- Email: [email protected]
Fatigue behavior of uncorroded butt welded joints made of bridge weathering steel
Structures 24 (2020) 377–385
Contents lists available at ScienceDirect
Structures journal homepage: www.elsevier.com/locate/structures
Fatigue behavior of uncorroded butt welded joints made of bridge weathering steel
T
⁎
Han Su, Jian Wang, Jinsheng Du
School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Uncorroded bridge weathering steel Butt welded joint Fatigue behavior Fracture mechanics Mixed-mode fatigue crack propagation simulation
Bridge weathering steel produced in China has been employed in bridges worldwide, among them Q345qNH is the most commonly used steel grade. Fatigue behavior of uncorroded butt welded joints made of bridge weathering steel Q345qNH was explored in this paper. Fatigue tests were conducted on 13 specimens involving 9 stress ranges, S-N curve and its lower bound of 95% survival probability were established. It was observed that the design S-N curve for butt welded joint in Eurocode 3 is suitable for fatigue assessment of this batch of specimens and provides a considerable safety margin. Numerical simulation of mixed-mode fatigue crack propagation and analytical investigation of fatigue crack propagation were conducted, it was found that numerical simulation is preferred since it considers the variation in stress due to crack propagation. The influences of initial crack size, initial crack shape, initial crack location and angular misalignment of plates on fatigue behavior of butt welded joints were investigated, the expression between fatigue life and initial crack size was derived. Additionally, it is recommended that a semi-elliptical crack with initial crack depth of 0.2 mm and initial aspect ratio of 1/4 to be adopted when information on initial crack is unavailable. The fatigue test results provide reference for fatigue design of steel bridges made of coated weathering steel and serve as control for analysis of deterioration of fatigue behavior due to corrosion for corroded butt welded joints made of uncoated weathering steel.
1. Introduction Addition of alloy elements including Copper, Nickle, Chrome and others gives weathering steel better corrosion resistance than normal carbon steel [1,2]. Weathering steel can be used as coated, uncoated and rust layer stabilized [3]. When weathering steel is uncoated, dense and protective rust layer is formed on top of substrate base metal which protects itself from further corrosion; when weathering steel is coated in severely corrosive environments, it provides extended coating service life since the dense and protective rust layer prevents the coating from falling off [4,5]. It is gaining increasing popularity in China and worldwide due to its reduced overall costs of steel structures in their lifecycles [6]. In design codes such as Eurocode 3 [7] and AASHTO [8], S-N curves which are derived from nominal stress and hot spot stress [9–13] and the Palmgren-Miner accumulative damage rule [14] are adopted to assess fatigue damage, however this approach becomes ineffective when fatigue details are not covered in design codes or fatigue details experience multiaxial stresses [15]. Notch stress method [16–18] has been proposed as an alternative to assess fatigue performance, IIW [19]
⁎
proposes the universal design S-N curve derived from notch stress, which is applicable to all types of fatigue details. However, the aforementioned approaches are based entirely on S-N curves which are time and capital consuming to establish, and these approaches become difficult to use when the loading history is unknown [20]. Due to the limitations of S-N curve based approaches, fracture mechanics method [21–23] which focuses on crack initiation and crack propagation has been applied in fatigue assessment. Since welding inevitably introduces initial cracks in steel bridges, and steel bridges are mostly in a fully elastic static when they are under the actions of vehicle loads, linear elastic fracture mechanics (LEFM) is especially suitable for fatigue assessment of steel bridges. Analytical stress intensity factor solutions for plates have been developed by Newman and Raju [24], these factors can be revised by modification factors to account for stress concentration caused by the presence of weld or attachment [25–27], thereafter fatigue assessment of welds can be conducted. Numerical simulations of 3D mixed-mode crack propagation were performed by Barsoum [28] and Zong [20,29,30], and simulation results agreed well with experimental results. Since steel bridges undergo long-term repeated traffic loads, they
Corresponding author. E-mail address: [email protected] (J. Du).
https://doi.org/10.1016/j.istruc.2020.01.032 Received 30 September 2019; Received in revised form 20 January 2020; Accepted 23 January 2020 2352-0124/ © 2020 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved.
