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Effects of characteristic parameters of corrosion pits on the fatigue life of the steel wires
JCSR-105879; No of Pages 10 Journal of Constructional Steel Research xxx (2019) xxx
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Journal of Constructional Steel Research
Effects of characteristic parameters of corrosion pits on the fatigue life of the steel wires Changqing Miao a,b, Rou Li b,⁎, Jie Yu b a b
Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, Southeast University, Nanjing 210096, China School of Civil Engineering, Southeast University, Nanjing 210096, China
a r t i c l e
i n f o
Article history: Received 18 September 2019 Received in revised form 18 November 2019 Accepted 25 November 2019 Available online xxxx Keywords: Corrosion pits Steel wire Fatigue life Prediction model S-N curve
a b s t r a c t To study the influence of corrosion pits on fatigue life of high-strength steel wire, 69 cable steel wires with different characteristic parameters of pits were obtained by manual prefabrication. The effects of pit depth, width, location and stress amplitude on the fatigue life of steel wires were investigated through the fatigue test. Then, the prediction model of fatigue life of steel wire with corrosion pits was established. Finally, 236 finite element models (FEM) of steel wire with corrosion pits were established by the software ANSYS and nCode designLife, and the S\\N curves of steel wires with different sizes of pit and stress ratios were also analyzed. The results showed that the fatigue life of steel wire decreased significantly when the depth of pit was in the range of 0.2– 0.6 mm, with a maximum reduction of 99.25%. The slight change of stress amplitude would result in the fatigue life by several times or even ten times. The superposition effect of pits would slightly increase the fatigue life of steel wire. In addition, when the stress ratio increased from −1 to 0.44, the S\\N curve of steel wire with 0.16 of depth-width ratio of pits would move down more than twice than that of steel wire with 0.75 of depth-width ratio of pits. For finite life design, the fatigue life of steel wire changed from high cycle fatigue to low cycle fatigue with the increase of depth-width ratio of pits. When the depth-width ratio was N1, the corresponding stress amplitude was not affected by the pit sizes under the same fatigue life. The effect of stress ratio on wide-shallow pits was greater than that on deep-narrow pits. © 2019 Elsevier Ltd. All rights reserved.
1. Introduction Modern cable-stayed bridges have been used worldwide for large span capacity, large-scale construction and beautiful radial shape [1]. Cable-stayed cables are the main structural components that transfer the weight and load of the main girder and bridge deck to the pylon. Whether they can be used normally and safely directly determines the reliability of the whole cable-stayed bridge [2–4]. However, bridges has always suffered from the alternating effects of vehicles, wind and rain during service, and at the same time due to the existence of corrosion media, it is easy to cause corrosion damage on the fatigue, thus bringing a severe test to the safe service and normal use of cablestayed bridges. Based on the external investigation of cable-stayed bridges, Stafford and Watson [5] found that nearly 200 cable-stayed bridges were facing danger due to the corrosion. It has also been proved that the corrosion played a significant role in the catastrophic collapse of both the Silver Bridge in 1967 and the Mianus River Bridge in 1983 [6]. Corrosion degradation and fatigue attenuation of cables have become one
⁎ Corresponding author. E-mail address: [email protected] (R. Li).
of the most important factors affecting the service life and seriously threatening the service safety of bridge structures. Local corrosion was the most common failure mode of metal materials. As the initial stage of corrosion, pitting corrosion had the macroscopic characteristics of acicular pinhole corrosion, which was a kind of local corrosion with great harm [7,8]. Under the fatigue load, corrosion pits would produce stress concentration, and then cause cracks to sprout quickly from corrosion pits, which was the main reason for the significant decrease of fatigue life with corrosion damage. Research showed that the fatigue life of untreated original specimens can be reduced by 40%–50% under the corrosion environment [9]. Sankaran et al. [10] studied the effect of pitting on fatigue behavior of aluminum alloy 7075-T6 by simulation and experiment. It was found that pitting corrosion decreased the fatigue lives by a factor of about 6 to 8. Chlistovsky and Heffernan [11] pointed out that the fatigue life reduction mainly depended on the formation of pits and the joint action of anodic dissolution at crack tip and oxygen embrittlement. In addition, P. Shi and Skanaran [12] used the damage tolerance method to study and predict the probabilistic fatigue life of pitting corrosion. It was found that the nucleation time of pits and the material constant of short crack propagation were the two most important factors affecting the fatigue life.
https://doi.org/10.1016/j.jcsr.2019.105879 0143-974X/© 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: C. Miao, R. Li and J. Yu, Effects of characteristic parameters of corrosion pits on the fatigue life of the steel wires, J Constr Steel Res, https://doi.org/10.1016/j.jcsr.2019.105879
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Nomenclature H L E ν Kt Sm f σ’f σm εa K′ σa ρ b⁎ W fy fu σ Sa R N ε’f c Kf n’ a γ
depth of pit clearance of pits on the same side elastic modulus poisson's ratio stress concentration factor average stress frequency fatigue strength coefficient average stress total strain cyclic strength coefficient cyclic stress amplitude notch root radius fatigue strength index considering the effect of stress gradient width of pit yield strength ultimate strength stress stress amplitude stress ratio fatigue life fatigue ductility coefficient fatigue ductility exponent fatigue notch factor cyclic strain hardening index material constants fatigue life increase coefficient
Many researches have also been performed on the fatigue properties of corroded cable steel wire. Nakamura et al. [13] confirmed the rule that the more serious the corrosion was, the shorter the fatigue life was according to the fatigue test results of artificially corroded steel wires. Suzumura et al. [14] considered that the main reason for the deterioration of fatigue properties of steel wire was corrosion pits on the surface of steel wire, which accelerated the crack initiation of fatigue damage and reduced fatigue life due to the stress concentration. Nakamura et al. [15] according to the comparison of the test results of mechanical properties between the notched steel wire and the corroded steel wire, it is considered that the sharper the notch shape was, the shorter the fatigue life of the notched steel wire was. Rusk & Hoppe [16] proposed a new method for predicting fatigue life of high strength steel wire after corrosion by using equivalent stress growth model. Sih & Tange [17] aiming at the durability of the stay cables of Runyang Bridge, the propagation mechanism of fatigue crack of the stay cables and high strength steel wires was also studied. The above fatigue testes of the corroded steel wire showed that the fatigue life of the cable steel wire was significantly related to the development and change of the corrosion pits on the surface of the steel wire [18]. Corrosion pits on the surface of steel wire would lead to brittle failure and result in decreasing fatigue life. The size parameters of corrosion pits directly determined the stress concentration factor, which directly leaded to the reduction of fatigue strength of structural member [19]. However, the overview of the state of the art showed that most of them did not consider the effect of pit size and number on the fatigue life. The relationship between fatigue life of cable steel wire and the distribution of corrosion pits had not been established. Especially for steel wire with specific type of pit distribution which was difficult to accurately study by the fatigue test, so the fatigue life cannot be predicted by the effective method. It was necessary to study the effect of pits size and shape on the fatigue life of steel wire. Therefore, 69 steel wires with corrosion pits were manually prefabricated, and the fatigue life of the steel wires was investigated
by the fatigue test. The relationships between the fatigue life of the steel wires and the depth, width, location and stress amplitude of corrosion pits were studied. On this basis, the prediction model of fatigue life of steel wire with corrosion pits was also established. Finally, a total of 236 FEMs of steel wire with corrosion pits were established by ANSYS software, and the S\\N curves of cable steel wires with different sizes of pit and stress ratios were analyzed through the expansion of the software nCode DesignLife. 2. Experiment procedure 2.1. Specimens descriptions In order to study the relationship between pit depth, width, location, stress amplitude and fatigue life of cable steel wire, 69 cable steel wires with different depths, widths and spacing of pits were obtained by cutting with precision machine tools. Then, through the fatigue tests of different stress amplitudes, the effects of pit parameters and stress state on the fatigue properties of cable steel wire were also studied. The steel wires with prefabricated pits were made of high strength steel wires commonly used in the long-span bridges. The material properties of the steel wires were shown in Table 1. According to the researches on the shape and formation process of pits [20], and considering the difficulty of processing, the pit shape was simplified to elliptical sphere. The specimens design was shown in Fig. 1. The characteristic parameters of the pits of the specimens were shown in Table 2. 2.2. Experimental setup The PLG-200 high frequency fatigue testing machine was used for the fatigue test, as shown in Fig. 2(a). The total length of the specimens was 400 mm, and the effective length of the non-clamping section was about 260 mm. The value of the R was determined based on the service condition of the cables. According to the time histories of the axial force in cables [21–23], R was set to be 0.44. In addition, to alleviate the fracture of steel wire at the clamping position caused by the stress concentration, the clamping area at both ends of steel wire was sprayed (See Fig. 2 (b)). 3. Results and discussion 3.1. Experimental results Some representative fractures of specimens were selected, shown in Fig. 3. It can be seen that the fatigue core was located in the surface of corrosion pit, and the outer side of the fatigue area was the instantaneous fracture area with obvious radiation pattern. Fig. 3 (a) showed the fatigue fracture of the steel wire without corrosion. It can be seen that the fatigue area accounted for nearly 1/2 of the total area. When corrosion pits appeared on the surface of steel wire, and the width of corrosion pits decreased gradually in Fig. 3 (b), (c) and (d), the fatigue area decreased from 1/2 to 1/3, while the area of instantaneous fault area increased, indicating that the fatigue life decreased. Under the high stress amplitude, the fatigue crack growth was insufficient. The smaller the fatigue area and the larger the instantaneous fracture area, the shorter the fatigue life, shown in Fig. 3(e) (Sa = 252 MPa); However, under the low stress amplitude, the fatigue crack growth was sufficient. The larger the fatigue area was, the smaller the instantaneous fracture area was, and the longer the fatigue life was, shown in Fig. 3 (f) (Sa = 196 MPa). Table 1 The material properties of high strength steel wires. Materials
E/GPa
fu/MPa
fy/MPa
ν
Hot-dip galvanized steel wire
205
1670
1540
0.3
Please cite this article as: C. Miao, R. Li and J. Yu, Effects of characteristic parameters of corrosion pits on the fatigue life of the steel wires, J Constr Steel Res, https://doi.org/10.1016/j.jcsr.2019.105879
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Fig. 1. Specimens descriptions.
