Tribology International 44 (2011) 1417–1426
Contents lists available at ScienceDirect
Tribology International journal homepage: www.elsevier.com/locate/triboint
An experimental study on bending fretting fatigue characteristics of 316L austenitic stainless steel J.F. Peng, C. Song, M.X. Shen, J.F. Zheng, Z.R. Zhou, M.H. Zhu n Tribology Research Institute, Traction Power State Key Laboratory, Southwest Jiaotong University, Chengdu 610031, China
a r t i c l e in f o
abstract
Article history: Received 7 May 2010 Received in revised form 25 September 2010 Accepted 23 November 2010 Available online 2 December 2010
Bending fretting fatigue tests of 316L austenitic stainless steel plates against 52100 steel cylinders have been carried out under same normal load and varied bending loads. Tests of plain bending fatigue were carried out as a control group. The S–N curves of the bending fatigue were made. The results indicated that there was an obvious drop of life under the condition of bending fretting fatigue due to higher local contact stress. A dislocation model of micro-crack nucleation mechanism, as a manner of zig-zag mode, was created to explain the nucleation of fretting fatigue cracks. Crown Copyright & 2010 Published by Elsevier Ltd. All rights reserved.
Keywords: Fretting damage Bending Fretting fatigue Microstructure Dislocation model
1. Introduction Fretting refers to small amplitude oscillatory movement between two surfaces in contact [1,2], and may lead to surface damages [3–6]. If the relative movement is the consequence of a cyclic bending load to the contacting components, fretting will act conjointly with the cyclic bending stress, which is referred to as bending fretting fatigue, and the fatigue strength of the component will be much reduced. The investigation [7,8] displayed that the fatigue strength during fretting decreased to less than one-third of that without fretting. Bending fretting fatigue may occur such as in bolts, overhead electrical conductors, wheel-sets, and so on, but more studies have been extensively focused on the wheel-on-axle assembly, especially axle of railway vehicles [9–12]. In order to enhance the reliability and the service life of a railway axle, the behaviors of fretting fatigue under condition of bending are worth studying in detail. Under the fatigue condition, the initiation and propagation of fatigue cracks are strongly dependent on the microstructure of materials, especially on the variation in dislocation configuration. The dislocated structures significantly affect plastic deformation, and the relationship between dislocated structures and plastic deformation is a basic topic [13]. Many researchers [13–15] have reported the relationship between the plain fatigue and the dislocated structure; however, a few focused on fretting fatigue [16], and almost no study on the relationship between the bending
n
Corresponding author. Tel.: + 86 28 87600715; fax: +86 28 87601304. E-mail address:
[email protected] (M.H. Zhu).
fretting fatigue and the dislocated structure can be found. Therefore, it is significant to investigate the relationship under the condition of the bending fretting fatigue. A 316L austenitic stainless steel was chosen as the testing material as it presents crystal structure of face centered cubic (FCC) lattice, and its dislocation configurations are easy to identify.
2. Materials and Methods 2.1. Materials and specimen geometry 316L austenitic stainless steel was used as the testing material in this study in order to understand the behavior of the microstructure under the condition of bending fretting fatigue. It was annealed at 1100 1C for 10 h and then quenched in water before machining. The specimens for the bending fretting fatigue tests were designed and machined as a half dog-bone geometry [9] as shown in Fig. 1, and were cut out from a single rolled plate of 6000 mm 1500 mm 16 mm. The fretting pads were made of AISI 52100 steel cylinders of diameter10 mm. The chemical composition and mechanical properties of material are listed in Tables 1 and 2, respectively. For the specimens of bending fretting fatigue, the gage crosssection (sites A–B in Fig. 1) was selected to the loading capability of the test frame and a generous gage-to-grip bending radius to minimize the stress concentration and guarantee the non-frettinginduced failure occurred outside the gage section. The bending load was applied at the sites C–D in Fig. 1. The distance between the
0301-679X/$ - see front matter Crown Copyright & 2010 Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.triboint.2010.11.013
1418
J.F. Peng et al. / Tribology International 44 (2011) 1417–1426
Fig. 1. Bending fretting fatigue specimen geometry.