Structures 24 (2020) 377–385
H. Su, et al.
are prone to have fatigue problems, and fatigue of materials could cause abrupt destruction of steel bridges which results in disasters [31], as evidenced by the sudden collapse of Seongsu Bridge in Korea in 1994 which was caused by fatigue crack initiated from a welded vertical member [32]. Butt welded joint is among the most widely used types of connections in practical fabrication of bridges [15,30]. Since bridges experience cyclic fatigue loads and butt welded joints are vulnerable to fatigue damage [33], fatigue behavior of butt welded joints should be investigated. Fatigue behavior of butt welded joints have been investigated by many researchers. Kaufmann et al. [34] investigated fatigue behavior of butt welded joints made of S355N, S355M, S690Q and S960Q, it was found that butt welded joints made of S960Q performed better under variable amplitude loading and in the case of overloads. Zong et al. [30] assessed fatigue behavior of butt welded joints connecting plates with different thicknesses made of normal carbon steel Q345qD, and found that all specimens satisfied the fatigue requirements of Eurocode 3. Akyel et al. [35] tested fatigue strength of repaired butt welded joints made of S690 and S890, and found that repair procedure recovered fatigue strength of damaged butt welded joints. However, there are scarce researches regarding the fatigue behavior of butt welded joints made of weathering steel. This paper investigates the fatigue behavior of uncorroded butt welded joints made of bridge weathering steel Q345qDNH. Fatigue tests were conducted on 13 butt welded joint specimens which were under 9 stress ranges, S-N curve and its lower bound of 95% survival probability were established. Mixed-mode crack propagation was then simulated by ABAQUS [36] and FRANC3D [37] and then compared with analytical solution. The influences of initial crack size, initial crack shape, initial crack location and angular misalignment of plates on fatigue behavior of butt welded joints were analyzed and discussed, and suitable initial crack was recommended. The results provide reference for fatigue design of steel bridges made of coated weathering steel and for comparison with corroded butt welded joints made of uncoated weathering steel, and they could serve as control to analyze deterioration of fatigue behavior due to corrosion in the future study.
Fig. 2. Design geometry of butt welded joint.
2. Experimental details 2.1. Specimen preparation Fatigue detail of butt welded joint with temporary ceramic backing in Eurocode 3 [7] with a fatigue strength of 71 MPa was chosen to investigate the fatigue behavior of butt welded joint, as indicated in Fig. 1. The design geometry of butt welded joint specimen is illustrated in Fig. 2, and a typical finished butt welded joint is illustrated in Fig. 3. The butt welded joints were made from the same batch of steel plates and welding wires as in [38], the mechanical properties are included in Table 1. The butt welded joint specimens were fabricated by CO2 arc welding with welding current of 240 ± 20 A and welding voltage of 30 ± 2 V. The design geometry of the weld is shown in Fig. 4, the groove was welded from the top by seven weld beads with a temporary ceramic backing on the bottom. The butt welded joints were proved to be of good quality by non-destructive testing. The variations in straightness of specimens were checked and the requirements of American Standard AASHTO/AWS D1.5M/D1.5 “Bridge Welding Code” were met [39]. Before fatigue tests, geometric dimensions of butt welded joints
Fig. 3. A typical finished butt welded joint. Table 1 Mechanical properties of Q345qDNH base metal and CHT71NHQ welding wire. Content
fy (MPa)
fu (MPa)
A (%)
Yield strength ratio
E (GPa)
Base metal Welding wire
413 485
550 561
30 24.5
0.75 0.86
206 –
Fig. 4. Design geometry of butt welds.
were measured by image processing approach to facilitate establishment of finite element model, as shown in Fig. 5, Measured geometric dimensions are tabulated in Table 2. Fig. 1. Typical butt welded joint with temporary ceramic backing. 378
Structures 24 (2020) 377–385
H. Su, et al.
Fig. 5. Geometric profile of butt welded joints.