The fatigue life of steel wires under different characteristic parameters was shown in Table 3. It can be found that the change of pit depth, width, location and stress amplitude would result in the change of fatigue life. The relationship between fatigue life and pit depth, width, location and stress amplitude was shown in Fig. 4. Fig. 4 (a) showed the relationship between fatigue life of steel wire and pit depth. As can be seen from Fig. 4 (a), the fatigue life of steel wire decreased sharply with the increase of pit depth. When the pit depth was 0.2 mm, the steel wire could still meet the performance requirements of 2 million fatigue cycles. However, when pit depth increased from 0.4 mm to 0.6 mm, the average fatigue life of steel wire decreased sharply, from about 800,000 times to about 66,000 times, with a decrease of 99.25%, indicating that pit depth of steel wire had a serious impact on the fatigue life. When the pit depth was N0.6 mm, the fatigue life of steel wire was far b100,000 times, which belonged to the low cycle fatigue. With the further increase of pit depth, when pit depth reached 1.2 mm, there was almost no fatigue life compared to the un-corrosion steel wire. Fig. 4 (b) showed the relationship between fatigue life of steel wire and pit width. It was found that fatigue life of steel wire increased with pit width. The reason was that pit width determined the stress concentration at the bottom of the pit when the pit depth remained unchanged. The larger the pit width was, the smaller the stress concentration at the bottom of the pit was. The smaller the local stress and strain at the bottom of the pit was, so the greater the fatigue life of the steel wire was. Therefore, when the pit width reached 6 mm, compared to
Table 2 The characteristic parameters of specimens. Characteristic parameters
Number Parameter value
Quantity of specimens
Constant parameters
Pit depth H/mm
H-0.2 H-0.4 H-0.6 H-0.8 H-1.0 H-1.2 W-2.0 W-3.0 W-4.0 W-5.0 W-6.0 Sa-252 Sa-224 Sa-196 Sa-182 Sa-168 L-0 L-1 L-2 L-3 L-5 L-10 L-15
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
Sa = 252 MPa Sm = 648 MPa R = 0.44 f = 80 HZ W = 5 mm
Pit width W/mm
Stress amplitude Sa (Sm)/MPa
Pit spacing L/mm
0.2 0.4 0.6 0.8 1 1.2 2 3 4 5 6 252(648) 224(576) 196(504) 182(468) 168(432) 0 1 2 3 5 10 15
Sa = 196 MPa Sm = 504 MPa R = 0.44 f = 80 HZ H = 1 mm R = 0.44 f = 80 HZ H = 1 mm W = 5 mm Sa = 196 MPa Sm = 504 MPa R = 0.44 f = 80 HZ H = 1 mm W = 5 mm
Please cite this article as: C. Miao, R. Li and J. Yu, Effects of characteristic parameters of corrosion pits on the fatigue life of the steel wires, J Constr Steel Res, https://doi.org/10.1016/j.jcsr.2019.105879
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Fig. 2. Fatigue test device.
the steel wire with 2 mm of pit width, the fatigue life increased about 90,000 times. Therefore, it can be seen that corrosion pits with smaller width had greater impact on fatigue life, which should be paid attention to. Fig. 4 (c) showed the relationship between the fatigue life of steel wire and the stress amplitude. It was found that the stress amplitude had greater influence on fatigue life of steel wire with pits than that of steel wire without pits. With the increase of stress amplitude, the fatigue life of steel wire decreased exponentially. The slight change of stress amplitude would reduce the fatigue life several times or even ten times, so the corrosion of steel wire with high stress amplitude should be paid attention to. Fig. 4 (d) showed the relationship between fatigue life of steel wire and pit spacing. It was found that the fatigue life of steel wire was slightly higher than that of steel wire with single pit when pit spacing was b6 mm. However, with the increase of pit spacing, the gap decreased gradually and tended to be equal. Therefore, pit spacing had little effect on the fatigue life of steel wire.
Table 3 The fatigue life of steel wires under different characteristic parameters. Parameters Number Fatigue life H
W
Sa
3.2. Theoretical calculation of fatigue life Based on the modified Manson-Coffin formula [24] considering average stress and stress gradient, the formula for predicting fatigue life of steel wire with pits was proposed. The expressions were as follows: 8 ( 0 ) σ f −σ m > 0 > b c > ε ð 2N Þ ¼ γ þ ε ð 2N Þ > a f > > E > > > < 2 H γ¼ > > W 2R ðL þ 1Þ > > > > > lg K t =K f > > :b ¼ b þ ≈ b þ 0:137 lg K t =K f lg2 þ 7
ð1Þ
L
H -0.2 H -0.4 H -0.6 H -0.8 H -1.0 H -1.2 W -2.0 W -3.0 W -4.0 W -5.0 W -6.0 Sa − 252 Sa − 224 Sa − 196 Sa − 182 Sa − 168 L−0 L−1 L−2 L−3 L−5 L − 10 L − 15
Fig. 3. The fracture of steel wire with corrosion pit.
Average life
N 2 million (unbroken) 1,135,258 4351 4497 391 531 827 3450 8279 49,860 89,735 391
N 2 million (unbroken) 662,517 8873 2325 1135 462 2644 5649 13,247 31,084 126,895 1135
N 2 million (unbroken) 806,983 6921 2103 960 385 3875 4479 16,982 19,360 68,725 960
N 2 million (unbroken) 868,252 6715 2975 828 459 2448 4526 12,836 33,434 95,118 828
1450
2649
3479
2526
49,860
31,084
19,360
33,434
498,260
315,084
219,360
344,234
N 2 million (unbroken) 22,659 36,587 48,565 35,628 35,841 26,547 22,356
N 2 million (unbroken) 69,834 54,684 25,427 32,451 54,623 35,894 56,421
2 million
N 2 million (unbroken) 43,990 39,287 34,244 44,657 41,707 30,668 31,487
39,478 26,589 28,742 65,894 34,658 29,564 15,684
C. Miao et al. / Journal of Constructional Steel Research xxx (2019) xxx
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5.5 lg(N) Mean of lg(N) H-Mean of lg(N)
7
5.0 4.5 lg(N)
lg(N)
6 5
4.0
4
3.5
3
3.0
2
0.2
0.4
0.6
0.8
1.0
H/mm
2.5
1.2
lg(N) Mean of lg(N) W-mean of lg(N)
2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 W/mm
˄a˅H-lg(N) 9 8
˄b˅W-lg(N) 6.0
The fatigue life of non-corroded steel wire with different stress amplitude is more than 2 million times.