Table 1 Chemical composition of the materials (wt%). Materials
Fe (%)
C (%)
S (%)
Si (%)
Mn (%)
P (%)
Cr (%)
Ni (%)
Cu (%)
316L 52100
Balance Balance
0.0212 1.00
0.015 0.03
0.45 0.25
1.116 0.30
0.0258 0.027
16.681 1.5
10.163 0.2
0.3020 0.30
Table 2 Main mechanical properties of the materials. Mechanical properties
s0.2 (MPa)
sb (MPa)
E (GPa)
HV
316L 52100
282 1600
555 2000
191 210
135 890
Load cell
Cyclic bending load
Specimen
Fig. 3. S–N data for the bending fretting fatigue and plain bending fatigue of 316L steel.
Fretting pad
Fig. 2. Bending fretting fatigue test rig.
center of the fretting scar and the bending load was fixed at 40 mm for all fretting fatigue tests.
2.2. Fretting fatigue tests The bending fretting fatigue experiments were carried out on a commercial servo hydraulic uni-axial fatigue tester (SHIMADZU EHF-UM100K2 servo fatigue machine). The test rig shown in Fig. 2 was mounted on the pedestal of the fatigue machine. A fastening bolt was used to impose the normal load to the plate specimen at A–B line (Fig. 1) during the tests. The normal load was measured
and controlled through a small load cell, as seen in Fig. 2. The fatigue tests transformed to the plain bending fatigue when no normal load was imposed. The bending load was applied at the site of C–D line, as shown in Fig. 1 for all tests. The bending load applied to the specimen caused an axial deflection, the specimen was bent downwards, resulting in a tangential force that is transmitted between the pad and the specimen. The cyclical bending loads (W) were imposed at the C–D line in Fig. 1 by the servo fatigue machine. For the bending fatigue tests, the bending peak loads were 5.5, 5.75, 6.0, 6.125, 6.25, and 6.5 KN, respectively. Maximum cyclical bending stresses in this study were 509.3, 532.4, 555.6, 567.1, 578.7, and 601.9 MPa, respectively, according to the calculation of the formula of material mechanics:
sa,max ¼ 6WL=bh2 here, sa,max is the maximum bending stress, W is the cyclical bending load, L is the distance between the sites of bending load
J.F. Peng et al. / Tribology International 44 (2011) 1417–1426
and the fretting pads, b is the width of the specimen and h is the height of the specimen. In addition, the normal load imposed on the fretting pads was fixed at 1 KN for all fretting fatigue tests. According to the calculation of the Hertz contact theory [17,18], the maximum contact stress was 191.64 MPa with maximum contact depth of 45.37 um. The testing frequency was set at 20 Hz, and the stress ratio R was 0.1 in sine waveform. The fretting fatigue limit was defined as the fretting fatigue strength at 1 107 cycles.
2.3. Micro-examination The upper regions of fretting contact of the specimen and the fracture surfaces of the failed specimens after fretting fatigue test were examined by optical microscopy (OM), scanning electron microscopy (SEM, Quanta 2000), and energy dispersive X-ray spectroscopy (EDX, EDAX-7760/68 ME). Before the examination,
1419
the fretting regions were cleaned using acetone to remove fretting debris and to make it easier for observation. The fretting scars and fracture surfaces at the failure section were examined under OM to determine the locations of the crack initiated and the severity of fretting damage. For observation of fretting cracks, specimens were cut by a wire-electrode cutting machine. Cross-sections of the fretting specimens were etched with the solution of 33.3% HNO3 and 33.3% HCl for 20 s and then cleaned with acetone using ultrasonic, and lastly dehydrated in air. After the tests of bending fretting fatigue, the fretting contact zones were covered by some oxidative debris. In order to observe the fretting damage zones under SEM, the 316L austenitic stainless steel specimens were first cut by a wire-electrode cutting machine at the two sides of fretting contact zone, then cleaned with acetone until nearly no contamination and debris was left on them. In order to analyze the microstructure evolution of the 316 L steel specimen under the condition of bending fretting fatigue, transmission electron microscopy (TEM) specimens were prepared. The original
Fig. 4. (a)–(c) SEM images of fretting damage zone and EDX spectrum of oxidative debris and (d): W¼ 5.50 KN, sa,max ¼ 509.3 MPa, 107 cycles.
