- Email: [email protected]
Experimental study on fretting-fatigue of bridge cable wires
International Journal of Fatigue 131 (2020) 105321
Contents lists available at ScienceDirect
International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Experimental study on fretting-fatigue of bridge cable wires a,⁎
a
b
T
c
Tong Guo , Zhongxiang Liu , José Correia , Abílio M.P. de Jesus a b c
Key Laboratory of Concrete and Prestressed Concrete Structures, Ministry of Education, Southeast University, Nanjing 210096, PR China CONSTRUCT & Faculty of Engineering, University of Porto, Porto, Portugal Faculty of Engineering, University of Porto, Porto, Portugal
A R T I C LE I N FO
A B S T R A C T
Keywords: Fretting-fatigue Wear scar Fracture surface Cable wire Friction coefficient
Bridge cables are subjected to small relative sliding and high contact stresses among wires under fluctuating loads and repeated bending, eventually leading to fretting-fatigue failure. This paper presents a series of fretting fatigue tests with different fretting and fatigue parameters to investigate the tribological properties, fretting fatigue characteristics and fracture failure mechanism. Results show that the fretting-fatigue failure evolved from surface micro cracks at the trailing edges generated from a mixed slip regime. Larger fretting amplitude induced larger tangential force and coefficient of friction, and decreased life. Fretting scar depth increased as fretting-fatigue proceeded while the growth rate was declining.
1. Introduction Bridge cables that bear large axial loads with comparatively small bending and torsional stiffness have been widely used in cable-supported bridges, such as suspension bridges, cable-stayed bridges and tied-arch bridges [1]. The cables primarily consist of parallel wires, parallel strands or helical strands, as shown in Fig. 1. Essentially, bridge cables are commonly manufactured from high strength steel wires through clustering or knitting. Those wires are cold drawn high-carbon steel with a diameter ranging between 2 mm and 7 mm. Wires of bridge cables, especially those near the anchorage, are generally subjected to fluctuating loads and repeated bending [2,3], which can result into small relative sliding and high contact stresses among wires. As friction exists between wires, the relative sliding can induce fretting wear in the contact interfaces, generating cracking sources. Fretting-fatigue is a contact fatigue process triggered by cyclic relative sliding and fretting contact stress between compacted structural members, which can lead to the decrease of fatigue strength and premature fracture. Due to the interaction of cyclic internal stresses and external fretting wear, the wires are susceptive to fretting-fatigue, where tensile fatigue along the wire axis, micro-slip at the contact surface and cyclic fretting contact stresses work together. This results in the cracking of wires and a reduction of the cable bearing capacity leading, eventually, to its final fracture [4]. Moreover, such fracture can result in premature failure of suspension cables, which in extreme cases, may lead to progressive collapse of a structure. The fretting-fatigue of wires has been already discussed in several
⁎
studies. Hobbs and Raoof [5] presented a detailed discussion of the different mechanisms of inter-wire fretting-fatigue of steel cables, finding that more failures occurred in wires at quasi-punctual contact areas than in linear contact areas. The reason is that smaller contact area induces higher contact stresses. According to experimental studies, Siegert and Brevet [6] observed that fracture was concentrated in the bending plane and most of the fracture were locally originated in wear areas due to inter-wire fretting. Wang et al. [7] demonstrated that fretting can worsen the contact surfaces and accelerate the fatigue process, resulting in abrupt change of tensile stresses, cross-section reduction and high stress concentration. Additionally, Liu et al. [8] conducted a comparative study on failure of suspension cables of two similar long-span suspension bridges. The shortest suspension cables of one of the bridges were replaced by rigid central clamps; based on field measurements, notable wear between several wires in the rope of the suspension cables and its failure mechanism under repetitive traffic loading were discussed. Due to the importance of contact surface in fretting-fatigue process, the condition and mechanical characteristics of contact surfaces have been extensively studied. Nawrocki and Labrosse [9] identified that the inter-wire pivoting and sliding dominates the response of rope under the axial and bending loads. Siegert [10] analyzed the normal force and relative displacement amplitude between the contact areas in a multilayer strand. Based on experimental data, Waterhouse et al. [11] noticed that the lubrication effect provided by zinc coating can significantly alleviate the fretting-fatigue, maintaining the friction coefficient at a low value, at least during the early stages of fretting. The
Corresponding author. E-mail addresses: [email protected] (T. Guo), [email protected] (Z. Liu), [email protected] (J. Correia), [email protected] (A.M.P. de Jesus).
https://doi.org/10.1016/j.ijfatigue.2019.105321 Received 25 May 2019; Received in revised form 9 September 2019; Accepted 3 October 2019 Available online 04 October 2019 0142-1123/ © 2019 Published by Elsevier Ltd.
International Journal of Fatigue 131 (2020) 105321
T. Guo, et al.
(a) Parallel wire cable
(b) Spiral strand cable
Fig. 1. Configuration of typical bridge cables.
Fig. 2(b) presents a schematic of the aforementioned fretting-fatigue testing, where the normal force between wires (Fn) is equal to the gravity of mass blocks. The distance between the lower gripping head and the axis of the loading wire, i.e., the length of the lower wire segment, is S. Under a mean displacement (Δ0) and a displacement range (Δ), the tested wire deforms cyclically. The strain variations are obtained by two strain gauges attached on the lower and upper wire segment apart from the necking region, respectively. The relative displacement between the tested wire and loading wire can be expressed as Eq. (1a), which can be alternatively estimated by Eq. (1b). Also, the tangential force (Q) can be evaluated according to the strain difference of the upper and lower wire segment, as shown in Eq. (2).
friction phenomenon between the contact surfaces that affects the fretting-fatigue behavior of wires has been identified by reference [12], where the endurance limits of bright, galvanized and lubricated wires were experimentally determined to be about 100 MPa, 170 MPa and 250 MPa. Besides, the effects of protecting measures (i.e., lubrication and zinc coating) on reducing the friction between the fretting surfaces and corrosive environments on the fretting-fatigue were also discussed [13]. To better understand the tribological properties, fretting-fatigue characteristics and fracture failure mechanism of cable wires, this paper presents a series of fretting fatigue tests with various fretting and fatigue parameters. The fretting scar and fracture surface were checked using both optical microscopy and scanning electron microscope (SEM). Besides, the primary wear properties, i.e., tangential force and friction coefficient, under various fretting amplitudes and normal forces were discussed to understand the slip regime and wear mechanisms. Additionally, the evolution of fretting scar morphologies, including scar depth profiles and maximum scar depths, under different normal forces were quantitatively analyzed using the white light interferometer. Furthermore, the fretting fatigue lives of wires due to different displacement ranges and normal forces were used to quantitatively identify the characteristics of fretting damage. The presented study provides references to the design and maintenance of cable wires, besides lifetime prediction.
δ = ε1 S
δ = Δ· Q=
S L
1 EA (ε2 − ε1) 2
(1a) (1b) (2)
where δ is the amplitude of relative displacement between the tested wire and loading wire, i.e., fretting amplitude; ε1 and ε2 are the strain of the lower and upper wire segments, which are assumed to be uniform between the gripping head and contact surface; E is the elasticity modulus, which can be determined according to material tests; and A is the cross-section area of the wire.
2. Material and fretting fatigue testing
2.2. Tensile material properties
2.1. Test device and theory
Fundamental constituent elements of bridge cable wires were used to produce the specimens required for this study, including the tested wires and loading wires. Those steel wires are high strength low alloy steel with a diameter of 5 mm, manufactured by high-quality carbon structural steel through cold drawing. The general chemical composition of the alloy is listed in Table 1. Suitable tensile tests were designed and implemented on specimens (total length of 500 mm) to capture the mechanical properties of the studied wire. Fig. 3(a) shows the stressstrain curves of some studied wires, revealing that the elastic modulus (E) of the wire was 2.025 × 105 MPa, and the yield strength (σy), ultimate strength (σu) and elongation (δ) at fracture were 1620 MPa, 1835 MPa and 5.78%, respectively. As shown in Fig. 3(b), the wire presented slight plastic deformation prior to the fracture with a final cross section reduction of 6.25%. The tensile fracture surface in Fig. 3(b) consisted of central rough fibrous region, peripheral smooth shear lip and coarse radial region with radial marks. Fracture surface examinations show that fracture initiated in the center of the specimens [14,15]. Once the necking begun, the tri-axial stress developed in the center of the neck region promoted the nucleation and growth of microcracks. Subsequently, the cracks initially occurring in the center of the plane perpendicular to the wire axis propagated to the periphery
Fretting fatigue testing was conducted on a fatigue testing machine, where an auxiliary friction device was developed to provide external fretting wear, as shown in Fig. 2(a). The fatigue testing machine provided fatigue loads applied to the wire through the cyclic movement of gripping heads. The auxiliary friction device consists of a loading fixture, a support fixture, a pair of sliding guides, a sliding plate, a pair of cantilevers, a pair of fixed splints and mass blocks. This experimental device was used to reproduce the loading conditions of wires in a spiral strand, like the bending of suspender cable ends. Loading wires were installed at the same level on the loading and support fixture through bolts, respectively, which were made of the same wire as the tested wire. The loading fixture was placed in the sliding guides, while the support fixture was fixed on the sliding plate that can slide straight along the oblong holes on the cantilevers. Hence, under the traction of mass blocks, the two fixtures moved toward the tested wire in the middle, making the loading wires contact with the tested wire and simultaneously providing constant normal force between wires. This setup is capable of implementing fretting fatigue testing under constant normal force. 2
International Journal of Fatigue 131 (2020) 105321
T. Guo, et al.
(a) Testing device
(b) Testing theory model
Fig. 2. Fretting fatigue device and theory.