2.2. Experimental details The tests were carried out at room temperature. The specimens were loaded on QBG-250 High Frequency Fatigue Tester with constant amplitude, the experimental setup was shown in Fig. 6. The loading capacity of the machine is ± 25 tons. The stiffness of the specimen determines the loading frequency, the stiffness of the specimen decreases as the crack propagates, leading to a decrease in loading frequency. The specimens were tested under initial loading frequency of 101.4–114.9 Hz. The boundary conditions were that the bottom plate was fixed while the axial tensile stress was applied on the top plate. The stress ratio was set to be 0.1 for all specimens. The maximum number of loading cycles was set to be 5 million. The fatigue test would terminate if either the loading frequency decreases by 10 Hz or the number of loading cycles reaches 5 million. If the latter case happens, the specimen will be labelled as run out. The maximum stress was set to be 100 MPa for the first specimen, which corresponds to a stress range of 90 MPa. If the specimen fails, the maximum stress would increase by 10 MPa for the next test, otherwise the maximum stress would increase by 20 MPa. 13 specimens were tested and results for 9 stress ranges were obtained. For each test, the loading machine was momentarily paused when loading frequency decreases by 2 Hz, which indicated that the crack might have propagated to a visible size. The location of the visible crack was measured and recorded, and the location was deemed to be the location of crack initiation.
Fig. 6. Experimental setup.
Fig. 7. Fatigue test results and S-N curve from Eurocode 3.
3. Experimental observations and results
130.4 MPa, the computed fatigue strength according to lower bound of 95% survival probability is 111.4 MPa, which are both considerably larger than the design fatigue strength of 71 MPa. It is observed that the S-N curve in Eurocode 3 safely covers all the test results for this batch of specimens and also offers a considerable safety margin.
3.1. Fatigue test results Among the test results of 13 specimens, 9 specimens failed, and 4 specimens were run outs. The test results along with the S-N curve corresponding to this specific fatigue detail in Eurocode 3 [7] were plotted in logarithmic coordinates in Fig. 7. The 9 valid test results were linearly fitted with a fixed slope of m = 3, the lower bound of 95% survival probability was also derived according to the test data evaluation approach recommended by Hobbacher [19]. The average ratio between the recorded fatigue life and the computed fatigue life according to the lower bound of 95% survival probability is 2.16, the average ratio between the recorded fatigue life and the computed fatigue life according to design S-N curve from Eurocode 3 is 8.36, the average ratio between the computed fatigue life according to lower bound of 95% survival probability and the computed fatigue life according to design S-N curve from Eurocode 3 is 3.86. The computed fatigue strength according to linearly fitted S-N curve of test results is
3.2. Initial crack location and critical crack depth Locations of crack initiation of every failed specimens were observed and recorded. It was found that all cracks initiated from the intersection line between butt weld and base metal, as shown in Fig. 8. A local measuring coordinate was established to facilitate measurement and recording of crack initiation locations, as illustrated in Fig. 9(a). The average measured location of crack initiation was found to be 5.44 mm away from the longitudinal edge of the specimen and is illustrated in Fig. 9(b). When the fatigue tests finished, the cracked specimens were loaded to complete fracture to facilitate observing the depth of the crack, it was observed that the crack occupied
Table 2 Average geometric dimensions of butt welded joints. Category
t/mm
B1/mm
C1/mm
B2/mm
C2/mm
α/degrees
θ/degrees
Mean value
16.24
32.62
2.97
17.43
2.15
0.04
19.98
379
Structures 24 (2020) 377–385
H. Su, et al.
b) Critical crack size acr, c) Appropriate fatigue crack growth rate parameters C and m, d) Stress intensity factor ΔK.
