society for Testing and Materials, Philadelphia, pp.184-202, (1985). [8] L. P. Pook, A. F. Greenan, “Mode II Fatigue Crack Growth Threshold in Mild Steel”, Proceedings Fatigue Testing and Design Conference, London, Society of Environmental Engineers,pp.30.1-30.33, (1976).