Single pit
5
lg(N)
lg(N)
5.0
lg(N) Mean of lg(N) Sa-Mean of lg(N)
6
4.5 4.0
W=5, H=1 3.5
3 2 160
lg(N) Mean of lg(N) L-Mean of lg(N)
5.5
7
4
5
180
200 220 Sa/MPa
240
260
˄c˅Sa-lg(N)
3.0 -2
0
2
4
6
8 10 L/mm
12
14
16
˄d˅L-lg(N)
Fig. 4. The relationship between fatigue life and pit characteristic parameters.
where, σ'f is the fatigue strength coefficient, ε'f is the fatigue continuity coefficient, b⁎ is the fatigue strength index considering the effect of stress gradient, and γ is the correction factor of fatigue life of steel wire with corrosion pits. c is the fatigue ductility index, N is the fatigue life, σm is the average stress, E is the elastic modulus, εa is the total strain, Kt is the stress concentration factor, and Kf is the fatigue notch factor. The value εa was determined by the approximate expression of the steady-state cyclic stress-strain curve:
εa ¼
1 σa σa n þ 0 E K
0
ð2Þ
where, K' is the cyclic strength coefficient, n' is the cyclic strain hardening index and σa is the cyclic stress amplitude. The fatigue notch coefficient Kf was calculated according to Peterson's formula.
Kf ¼ 1 þ
K t −1 1 þ a=ρ
4. Parameter analysis of fatigue life 4.1. Finite element model Taking the pit size W = 5 mm, H = 0.8 mm as an example, the finite element model was established by ANSYS according to the size in Fig. 1 (a). The mesh size was 0.2 mm, and the element type was SOLID45, which was meshed freely. The modulus of elasticity was 205 MPa, Poisson's ratio was 0.3, and the density was 7.850 g/cm3. The loading mode of the model was constrained at one end and applied with axial load at the other end. The finite element results were shown in Fig. 6 (a). Then the analysis results (.RST file) obtained by ANSYS were imported into the FE Input module of software nCode DesignLife, shown in Fig. 6 (b). In the S\\N analysis module, the maximum ratio of load was set to 900 and the minimum ratio of load was set to 0.44. Material properties of the steel wire were based on the fatigue performance curve of 1670 MPa steel wire, as shown in Fig. 6 (c). The final calculation results of the fatigue life were shown in Fig. 6 (d).
ð3Þ
where, a is a material constant, which is related to the tensile strength of the material. For the steel wire with strength grade 1670 MPa, a is 0.043 mm and ρ is the radius of the notch root. The comparison between the fatigue life of test result and the modified theoretical result was shown in Fig. 5. It can be concluded that the modified fatigue life of the steel wire with corrosion pits was closer to the test result than that of unmodified calculation result, and the maximum accuracy can be increased by about 10%. Therefore, the modified formula obviously improved the prediction accuracy of fatigue life of steel wire with corrosion pits.
4.2. Analysis result The results of fatigue life and stress distribution of steel wire were shown in Fig. 7. As can be seen from Fig. 7 (a), the fatigue life of the pits was obviously lower than that of other parts. The dangerous area was concentrated at the bottom of the pits and distributed in strips perpendicular to the tensile direction. The minimum life of the pits was only 2836 times. From Fig. 7 (b), it can be seen that the stress at the pit was obviously higher than that at other parts, in which the dangerous areas were concentrated at the bottom of the pit and distributed in strips perpendicular to the tensile direction, with the maximum stress of 3.266 MPa. In summary, the stress at the bottom of the pit
Please cite this article as: C. Miao, R. Li and J. Yu, Effects of characteristic parameters of corrosion pits on the fatigue life of the steel wires, J Constr Steel Res, https://doi.org/10.1016/j.jcsr.2019.105879
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6.0
1.13%
4.0
3.81% 4.0
1.78%
3.5
4.77%
9.5%
3.0
3.5
2.54%
6.29%
2.5 2.0
3.18
4.5
4.5
lg(N)
lg(N)
5.0
Experiment Manson-Coffin Modified formula
5.0
Experiment Manson-Coffin Modified formula
5.5
3.71% 0.4
0.6
0.8
H/mm
1.0
4.73% 1.2
3.0
6.0
2
3
4
5
W/mm
6
6.0 Experiment Manson-Coffin Modified formula
3.68%
5.5
Experiment Manson-Coffin Modified formula
5.5
5.0
5.0
3.69%
lg(N)
lg(N)
4.5 4.0 3.5
3.81%
3.0
3.88% 1.32%
4.5
0.64%
1.96% 0.96%
0.36%
0.25%
4.0 3.5
3.92%
2.5 180
190
200
210
220
Sa/MPa
230
240
250
260
3.0 -2
0
2
4
6
8
L/mm
10
12
14
16
Fig. 5. The comparison between the fatigue life of test result and the modified theoretical result.
was the largest and the fatigue life was the lowest, indicating that fatigue cracks first formed at the bottom of the pit. The fatigue life and stress from bottom to edge of pit along the length of steel wire were shown in Fig. 8. It can be found that from the bottom to the edge of the pit, the fatigue life increased and the stress decreased.
Both of them were axisymmetrical along the bottom of the pits. Secondly, the stress near the bottom of the pit varied greatly, while the fatigue life remained basically unchanged (See the shadow part in the Fig. 8). With the distance increasing, the stress decreased linearly and the fatigue life increased exponentially.
Fig. 6. Analysis process of fatigue life of steel wire with corrosion pits.
Please cite this article as: C. Miao, R. Li and J. Yu, Effects of characteristic parameters of corrosion pits on the fatigue life of the steel wires, J Constr Steel Res, https://doi.org/10.1016/j.jcsr.2019.105879
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Fig. 7. The results of fatigue life and stress distribution.
4.3. Verification of finite element model The comparisons of test results, theoretical calculation results and finite element results of fatigue life of some specimens were shown in Table 4 and Fig. 9. It can be seen that the ratios of test, formula and finite element results were approximately 1, and the maximum error was only 6%, which verified the correctness of the finite element model. The fatigue life of steel wire with corrosion pits can be predicted accurately by the finite element model and the calculation theory of fatigue life established in this paper.
4.4. Parameter analysis
Table 4 The comparison of test, theoretical and finite element result.
Previous experimental studies have found that the main factors affecting the fatigue life of steel wire with pits were the width and depth of corrosion pits. Therefore, in order to obtain the S\\N curves of steel wires with different sizes of pits and the effects of stress ratio on the S\\N curves of steel wires with pits, 236 finite element models were established by the finite element software for more comprehensive extension analysis of fatigue life.
6x105
Number
Test/time
Theoretical/time
FEA/time
FEA-Test Test
FEA-Theoretical Theoretical
H-0.8 H-1.0 H-1.2 W-2.0 W-3.0 W-4.0
2975 828 459 2448 4526 12,836
2686 770.9 438.29 2532 4413 12,578
2836 823.6 434.4 2398 4432 12,732
4.8% 0.5% 5.4% 2.0% 2.1% 0.8%
5.6% 6.8% 0.9% 5.3% 0.4% 1.2%
3.5 Fatigue Life Stress
3.0 2.5
4x105
σ/MPa
N/times
2.0
3x105
1.5
2x105
1.0
1x105
0.5
0
0.0 Edge of pit
Bottom of pit
Edge of pit
Different parts of pits along the length of steel wire Fig. 8. The fatigue life and stress from bottom to edge of pit along the length of steel wire.
14000 Test Theoretical FEA
12000 10000
N/times
5x105
4.4.1. Different pit sizes The S\\N curves of steel wires with different sizes of pits were shown in Fig. 10. Fig. 10 (a) showed that with the increase of pit depth, the S\\N curve moved downward as a whole, indicating that the fatigue life of steel wire decreased gradually with the pit depth. When the pit depth was b1.2 mm, the S\\N curve decreased slightly. While the pit depth was N1.2 mm, the S\\N curve decreased sharply. Therefore, when the pit depth was within 1.2 mm, the pit depth had little effect on the S\\N curve. In addition, the fatigue life decreased with the increase of pit depth under the same stress amplitude. For example, when the stress amplitude was equal to 95 MPa, the fatigue life
8000 6000 4000 2000 0
H-0.8
H-1.0
H-1.2 W-2.0 Specimens
W-3.0
W-4.0
Fig. 9. The comparison of test, theoretical and finite element result.