4.2. Simulation details The finite element model of the butt welded joint was established according to the geometric dimensions tabulated in Table 2. The bottom plate was fixed, the axial stress was applied on the end of the top plate, which were in line with actual experimental boundary conditions. The applied stresses were also consistent with fatigue tests. The material was assumed to be perfectly elastic. Element type C3D20 was chosen. Ibsø and Agerskov [41] investigated the initial crack geometry and determined that the initial aspect ratio a0/c0 to be 1/4, the initial crack depth a0 scatters from 0.075 mm to 0.4 mm. Thus, different initial crack depths which are 0.075 mm, 0.1 mm, 0.2 mm, 0.3 mm and 0.4 mm were considered, and initial aspect ratio was taken as 1/4. When the fatigue tester stopped due to a drop in loading frequency of 10 Hz caused by rapid propagation of fatigue crack, the crack depth occupied approximately half of the plate depth, therefore the critical crack size acr is determined to be 8 mm to be consistent with experimental observations. The fatigue crack growth rate parameters of the same batch of Q345qDNH have been measured in [38], the results derived from group specimen method were adopted in this analysis, where logC is taken as −10.37 and m is taken as 2.38. Fatigue crack growth threshold is assumed to be non-existent, which results in a conservative prediction of fatigue life, and the Paris Law becomes applicable to propagation of tiny cracks under this assumption. After the crack was inserted in FRANC3D, the model was re-meshed, as shown in Fig. 10. The stress intensity factor was calculated by the interaction integral method. Due to angular misalignment of plates and geometric asymmetry after insertion of crack, the crack is a mixedmode crack, thus the maximum tensile stress (MTS) criterion was applied to account for mixed-mode crack, and the corresponding effective stress intensity factor range was calculated by [42]:
Fig. 8. Location of crack initiation and crack propagation.
approximately half of the plate depth. 4. Numerical simulation 4.1. Fatigue crack simulation First of all, the finite element model is established and boundary conditions are applied in ABAQUS. Secondly, the model is exported to FRANC3D for inserting the crack. Thereafter, the model is being remeshed by wedge and hex elements near the crack tip, while remaining areas will be re-meshed by tet elements, and displacements will be calculated. Finally, the crack front will be repeatedly updated by using the calculated displacements, and the model will be iteratively re-meshed accordingly. Crack propagation direction, which is also called kink angle, and the equivalent stress intensity range model are two criteria which need to be determined for numerical simulation to progress. The size of crack extension is predetermined in FRANC3D, the number of loading cycles is calculated by Paris Law [40]:
Ni =
∫a
ai + 1
i
da C (ΔK )m
(i = 1, 2, 3, ...,n)
(1)
where Ni is the number of loading cycles, ai is the initial crack size of the ith step, ai+1 is the predetermined size of crack extension, C and m are fatigue crack growth rate parameters. The fatigue life can be calculated by n
N=
acr
∑ Ni = ∫a0 1
da C (ΔK )m
(2)
where N is the fatigue life, a0 is the initial crack size, acr is the critical crack size. As can be seen from Eq. (2), to predict the fatigue life accurately, four sets of parameters need to be determined:
ΔK eff =
a) Initial crack size a0,
ΔK eff =
KI2 + KII2 +
2 KIII (1 − ν )
(3)
where ν is Poisson’s ratio, which is 0.3 for steel, thus 2 KI2 + KII2 + 1.429KIII
Fig. 9. Measurement of initial crack location. 380
(4)
Structures 24 (2020) 377–385
H. Su, et al.
Fig. 10. Crack insertion of butt welded joint by FRANC3D.
4.3. Simulation results and determination of initial crack
5. Discussion
The simulation results of different initial crack sizes are presented in Fig. 11. The test results, the design S-N curve corresponding to this specific fatigue detail in Eurocode 3, the fitted experimental S-N curve of test results and the lower bound of 95% survival probability are also presented. The fatigue strengths for initial crack sizes of 0.075 mm, 0.1 mm, 0.2 mm, 0.3 mm and 0.4 mm are 111.3 MPa, 106.5 MPa, 94.2 MPa, 86.8 MPa and 81.1 MPa respectively. It is found that when the initial semi-elliptical crack depth is 0.2 mm for this batch of specimens, the numerical simulation could cover all the test results and provide reasonably accurate predictions of fatigue lives.