adopted in the tests, i.e., 60 N and 120 N, to consider the effect of contact stresses, which can represent approximately the contact force between strands of a rope cable. The loading frequency is fixed to 5 Hz in all tests. This loading frequency is a compromise between test duration, kinetics of fretting-fatigue and capacity of loading system, so that the tests may be as reproducible as possible. The experimental parameters are listed in Table 2. The fretting-fatigue tests were conducted in the laboratory at ambient atmosphere and room temperature, as shown in Fig. 4. Strains were recorded using a dynamic signal data acquisition unit (Model: TST-3000). To eliminate the effect of surface oil, alcohol was used to clean specimens’ surface before each test. After the tests, fretting scars and fracture surfaces of wires were observed using SEM, and the hysteresis loop, tangential force, friction coefficient (i.e., the ratio of maximum tangential force to normal force in a cycle) and lifetime were extracted for comparative analyses. Besides, the morphologies and profiles of fretting scars were measured using a white light interferometer.
Table 1 Chemical composition of the tested wires. Element
Fe
C
Si
Mn
S
P
Cr
Weight percent (%)
98.5
0.8
0.23
0.42
0.018
< 0.017
0.017
inclining at about 45° to its axis, leading to a final fracture. 2.3. Fatigue experimental procedure A displacement-based loading protocol [16,17] with a sinusoidal loading mode was applied. The basis loading protocol adopted here corresponds to the fatigue test protocol specified in the standard GB/T 17101 [18], which stipulates that the wire with qualified fatigue property should be able to resist 2 × 106 fatigue cycles under a mean stress of 0.45σu–180 MPa and a stress range of 180 MPa, respectively. According to the stress-strain curve shown in Fig. 3(a), the steel wire will remain at linear elasticity stage. Therefore, the mean displacement and displacement range of the basis loading protocol are 1.37 mm and 0.44 mm, respectively, when the length of tested wire is 500 mm, based on the Hooke's law. The fretting amplitude between the wires can be estimated according to Eq. (1b). Fretting fatigue tests of the steel wires were conducted at different displacement ranges in order to investigate the influence of the fretting amplitudes. Besides, two levels of Fn were
3. Results and discussion 3.1. Fretting scars and fracture surfaces The fretting scars of 5 mm wires were checked by optical microscopy, as shown in Fig. 5. In general, the fretting scars presented an
2000
Stress (MPa)
1500
1000
500
0
Tensile test #1 Tensile test #2
0.2% 0
1
2
3
4
5
6
Strain (%)
(a) Stress-strain curves
(b) Fracture appearance Fig. 3. Tensile test data. 3
International Journal of Fatigue 131 (2020) 105321
T. Guo, et al.
Table 2 Fatigue experimental parameters. Mean displacement, Δ0 (mm)
Displacement Range, Δ (mm)
Fretting amplitude, δ (μm)
Normal force, Fn (N)
1.37
0.44, 0.66, 0.88
220, 330, 440
60, 120
Fig. 6. Wear fragment in the early stage of the test.
another crack existed on the same scar, indicating that such fracture evolved from a surface micro crack at the trailing edge. In frettingfatigue process, the fretting wear can damage the wire surface, so that micro cracks may initiate in the wear scar, centrally around the trailing edge. During the process, some formed micro cracks may be worn off, while one of the primary cracks probably around the trailing edge, together with secondary cracks nearby, may gradually develop and finally form a macro-crack. Compared with the tested wire, the loading wire that suffered from wear without fatigue loads did not show any fracture, which is an evidence of the accelerated damage of the tested wire due to the fretting-fatigue. Fig. 7(b) presents typical fracture surfaces of the tested wire due to fretting-fatigue damage. For the first type of fracture surfaces, the crack propagated inclined to the wire axis until a sudden static break occurred due to insufficient cross-section. In another type of fracture surfaces, obvious change of the crack propagation direction was observed. This is due to that cold drawing facilitated the grain structures alignments and weak colony interfaces orienting along the wire axis [22]. The colony interfaces are prone to damage, which can lead to the cracking initiating normal to the wire axis but branching towards the axis direction.
Fig. 4. Fretting fatigue test in the laboratory.
elliptical shape with the long axis along the sliding direction especially that of the tested wire in Fig. 5(a). It is observed that the contact surface of the tested wire was composed with a deep central zone and two shallow end zones, which corresponds to the stick zone and slip zone [19]. The formation of variant scar depths was due to larger contact pressure and more wear time in the stick zone than in the slip zone. In the stick zone, detached particles and furrows along the sliding direction indicate that this fretting damage resulted from adhesive and abrasive wear. The reason for the polishing is that the wear fragments were initially generated in the adhesive wear and then acted as the third body in the abrasive wear [20]. According to Fig. 6, some wear fragments were squeezed out of the fretting scar in the early stage of the fretting-fatigue test, which can prove the existing of wear fragments. Besides, wear fragments on the contact surfaces can be oxidized generating iron oxides during the fretting-fatigue test, which can be determined by the brown-red on the contact surfaces in Fig. 5. This phenomenon has been confirmed by the results of X-ray energy spectrum analysis [7]. According to the fretting scar of the failed wire shown in Fig. 7(a), the fracture (i.e. the through cross section crack) was located at the boundary between the slip and stick zone (i.e., the trailing edge), perpendicular to the sliding direction. Large stress abrupt change at the trailing edges due to significant geometry change and comparatively serious fretting wear may be the primary reason [21]. Meanwhile,
3.2. Tangential force and friction coefficient Tangential force varies with the development of the slip regime, accusing the change in the contact condition during the fretting process [23]. A perfect hysteresis loop represents a gross slip, a less opened indicates a stick-slip and a line is characteristics of a stick regime [24]. To identify the slip regimes, dynamic response of tangential force and relative slip amplitude can be utilized. Fig. 8 shows the evolution of the
(a) Intested wire
(b) In loading wire Fig. 5. Wear scars after fretting-fatigue testing. 4
International Journal of Fatigue 131 (2020) 105321
T. Guo, et al.
(b) Fracture surfaces
(a) Cracking location
Fig. 7. Fretting-fatigue failure of the tested wire.
it. Subsequently, the contact area was enlarged due to the fretting wear, making the partial slip regime generated. As fretting wear increased, the wear scar deepened and the areas of hysteresis loops continuously decreased [25]. Meanwhile, the hysteresis loops in the test conducted at Fn = 120 N and Δ = 0.44 mm are also presented in Fig. 8. It is observed that those hysteresis loops obeyed the same evolution trend as that conducted at Fn = 120 N and Δ = 0.88 mm and the fretting developed into a mixed slip regime (i.e. stick-slip) as the test lasted, which has been confirmed
hysteresis loops, relating the tangential force and displacement, with fatigue cycles during the test conducted at Fn = 120 N and Δ = 0.88 mm. As the cycling increased, the contact condition changed from initial gross slip to stick-slip, i.e. a perfect hysteresis loop with rectangular shape changed into a less opened one. This evolution has been identified by the experimental results [7]. Regarding to the tangential force, it significantly increased initially and then gradually decreased as the fretting fatigue test proceeded. In the early stage of cycling, the contact area was small and small tangential force went with
Fig. 8. Hysteresis loops with increasing fretting cycles. 5
International Journal of Fatigue 131 (2020) 105321
T. Guo, et al.
0.8
Friction coefficient
to fretting fatigue may be the primary reason. For the tests conducted at Δ = 0.44 mm and Δ = 0.66 mm, the evolution trends of the friction coefficient were similar to that test conducted at Δ = 0.88 mm in general; however, unneglectable differences existed in the magnitudes. The reason for the phenomenon is that the increase of displacement range can inevitably result in the reduction of the stick zone, i.e., the increase of slip zone, which promoted the coefficient of friction [29]. Besides, the test conducted at Fn = 60 N and Δ = 0.88 mm had larger friction coefficients than that conducted at Fn = 120 N and Δ = 0.88 mm, as presented in Fig. 9, which is in accordance with the conclusions reported in past studies [30,31]. The reason for this phenomenon is that larger normal forces can be more effective in reducing micro convex bodies and rough peaks, thus reducing the frictional resistance between the contact surfaces. Hence, larger normal forces can result in smaller friction coefficient.
Wire fracture
0.7 0.6 0.5 0.4
Fn=120N, Δ=0.88mm
0.3
Fn=120N, Δ=0.66mm
0.2
Fn=120N, Δ=0.44mm
0.1
Fn= 60N, Δ=0.88mm
0.0
0
1x105
2x105
3x105
4x105
Number of cycles Fig. 9. Influence of displacement range and normal force on the coefficient of friction.