Please cite this article as: C. Miao, R. Li and J. Yu, Effects of characteristic parameters of corrosion pits on the fatigue life of the steel wires, J Constr Steel Res, https://doi.org/10.1016/j.jcsr.2019.105879
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350 300
160 140
250
120
200
100 80
R=0.44 W=5 mm
100
W=2.5 W=2.0 W=1.5 W=1.0 W=0.5
60
H=0.8 H=1.0 H=1.2 H=1.5 H=2.0
50 0 10
H=1.5 mm R=0.44
Sa/MPa
Sa/MPa
150
40
101
102
103 N/times
104
105
106
100
101
(a) Pit depth
102
103
N/times
104
105
106
(b) Pit width
Fig. 10. The S\ \N curves of steel wires with different pit sizes.
decreased by 99%, and the fatigue life changed from high cycle fatigue to low cycle fatigue (The high cycle fatigue was N104 times). Therefore, for the design of finite fatigue life, the effect of pit depth was particularly important. For larger depth pits, brittle fracture even occurred under higher stress amplitude. Fig. 10 (b) showed the S\\N curve of steel wire with different pit widths. As can be seen from Fig. 10 (b), with the pit width decreased, the S\\N curve moved downward as a whole, and the decreasing range was basically unchanged. Under the same stress amplitude, the fatigue life decreased with the decrease of pit width. For example, when the stress amplitude was 88 MPa, the fatigue life of steel wires decreased by 94%, and changed from high cycle fatigue to low cycle fatigue. Through the S\\N curve of steel wire with different depths and widths of pits, it can be found that the fatigue life of steel wire decreased with the increase of pit depth and the decrease of pit width. Therefore, in order to obtain the effect of pit shape on the fatigue life of steel wire, the relationship of pit depth-width ratio and fatigue life was established, as shown in Fig. 11. It can be found that on the same fatigue life curve (N = 103, 104, 105, 106), with the increase of pit depth-width ratio (i.e. the pit shape changed from the wide-shallow to the deepnarrow), the corresponding stress amplitude gradually decreased, especially in the range of 0 to 0.5. While N1, it tended to be flat and converged to a certain value. Therefore, when the pit depth-width ratio was N1, under the same fatigue life, the required stress amplitude had nothing to do with the pit sizes. In addition, the fatigue life decreased gradually with the increase of depth-width ratio of pit at the same stress amplitude of 110 MPa (See Fig. 11), and the fatigue life decreased from 106 times to 103 times. When the depth-width ratio of pit was 1.5, the stress amplitude increased from 45 MPa to 105 MPa, and the fatigue life decreased from 106 times to 103 times, but the fatigue life of the smooth steel wire
was all N106 with the same change of stress amplitude, which indicated that pit depth-width ratio was an important factor affecting the fatigue life of steel wire.
4.4.2. Different stress ratios Taking the steel wire with depth-width ratio of 0.16 (wide-shallow) and 0.75 (deep-narrow) as examples, the S\\N curves of steel wire under stress ratios of R = −1, 0 and 0.44 were obtained, shown in Fig. 12. It can be seen that under the same pit size, the S\\N curve of steel wire decreased with the stress ratio increased. Therefore, the greater the stress ratio, the more significant the effect of pit on the fatigue life was. When the stress ratio increased from −1 to 0.44, the S\\N curve of steel wire with depth-width ratio of 0.16 would move down more than twice the depth-width ratio of 0.75, which indicated that the influence of wide-shallow pits on the fatigue life was more obvious. In order to more intuitively reflect the relationship between fatigue life, stress ratio, stress amplitude and pit size, taking the steel wire with pit depth-width ratio of 0.16 as an example, the S-N-R diagram of steel wire was obtained according to the S\\N curves of steel wire with different stress ratios. The specific method was shown in Fig. 13. From Fig. 13 (b), it can be found that with the increase of stress ratio, the stress amplitude corresponding to the same fatigue life was smaller. In addition, with the increase of fatigue life, the relationship between stress amplitude and stress ratio became smoother, which indicated that the low cycle fatigue of steel wire with corrosion pits was more sensitive than the high cycle fatigue.
H/W=0.16
1000 300
R= -1 (H/W=0.16) R=0 (H/W=0.16) R=0.44(H/W=0.16) R= -1 (H/W=0.75) R=0 (H/W=0.75) R=0.44 (H/W=0.75)
1200
0.7 0.6
800
Deep and Narrow N=103
N=104
N=10
N=10
(a) Sa=110MPa
150
(b) H/W=1.5
100 50
0.1 100
6
1.0
1.5 H/W
N=103 N=104 N=105
2.0
101
102
103
104
N/times (a) Sa=110MPa
105
106
100
2.5
3.0
H/W=0.16 H/W=0.75
400
110 100 90 80 70 60 50 40
N=10
0.5
600
0.2
6
0.0
0.3
H/W=0.16 H/W=0.75
200
sa/MPa
Sa/MPa
5
0.4
Sa/MPa
Shallow and Wide
200
H/W
0.5
250
H/W=0.75 101
102
103
104
N/times
(b) H/W=1.5
Fig. 11. The relationship of fatigue life and the depth-width ratio of pits.
105
106
0 100
101
102
103
N/times
104
105
106
Fig. 12. The S\ \N curves of steel wire under different stress ratios.
Please cite this article as: C. Miao, R. Li and J. Yu, Effects of characteristic parameters of corrosion pits on the fatigue life of the steel wires, J Constr Steel Res, https://doi.org/10.1016/j.jcsr.2019.105879
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Sa/MPa Sa/MPa
1200
N=103 N=106
1000
1000
R=-1 R=0 R=0.44
800 600
600
400
400
200
200
0 0 10
101
N=103
800
102
103
104
(a) S-N
105
106
N/times
N=106
0 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
(b) S-N-R
R
Fig. 13. The S-N-R curves of the steel wires.
H/W=0.16, N=103 H/W=0.75, N=103 H/W=0.16, N=106 H/W=0.75, N=106
1000 800
Sa/MPa
600 400 200 0 -1.0
-0.8
-0.6
-0.4
-0.2
R
0.0
0.2
0.4
0.6
Fig. 14. The S-N-R curves of pits with different depth to width ratios.
The S-N-R curves of steel wire with different depth to width ratios of pits were shown in Fig. 14. It can be seen that under the same fatigue life, the S-N-R curves of steel wires with larger depth-width ratio of pit were all located below the steel wires with smaller depth-width ratio of pit, indicating that the larger depth-width ratio of pit was, the smaller the stress amplitude was under the same stress ratio. Therefore, under the same load, the steel wire with larger depth-width ratio had shorter fatigue life. In addition, under the same fatigue life, the S-N-R curve of steel wire with larger pit depth and width was smoother, indicating that the change rate of stress ratio and stress amplitude was related to depth-width ratio of pit under the same fatigue life.
increase of stress amplitude, the fatigue life of steel wire decreased exponentially. In addition, the study of pit spacing showed that the superposition effect of pits can slightly improve the fatigue life of steel wire. (3) The modified fatigue life of the steel wire with corrosion pits was closer to the test result than that of unmodified calculation result, and the maximum accuracy can be increased by about 10%. The modified formula obviously improved the prediction accuracy of fatigue life of steel wire with corrosion pits. (4) With the increase of pit depth, the S\\N curve moved downward as a whole, indicating that the fatigue life of steel wire decreased gradually with the pit depth. For the design of finite fatigue life, the effect of pit depth was particularly important. For larger depth pits, brittle fracture even occurred under higher stress amplitude. Corrosion pits with larger depth to width ratio had greater impact on fatigue life of the steel wire, which should be paid attention to. When the depth to width ratio of pit was N1, under the same fatigue life, the required stress amplitude had nothing to do with the pit size. (5) The greater the stress ratio, the more significant the effect of pit on the fatigue life was. When the stress ratio increased from - 1 to 0.44, the S\\N curve of steel wire with depth-width ratio of 0.16 would move down more than twice the depth-width ratio of 0.75, which indicated that the influence of wide-shallow pits on fatigue life was more obvious. In addition, under the same fatigue life, the S-N-R curve of steel wire with larger depth and width of pit was smoother, indicating that the change of stress ratio and stress amplitude was related to depth-width ratio of pit.