5.1. Size of initial crack The initial crack size influences fatigue behavior significantly, thus its influence on fatigue behavior needs to be analyzed. The predicted fatigue lives of butt welded joint specimens when the stress range is 110 MPa with initial crack depths of 0.075 mm, 0.1 mm, 0.2 mm, 0.3 mm and 0.4 mm are derived and plotted in Fig. 12. Regression analysis was conducted and the expression between fatigue life and initial crack depth is derived as
N = (2.534 − 7.421a0 + 8.856a0 2)·106 (0.075 ⩽ a0 ⩽ 0.4)
(5)
It can be seen that as the initial crack depth increases, the predicted fatigue life decreases dramatically. The reason is that stress intensity factors correspond to tiny cracks are low, therefore cracks propagate at extraordinarily slow rates, consequently considerable number of
Fig. 11. Predicted S-N curves by numerical simulation. 381
Structures 24 (2020) 377–385
H. Su, et al.
However, for this batch of specimens, aspect ratio of 1/4 is still recommended as it better reflects their fatigue behavior. 5.3. Location of initial crack The aforementioned analyses assumed that the crack initiated from the average measured location of crack initiation. However, crack could initiate from various locations in reality, ranging from the center of the plate to the corner of the plate, as shown in Fig. 14. Thus, the influence of initial crack location on fatigue behavior of butt welded joints needs to be investigated. The S-N curves and a-N curves of center crack, average measured crack and corner with an initial crack size of 0.2 mm and initial aspect ratio of 1/4 are derived by numerical simulation and plotted in Fig. 15. The fatigue strengths for center crack, average measured crack and corner crack are 97.9 MPa, 97.3 MPa and 94.2 MPa respectively, the differences between fatigue strengths for center crack, corner crack and fatigue strength for average measured crack are 3.8%, and 3.2%, the differences between fatigue lives for center crack, corner crack and fatigue life for average measured crack are 9.2% and 7.8%. Therefore, it was found that the influence of initial crack location on fatigue behavior of butt welded joint is insignificant. The influence of initial crack location on fatigue behavior of butt welded joints can also be investigated analytically. Newman and Raju [24] have developed analytical stress intensity factor solutions for semielliptical center and corner surface flaws in plates, and these solutions are adopted by BS 7910 [43]. The stress intensity factor is calculated by:
Fig. 12. Influence of size of initial crack on fatigue behavior of butt welded joints.
loading cycles is required to propagate the crack a short distance. The importance of accurately measuring the initial crack size by non-destructive testing techniques is thus being stressed. 5.2. Shape of initial crack The aforementioned analyses were conducted under the assumption that the aspect ratio a0/c0 is 1/4. Although this assumption is supported by Ibsø and Agerskov [41], the exact aspect ratio may vary in reality. Thus, the influence of initial crack shape on fatigue behavior of butt welded joints needs to be investigated. The S-N curves and a-N curves with aspect ratio ranging from 1/1 to 1/4 and initial crack size of 0.2 mm are derived by numerical simulation and plotted in Fig. 13. The fatigue strengths for initial crack aspect ratio of 1/1, 1/2, 1/3 and 1/4 are 107.8 MPa, 101.3 MPa, 97.2 MPa and 94.2 MPa respectively, the differences between fatigue strengths for initial crack aspect ratio of 1/1, 1/2, 1/3 and fatigue strength for initial crack aspect ratio of 1/4 are 12.6%, 7.0% and 3.1%, the differences between fatigue lives for initial crack aspect ratio of 1/1, 1/2, 1/3 and fatigue life for initial crack aspect ratio of 1/4 are 38.5%, 15.9% and 7.7%. Therefore, it can be concluded that the influence of initial crack shape on fatigue behavior of butt welded joint is relatively significant.
K = (Mkt St + Mkb HSb) π
a a a c F ⎛ , , , ϕ⎞ Q ⎝t c b ⎠
(6)
where St and Sb are the tension and bending stresses respectively. Mkt and Mkb are the magnification factors for applied tension and bending stresses respectively, which are functions of a/t, c/a, B1/t and θ [25], where θ is the weld angle and θ is taken as 0.349 for this batch of specimens. H is a function of H1, H2 and p that can be calculated by Eq. (7). Q is the shape factor for elliptical crack that can be calculated by Eq. (8). F is the stress intensity boundary correction factor which is a function of a/t, a/c, c/b and ϕ that can be calculated by Eq. (9).
H = H1 + (H2 − H1)sinp ϕ
(7)
where H1 and H2 are functions of a/t. p is a function of a/c and a/t.