3.3. Fretting scar profile To identify fretting damage quantitatively, the coordinates of wear scar surfaces were measured by using a white light interferometer (Model: MicroXAM-100), which can be used to restructure the morphologies of fretting scars and then estimated the wear volumes. The white interferometer can measure the 3D topography of surfaces at the nanometer level with a vertical resolution of 0.1 nm and a scan speed of 2.1 μm/sec. Fig. 10 shows the restructured models of fretting scar morphologies during the fretting fatigue test conducted at Fn = 120 N, Δ = 0.88 mm. According to Fig. 10, fretting scar surfaces exhibited the material adhesion, plastic deformation, particle detaching and ploughing [32]. The fretting scar gradually developed into an approximate semi-ellipsoid, which is consistent with the experimental results in the reference [33]. In order to investigate the evolution of the fretting scar profile, the scar depths of the tested wire shown in Fig. 10, at distinct fatigue cycles, were obtained from their morphologies, as illustrated in Fig. 11. Those
by the reference [26]. However, the mixed slip regimes in the test conducted at Fn = 120 N and Δ = 0.44 mm developed faster, which is primarily due to smaller slip amplitude [27]. Moreover, its tangential forces were less than those conducted at Fn = 120 N and Δ = 0.88 mm. To further investigate the contact condition during the fretting process, the friction coefficient that corresponds to the ratio of maximum tangential force to normal force in a cycle was calculated, as shown in Fig. 9. At the beginning of the test conducted at Fn = 120 N and Δ = 0.88 mm, the friction coefficient is in a low level, about 0.13, which may be attributed to the initial un-rough surface of the steel wire with protective film. As the fretting effect made the contact surface rough due to detached particles and furrows [28], this coefficient rose dramatically to the maximum value about 0.65. After 1.15 × 104 cycles, it declined continuously to about 0.58 until wire fracture. Progressive material loss and crack propagation in the contact surface due
Fig. 10. Restructured wear scars of the tested wire during the fretting fatigue test. 6
International Journal of Fatigue 131 (2020) 105321
T. Guo, et al.
Fig. 11. Scar depth profiles of tested wires during fretting fatigue tests under different normal forces.
Maximum scar depth (μm)
0 -20
scar depth profiles are along the axis of the tested wire with its x-coordinates equal to zero and the z-coordinates of the original wire surface were set to be zero as a baseline. Accumulation of the wear fragment and plastic flow of the material can bring about irregular elliptical profile [34], especially in the initial state, such as the profile shown in Fig. 11(a). It is observed that the scar depth increased with cycling. Besides, these profiles show that the scar had a significant drop at the trailing edges than at any other locations. This phenomenon became more apparent as the fatigue test proceeded. Such notable changes in the scar can induce significant stress concentration at trailing edges, making it the most vulnerable zone to fracture. In addition, Fig. 11 also presents the scar depth profiles of the tested wire during the fretting fatigue test that was conducted at Fn = 60 N, Δ = 0.88 mm. It reveals that larger normal force resulted in considerably deeper surface damage. Furthermore, the maximum scar depth of the profile shown in Fig. 11 was extracted, as illustrated in Fig. 12. The maximum scar depths increase exponentially with the number of cycles, while their growth rates were declining. These characteristics of the depth growth rates were similar at both normal forces. Those reveals severe wear at the initial stage, which gradually tended to be stable. This phenomenon has an agreement with the development trend of the friction coefficient shown in Fig. 9.
18.5
-40
52.1
-60 -80
77.4
-100 -120
96.8 0
2000
4000
6000
8000
10000
12000
Number of cycles Fig. 12. Maximum scar depth of depth profiles with x = 0.
Displacement range (mm)
0.72
Fn=120Ν, Δ=0.44mm Fn=120Ν, Δ=0.66mm
0.54
Fn=120Ν, Δ=0.88mm
3.4. Fretting fatigue life
Fn= 60Ν, Δ=0.88mm
Fig. 13 illustrates the fretting fatigue lives of tested wires as the displacement range increased from 0.44 mm to 0.88 mm with the normal force equal to 120 N. The fretting fatigue lives of tested wires at Δ = 0.88 mm were ranged between 3.6 × 105 cycles and 4.2 × 105 cycles. Besides, fretting fatigue lives of tested wires at Δ = 0.66 mm were ranged between 6.8 × 105 cycles and 8.2 × 105 cycles, while those at Δ = 0.44 mm were ranged between 1.50 × 106 cycles and 1.87 × 106 cycles. It is observed that fretting fatigue life decreases
0.36 0.0
4.0x10
5
8.0x10
5
6
1.2x10
1.6x10
6
2.0x10
6
Number of cycles Fig. 13. Fretting-fatigue lives at different displacement ranges.
7
International Journal of Fatigue 131 (2020) 105321
T. Guo, et al.
Acknowledgements
rapidly with the increase of displacement range (i.e., fretting amplitude). The increase of displacement range can inevitably result in the increase of slip zone and fretting damage, which makes the partial slip significant. As the most dangerous slip regime [35], the partial slip regime can accelerate crack initiation and propagation, causing significant decrease of the fretting fatigue life. Therefore, the fretting fatigue life decreases with the increase of displacement range in a certain range [36]. In order to investigated the effect of normal force, several tests were conducted at Fn = 60 N and Δ = 0.88 mm, whose average fretting fatigue life was about 1.15 × 106 cycles. Compared with tests conducted at Fn = 120 N and Δ = 0.88 mm, it is found that larger normal force can dramatically decrease the life of wires in fretting fatigue tests [37]. Although larger normal force caused smaller friction coefficient in the fretting fatigue tests, the aggravated fretting wear of the contact surfaces leads to shorter life. The reason is that larger normal force can make more brittle material phases to detach due to continuous hardening and ploughing of the contact surface [26]. Fretting fatigue tests also show an important dispersion in terms of lifetime. The primary reason is related to the complexity of the fretting fatigue device accompanied with the classic scattering in fatigue tests. The scattering of lifetime in fatigue tests is attributed to the stochastic distribution of microdefects in material [38,39]. The crack propagation changing from the transverse to the longitudinal directions, which is due to cold drawing grain structures anisotropy facilitating weaker colony interfaces oriented along the direction of the wire axis [40,41], may also increase results dispersion. Note that the tested wires fractured in completed tests, while no visible cracking or fracture has been observed in the fretting scars of the loading wires in all these tests. Compared with the tested wire, the loading wire suffered from wear without fatigue cracks; an accelerated damage on the tested wire due to the coupled effect of fretting wear and fatigue was verified.