1420
J.F. Peng et al. / Tribology International 44 (2011) 1417–1426
TEM specimens of 0.1 mm thickness were cut from the upper contact stress zones of the fretting specimens, which were 0.1 mm beneath the contact surface and were parallel to the contact surface. The sheets were ground and polished to the thickness less than 50 mm, and then punched into small disks of 3 mm diameter. Before the observation by the TEM (Hitachi H-800), the TEM samples were prepared by a twin jet apparatus at a potential of
80 V and a temperature of 248 K, in a solution with 5 vol% of perchloric acid and 95 vol% alcohol.
3. Results and discussion 3.1. Bending fretting fatigue test results
Fig. 5. SEM image of fretting damage zone: W ¼ 5.75 KN, sa,max ¼532.4 MPa, N¼ 107 cycles.
Fig. 3 shows the S–N (details) results of the bending fretting fatigue and the plain bending fatigue. It illustrated that the lifetime presented a significant trend of dramatically decreasing with the increase in the cyclical bending stress amplitude. In other words, the lifetime of fretting fatigue was distinctly less than that of plain fatigue under the same cyclical bending stress. Due to the combined action of the cyclical bending stress and local contact stress of the bending fretting fatigue, the micro-cracks were accelerated to nucleate, which the shortened the initiation stage of fatigue cracks as compared to plain fatigue and then the specimen ruptured ahead of schedule. With the increase in the cyclical bending stress amplitude, the distinction of lifetime was gradually changing to inconspicuous. The rationale is that, as the cyclical bending stress amplitude increased near to the yield stress of the specimen, the local plastic deformation and stress concentration occurred severely to promote the initiation and propagation of micro-cracks, and the influence of the fretting wear between the specimens and fretting pads was weakened accordingly. The lifetime of fretting fatigue can be divided into two stages: (a) fretting cracks initiation and propagation caused by local contact stress, and (b) macro-cracks propagation caused by the cyclical bending stress. Stage (a) could be shortened due to higher bending of stress amplitude. It was also the reason why the lifetime of both fretting fatigue and plain fatigue was limited under the conditions of high bending loads.
Fig. 6. SEM images of the fretting contact zones, W ¼5.5 KN, sa,max ¼ 509.26 MPa: (a) 1 105 cycles, (b) 1 106 cycles, (c) 2 106 cycles, and (d) 5 106 cycles.
J.F. Peng et al. / Tribology International 44 (2011) 1417–1426
3.2. Fretting damage analyses Fig. 4 displayed the SEM images of the fretting fatigue specimen under low bending cyclic peak stress (W¼5.50 KN, sa,max ¼509.3 MPa) after 107 cycles. The relative displacement between the specimen contact zone and upper fretting pad occurred when the cyclical bending stress was applied. Accordingly, the plastic deformation and work-hardening in the contact zone occurred. As a result, the material was embrittled, and white layers formed at the meantime [19]. The material surface of the contact zone underwent alternative tangential forces, which induced the material detachment to form the debris. For the cross-section of specimens, the wear zones presented a shape deviated from a rectangle due to the buckling of the specimen (Fig. 4(a)). In the severe damage region, the plastic flow and detachment by delamination can be observed as seen in Fig. 4(b), then the detached particles were ground and oxidized repeatedly to form the fine oxidative debris bed. Fig. 4(c) showed the debris bed at the contact edge, indicating that the debris was oxidized deeply through the detection of the EDX (Fig. 4(d)). With the increase in the bending fatigue load, the fretting contact zone not only presented wear and debris, but also generated microscopic cracks in shape of a zig-zag, which was perpendicular to the direction of the micro-slip, as seen in Fig. 5. The cracks may be propagated in further cycles and finally induce fracture of the specimen. Some ploughing grooves also appeared as shown in Fig. 5. The damage levels of the contact zones were strongly dependent on the evolution of the number of cycles. Fig. 6 presents the evolution of the fretting fatigue damage as a function of the number of cycles (the SEM images from four different specimens) under the maximum bending load of 5.5 KN (sa,max ¼509.26 MPa). In Fig. 6(a), after 1 105 cycles, a mild damage with a few pieces of detachment and some traces of ploughing occurred at the contact zones. After 1 106 cycles (Fig. 6(b)), the width of the damaged region enlarged, and the damage became more severe. Meanwhile, the feature of ploughing was disappeared, local severe wear appeared at the center and an obvious debris bed formed. With the further increase in the number of cycles (N ¼2 106 cycles, Fig. 6(c)), the damaged region obviously broadened and more debris covered on it. There was a shallow notch with severe damage located at the center of the damage region. When the number of the cycles reached 5 106 (Fig. 6(d)), a thick oxidative debris layer covered the center of the contact zone, and the depth of the shallow notch increased accordingly. The deep notch may be the result of the fretting pad operating on the thick debris layer at higher cycles; therefore, the wear mechanisms in the fretting damaged zones mainly were abrasive wear, oxidative wear and delamination according to the morphology observation and EDX examination.