5. Conclusion
Declaration of Competing Interest
In this paper, 69 cable steel wires with different characteristic parameters of pit were obtained by manual prefabrication. The effects of pit depth, width, location and stress amplitude on the fatigue life of cable steel wires were discussed through the fatigue test. Then, the fatigue life prediction model of cable steel wire with corrosion pits was established. Finally, 236 steel wire models with corrosion pits were established by the software ANSYS and nCode designLife, and the S\\N curves of cable steel wires with different sizes of pit and stress ratios were analyzed and compared. The main conclusions were as follows:
The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Acknowledgments The financial support provided by National Natural Science Foundation of China under Grant Nos. NSFC-51078080. The supports were highly acknowledged. The authors also would like to express gratitude to the viewers for their comments. References
(1) When pit depth increased from 0.4 mm to 0.6 mm, the fatigue life of steel wire decreased by 99.25%. When the width of pit increased from 2 mm to 6 mm, the fatigue life of the steel wire increased by 97.42%. The fatigue life of steel wire decreased with the increase of pit depth and the decrease of pit width. (2) The stress amplitude had greater influence on fatigue life of steel wire with pits than that of steel wire without pits. With the
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Contents lists available at ScienceDirect
Journal of Constructional Steel Research
Effects of characteristic parameters of corrosion pits on the fatigue life of the steel wires Changqing Miao a,b, Rou Li b,⁎, Jie Yu b a b
Key Laboratory of Concrete and Prestressed Concrete Structures of Ministry of Education, Southeast University, Nanjing 210096, China School of Civil Engineering, Southeast University, Nanjing 210096, China
a r t i c l e
i n f o
Article history: Received 18 September 2019 Received in revised form 18 November 2019 Accepted 25 November 2019 Available online xxxx Keywords: Corrosion pits Steel wire Fatigue life Prediction model S-N curve
a b s t r a c t To study the influence of corrosion pits on fatigue life of high-strength steel wire, 69 cable steel wires with different characteristic parameters of pits were obtained by manual prefabrication. The effects of pit depth, width, location and stress amplitude on the fatigue life of steel wires were investigated through the fatigue test. Then, the prediction model of fatigue life of steel wire with corrosion pits was established. Finally, 236 finite element models (FEM) of steel wire with corrosion pits were established by the software ANSYS and nCode designLife, and the S\\N curves of steel wires with different sizes of pit and stress ratios were also analyzed. The results showed that the fatigue life of steel wire decreased significantly when the depth of pit was in the range of 0.2– 0.6 mm, with a maximum reduction of 99.25%. The slight change of stress amplitude would result in the fatigue life by several times or even ten times. The superposition effect of pits would slightly increase the fatigue life of steel wire. In addition, when the stress ratio increased from −1 to 0.44, the S\\N curve of steel wire with 0.16 of depth-width ratio of pits would move down more than twice than that of steel wire with 0.75 of depth-width ratio of pits. For finite life design, the fatigue life of steel wire changed from high cycle fatigue to low cycle fatigue with the increase of depth-width ratio of pits. When the depth-width ratio was N1, the corresponding stress amplitude was not affected by the pit sizes under the same fatigue life. The effect of stress ratio on wide-shallow pits was greater than that on deep-narrow pits. © 2019 Elsevier Ltd. All rights reserved.
1. Introduction Modern cable-stayed bridges have been used worldwide for large span capacity, large-scale construction and beautiful radial shape [1]. Cable-stayed cables are the main structural components that transfer the weight and load of the main girder and bridge deck to the pylon. Whether they can be used normally and safely directly determines the reliability of the whole cable-stayed bridge [2–4]. However, bridges has always suffered from the alternating effects of vehicles, wind and rain during service, and at the same time due to the existence of corrosion media, it is easy to cause corrosion damage on the fatigue, thus bringing a severe test to the safe service and normal use of cablestayed bridges. Based on the external investigation of cable-stayed bridges, Stafford and Watson [5] found that nearly 200 cable-stayed bridges were facing danger due to the corrosion. It has also been proved that the corrosion played a significant role in the catastrophic collapse of both the Silver Bridge in 1967 and the Mianus River Bridge in 1983 [6]. Corrosion degradation and fatigue attenuation of cables have become one
⁎ Corresponding author. E-mail address: [email protected] (R. Li).
of the most important factors affecting the service life and seriously threatening the service safety of bridge structures. Local corrosion was the most common failure mode of metal materials. As the initial stage of corrosion, pitting corrosion had the macroscopic characteristics of acicular pinhole corrosion, which was a kind of local corrosion with great harm [7,8]. Under the fatigue load, corrosion pits would produce stress concentration, and then cause cracks to sprout quickly from corrosion pits, which was the main reason for the significant decrease of fatigue life with corrosion damage. Research showed that the fatigue life of untreated original specimens can be reduced by 40%–50% under the corrosion environment [9]. Sankaran et al. [10] studied the effect of pitting on fatigue behavior of aluminum alloy 7075-T6 by simulation and experiment. It was found that pitting corrosion decreased the fatigue lives by a factor of about 6 to 8. Chlistovsky and Heffernan [11] pointed out that the fatigue life reduction mainly depended on the formation of pits and the joint action of anodic dissolution at crack tip and oxygen embrittlement. In addition, P. Shi and Skanaran [12] used the damage tolerance method to study and predict the probabilistic fatigue life of pitting corrosion. It was found that the nucleation time of pits and the material constant of short crack propagation were the two most important factors affecting the fatigue life.
https://doi.org/10.1016/j.jcsr.2019.105879 0143-974X/© 2019 Elsevier Ltd. All rights reserved.
Please cite this article as: C. Miao, R. Li and J. Yu, Effects of characteristic parameters of corrosion pits on the fatigue life of the steel wires, J Constr Steel Res, https://doi.org/10.1016/j.jcsr.2019.105879
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Nomenclature H L E ν Kt Sm f σ’f σm εa K′ σa ρ b⁎ W fy fu σ Sa R N ε’f c Kf n’ a γ
depth of pit clearance of pits on the same side elastic modulus poisson's ratio stress concentration factor average stress frequency fatigue strength coefficient average stress total strain cyclic strength coefficient cyclic stress amplitude notch root radius fatigue strength index considering the effect of stress gradient width of pit yield strength ultimate strength stress stress amplitude stress ratio fatigue life fatigue ductility coefficient fatigue ductility exponent fatigue notch factor cyclic strain hardening index material constants fatigue life increase coefficient
Many researches have also been performed on the fatigue properties of corroded cable steel wire. Nakamura et al. [13] confirmed the rule that the more serious the corrosion was, the shorter the fatigue life was according to the fatigue test results of artificially corroded steel wires. Suzumura et al. [14] considered that the main reason for the deterioration of fatigue properties of steel wire was corrosion pits on the surface of steel wire, which accelerated the crack initiation of fatigue damage and reduced fatigue life due to the stress concentration. Nakamura et al. [15] according to the comparison of the test results of mechanical properties between the notched steel wire and the corroded steel wire, it is considered that the sharper the notch shape was, the shorter the fatigue life of the notched steel wire was. Rusk & Hoppe [16] proposed a new method for predicting fatigue life of high strength steel wire after corrosion by using equivalent stress growth model. Sih & Tange [17] aiming at the durability of the stay cables of Runyang Bridge, the propagation mechanism of fatigue crack of the stay cables and high strength steel wires was also studied. The above fatigue testes of the corroded steel wire showed that the fatigue life of the cable steel wire was significantly related to the development and change of the corrosion pits on the surface of the steel wire [18]. Corrosion pits on the surface of steel wire would lead to brittle failure and result in decreasing fatigue life. The size parameters of corrosion pits directly determined the stress concentration factor, which directly leaded to the reduction of fatigue strength of structural member [19]. However, the overview of the state of the art showed that most of them did not consider the effect of pit size and number on the fatigue life. The relationship between fatigue life of cable steel wire and the distribution of corrosion pits had not been established. Especially for steel wire with specific type of pit distribution which was difficult to accurately study by the fatigue test, so the fatigue life cannot be predicted by the effective method. It was necessary to study the effect of pits size and shape on the fatigue life of steel wire. Therefore, 69 steel wires with corrosion pits were manually prefabricated, and the fatigue life of the steel wires was investigated
by the fatigue test. The relationships between the fatigue life of the steel wires and the depth, width, location and stress amplitude of corrosion pits were studied. On this basis, the prediction model of fatigue life of steel wire with corrosion pits was also established. Finally, a total of 236 FEMs of steel wire with corrosion pits were established by ANSYS software, and the S\\N curves of cable steel wires with different sizes of pit and stress ratios were analyzed through the expansion of the software nCode DesignLife. 2. Experiment procedure 2.1. Specimens descriptions In order to study the relationship between pit depth, width, location, stress amplitude and fatigue life of cable steel wire, 69 cable steel wires with different depths, widths and spacing of pits were obtained by cutting with precision machine tools. Then, through the fatigue tests of different stress amplitudes, the effects of pit parameters and stress state on the fatigue properties of cable steel wire were also studied. The steel wires with prefabricated pits were made of high strength steel wires commonly used in the long-span bridges. The material properties of the steel wires were shown in Table 1. According to the researches on the shape and formation process of pits [20], and considering the difficulty of processing, the pit shape was simplified to elliptical sphere. The specimens design was shown in Fig. 1. The characteristic parameters of the pits of the specimens were shown in Table 2. 2.2. Experimental setup The PLG-200 high frequency fatigue testing machine was used for the fatigue test, as shown in Fig. 2(a). The total length of the specimens was 400 mm, and the effective length of the non-clamping section was about 260 mm. The value of the R was determined based on the service condition of the cables. According to the time histories of the axial force in cables [21–23], R was set to be 0.44. In addition, to alleviate the fracture of steel wire at the clamping position caused by the stress concentration, the clamping area at both ends of steel wire was sprayed (See Fig. 2 (b)). 3. Results and discussion 3.1. Experimental results Some representative fractures of specimens were selected, shown in Fig. 3. It can be seen that the fatigue core was located in the surface of corrosion pit, and the outer side of the fatigue area was the instantaneous fracture area with obvious radiation pattern. Fig. 3 (a) showed the fatigue fracture of the steel wire without corrosion. It can be seen that the fatigue area accounted for nearly 1/2 of the total area. When corrosion pits appeared on the surface of steel wire, and the width of corrosion pits decreased gradually in Fig. 3 (b), (c) and (d), the fatigue area decreased from 1/2 to 1/3, while the area of instantaneous fault area increased, indicating that the fatigue life decreased. Under the high stress amplitude, the fatigue crack growth was insufficient. The smaller the fatigue area and the larger the instantaneous fracture area, the shorter the fatigue life, shown in Fig. 3(e) (Sa = 252 MPa); However, under the low stress amplitude, the fatigue crack growth was sufficient. The larger the fatigue area was, the smaller the instantaneous fracture area was, and the longer the fatigue life was, shown in Fig. 3 (f) (Sa = 196 MPa). Table 1 The material properties of high strength steel wires. Materials
E/GPa
fu/MPa
fy/MPa
ν
Hot-dip galvanized steel wire
205
1670
1540
0.3
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Fig. 1. Specimens descriptions.