Support from the Natural Science Foundation of China under Grant No. 51978156 and the Scientific Research Foundation of the Graduate School of Southeast University under grant No. YBJJ1818 is gratefully acknowledged. Additionally, this work was also supported by: UID/ ECI/04708/2019 - CONSTRUCT – Instituto de I&D em Estruturas e Construções; and POCI-01-0145-FEDER-030103 FiberBridge – Fatigue strengthening and assessment of railway metallic bridges using fiberreinforced polymers funded by national funds through the FCT/MCTES (PIDDAC). References [1] Liu Z, Guo T, Huang L, Pan Z. Fatigue life evaluation on short suspenders of longspan suspension bridge with Central Clamps. J Bridge Eng 2017;22(10):04017074. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001097. [2] Kondoh M, Okuda M, Kawaguchi K, Yamazaki T. Design method of a hanger system for long-span suspension bridge. J Bridge Eng 2001;6(3):176–82. https://doi.org/ 10.1061/(ASCE)1084-0702(2001) 6:3(176). [3] Liu Z, Guo T, Hebdon MH, Zhang Z. Corrosion fatigue analysis and reliability assessment of short suspenders in suspension and arch bridges. J Perform Constr Facil 2018;32(5):04018060. https://doi.org/10.1061/(ASCE)CF.1943-5509.0001203. [4] Mouradi H, El Barkany A, El Biyaali A. Investigation on the main degradation mechanisms of steel wire ropes. J Eng Appl Sci 2016;100(6):1206–17. https://doi. org/10.3923/jeasci.2016.1206.1217. [5] Hobbs RE, Raoof M. Mechanism of fretting fatigue in steel cables. Int J Fatigue 1994;16:273–80. https://doi.org/10.1016/0142-1123(94)90341-7. [6] Siegert D, Brevet P. Fatigue of stay cables inside end fittings: high frequencies of wind induced vibrations. Bull Int Organis Study Endurance of Ropes 2005;89:43. [7] Wang D, Zhang D, Ge S. Fretting–fatigue behavior of steel wires in low cycle fatigue. Mater Des 2011;32(10):4986–93. https://doi.org/10.1016/j.matdes.2011.06.037. [8] Liu Z, Guo T, Hebdon MH, Han W. Measurement and comparative study on movements of suspenders in long-span suspension bridges. J Bridge Eng 2019;24(5):04019026. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001386. [9] Nawrocki A, Labrosse M. A finite element model for simple straight wire rope strands. Comput Struct 2000;77(4):345–59. https://doi.org/10.1016/S00457949(00)00026-2. [10] Siegert D. Initiation of fretting fatigue cracks in spiral multi-layer strands. Bulletin 1999;78:27–44. [11] Waterhouse RB, McColl IR, Harris SJ, Tsujikawa T. Fretting wear of a high-strength heavily work-hardened eutectoid steel. Wear 1994;175(1–2):51–7. https://doi.org/ 10.1016/0043-1648(94)90167-8. [12] Périer V, Dieng L, Gaillet L, Fouvry S. Influence of an aqueous environment on the fretting behaviour of steel wires used in civil engineering cables. Wear 2011;271(9–10):1585–93. https://doi.org/10.1016/j.wear.2011.01.095. [13] McColl IR, Waterhouse RB, Harris SJ, Tsujikawa M. Lubricated fretting wear of a high-strength eutectoid steel rope wire. Wear 1995;185(1–2):203–12. https://doi. org/10.1016/0043-1648(95)06616-0. [14] Wei S, Wang G, Yu J, Rong Y. Competitive failure analysis on tensile fracture of laser-deposited material for martensitic stainless steel. Mater Des 2007;118:1–10. https://doi.org/10.1016/j.matdes.2017.01.014. [15] Saeidi N, Ekrami A. Comparison of mechanical properties of martensite/ferrite and bainite/ferrite dual phase 4340 steels. Mater Sci Eng A 2009;523(1–2):125–9. https://doi.org/10.1016/j.msea.2009.06.057. [16] YuanZhou Z, Ji B, Fu Z, Kainuma S, Tsukamoto S. Fatigue crack retrofitting by closing crack surface. Int J Fatigue 2019;119:229–37. https://doi.org/10.1016/j. ijfatigue.2018.10.006. [17] Fu Z, Wang Y, Ji B, Jiang F. Effects of multiaxial fatigue on typical details of orthotropic steel bridge deck. Thin-Walled Struct 2019;135:137–46. https://doi.org/ 10.1016/j.tws.2018.10.035. [18] GB/T 17101-2008, Hot-dip Galvanized Steel Wires for Bridge Cables, Standards Press of China; 2008. [19] Fouvry S, Elleuch K, Simeon G. Prediction of crack nucleation under partial slip fretting conditions. J Strain Anal Eng Des 2002;37(6):549–64. https://doi.org/10. 1243/030932402320950152. [20] Basseville S, Héripré E, Cailletaud G. Numerical simulation of the third body in fretting problems. Wear 2011;270(11–12):876–87. https://doi.org/10.1016/j. wear.2011.02.016. [21] Hojjati-Talemi R, Wahab MA. Fretting fatigue crack initiation lifetime predictor tool: using damage mechanics approach. Tribol Int 2013;60:176–86. https://doi. org/10.1016/j.triboint.2012.10.028. [22] Perier V, Dieng L, Gaillet L, Tessier C, Fouvry S. Fretting-fatigue behaviour of bridge engineering cables in a solution of sodium chloride. Wear 2009;267(1–4):308–14. https://doi.org/10.1016/j.wear.2008.12.107. [23] Ramesh R, Gnanamoorthy R. Development of a fretting wear test rig and preliminary studies for understanding the fretting wear properties of steels. Mater Des 2006;27(2):141–6. https://doi.org/10.1016/j.matdes.2004.09.017. [24] Siegfried F, Philippe K, Hassan Z, Fouvry S, Kapsa P, Zahouani H, et al. Wear analysis in fretting of hard coatings through a dissipated energy concept. Wear 1997;203:393–403. https://doi.org/10.1016/S0043-1648(96)07436-4.
4. Conclusions The present studies of the tribological properties, fretting fatigue characteristics and fracture/failure mechanisms of cable wires under different fretting parameters and fatigue parameters revealed the following findings: 1. The contact surface of the tested wire was composed with a deep central zone and two shallow end zones, due to a mixed slip regime that resulted in variant scar depths at the trailing edges of the scar and significant decrease of the fretting fatigue life. As significant stress concentration due to variant scar profile change is expected, the fretting-fatigue failure evolved from surface micro cracks at the trailing edges towards the interior of the cross-section. 2. The tangential force as well as the friction coefficient increased as the displacement range (i.e., fretting amplitude) increased, those maximum magnitudes were significantly relevant to the contact stress dependent of the normal force. 3. Fretting scar depth increased with the increase of fatigue cycles, while the growth rate of maximum scar depth was declining significantly, indicating severe wear damage at the initial stage and that subsequent stabilization of wear damage rate. Besides, larger normal force can result in considerably deeper wear damage. 4. The fretting fatigue life decreased rapidly with larger increase of the fretting amplitude in a certain range and normal force. Larger fretting amplitudes make the mixed slip regime significant in the present study, leading to increase of slip zone and fretting damage. Meanwhile, larger normal forces made brittle/hard material phases to detach due to continuous hardening and ploughing of the contact surface. In addition, the lifetime in fretting fatigue tests showed an important dispersion, which may be relate to the complexity of the fretting fatigue failure mechanisms and the fretting fatigue device accompanied with the classic scattering in fatigue tests. 8
International Journal of Fatigue 131 (2020) 105321
T. Guo, et al.
[25] Fouvry S, Kapsa P, Vincent L. Quantification of fretting damage. Wear 1996;200:186–205. https://doi.org/10.1016/S0043-1648(96)07306-1. [26] Zhang D, Shen Y, Xu L, Ge S. Fretting wear behaviors of steel wires in coal mine under different corrosive mediums. Wear 2011;271(5–6):866–74. https://doi.org/ 10.1016/j.wear.2011.03.028. [27] Yark YW, Sankara Narayanan TSN, Lee KY. Effect of fretting amplitude and frequency on the fretting corrosion behaviour of tin plated contacts. Surf Coat Technol 2006;201:2181–92. https://doi.org/10.1016/j.surfcoat.2006.03.031. [28] Zhou ZR, Vincent L. Mixed fretting regime. Wear 1995;181:531–6. https://doi.org/ 10.1016/0043-1648(95)90168-X. [29] Jin O, Mall S. Influence of contact configuration on fretting fatigue behavior of Ti–6Al–4V under independent pad displacement condition. Int J Fatigue 2002;24(12):1243–53. https://doi.org/10.1016/S0142-1123(02)00041-5. [30] McColl IR, Ding J, Leen SB. Finite element simulation and experimental validation of fretting wear. Wear 2004;256(11–12):1114–27. https://doi.org/10.1016/j.wear. 2003.07.001. [31] Chen Y, Meng F, Gong X. Interwire wear and its influence on contact behavior of wire rope strand subjected to cyclic bending load. Wear 2016;368:470–84. https:// doi.org/10.1016/j.wear.2016.10.020. [32] Velkavrh I, Ausserer F, Klien S, Voyer J, Ristow A, Brenner J, et al. The influence of temperature on friction and wear of unlubricated steel/steel contacts in different gaseous atmospheres. Tribol Int 2016;98:155–71. https://doi.org/10.1016/j. triboint.2016.02.022. [33] Cruzado A, Urchegui MA, Gómez X. Finite element modeling and experimental
[34]
[35]
[36]
[37] [38]
[39]
[40]
[41]
9
validation of fretting wear scars in thin steel wires. Wear 2012;289:26–38. https:// doi.org/10.1016/j.wear.2012.04.018. Wang D, Li X, Wang X, Zhang D, Wang D. Dynamic wear evolution and crack propagation behaviors of steel wires during fretting-fatigue. Tribol Int 2016;101:348–55. https://doi.org/10.1016/j.triboint.2016.05.003. Jayaprakash M, Raman SGS. Influence of pad span on fretting fatigue behaviour of AISI 304 stainless steel. J Mater Sci 2007;42(12):4308–15. https://doi.org/10. 1007/s10853-006-0653-z. Zhou ZR, Nakazawa K, Zhu MH, Maruyama N, Kapsa Ph, Vincent L. Progress in fretting maps. Tribol Int 2006;39:1068–73. https://doi.org/10.1016/j.triboint. 2006.02.001. Gnanamoorthy R, Reddy RR. Fretting fatigue in AISI 1015 steel. Bull Mater Sci 2002;25(2):109–14. https://doi.org/10.1007/BF02706229. Qian G, Lei WS. A statistical model of fatigue failure incorporating effects of specimen size and load amplitude on fatigue life. Phil Mag 2019:1–37. https://doi.org/ 10.1080/14786435.2019.1609707. Qian G, Lei WS, Tong Z, Yu Z. A Statistical model of cleavage fracture toughness of ferritic steels DIN 22NiMoCr37 at different temperatures. Materials 2019;12(6):982. https://doi.org/10.3390/ma12060982. Qian G, Lei WS, Yu Z, Berto F. Statistical size scaling of breakage strength of irregularly-shaped particles. Theor Appl Fract Mech 2019;102:51–8. https://doi.org/ 10.1016/j.tafmec.2019.04.008. Zelin M. Microstructure evolution in pearlitic steels during wire drawing. Acta Mater 2002;50(17):4431–47. https://doi.org/10.1016/S1359-6454(02)00281-1.