1421
When the maximum cyclical bending load reached 6.0 KN (sa,max ¼555.56 MPa), the specimen would fracture at the number of cycles less than 107. Its SEM images of the cross-section (Fig. 7) exhibited that the microscopic crack initiated along a direction of about 30–451 to the surface at the beginning stage (Fig. 7(b)), and propagated perpendicular to the contact surface with the increase in the number of the cycles. The crack orientation took a sudden transition to a perpendicular direction in length of about 90 mm, and the crack propagation was mainly transgranular (Fig. 8). In Fig. 7(b), it showed that the depth of the turning point of the crack was about 72 mm, which fell in between the depth of maximum Hertz stress (45.37 mm) and the depth of the contact stress influence area (about 113 mm calculated by Hertz contact theory). Thus, as mentioned above, the stage of initiation and propagation of the oblique crack was controlled by the local contact stress of fretting, and the perpendicular stage of the propagation was controlled by the bending fatigue stress. In other words, the initiation of the cracks was mainly dependent on the local fretting action and the propagation was dependent on the whole fatigue [19]. When the cyclical bending stress increased further to a higher level, the lifetime of the fretting fatigue subsequently shortened; however, the feature of two stages was still unchanged.
Fig. 8. SEM image of the cross-section of the fretting damage zone: W ¼ 6.25 KN, sa,max ¼578.7 MPa, and 107 cycles.
Fig. 7. SEM images of the cross-section of the fretting damage zone: W¼ 6.0 KN, sa,max ¼555.6 MPa, and 107 cycles.
1422
J.F. Peng et al. / Tribology International 44 (2011) 1417–1426
Fig. 9. SEM images of the fretting crack sources: (a) W¼ 6.25 KN, sa,max ¼ 578.7 MPa and (b) W¼ 6.5 KN, sa,max ¼601.9 MPa.
Fig. 10. SEM images of the fretting fracture surface: (a) W ¼ 6.25 KN, sa,max ¼ 578.7 MPa and (b) W ¼ 6.5 KN, sa,max ¼601.9 MPa.
Fig. 11. TEM images of the dislocation configuration of the original 316L austenitic stainless steel; W¼ 0 KN, Fn ¼0 KN: (a) cross-slip of dislocations and (b) stacking faults.
For the conventional fatigue testing, the crack sources usually locate at the surface of the specimen where some defects are present [20]; however, for the fretting fatigue, the crack sources are found beneath the contact surface of the fretting scars. Same results were obtained under the bending fretting fatigue condition. As shown in Fig. 9(a), a white layer (dark region at the top area of the image) has been formed at the surface of the contact zone, and the fretting fatigue crack initiated beneath the white layer where the contact stress was the highest. Also, in Fig. 9(b), the white layer was removed to form a worn pit, which corresponded to a higher bending load and a higher tangential force at the fretting contact zone. In the same way, the fretting fatigue crack
sources are located in the plastic deformation zone beneath the white layer although higher bending loads are imposed. When the bending stress was high enough (W¼6.25 KN, sa,max ¼578.7 MPa), the second cracks perpendicular to the fracture surface can be observed (Fig. 10(a)). With the bending stress further increasing, the size and amount of the second cracks increased obviously (Fig. 10(b)). It illustrated that many independent crack sources can be generated under higher stress levels. The local stress would be relaxed during the propagating of the second cracks and linking to the main crack. However, this process was not the principal aspect of the damage.