The fatigue life of steel wires under different characteristic parameters was shown in Table 3. It can be found that the change of pit depth, width, location and stress amplitude would result in the change of fatigue life. The relationship between fatigue life and pit depth, width, location and stress amplitude was shown in Fig. 4. Fig. 4 (a) showed the relationship between fatigue life of steel wire and pit depth. As can be seen from Fig. 4 (a), the fatigue life of steel wire decreased sharply with the increase of pit depth. When the pit depth was 0.2 mm, the steel wire could still meet the performance requirements of 2 million fatigue cycles. However, when pit depth increased from 0.4 mm to 0.6 mm, the average fatigue life of steel wire decreased sharply, from about 800,000 times to about 66,000 times, with a decrease of 99.25%, indicating that pit depth of steel wire had a serious impact on the fatigue life. When the pit depth was N0.6 mm, the fatigue life of steel wire was far b100,000 times, which belonged to the low cycle fatigue. With the further increase of pit depth, when pit depth reached 1.2 mm, there was almost no fatigue life compared to the un-corrosion steel wire. Fig. 4 (b) showed the relationship between fatigue life of steel wire and pit width. It was found that fatigue life of steel wire increased with pit width. The reason was that pit width determined the stress concentration at the bottom of the pit when the pit depth remained unchanged. The larger the pit width was, the smaller the stress concentration at the bottom of the pit was. The smaller the local stress and strain at the bottom of the pit was, so the greater the fatigue life of the steel wire was. Therefore, when the pit width reached 6 mm, compared to
Table 2 The characteristic parameters of specimens. Characteristic parameters
Number Parameter value
Quantity of specimens
Constant parameters
Pit depth H/mm
H-0.2 H-0.4 H-0.6 H-0.8 H-1.0 H-1.2 W-2.0 W-3.0 W-4.0 W-5.0 W-6.0 Sa-252 Sa-224 Sa-196 Sa-182 Sa-168 L-0 L-1 L-2 L-3 L-5 L-10 L-15
3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3 3
Sa = 252 MPa Sm = 648 MPa R = 0.44 f = 80 HZ W = 5 mm
Pit width W/mm
Stress amplitude Sa (Sm)/MPa
Pit spacing L/mm
0.2 0.4 0.6 0.8 1 1.2 2 3 4 5 6 252(648) 224(576) 196(504) 182(468) 168(432) 0 1 2 3 5 10 15
Sa = 196 MPa Sm = 504 MPa R = 0.44 f = 80 HZ H = 1 mm R = 0.44 f = 80 HZ H = 1 mm W = 5 mm Sa = 196 MPa Sm = 504 MPa R = 0.44 f = 80 HZ H = 1 mm W = 5 mm
Please cite this article as: C. Miao, R. Li and J. Yu, Effects of characteristic parameters of corrosion pits on the fatigue life of the steel wires, J Constr Steel Res, https://doi.org/10.1016/j.jcsr.2019.105879
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Fig. 2. Fatigue test device.
the steel wire with 2 mm of pit width, the fatigue life increased about 90,000 times. Therefore, it can be seen that corrosion pits with smaller width had greater impact on fatigue life, which should be paid attention to. Fig. 4 (c) showed the relationship between the fatigue life of steel wire and the stress amplitude. It was found that the stress amplitude had greater influence on fatigue life of steel wire with pits than that of steel wire without pits. With the increase of stress amplitude, the fatigue life of steel wire decreased exponentially. The slight change of stress amplitude would reduce the fatigue life several times or even ten times, so the corrosion of steel wire with high stress amplitude should be paid attention to. Fig. 4 (d) showed the relationship between fatigue life of steel wire and pit spacing. It was found that the fatigue life of steel wire was slightly higher than that of steel wire with single pit when pit spacing was b6 mm. However, with the increase of pit spacing, the gap decreased gradually and tended to be equal. Therefore, pit spacing had little effect on the fatigue life of steel wire.
Table 3 The fatigue life of steel wires under different characteristic parameters. Parameters Number Fatigue life H
W
Sa
3.2. Theoretical calculation of fatigue life Based on the modified Manson-Coffin formula [24] considering average stress and stress gradient, the formula for predicting fatigue life of steel wire with pits was proposed. The expressions were as follows: 8 ( 0 ) σ f −σ m > 0 > b c > ε ð 2N Þ ¼ γ þ ε ð 2N Þ > a f > > E > > > < 2 H γ¼ > > W 2R ðL þ 1Þ > > > > > lg K t =K f > > :b ¼ b þ ≈ b þ 0:137 lg K t =K f lg2 þ 7
ð1Þ
L
H -0.2 H -0.4 H -0.6 H -0.8 H -1.0 H -1.2 W -2.0 W -3.0 W -4.0 W -5.0 W -6.0 Sa − 252 Sa − 224 Sa − 196 Sa − 182 Sa − 168 L−0 L−1 L−2 L−3 L−5 L − 10 L − 15
Fig. 3. The fracture of steel wire with corrosion pit.
Average life
N 2 million (unbroken) 1,135,258 4351 4497 391 531 827 3450 8279 49,860 89,735 391
N 2 million (unbroken) 662,517 8873 2325 1135 462 2644 5649 13,247 31,084 126,895 1135
N 2 million (unbroken) 806,983 6921 2103 960 385 3875 4479 16,982 19,360 68,725 960
N 2 million (unbroken) 868,252 6715 2975 828 459 2448 4526 12,836 33,434 95,118 828
1450
2649
3479
2526
49,860
31,084
19,360
33,434
498,260
315,084
219,360
344,234
N 2 million (unbroken) 22,659 36,587 48,565 35,628 35,841 26,547 22,356
N 2 million (unbroken) 69,834 54,684 25,427 32,451 54,623 35,894 56,421
2 million
N 2 million (unbroken) 43,990 39,287 34,244 44,657 41,707 30,668 31,487
39,478 26,589 28,742 65,894 34,658 29,564 15,684
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8
5.5 lg(N) Mean of lg(N) H-Mean of lg(N)
7
5.0 4.5 lg(N)
lg(N)
6 5
4.0
4
3.5
3
3.0
2
0.2
0.4
0.6
0.8
1.0
H/mm
2.5
1.2
lg(N) Mean of lg(N) W-mean of lg(N)
2.0 2.5 3.0 3.5 4.0 4.5 5.0 5.5 6.0 W/mm
˄a˅H-lg(N) 9 8
˄b˅W-lg(N) 6.0
The fatigue life of non-corroded steel wire with different stress amplitude is more than 2 million times.