Contents lists available at ScienceDirect
International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Experimental study on fretting-fatigue of bridge cable wires a,⁎
a
b
T
c
Tong Guo , Zhongxiang Liu , José Correia , Abílio M.P. de Jesus a b c
Key Laboratory of Concrete and Prestressed Concrete Structures, Ministry of Education, Southeast University, Nanjing 210096, PR China CONSTRUCT & Faculty of Engineering, University of Porto, Porto, Portugal Faculty of Engineering, University of Porto, Porto, Portugal
A R T I C LE I N FO
A B S T R A C T
Keywords: Fretting-fatigue Wear scar Fracture surface Cable wire Friction coefficient
Bridge cables are subjected to small relative sliding and high contact stresses among wires under fluctuating loads and repeated bending, eventually leading to fretting-fatigue failure. This paper presents a series of fretting fatigue tests with different fretting and fatigue parameters to investigate the tribological properties, fretting fatigue characteristics and fracture failure mechanism. Results show that the fretting-fatigue failure evolved from surface micro cracks at the trailing edges generated from a mixed slip regime. Larger fretting amplitude induced larger tangential force and coefficient of friction, and decreased life. Fretting scar depth increased as fretting-fatigue proceeded while the growth rate was declining.
1. Introduction Bridge cables that bear large axial loads with comparatively small bending and torsional stiffness have been widely used in cable-supported bridges, such as suspension bridges, cable-stayed bridges and tied-arch bridges [1]. The cables primarily consist of parallel wires, parallel strands or helical strands, as shown in Fig. 1. Essentially, bridge cables are commonly manufactured from high strength steel wires through clustering or knitting. Those wires are cold drawn high-carbon steel with a diameter ranging between 2 mm and 7 mm. Wires of bridge cables, especially those near the anchorage, are generally subjected to fluctuating loads and repeated bending [2,3], which can result into small relative sliding and high contact stresses among wires. As friction exists between wires, the relative sliding can induce fretting wear in the contact interfaces, generating cracking sources. Fretting-fatigue is a contact fatigue process triggered by cyclic relative sliding and fretting contact stress between compacted structural members, which can lead to the decrease of fatigue strength and premature fracture. Due to the interaction of cyclic internal stresses and external fretting wear, the wires are susceptive to fretting-fatigue, where tensile fatigue along the wire axis, micro-slip at the contact surface and cyclic fretting contact stresses work together. This results in the cracking of wires and a reduction of the cable bearing capacity leading, eventually, to its final fracture [4]. Moreover, such fracture can result in premature failure of suspension cables, which in extreme cases, may lead to progressive collapse of a structure. The fretting-fatigue of wires has been already discussed in several
⁎
studies. Hobbs and Raoof [5] presented a detailed discussion of the different mechanisms of inter-wire fretting-fatigue of steel cables, finding that more failures occurred in wires at quasi-punctual contact areas than in linear contact areas. The reason is that smaller contact area induces higher contact stresses. According to experimental studies, Siegert and Brevet [6] observed that fracture was concentrated in the bending plane and most of the fracture were locally originated in wear areas due to inter-wire fretting. Wang et al. [7] demonstrated that fretting can worsen the contact surfaces and accelerate the fatigue process, resulting in abrupt change of tensile stresses, cross-section reduction and high stress concentration. Additionally, Liu et al. [8] conducted a comparative study on failure of suspension cables of two similar long-span suspension bridges. The shortest suspension cables of one of the bridges were replaced by rigid central clamps; based on field measurements, notable wear between several wires in the rope of the suspension cables and its failure mechanism under repetitive traffic loading were discussed. Due to the importance of contact surface in fretting-fatigue process, the condition and mechanical characteristics of contact surfaces have been extensively studied. Nawrocki and Labrosse [9] identified that the inter-wire pivoting and sliding dominates the response of rope under the axial and bending loads. Siegert [10] analyzed the normal force and relative displacement amplitude between the contact areas in a multilayer strand. Based on experimental data, Waterhouse et al. [11] noticed that the lubrication effect provided by zinc coating can significantly alleviate the fretting-fatigue, maintaining the friction coefficient at a low value, at least during the early stages of fretting. The
Corresponding author. E-mail addresses: [email protected] (T. Guo), [email protected] (Z. Liu), [email protected] (J. Correia), [email protected] (A.M.P. de Jesus).
https://doi.org/10.1016/j.ijfatigue.2019.105321 Received 25 May 2019; Received in revised form 9 September 2019; Accepted 3 October 2019 Available online 04 October 2019 0142-1123/ © 2019 Published by Elsevier Ltd.
International Journal of Fatigue 131 (2020) 105321
T. Guo, et al.
(a) Parallel wire cable
(b) Spiral strand cable
Fig. 1. Configuration of typical bridge cables.
Fig. 2(b) presents a schematic of the aforementioned fretting-fatigue testing, where the normal force between wires (Fn) is equal to the gravity of mass blocks. The distance between the lower gripping head and the axis of the loading wire, i.e., the length of the lower wire segment, is S. Under a mean displacement (Δ0) and a displacement range (Δ), the tested wire deforms cyclically. The strain variations are obtained by two strain gauges attached on the lower and upper wire segment apart from the necking region, respectively. The relative displacement between the tested wire and loading wire can be expressed as Eq. (1a), which can be alternatively estimated by Eq. (1b). Also, the tangential force (Q) can be evaluated according to the strain difference of the upper and lower wire segment, as shown in Eq. (2).
friction phenomenon between the contact surfaces that affects the fretting-fatigue behavior of wires has been identified by reference [12], where the endurance limits of bright, galvanized and lubricated wires were experimentally determined to be about 100 MPa, 170 MPa and 250 MPa. Besides, the effects of protecting measures (i.e., lubrication and zinc coating) on reducing the friction between the fretting surfaces and corrosive environments on the fretting-fatigue were also discussed [13]. To better understand the tribological properties, fretting-fatigue characteristics and fracture failure mechanism of cable wires, this paper presents a series of fretting fatigue tests with various fretting and fatigue parameters. The fretting scar and fracture surface were checked using both optical microscopy and scanning electron microscope (SEM). Besides, the primary wear properties, i.e., tangential force and friction coefficient, under various fretting amplitudes and normal forces were discussed to understand the slip regime and wear mechanisms. Additionally, the evolution of fretting scar morphologies, including scar depth profiles and maximum scar depths, under different normal forces were quantitatively analyzed using the white light interferometer. Furthermore, the fretting fatigue lives of wires due to different displacement ranges and normal forces were used to quantitatively identify the characteristics of fretting damage. The presented study provides references to the design and maintenance of cable wires, besides lifetime prediction.
δ = ε1 S
δ = Δ· Q=
S L
1 EA (ε2 − ε1) 2
(1a) (1b) (2)
where δ is the amplitude of relative displacement between the tested wire and loading wire, i.e., fretting amplitude; ε1 and ε2 are the strain of the lower and upper wire segments, which are assumed to be uniform between the gripping head and contact surface; E is the elasticity modulus, which can be determined according to material tests; and A is the cross-section area of the wire.
2. Material and fretting fatigue testing
2.2. Tensile material properties
2.1. Test device and theory
Fundamental constituent elements of bridge cable wires were used to produce the specimens required for this study, including the tested wires and loading wires. Those steel wires are high strength low alloy steel with a diameter of 5 mm, manufactured by high-quality carbon structural steel through cold drawing. The general chemical composition of the alloy is listed in Table 1. Suitable tensile tests were designed and implemented on specimens (total length of 500 mm) to capture the mechanical properties of the studied wire. Fig. 3(a) shows the stressstrain curves of some studied wires, revealing that the elastic modulus (E) of the wire was 2.025 × 105 MPa, and the yield strength (σy), ultimate strength (σu) and elongation (δ) at fracture were 1620 MPa, 1835 MPa and 5.78%, respectively. As shown in Fig. 3(b), the wire presented slight plastic deformation prior to the fracture with a final cross section reduction of 6.25%. The tensile fracture surface in Fig. 3(b) consisted of central rough fibrous region, peripheral smooth shear lip and coarse radial region with radial marks. Fracture surface examinations show that fracture initiated in the center of the specimens [14,15]. Once the necking begun, the tri-axial stress developed in the center of the neck region promoted the nucleation and growth of microcracks. Subsequently, the cracks initially occurring in the center of the plane perpendicular to the wire axis propagated to the periphery
Fretting fatigue testing was conducted on a fatigue testing machine, where an auxiliary friction device was developed to provide external fretting wear, as shown in Fig. 2(a). The fatigue testing machine provided fatigue loads applied to the wire through the cyclic movement of gripping heads. The auxiliary friction device consists of a loading fixture, a support fixture, a pair of sliding guides, a sliding plate, a pair of cantilevers, a pair of fixed splints and mass blocks. This experimental device was used to reproduce the loading conditions of wires in a spiral strand, like the bending of suspender cable ends. Loading wires were installed at the same level on the loading and support fixture through bolts, respectively, which were made of the same wire as the tested wire. The loading fixture was placed in the sliding guides, while the support fixture was fixed on the sliding plate that can slide straight along the oblong holes on the cantilevers. Hence, under the traction of mass blocks, the two fixtures moved toward the tested wire in the middle, making the loading wires contact with the tested wire and simultaneously providing constant normal force between wires. This setup is capable of implementing fretting fatigue testing under constant normal force. 2
International Journal of Fatigue 131 (2020) 105321
T. Guo, et al.
(a) Testing device
(b) Testing theory model
Fig. 2. Fretting fatigue device and theory.