J.F. Peng et al. / Tribology International 44 (2011) 1417–1426
3.3. TEM analyses After the fatigue tests, the microstructures of the fatigue specimens were observed by the TEM, which provided information on the dislocation distribution and configuration under the conditions of the bending loads and normal load. Fig. 11. showed that there was very low dislocation density for the annealing metal. The cross-slip of dislocation (Fig. 11(a)) and stacking fault of the FCC structure of the austenite (Fig. 11(b)) can be observed. No twins appeared in the microstructure of the specimen prepared. When the 316L austenitic stainless steel was tested under the lower bending load of 5.5 KN and 106 cycles, the microstructure of the specimen changed greatly, as the TEM images of the dislocation configuration shown in Fig. 12. In Fig. 12(a), it showed that the dislocation density and the amount of the cross-slip of dislocation increased in comparison with the original material. At the boundary of the grains, the dislocations piled up obviously and greatly to lead to the bending of the grain boundary due to the stress concentration induced by the accumulation of dislocations (Fig. 12(b) and (c)). Under this test condition, some deformation twins passing through whole grains can be found in partial grains (Fig. 12(d)). The spots of electron diffraction shown in Fig. 12(d) proved that the fine strips were the deformation twins. In general, the plastic deformation is in progress by the slip of dislocation, and the deformation twins generate due to the slip stopped by some impediments. Here, the formation of the deformation twins illustrated that the dislocation slip cannot continue to occur when the plastic deformation accumulated to a certain degree. When the number of cycles further increased to 107 under the same bending load, the amount of twins multiplied rapidly, and the single directional twins transformed to trifurcate twins, as seen in Fig. 13. It means that the single twinning system (corresponding to only one twinning plane and twinning direction) was started for
1423
lower cycles; however, more twinning systems (corresponding to varied twinning planes and twinning directions) were switched on by the accumulation of plastic deformation at higher cycles. Because of the impact of the deformation twins, the grain boundaries were changed to polygonal lines (Fig. 13(b)). For the deformation twins, they presented higher dislocation density in the twin strip (Fig. 13(c)). The grids, the area surrounded by the trifurcate twins, appeared to have higher dislocation tangles as shown in Fig. 13(d) and (e). With the increase in the degree of the dislocation tangles, the stress concentration in the triangle zone of the grids increased tremendously (Fig. 13(e)). As the stress concentration exceeded the strength of the material, the material was torn to form a crack nucleus. With the linking of the adjacent crack nuclei, as seen in Fig. 13(f), the micro-crack propagated in a zig-zag manner. It can be concluded that this was the mechanism of the micro-crack initiation under the condition of bending fretting fatigue. Similar results were obtained under higher bending loads. For example, even under W¼6.5 KN and N ¼1.0 105, some dislocation tangles in cellular structure were formed, as shown in Fig. 14(a). The dislocation density was higher than that in Fig. 12(a), and some deformation twins with different twinning systems were formed (Fig. 14(b)). It revealed that the higher bending stress accelerated the damage of the material. In comparison to details in Fig. 13, the dislocation density and diameters of the dislocation cells of the plain bending fatigue were still lower than that of the bending fretting fatigue under same load level even after 6.7 105 cycles (Fig. 15). In the TEM samples of the plain bending fatigue, it showed that the fretting contact stress immensely accelerated the evolution of the microstructure and induced severe damage to the material. According to the TEM observations of the specimens of fatigue testing, the biggest difference between the bending fretting fatigue and plain fretting was the twinning deformation turning into the
Fig. 12. TEM images of the dislocation configuration of the bending fretting specimen; W ¼5.5 KN, sa,max ¼ 509.3 MPa, N ¼106 cycles: (a) cross-slip of dislocations, (b) dislocations pile up on the grain boundary, (c) grain boundary bends, and (d) deformation twins.