Single pit
5
lg(N)
lg(N)
5.0
lg(N) Mean of lg(N) Sa-Mean of lg(N)
6
4.5 4.0
W=5, H=1 3.5
3 2 160
lg(N) Mean of lg(N) L-Mean of lg(N)
5.5
7
4
5
180
200 220 Sa/MPa
240
260
˄c˅Sa-lg(N)
3.0 -2
0
2
4
6
8 10 L/mm
12
14
16
˄d˅L-lg(N)
Fig. 4. The relationship between fatigue life and pit characteristic parameters.
where, σ'f is the fatigue strength coefficient, ε'f is the fatigue continuity coefficient, b⁎ is the fatigue strength index considering the effect of stress gradient, and γ is the correction factor of fatigue life of steel wire with corrosion pits. c is the fatigue ductility index, N is the fatigue life, σm is the average stress, E is the elastic modulus, εa is the total strain, Kt is the stress concentration factor, and Kf is the fatigue notch factor. The value εa was determined by the approximate expression of the steady-state cyclic stress-strain curve:
εa ¼
1 σa σa n þ 0 E K
0
ð2Þ
where, K' is the cyclic strength coefficient, n' is the cyclic strain hardening index and σa is the cyclic stress amplitude. The fatigue notch coefficient Kf was calculated according to Peterson's formula.
Kf ¼ 1 þ
K t −1 1 þ a=ρ
4. Parameter analysis of fatigue life 4.1. Finite element model Taking the pit size W = 5 mm, H = 0.8 mm as an example, the finite element model was established by ANSYS according to the size in Fig. 1 (a). The mesh size was 0.2 mm, and the element type was SOLID45, which was meshed freely. The modulus of elasticity was 205 MPa, Poisson's ratio was 0.3, and the density was 7.850 g/cm3. The loading mode of the model was constrained at one end and applied with axial load at the other end. The finite element results were shown in Fig. 6 (a). Then the analysis results (.RST file) obtained by ANSYS were imported into the FE Input module of software nCode DesignLife, shown in Fig. 6 (b). In the S\\N analysis module, the maximum ratio of load was set to 900 and the minimum ratio of load was set to 0.44. Material properties of the steel wire were based on the fatigue performance curve of 1670 MPa steel wire, as shown in Fig. 6 (c). The final calculation results of the fatigue life were shown in Fig. 6 (d).
ð3Þ
where, a is a material constant, which is related to the tensile strength of the material. For the steel wire with strength grade 1670 MPa, a is 0.043 mm and ρ is the radius of the notch root. The comparison between the fatigue life of test result and the modified theoretical result was shown in Fig. 5. It can be concluded that the modified fatigue life of the steel wire with corrosion pits was closer to the test result than that of unmodified calculation result, and the maximum accuracy can be increased by about 10%. Therefore, the modified formula obviously improved the prediction accuracy of fatigue life of steel wire with corrosion pits.
4.2. Analysis result The results of fatigue life and stress distribution of steel wire were shown in Fig. 7. As can be seen from Fig. 7 (a), the fatigue life of the pits was obviously lower than that of other parts. The dangerous area was concentrated at the bottom of the pits and distributed in strips perpendicular to the tensile direction. The minimum life of the pits was only 2836 times. From Fig. 7 (b), it can be seen that the stress at the pit was obviously higher than that at other parts, in which the dangerous areas were concentrated at the bottom of the pit and distributed in strips perpendicular to the tensile direction, with the maximum stress of 3.266 MPa. In summary, the stress at the bottom of the pit
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6.0
1.13%
4.0
3.81% 4.0
1.78%
3.5
4.77%
9.5%
3.0
3.5
2.54%
6.29%
2.5 2.0
3.18
4.5
4.5
lg(N)
lg(N)
5.0
Experiment Manson-Coffin Modified formula
5.0
Experiment Manson-Coffin Modified formula
5.5
3.71% 0.4
0.6
0.8
H/mm
1.0
4.73% 1.2
3.0
6.0
2
3
4
5
W/mm
6
6.0 Experiment Manson-Coffin Modified formula
3.68%
5.5
Experiment Manson-Coffin Modified formula
5.5
5.0
5.0
3.69%
lg(N)
lg(N)
4.5 4.0 3.5
3.81%
3.0
3.88% 1.32%
4.5
0.64%
1.96% 0.96%
0.36%
0.25%
4.0 3.5
3.92%
2.5 180
190
200
210
220
Sa/MPa
230
240
250
260
3.0 -2
0
2
4
6
8
L/mm
10
12
14
16
Fig. 5. The comparison between the fatigue life of test result and the modified theoretical result.
was the largest and the fatigue life was the lowest, indicating that fatigue cracks first formed at the bottom of the pit. The fatigue life and stress from bottom to edge of pit along the length of steel wire were shown in Fig. 8. It can be found that from the bottom to the edge of the pit, the fatigue life increased and the stress decreased.
Both of them were axisymmetrical along the bottom of the pits. Secondly, the stress near the bottom of the pit varied greatly, while the fatigue life remained basically unchanged (See the shadow part in the Fig. 8). With the distance increasing, the stress decreased linearly and the fatigue life increased exponentially.
Fig. 6. Analysis process of fatigue life of steel wire with corrosion pits.
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7
Fig. 7. The results of fatigue life and stress distribution.
4.3. Verification of finite element model The comparisons of test results, theoretical calculation results and finite element results of fatigue life of some specimens were shown in Table 4 and Fig. 9. It can be seen that the ratios of test, formula and finite element results were approximately 1, and the maximum error was only 6%, which verified the correctness of the finite element model. The fatigue life of steel wire with corrosion pits can be predicted accurately by the finite element model and the calculation theory of fatigue life established in this paper.
4.4. Parameter analysis
Table 4 The comparison of test, theoretical and finite element result.
Previous experimental studies have found that the main factors affecting the fatigue life of steel wire with pits were the width and depth of corrosion pits. Therefore, in order to obtain the S\\N curves of steel wires with different sizes of pits and the effects of stress ratio on the S\\N curves of steel wires with pits, 236 finite element models were established by the finite element software for more comprehensive extension analysis of fatigue life.
6x105
Number
Test/time
Theoretical/time
FEA/time
FEA-Test Test
FEA-Theoretical Theoretical
H-0.8 H-1.0 H-1.2 W-2.0 W-3.0 W-4.0
2975 828 459 2448 4526 12,836
2686 770.9 438.29 2532 4413 12,578
2836 823.6 434.4 2398 4432 12,732
4.8% 0.5% 5.4% 2.0% 2.1% 0.8%
5.6% 6.8% 0.9% 5.3% 0.4% 1.2%
3.5 Fatigue Life Stress
3.0 2.5
4x105
σ/MPa
N/times
2.0
3x105
1.5
2x105
1.0
1x105
0.5
0
0.0 Edge of pit
Bottom of pit
Edge of pit
Different parts of pits along the length of steel wire Fig. 8. The fatigue life and stress from bottom to edge of pit along the length of steel wire.
14000 Test Theoretical FEA
12000 10000
N/times
5x105
4.4.1. Different pit sizes The S\\N curves of steel wires with different sizes of pits were shown in Fig. 10. Fig. 10 (a) showed that with the increase of pit depth, the S\\N curve moved downward as a whole, indicating that the fatigue life of steel wire decreased gradually with the pit depth. When the pit depth was b1.2 mm, the S\\N curve decreased slightly. While the pit depth was N1.2 mm, the S\\N curve decreased sharply. Therefore, when the pit depth was within 1.2 mm, the pit depth had little effect on the S\\N curve. In addition, the fatigue life decreased with the increase of pit depth under the same stress amplitude. For example, when the stress amplitude was equal to 95 MPa, the fatigue life
8000 6000 4000 2000 0
H-0.8
H-1.0
H-1.2 W-2.0 Specimens
W-3.0
W-4.0
Fig. 9. The comparison of test, theoretical and finite element result.