adopted in the tests, i.e., 60 N and 120 N, to consider the effect of contact stresses, which can represent approximately the contact force between strands of a rope cable. The loading frequency is fixed to 5 Hz in all tests. This loading frequency is a compromise between test duration, kinetics of fretting-fatigue and capacity of loading system, so that the tests may be as reproducible as possible. The experimental parameters are listed in Table 2. The fretting-fatigue tests were conducted in the laboratory at ambient atmosphere and room temperature, as shown in Fig. 4. Strains were recorded using a dynamic signal data acquisition unit (Model: TST-3000). To eliminate the effect of surface oil, alcohol was used to clean specimens’ surface before each test. After the tests, fretting scars and fracture surfaces of wires were observed using SEM, and the hysteresis loop, tangential force, friction coefficient (i.e., the ratio of maximum tangential force to normal force in a cycle) and lifetime were extracted for comparative analyses. Besides, the morphologies and profiles of fretting scars were measured using a white light interferometer.
Table 1 Chemical composition of the tested wires. Element
Fe
C
Si
Mn
S
P
Cr
Weight percent (%)
98.5
0.8
0.23
0.42
0.018
< 0.017
0.017
inclining at about 45° to its axis, leading to a final fracture. 2.3. Fatigue experimental procedure A displacement-based loading protocol [16,17] with a sinusoidal loading mode was applied. The basis loading protocol adopted here corresponds to the fatigue test protocol specified in the standard GB/T 17101 [18], which stipulates that the wire with qualified fatigue property should be able to resist 2 × 106 fatigue cycles under a mean stress of 0.45σu–180 MPa and a stress range of 180 MPa, respectively. According to the stress-strain curve shown in Fig. 3(a), the steel wire will remain at linear elasticity stage. Therefore, the mean displacement and displacement range of the basis loading protocol are 1.37 mm and 0.44 mm, respectively, when the length of tested wire is 500 mm, based on the Hooke's law. The fretting amplitude between the wires can be estimated according to Eq. (1b). Fretting fatigue tests of the steel wires were conducted at different displacement ranges in order to investigate the influence of the fretting amplitudes. Besides, two levels of Fn were
3. Results and discussion 3.1. Fretting scars and fracture surfaces The fretting scars of 5 mm wires were checked by optical microscopy, as shown in Fig. 5. In general, the fretting scars presented an
2000
Stress (MPa)
1500
1000
500
0
Tensile test #1 Tensile test #2
0.2% 0
1
2
3
4
5
6
Strain (%)
(a) Stress-strain curves
(b) Fracture appearance Fig. 3. Tensile test data. 3
International Journal of Fatigue 131 (2020) 105321
T. Guo, et al.
Table 2 Fatigue experimental parameters. Mean displacement, Δ0 (mm)
Displacement Range, Δ (mm)
Fretting amplitude, δ (μm)
Normal force, Fn (N)
1.37
0.44, 0.66, 0.88
220, 330, 440
60, 120
Fig. 6. Wear fragment in the early stage of the test.
another crack existed on the same scar, indicating that such fracture evolved from a surface micro crack at the trailing edge. In frettingfatigue process, the fretting wear can damage the wire surface, so that micro cracks may initiate in the wear scar, centrally around the trailing edge. During the process, some formed micro cracks may be worn off, while one of the primary cracks probably around the trailing edge, together with secondary cracks nearby, may gradually develop and finally form a macro-crack. Compared with the tested wire, the loading wire that suffered from wear without fatigue loads did not show any fracture, which is an evidence of the accelerated damage of the tested wire due to the fretting-fatigue. Fig. 7(b) presents typical fracture surfaces of the tested wire due to fretting-fatigue damage. For the first type of fracture surfaces, the crack propagated inclined to the wire axis until a sudden static break occurred due to insufficient cross-section. In another type of fracture surfaces, obvious change of the crack propagation direction was observed. This is due to that cold drawing facilitated the grain structures alignments and weak colony interfaces orienting along the wire axis [22]. The colony interfaces are prone to damage, which can lead to the cracking initiating normal to the wire axis but branching towards the axis direction.
Fig. 4. Fretting fatigue test in the laboratory.
elliptical shape with the long axis along the sliding direction especially that of the tested wire in Fig. 5(a). It is observed that the contact surface of the tested wire was composed with a deep central zone and two shallow end zones, which corresponds to the stick zone and slip zone [19]. The formation of variant scar depths was due to larger contact pressure and more wear time in the stick zone than in the slip zone. In the stick zone, detached particles and furrows along the sliding direction indicate that this fretting damage resulted from adhesive and abrasive wear. The reason for the polishing is that the wear fragments were initially generated in the adhesive wear and then acted as the third body in the abrasive wear [20]. According to Fig. 6, some wear fragments were squeezed out of the fretting scar in the early stage of the fretting-fatigue test, which can prove the existing of wear fragments. Besides, wear fragments on the contact surfaces can be oxidized generating iron oxides during the fretting-fatigue test, which can be determined by the brown-red on the contact surfaces in Fig. 5. This phenomenon has been confirmed by the results of X-ray energy spectrum analysis [7]. According to the fretting scar of the failed wire shown in Fig. 7(a), the fracture (i.e. the through cross section crack) was located at the boundary between the slip and stick zone (i.e., the trailing edge), perpendicular to the sliding direction. Large stress abrupt change at the trailing edges due to significant geometry change and comparatively serious fretting wear may be the primary reason [21]. Meanwhile,
3.2. Tangential force and friction coefficient Tangential force varies with the development of the slip regime, accusing the change in the contact condition during the fretting process [23]. A perfect hysteresis loop represents a gross slip, a less opened indicates a stick-slip and a line is characteristics of a stick regime [24]. To identify the slip regimes, dynamic response of tangential force and relative slip amplitude can be utilized. Fig. 8 shows the evolution of the
(a) Intested wire
(b) In loading wire Fig. 5. Wear scars after fretting-fatigue testing. 4
International Journal of Fatigue 131 (2020) 105321
T. Guo, et al.
(b) Fracture surfaces
(a) Cracking location
Fig. 7. Fretting-fatigue failure of the tested wire.
it. Subsequently, the contact area was enlarged due to the fretting wear, making the partial slip regime generated. As fretting wear increased, the wear scar deepened and the areas of hysteresis loops continuously decreased [25]. Meanwhile, the hysteresis loops in the test conducted at Fn = 120 N and Δ = 0.44 mm are also presented in Fig. 8. It is observed that those hysteresis loops obeyed the same evolution trend as that conducted at Fn = 120 N and Δ = 0.88 mm and the fretting developed into a mixed slip regime (i.e. stick-slip) as the test lasted, which has been confirmed
hysteresis loops, relating the tangential force and displacement, with fatigue cycles during the test conducted at Fn = 120 N and Δ = 0.88 mm. As the cycling increased, the contact condition changed from initial gross slip to stick-slip, i.e. a perfect hysteresis loop with rectangular shape changed into a less opened one. This evolution has been identified by the experimental results [7]. Regarding to the tangential force, it significantly increased initially and then gradually decreased as the fretting fatigue test proceeded. In the early stage of cycling, the contact area was small and small tangential force went with
Fig. 8. Hysteresis loops with increasing fretting cycles. 5
International Journal of Fatigue 131 (2020) 105321
T. Guo, et al.
0.8
Friction coefficient
to fretting fatigue may be the primary reason. For the tests conducted at Δ = 0.44 mm and Δ = 0.66 mm, the evolution trends of the friction coefficient were similar to that test conducted at Δ = 0.88 mm in general; however, unneglectable differences existed in the magnitudes. The reason for the phenomenon is that the increase of displacement range can inevitably result in the reduction of the stick zone, i.e., the increase of slip zone, which promoted the coefficient of friction [29]. Besides, the test conducted at Fn = 60 N and Δ = 0.88 mm had larger friction coefficients than that conducted at Fn = 120 N and Δ = 0.88 mm, as presented in Fig. 9, which is in accordance with the conclusions reported in past studies [30,31]. The reason for this phenomenon is that larger normal forces can be more effective in reducing micro convex bodies and rough peaks, thus reducing the frictional resistance between the contact surfaces. Hence, larger normal forces can result in smaller friction coefficient.
Wire fracture
0.7 0.6 0.5 0.4
Fn=120N, Δ=0.88mm
0.3
Fn=120N, Δ=0.66mm
0.2
Fn=120N, Δ=0.44mm
0.1
Fn= 60N, Δ=0.88mm
0.0
0
1x105
2x105
3x105
4x105
Number of cycles Fig. 9. Influence of displacement range and normal force on the coefficient of friction.