1424
J.F. Peng et al. / Tribology International 44 (2011) 1417–1426
Fig. 13. TEM images of the dislocation configuration of the bending fretting specimen; W¼ 5.5 KN, sa,max ¼ 509.3 MPa, N ¼ 107 cycles: (a) twins multiply, (b) grain boundary is polygonal line, (c) higher dislocation density in the twin strip, (d) higher dislocation tangles in the grids, (e) trifurcate twins, and (f) crack nuclei.
Fig. 14. TEM images of the dislocation configuration of the bending fretting specimen; W ¼6.5 KN, sa,max ¼ 601.9 MPa, N ¼ 1.0 105 cycles: (a) dislocation tangles in structure of cellular and (b) deformation twins.
J.F. Peng et al. / Tribology International 44 (2011) 1417–1426
1425
Fig. 15. TEM images of the dislocation configuration of the plain fatigue specimen; W ¼6.5 KN, sa,max ¼ 601.9 MPa, Fn ¼0 KN, N ¼6.7 105 cycles: (a) dislocation cells and (b) deformation twins.
Fig. 16. Physical model of the microscopic mechanism of the crack nucleation for the bending fretting fatigue.
main mechanism for the crack nucleation due to the local higher contact stress. The microscopic mechanism of the crack nucleation for the bending fretting fatigue can be drawn as a physical model as shown in Fig. 16. The process can be described as follows:
(h) Finally, the micro-crack nucleus connected together to form a fatigue micro-crack in the shape of a zig-zag.
4. Conclusions (a) Before the testing of the bending fretting fatigue, there is very low dislocation density for annealing 316L austenitic stainless steel. The cross-slip of the dislocations and stacking fault of the FCC structure can be observed. (b) In the early test stage of the bending fretting fatigue, the dislocation density increased with the increase in the number of cycles, which accompanied with the cross-slip of the dislocations and dislocation pile up at the grain boundaries. (c) With the increase in the number of cycles, the dislocation density multiplied to a high level to restrain the dislocation slip. The twinning became the main deformation mode, the single twinning system was started up and passed through the whole grain. (d) With further increase in the number of cycles, more twinning systems were brought into operation by the accumulation of plastic deformation; the intercrossing of the twin bands generated and the grids were formed in the grains. (e) With the further increase in the accumulation of plastic deformation, higher dislocation tangles with higher dislocation density appeared in the grids of the intercrossing regions of twins. (f) When the cycles increased to higher level, twinning systems of the austenite were adequately developed to transform the trifurcate twins within higher dislocation tangles. The stress concentration in the triangle zone of the grids increased step by step. (g) With the increase in the stress concentration, which exceeded the strength of the material, the micro-crack nucleus initiated at the corners of the triangular grids.
Based on the experimental results of the bending fretting fatigue of 316L austenitic stainless steel against 52100 steel, the fretting fatigue behaviors and damage mechanisms were analyzed in detail. The conclusions may be summarized as follows: (1) It showed that the 316L austenitic stainless steel life of the bending fretting fatigue was much smaller than that of the plain fatigue due to the local fretting damages. With the increase in the cyclical bend stress and the number of cycles, the effects of the fretting decreased and the width of damage zones increased. (2) After the tests of bending fretting fatigue, the fretting contact zones were covered by some oxidative debris in the severe damage region, and the plastic flow and detachment by delamination could be observed. With the increase in the bending fatigue load, the microscopic cracks generated in shape of a zig-zag, and the specimen ruptured ahead of schedule under higher bending fatigue loads. (3) The fretting fatigue cracks easily appeared at the upper fretting damage surface of the plate specimen, and initiated and propagated along the direction of about 30–451 to the surface at the beginning stage, which was controlled by the fretting contact stress. Then the crack orientation took a sudden transition in a perpendicular direction with about 72 mm controlled by the bending fatigue stress.