Fig. 13. Influence of shape of initial crack on fatigue behavior of butt welded joints. 382
Structures 24 (2020) 377–385
H. Su, et al.
Fig. 14. Center crack and corner crack.
Fig. 15. Influence of location of initial crack on fatigue behavior of butt welded joints by numerical simulation.
Fig. 16. Influence of location of initial crack on fatigue behavior of butt welded joints by analytical approach.
383
Structures 24 (2020) 377–385
H. Su, et al.
Fig. 17. Influence of misalignment of plates on fatigue behavior of butt welded joints by analytical approach.
a 1.65 Q = 1 + 1.464 ⎛ ⎞ ⎝c⎠
a ⎛ ⩽ 1⎞ ⎝c ⎠
2
straightness to be up to 1 mm/m. Since angular misalignment in plates introduces stress concentration, it could be extraordinarily harmful for fatigue behavior, hence the influence of angular misalignment on fatigue behavior of butt welded joints needs to be investigated. The effectiveness of analytical method to explore the influence of parameters on fatigue behavior has been illustrated in Section 5.3, therefore the influence of angular misalignment on fatigue behavior of butt welded joints are also investigated by analytical method. When the stress range is 110 MPa, the K-a curves and a-N curves of different variations in straightness with an initial center crack whose size is 0.2 mm and initial aspect ratio of 1/4 are derived analytically and plotted in Fig. 17. It can be seen that as the variation in straightness increases, the stress intensity factor also increases, resulting in decrease in fatigue life. The difference of stress intensity factors at fracture between 0 and 1 mm/m variation in straightness is 2.1%, the difference of fatigue life between 0 and 1 mm/m variation in straightness is 9.4%. Therefore, it can be concluded that as long as welding meets the fabrication requirements prescribed in AASHTO/AWS D1.5 M/D1.5, the influence of angular misalignment on fatigue behavior of butt welded joints can be regarded as relatively insignificant.
(8)
4
a a F = ⎡M1 + M2 ⎛ ⎞ + M3 ⎛ ⎞ ⎤ fϕ gfw ⎢ ⎝t ⎠ ⎥ ⎝t ⎠ ⎣ ⎦
(9)
where M1, M2 and M3 are functions of a/c. f ϕ is a function of a/c and ϕ. g is a function of a/t and ϕ. fw is a finite width correction factor which is a function of c/b and a/t. The bending stress Sb is caused by misalignment in butt welds. For the butt welded joints which have fixed ends, Sb can be calculated by [43]:
Sb = St
3α l ⎛ tanh(β /2) ⎞ ⎜ ⎟ t ⎝ β /2 ⎠
(10)
where l is half the length of the butt welded joint specimen. β is calculated by
β=
2 l ⎛ 3σmax, m ⎞0.5 t ⎝ E ⎠
(11)
where σmax,m is the membrane component of the maximum applied tensile stress which can be calculated with the assistance of the finite element model in Section 4. Consequently, when the stress range is 110 MPa, the K-a curves and a-N curves of center crack and corner with an initial crack size of 0.2 mm and initial aspect ratio of 1/4 are derived analytically and plotted in Fig. 16. The difference of stress intensity factors at fracture between center crack and corner crack is 10.4%, the difference of fatigue life between center crack and corner crack is 12.1%. Therefore, the finding is consistent with the conclusion drawn from numerical simulation that the influence of initial crack location on fatigue behavior of butt welded joint is insignificant. However, fatigue lives obtained analytically are considerably lower than those obtained numerically, the reason is that the local bending stress caused by misalignment decreases as crack propagates, however the decrease in local bending stress cannot be taken into account by analytical approach.