3.3. Fretting scar profile To identify fretting damage quantitatively, the coordinates of wear scar surfaces were measured by using a white light interferometer (Model: MicroXAM-100), which can be used to restructure the morphologies of fretting scars and then estimated the wear volumes. The white interferometer can measure the 3D topography of surfaces at the nanometer level with a vertical resolution of 0.1 nm and a scan speed of 2.1 μm/sec. Fig. 10 shows the restructured models of fretting scar morphologies during the fretting fatigue test conducted at Fn = 120 N, Δ = 0.88 mm. According to Fig. 10, fretting scar surfaces exhibited the material adhesion, plastic deformation, particle detaching and ploughing [32]. The fretting scar gradually developed into an approximate semi-ellipsoid, which is consistent with the experimental results in the reference [33]. In order to investigate the evolution of the fretting scar profile, the scar depths of the tested wire shown in Fig. 10, at distinct fatigue cycles, were obtained from their morphologies, as illustrated in Fig. 11. Those
by the reference [26]. However, the mixed slip regimes in the test conducted at Fn = 120 N and Δ = 0.44 mm developed faster, which is primarily due to smaller slip amplitude [27]. Moreover, its tangential forces were less than those conducted at Fn = 120 N and Δ = 0.88 mm. To further investigate the contact condition during the fretting process, the friction coefficient that corresponds to the ratio of maximum tangential force to normal force in a cycle was calculated, as shown in Fig. 9. At the beginning of the test conducted at Fn = 120 N and Δ = 0.88 mm, the friction coefficient is in a low level, about 0.13, which may be attributed to the initial un-rough surface of the steel wire with protective film. As the fretting effect made the contact surface rough due to detached particles and furrows [28], this coefficient rose dramatically to the maximum value about 0.65. After 1.15 × 104 cycles, it declined continuously to about 0.58 until wire fracture. Progressive material loss and crack propagation in the contact surface due
Fig. 10. Restructured wear scars of the tested wire during the fretting fatigue test. 6
International Journal of Fatigue 131 (2020) 105321
T. Guo, et al.
Fig. 11. Scar depth profiles of tested wires during fretting fatigue tests under different normal forces.
Maximum scar depth (μm)
0 -20
scar depth profiles are along the axis of the tested wire with its x-coordinates equal to zero and the z-coordinates of the original wire surface were set to be zero as a baseline. Accumulation of the wear fragment and plastic flow of the material can bring about irregular elliptical profile [34], especially in the initial state, such as the profile shown in Fig. 11(a). It is observed that the scar depth increased with cycling. Besides, these profiles show that the scar had a significant drop at the trailing edges than at any other locations. This phenomenon became more apparent as the fatigue test proceeded. Such notable changes in the scar can induce significant stress concentration at trailing edges, making it the most vulnerable zone to fracture. In addition, Fig. 11 also presents the scar depth profiles of the tested wire during the fretting fatigue test that was conducted at Fn = 60 N, Δ = 0.88 mm. It reveals that larger normal force resulted in considerably deeper surface damage. Furthermore, the maximum scar depth of the profile shown in Fig. 11 was extracted, as illustrated in Fig. 12. The maximum scar depths increase exponentially with the number of cycles, while their growth rates were declining. These characteristics of the depth growth rates were similar at both normal forces. Those reveals severe wear at the initial stage, which gradually tended to be stable. This phenomenon has an agreement with the development trend of the friction coefficient shown in Fig. 9.
18.5
-40
52.1
-60 -80
77.4
-100 -120
96.8 0
2000
4000
6000
8000
10000
12000
Number of cycles Fig. 12. Maximum scar depth of depth profiles with x = 0.
Displacement range (mm)
0.72
Fn=120Ν, Δ=0.44mm Fn=120Ν, Δ=0.66mm
0.54
Fn=120Ν, Δ=0.88mm
3.4. Fretting fatigue life
Fn= 60Ν, Δ=0.88mm
Fig. 13 illustrates the fretting fatigue lives of tested wires as the displacement range increased from 0.44 mm to 0.88 mm with the normal force equal to 120 N. The fretting fatigue lives of tested wires at Δ = 0.88 mm were ranged between 3.6 × 105 cycles and 4.2 × 105 cycles. Besides, fretting fatigue lives of tested wires at Δ = 0.66 mm were ranged between 6.8 × 105 cycles and 8.2 × 105 cycles, while those at Δ = 0.44 mm were ranged between 1.50 × 106 cycles and 1.87 × 106 cycles. It is observed that fretting fatigue life decreases
0.36 0.0
4.0x10
5
8.0x10
5
6
1.2x10
1.6x10
6
2.0x10
6
Number of cycles Fig. 13. Fretting-fatigue lives at different displacement ranges.
7
International Journal of Fatigue 131 (2020) 105321
T. Guo, et al.
Acknowledgements
rapidly with the increase of displacement range (i.e., fretting amplitude). The increase of displacement range can inevitably result in the increase of slip zone and fretting damage, which makes the partial slip significant. As the most dangerous slip regime [35], the partial slip regime can accelerate crack initiation and propagation, causing significant decrease of the fretting fatigue life. Therefore, the fretting fatigue life decreases with the increase of displacement range in a certain range [36]. In order to investigated the effect of normal force, several tests were conducted at Fn = 60 N and Δ = 0.88 mm, whose average fretting fatigue life was about 1.15 × 106 cycles. Compared with tests conducted at Fn = 120 N and Δ = 0.88 mm, it is found that larger normal force can dramatically decrease the life of wires in fretting fatigue tests [37]. Although larger normal force caused smaller friction coefficient in the fretting fatigue tests, the aggravated fretting wear of the contact surfaces leads to shorter life. The reason is that larger normal force can make more brittle material phases to detach due to continuous hardening and ploughing of the contact surface [26]. Fretting fatigue tests also show an important dispersion in terms of lifetime. The primary reason is related to the complexity of the fretting fatigue device accompanied with the classic scattering in fatigue tests. The scattering of lifetime in fatigue tests is attributed to the stochastic distribution of microdefects in material [38,39]. The crack propagation changing from the transverse to the longitudinal directions, which is due to cold drawing grain structures anisotropy facilitating weaker colony interfaces oriented along the direction of the wire axis [40,41], may also increase results dispersion. Note that the tested wires fractured in completed tests, while no visible cracking or fracture has been observed in the fretting scars of the loading wires in all these tests. Compared with the tested wire, the loading wire suffered from wear without fatigue cracks; an accelerated damage on the tested wire due to the coupled effect of fretting wear and fatigue was verified.