1426
J.F. Peng et al. / Tribology International 44 (2011) 1417–1426
(4) The fretting fatigue crack sources usually located at the plastic deformation zone beneath the white layer of fretting wear, and the crack propagation was mainly transgranular. (5) The TEM images displayed that the dislocation configuration of bending fretting fatigue was quite different from the plain bending fretting fatigue. With the increase in the cyclical bend stress and the number of cycles, the dislocation cellular structure transformed to twin–twin intersections. A dislocation model of micro-crack nucleation mechanism in the manner of a zig-zag mode was made.
Acknowledgements This work was supported by National Natural Science Foundation of China (50821063), Major State Basic Research Development Program of China (2007CB 714704), and Project of Traction Power State Key Laboratory of China (2008TPL_Z10). References [1] Hirakawa K, Toyama K, Kubota M. The analysis and prevention of failure in railway axles. Fatigue 1998;20(2):135–44. [2] Juuma Teuvo. Torsional fretting fatigue strength of a shrink-fitted shaft with a grooved hub. Tribology International 2000;33:537–43. [3] Juuma Teuvo. Torsional fretting fatigue strength of a shrink-fitted shaft. Wear 1999;231:310–8. [4] Gutkin R, Alfredsson.Growth B. of fretting fatigue cracks in a shrink-fitted joint subjected to rotatingbending. Engineering Failure Analysis 2008;15:582–96. [5] Waterhouse RB. Fretting fatigue. In: Lindley TC, editor. ESIS Publication 18, Mech. Eng. Publication; 1994.
[6] Waterhouse RB. Fretting fatigue. Appl. Sci. Publ.. 1981. [7] Hills DA, Nowell D. Mechanics of fretting fatigue. Dordrecht: Kluwer Academic Publishers; 1994. [8] Hoeppner DW, Chandrasekaran V, Elliot CB. Fretting fatigue: current technology and practices, ASTM STP 1367. American Society for Testing and Materials. 2000. (ISBN 0-8031-2851-7). [9] Ebara Ryuichiro, Fujimura Masanori. Fretting fatigue behaviour of Ti–6Al–4 V alloy under plane bending stress and contact stress. Tribology International 2006;39:1181–6. [10] Nowell D, Dini D, Hills DA. Recent developments in the understanding of fretting fatigue. Engineering Fracture Mechanics 2006;73:207–22. [11] Hattori T, Nakamura M, Watanabe T. Fretting fatigue analysis by using fracture mechanics. ASME paper no.84-WA/DE- 1984;10. [12] King R.N., Lindley T.C.. Fretting fatigue in a 312 Ni–Cr–Mo–V rotor steel. In: Proceedings of the ICF5 1980. p. 631. [13] Mayama Tsuyoshi, Sasaki Katsuhiko, Kuroda Mitsutoshi. Quantitative evaluations for strain amplitude dependent organization of dislocation structures due to cyclic plasticity in austenitic stainless steel 316L. Acta Materialia 2008;56:2735–43. [14] Yaguchi H, Mitani H, Nagano K, Fujii T, Kato M. Fatigue-damage evaluation in aluminum heat-transfer tubes by measuring dislocation cell-wall thickness. Materials Science and Engineering A 2001;315:189–94. [15] Gaudin C, Feaugas X. Cyclic creep process in AISI 316L stainless steel in terms of dislocation patterns and internal stresses. Acta Materialia 2004;52:3097–110. [16] Hutson Alisha, Sathish Shamachary, Nicholas Ted. Progression of fretting fatigue damage in Ti–6Al–4V. Tribology International 2006;39:1197–1205. [17] Johnson KL. Contact mechanics and the wear of metals. Wear 1995;190: 162–70. [18] Johnson KL, Greenwood. JA. An adhesion map for the contact of elastic spheres. Journal of Colloid and Interface Science 1997;192:326–33. [19] Zhou ZR , Zhu MH. Composite fretting wear. Shanghai University Publishing Company, 2004. [20] Sakaia Tatsuo, Satob Yosuke, Naganoc Yoshiyuki, Takedad Mitsuhiro, Ogumae Noriyasu. Effect of stress ratio on long life fatigue behavior of high carbon chromium bearing steel under axial loading. International Journal of Fatigue 2006;28:1547–54.