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C. Miao et al. / Journal of Constructional Steel Research xxx (2019) xxx
350 300
160 140
250
120
200
100 80
R=0.44 W=5 mm
100
W=2.5 W=2.0 W=1.5 W=1.0 W=0.5
60
H=0.8 H=1.0 H=1.2 H=1.5 H=2.0
50 0 10
H=1.5 mm R=0.44
Sa/MPa
Sa/MPa
150
40
101
102
103 N/times
104
105
106
100
101
(a) Pit depth
102
103
N/times
104
105
106
(b) Pit width
Fig. 10. The S\ \N curves of steel wires with different pit sizes.
decreased by 99%, and the fatigue life changed from high cycle fatigue to low cycle fatigue (The high cycle fatigue was N104 times). Therefore, for the design of finite fatigue life, the effect of pit depth was particularly important. For larger depth pits, brittle fracture even occurred under higher stress amplitude. Fig. 10 (b) showed the S\\N curve of steel wire with different pit widths. As can be seen from Fig. 10 (b), with the pit width decreased, the S\\N curve moved downward as a whole, and the decreasing range was basically unchanged. Under the same stress amplitude, the fatigue life decreased with the decrease of pit width. For example, when the stress amplitude was 88 MPa, the fatigue life of steel wires decreased by 94%, and changed from high cycle fatigue to low cycle fatigue. Through the S\\N curve of steel wire with different depths and widths of pits, it can be found that the fatigue life of steel wire decreased with the increase of pit depth and the decrease of pit width. Therefore, in order to obtain the effect of pit shape on the fatigue life of steel wire, the relationship of pit depth-width ratio and fatigue life was established, as shown in Fig. 11. It can be found that on the same fatigue life curve (N = 103, 104, 105, 106), with the increase of pit depth-width ratio (i.e. the pit shape changed from the wide-shallow to the deepnarrow), the corresponding stress amplitude gradually decreased, especially in the range of 0 to 0.5. While N1, it tended to be flat and converged to a certain value. Therefore, when the pit depth-width ratio was N1, under the same fatigue life, the required stress amplitude had nothing to do with the pit sizes. In addition, the fatigue life decreased gradually with the increase of depth-width ratio of pit at the same stress amplitude of 110 MPa (See Fig. 11), and the fatigue life decreased from 106 times to 103 times. When the depth-width ratio of pit was 1.5, the stress amplitude increased from 45 MPa to 105 MPa, and the fatigue life decreased from 106 times to 103 times, but the fatigue life of the smooth steel wire
was all N106 with the same change of stress amplitude, which indicated that pit depth-width ratio was an important factor affecting the fatigue life of steel wire.
4.4.2. Different stress ratios Taking the steel wire with depth-width ratio of 0.16 (wide-shallow) and 0.75 (deep-narrow) as examples, the S\\N curves of steel wire under stress ratios of R = −1, 0 and 0.44 were obtained, shown in Fig. 12. It can be seen that under the same pit size, the S\\N curve of steel wire decreased with the stress ratio increased. Therefore, the greater the stress ratio, the more significant the effect of pit on the fatigue life was. When the stress ratio increased from −1 to 0.44, the S\\N curve of steel wire with depth-width ratio of 0.16 would move down more than twice the depth-width ratio of 0.75, which indicated that the influence of wide-shallow pits on the fatigue life was more obvious. In order to more intuitively reflect the relationship between fatigue life, stress ratio, stress amplitude and pit size, taking the steel wire with pit depth-width ratio of 0.16 as an example, the S-N-R diagram of steel wire was obtained according to the S\\N curves of steel wire with different stress ratios. The specific method was shown in Fig. 13. From Fig. 13 (b), it can be found that with the increase of stress ratio, the stress amplitude corresponding to the same fatigue life was smaller. In addition, with the increase of fatigue life, the relationship between stress amplitude and stress ratio became smoother, which indicated that the low cycle fatigue of steel wire with corrosion pits was more sensitive than the high cycle fatigue.
H/W=0.16
1000 300
R= -1 (H/W=0.16) R=0 (H/W=0.16) R=0.44(H/W=0.16) R= -1 (H/W=0.75) R=0 (H/W=0.75) R=0.44 (H/W=0.75)
1200
0.7 0.6
800
Deep and Narrow N=103
N=104
N=10
N=10
(a) Sa=110MPa
150
(b) H/W=1.5
100 50
0.1 100
6
1.0
1.5 H/W
N=103 N=104 N=105
2.0
101
102
103
104
N/times (a) Sa=110MPa
105
106
100
2.5
3.0
H/W=0.16 H/W=0.75
400
110 100 90 80 70 60 50 40
N=10
0.5
600
0.2
6
0.0
0.3
H/W=0.16 H/W=0.75
200
sa/MPa
Sa/MPa
5
0.4
Sa/MPa
Shallow and Wide
200
H/W
0.5
250
H/W=0.75 101
102
103
104
N/times
(b) H/W=1.5
Fig. 11. The relationship of fatigue life and the depth-width ratio of pits.
105
106
0 100
101
102
103
N/times
104
105
106
Fig. 12. The S\ \N curves of steel wire under different stress ratios.
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9
Sa/MPa Sa/MPa
1200
N=103 N=106
1000
1000
R=-1 R=0 R=0.44
800 600
600
400
400
200
200
0 0 10
101
N=103
800
102
103
104
(a) S-N
105
106
N/times
N=106
0 -1.0 -0.8 -0.6 -0.4 -0.2 0.0 0.2 0.4 0.6 0.8 1.0
(b) S-N-R
R
Fig. 13. The S-N-R curves of the steel wires.
H/W=0.16, N=103 H/W=0.75, N=103 H/W=0.16, N=106 H/W=0.75, N=106
1000 800
Sa/MPa
600 400 200 0 -1.0
-0.8
-0.6
-0.4
-0.2
R
0.0
0.2
0.4
0.6
Fig. 14. The S-N-R curves of pits with different depth to width ratios.
The S-N-R curves of steel wire with different depth to width ratios of pits were shown in Fig. 14. It can be seen that under the same fatigue life, the S-N-R curves of steel wires with larger depth-width ratio of pit were all located below the steel wires with smaller depth-width ratio of pit, indicating that the larger depth-width ratio of pit was, the smaller the stress amplitude was under the same stress ratio. Therefore, under the same load, the steel wire with larger depth-width ratio had shorter fatigue life. In addition, under the same fatigue life, the S-N-R curve of steel wire with larger pit depth and width was smoother, indicating that the change rate of stress ratio and stress amplitude was related to depth-width ratio of pit under the same fatigue life.
increase of stress amplitude, the fatigue life of steel wire decreased exponentially. In addition, the study of pit spacing showed that the superposition effect of pits can slightly improve the fatigue life of steel wire. (3) The modified fatigue life of the steel wire with corrosion pits was closer to the test result than that of unmodified calculation result, and the maximum accuracy can be increased by about 10%. The modified formula obviously improved the prediction accuracy of fatigue life of steel wire with corrosion pits. (4) With the increase of pit depth, the S\\N curve moved downward as a whole, indicating that the fatigue life of steel wire decreased gradually with the pit depth. For the design of finite fatigue life, the effect of pit depth was particularly important. For larger depth pits, brittle fracture even occurred under higher stress amplitude. Corrosion pits with larger depth to width ratio had greater impact on fatigue life of the steel wire, which should be paid attention to. When the depth to width ratio of pit was N1, under the same fatigue life, the required stress amplitude had nothing to do with the pit size. (5) The greater the stress ratio, the more significant the effect of pit on the fatigue life was. When the stress ratio increased from - 1 to 0.44, the S\\N curve of steel wire with depth-width ratio of 0.16 would move down more than twice the depth-width ratio of 0.75, which indicated that the influence of wide-shallow pits on fatigue life was more obvious. In addition, under the same fatigue life, the S-N-R curve of steel wire with larger depth and width of pit was smoother, indicating that the change of stress ratio and stress amplitude was related to depth-width ratio of pit.
5. Conclusion
Declaration of Competing Interest
In this paper, 69 cable steel wires with different characteristic parameters of pit were obtained by manual prefabrication. The effects of pit depth, width, location and stress amplitude on the fatigue life of cable steel wires were discussed through the fatigue test. Then, the fatigue life prediction model of cable steel wire with corrosion pits was established. Finally, 236 steel wire models with corrosion pits were established by the software ANSYS and nCode designLife, and the S\\N curves of cable steel wires with different sizes of pit and stress ratios were analyzed and compared. The main conclusions were as follows:
The authors declared no potential conflicts of interest with respect to the research, authorship, and/or publication of this article. Acknowledgments The financial support provided by National Natural Science Foundation of China under Grant Nos. NSFC-51078080. The supports were highly acknowledged. The authors also would like to express gratitude to the viewers for their comments. References
(1) When pit depth increased from 0.4 mm to 0.6 mm, the fatigue life of steel wire decreased by 99.25%. When the width of pit increased from 2 mm to 6 mm, the fatigue life of the steel wire increased by 97.42%. The fatigue life of steel wire decreased with the increase of pit depth and the decrease of pit width. (2) The stress amplitude had greater influence on fatigue life of steel wire with pits than that of steel wire without pits. With the
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Please cite this article as: C. Miao, R. Li and J. Yu, Effects of characteristic parameters of corrosion pits on the fatigue life of the steel wires, J Constr Steel Res, https://doi.org/10.1016/j.jcsr.2019.105879