Support from the Natural Science Foundation of China under Grant No. 51978156 and the Scientific Research Foundation of the Graduate School of Southeast University under grant No. YBJJ1818 is gratefully acknowledged. Additionally, this work was also supported by: UID/ ECI/04708/2019 - CONSTRUCT – Instituto de I&D em Estruturas e Construções; and POCI-01-0145-FEDER-030103 FiberBridge – Fatigue strengthening and assessment of railway metallic bridges using fiberreinforced polymers funded by national funds through the FCT/MCTES (PIDDAC). References [1] Liu Z, Guo T, Huang L, Pan Z. Fatigue life evaluation on short suspenders of longspan suspension bridge with Central Clamps. J Bridge Eng 2017;22(10):04017074. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001097. [2] Kondoh M, Okuda M, Kawaguchi K, Yamazaki T. Design method of a hanger system for long-span suspension bridge. J Bridge Eng 2001;6(3):176–82. https://doi.org/ 10.1061/(ASCE)1084-0702(2001) 6:3(176). [3] Liu Z, Guo T, Hebdon MH, Zhang Z. Corrosion fatigue analysis and reliability assessment of short suspenders in suspension and arch bridges. J Perform Constr Facil 2018;32(5):04018060. https://doi.org/10.1061/(ASCE)CF.1943-5509.0001203. [4] Mouradi H, El Barkany A, El Biyaali A. Investigation on the main degradation mechanisms of steel wire ropes. J Eng Appl Sci 2016;100(6):1206–17. https://doi. org/10.3923/jeasci.2016.1206.1217. [5] Hobbs RE, Raoof M. Mechanism of fretting fatigue in steel cables. Int J Fatigue 1994;16:273–80. https://doi.org/10.1016/0142-1123(94)90341-7. [6] Siegert D, Brevet P. Fatigue of stay cables inside end fittings: high frequencies of wind induced vibrations. Bull Int Organis Study Endurance of Ropes 2005;89:43. [7] Wang D, Zhang D, Ge S. Fretting–fatigue behavior of steel wires in low cycle fatigue. Mater Des 2011;32(10):4986–93. https://doi.org/10.1016/j.matdes.2011.06.037. [8] Liu Z, Guo T, Hebdon MH, Han W. Measurement and comparative study on movements of suspenders in long-span suspension bridges. J Bridge Eng 2019;24(5):04019026. https://doi.org/10.1061/(ASCE)BE.1943-5592.0001386. [9] Nawrocki A, Labrosse M. A finite element model for simple straight wire rope strands. Comput Struct 2000;77(4):345–59. https://doi.org/10.1016/S00457949(00)00026-2. [10] Siegert D. Initiation of fretting fatigue cracks in spiral multi-layer strands. Bulletin 1999;78:27–44. [11] Waterhouse RB, McColl IR, Harris SJ, Tsujikawa T. Fretting wear of a high-strength heavily work-hardened eutectoid steel. Wear 1994;175(1–2):51–7. https://doi.org/ 10.1016/0043-1648(94)90167-8. [12] Périer V, Dieng L, Gaillet L, Fouvry S. Influence of an aqueous environment on the fretting behaviour of steel wires used in civil engineering cables. Wear 2011;271(9–10):1585–93. https://doi.org/10.1016/j.wear.2011.01.095. [13] McColl IR, Waterhouse RB, Harris SJ, Tsujikawa M. Lubricated fretting wear of a high-strength eutectoid steel rope wire. Wear 1995;185(1–2):203–12. https://doi. org/10.1016/0043-1648(95)06616-0. [14] Wei S, Wang G, Yu J, Rong Y. Competitive failure analysis on tensile fracture of laser-deposited material for martensitic stainless steel. Mater Des 2007;118:1–10. https://doi.org/10.1016/j.matdes.2017.01.014. [15] Saeidi N, Ekrami A. Comparison of mechanical properties of martensite/ferrite and bainite/ferrite dual phase 4340 steels. Mater Sci Eng A 2009;523(1–2):125–9. https://doi.org/10.1016/j.msea.2009.06.057. [16] YuanZhou Z, Ji B, Fu Z, Kainuma S, Tsukamoto S. Fatigue crack retrofitting by closing crack surface. Int J Fatigue 2019;119:229–37. https://doi.org/10.1016/j. ijfatigue.2018.10.006. [17] Fu Z, Wang Y, Ji B, Jiang F. Effects of multiaxial fatigue on typical details of orthotropic steel bridge deck. Thin-Walled Struct 2019;135:137–46. https://doi.org/ 10.1016/j.tws.2018.10.035. [18] GB/T 17101-2008, Hot-dip Galvanized Steel Wires for Bridge Cables, Standards Press of China; 2008. [19] Fouvry S, Elleuch K, Simeon G. Prediction of crack nucleation under partial slip fretting conditions. J Strain Anal Eng Des 2002;37(6):549–64. https://doi.org/10. 1243/030932402320950152. [20] Basseville S, Héripré E, Cailletaud G. Numerical simulation of the third body in fretting problems. Wear 2011;270(11–12):876–87. https://doi.org/10.1016/j. wear.2011.02.016. [21] Hojjati-Talemi R, Wahab MA. Fretting fatigue crack initiation lifetime predictor tool: using damage mechanics approach. Tribol Int 2013;60:176–86. https://doi. org/10.1016/j.triboint.2012.10.028. [22] Perier V, Dieng L, Gaillet L, Tessier C, Fouvry S. Fretting-fatigue behaviour of bridge engineering cables in a solution of sodium chloride. Wear 2009;267(1–4):308–14. https://doi.org/10.1016/j.wear.2008.12.107. [23] Ramesh R, Gnanamoorthy R. Development of a fretting wear test rig and preliminary studies for understanding the fretting wear properties of steels. Mater Des 2006;27(2):141–6. https://doi.org/10.1016/j.matdes.2004.09.017. [24] Siegfried F, Philippe K, Hassan Z, Fouvry S, Kapsa P, Zahouani H, et al. Wear analysis in fretting of hard coatings through a dissipated energy concept. Wear 1997;203:393–403. https://doi.org/10.1016/S0043-1648(96)07436-4.
4. Conclusions The present studies of the tribological properties, fretting fatigue characteristics and fracture/failure mechanisms of cable wires under different fretting parameters and fatigue parameters revealed the following findings: 1. The contact surface of the tested wire was composed with a deep central zone and two shallow end zones, due to a mixed slip regime that resulted in variant scar depths at the trailing edges of the scar and significant decrease of the fretting fatigue life. As significant stress concentration due to variant scar profile change is expected, the fretting-fatigue failure evolved from surface micro cracks at the trailing edges towards the interior of the cross-section. 2. The tangential force as well as the friction coefficient increased as the displacement range (i.e., fretting amplitude) increased, those maximum magnitudes were significantly relevant to the contact stress dependent of the normal force. 3. Fretting scar depth increased with the increase of fatigue cycles, while the growth rate of maximum scar depth was declining significantly, indicating severe wear damage at the initial stage and that subsequent stabilization of wear damage rate. Besides, larger normal force can result in considerably deeper wear damage. 4. The fretting fatigue life decreased rapidly with larger increase of the fretting amplitude in a certain range and normal force. Larger fretting amplitudes make the mixed slip regime significant in the present study, leading to increase of slip zone and fretting damage. Meanwhile, larger normal forces made brittle/hard material phases to detach due to continuous hardening and ploughing of the contact surface. In addition, the lifetime in fretting fatigue tests showed an important dispersion, which may be relate to the complexity of the fretting fatigue failure mechanisms and the fretting fatigue device accompanied with the classic scattering in fatigue tests. 8
International Journal of Fatigue 131 (2020) 105321
T. Guo, et al.
[25] Fouvry S, Kapsa P, Vincent L. Quantification of fretting damage. Wear 1996;200:186–205. https://doi.org/10.1016/S0043-1648(96)07306-1. [26] Zhang D, Shen Y, Xu L, Ge S. Fretting wear behaviors of steel wires in coal mine under different corrosive mediums. Wear 2011;271(5–6):866–74. https://doi.org/ 10.1016/j.wear.2011.03.028. [27] Yark YW, Sankara Narayanan TSN, Lee KY. Effect of fretting amplitude and frequency on the fretting corrosion behaviour of tin plated contacts. Surf Coat Technol 2006;201:2181–92. https://doi.org/10.1016/j.surfcoat.2006.03.031. [28] Zhou ZR, Vincent L. Mixed fretting regime. Wear 1995;181:531–6. https://doi.org/ 10.1016/0043-1648(95)90168-X. [29] Jin O, Mall S. Influence of contact configuration on fretting fatigue behavior of Ti–6Al–4V under independent pad displacement condition. Int J Fatigue 2002;24(12):1243–53. https://doi.org/10.1016/S0142-1123(02)00041-5. [30] McColl IR, Ding J, Leen SB. Finite element simulation and experimental validation of fretting wear. Wear 2004;256(11–12):1114–27. https://doi.org/10.1016/j.wear. 2003.07.001. [31] Chen Y, Meng F, Gong X. Interwire wear and its influence on contact behavior of wire rope strand subjected to cyclic bending load. Wear 2016;368:470–84. https:// doi.org/10.1016/j.wear.2016.10.020. [32] Velkavrh I, Ausserer F, Klien S, Voyer J, Ristow A, Brenner J, et al. The influence of temperature on friction and wear of unlubricated steel/steel contacts in different gaseous atmospheres. Tribol Int 2016;98:155–71. https://doi.org/10.1016/j. triboint.2016.02.022. [33] Cruzado A, Urchegui MA, Gómez X. Finite element modeling and experimental
[34]
[35]
[36]
[37] [38]
[39]
[40]
[41]
9
validation of fretting wear scars in thin steel wires. Wear 2012;289:26–38. https:// doi.org/10.1016/j.wear.2012.04.018. Wang D, Li X, Wang X, Zhang D, Wang D. Dynamic wear evolution and crack propagation behaviors of steel wires during fretting-fatigue. Tribol Int 2016;101:348–55. https://doi.org/10.1016/j.triboint.2016.05.003. Jayaprakash M, Raman SGS. Influence of pad span on fretting fatigue behaviour of AISI 304 stainless steel. J Mater Sci 2007;42(12):4308–15. https://doi.org/10. 1007/s10853-006-0653-z. Zhou ZR, Nakazawa K, Zhu MH, Maruyama N, Kapsa Ph, Vincent L. Progress in fretting maps. Tribol Int 2006;39:1068–73. https://doi.org/10.1016/j.triboint. 2006.02.001. Gnanamoorthy R, Reddy RR. Fretting fatigue in AISI 1015 steel. Bull Mater Sci 2002;25(2):109–14. https://doi.org/10.1007/BF02706229. Qian G, Lei WS. A statistical model of fatigue failure incorporating effects of specimen size and load amplitude on fatigue life. Phil Mag 2019:1–37. https://doi.org/ 10.1080/14786435.2019.1609707. Qian G, Lei WS, Tong Z, Yu Z. A Statistical model of cleavage fracture toughness of ferritic steels DIN 22NiMoCr37 at different temperatures. Materials 2019;12(6):982. https://doi.org/10.3390/ma12060982. Qian G, Lei WS, Yu Z, Berto F. Statistical size scaling of breakage strength of irregularly-shaped particles. Theor Appl Fract Mech 2019;102:51–8. https://doi.org/ 10.1016/j.tafmec.2019.04.008. Zelin M. Microstructure evolution in pearlitic steels during wire drawing. Acta Mater 2002;50(17):4431–47. https://doi.org/10.1016/S1359-6454(02)00281-1.