6. Conclusions This paper investigated the fatigue behavior of uncorroded butt welded joints made of bridge weathering steel Q345qDNH, the results provide reference for fatigue design of steel bridges made of coated weathering steel and serve as control for analysis of deterioration of fatigue behavior due to corrosion for corroded butt welded joints made of uncoated weathering steel. Fatigue tests were conducted on 13 butt welded joint specimens which were under 9 stress ranges, mixed-mode crack propagation was numerically simulated by ABAQUS and FRANC3D, and analytical analyses were conducted. The influences of initial crack size, initial crack shape, initial crack location and angular misalignment of plates on fatigue behavior of butt welded joints were analyzed and discussed, and suitable initial crack was recommended. Main conclusions are as follows: 1. 9 effective fatigue test data which were under 9 stress ranges were obtained, S-N curve and its lower bound of 95% survival probability were established. It was found that the design S-N curve for butt welded joint in Eurocode 3 is suitable for fatigue assessment of this batch of specimens made of bridge weathering steel Q345qDNH and provides a considerable safety margin. 2. Numerical simulation of mix-mode fatigue crack propagation and
5.4. Angular misalignment of plates The average measured angular misalignment between the two plates of specimens tested in this research is 0.04 degrees, as shown in Table 2, which corresponds to a variation in straightness of 0.7 mm/m. However, AASHTO/AWS D1.5 M/D1.5 [39] allows for the variation in 384
Structures 24 (2020) 377–385
H. Su, et al.
analytical investigation of fatigue crack propagation were conducted. It was observed that numerical simulation gives more accurate prediction results as it is able to take into account the variation in stress due to crack propagation while analytical method cannot, therefore numerical simulation can better reflect the stress redistribution and crack propagation. 3. The initial crack assumption was investigated, it is recommended that when information on initial crack is not available, a semi-elliptical crack with initial crack size of 0.2 mm and initial aspect ratio of 1/4 can be used to obtain reasonably accurate predicted fatigue life. 4. The influences of initial crack size, initial crack shape, initial crack location and angular misalignment of plates on fatigue behavior of butt welded joints were investigated. The initial crack size influences fatigue behavior significantly, the expression between fatigue life and initial crack depth was derived; the influence of initial crack shape on fatigue behavior of butt welded joint is relatively significant; the influence of initial crack location on fatigue behavior of butt welded joint is insignificant, and influence of angular misalignment on fatigue behavior of butt welded joints can be regarded as relatively insignificant as long as welding meets the fabrication requirements prescribed in standards.
[11] [12] [13] [14] [15]
[16] [17]
[18] [19] [20]
[21] [22]
[23] [24]
Declaration of Competing Interest
[25]
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
[26] [27]
Acknowledgments [28]
Funding: “Application Expressway” Construction
This work was sponsored by the research project of of High Performance Weathering Steel in Hai’an-Qidong from Jiangsu Provincial Transportation Engineering Bureau (No. C18L01160).
[29]
[30] [31]
References
[32]
[1] Diaz I, Cano H, de la Fuente D, Chico B, Vega JM, Morcillo M. Atmospheric corrosion of Ni-advanced weathering steels in marine atmospheres of moderate salinity. Corros Sci 2013;76:348–60. [2] Kamimura T, Hara S, Miyuki H, Yamashita M, Uchida H. Composition and protective ability of rust layer formed on weathering steel exposed to various environments. Corros Sci 2006;48(9):2799–812. [3] Guo XY, Kang JF, Zhu JS, Duan MH. Corrosion Behavior and Mechanical Property Degradation of Weathering Steel in Marine Atmosphere. J Mater Civ Eng 2019;31(9):04019181. [4] Qian Y, Ma C, Niu D, Xu J, Li M. Influence of alloyed chromium on the atmospheric corrosion resistance of weathering steels. Corros Sci 2013;74:424–9. [5] Damgaard N, Walbridge S, Hansson C, Yeung J. Corrosion protection and assessment of weathering steel highway structures. J Constr Steel Res 2010;66(10):1174–85. [6] McConnell J, Shenton III HW, Mertz DR, Kaur D. National Review on use and performance of uncoated weathering steel highway bridges. J Bridge Eng ASCE 2014;19(5):04014009. [7] European Committee for Standardization (CEN), EN 1993-1-9 Eurocode 3, Design of steel structures-part 1-9: fatigue, Brussels, 2009. [8] American Association of State Highway and Transportation Officials (AASHTO). LRFD Bridge Design Specifications. eighth ed. Washington, DC: AASHTO; 2017. [9] Niemi E, Fricke W, Maddox SJ. Structural Hot-Spot Stress Approach to Fatigue Analysis of Welded Components. 2nd ed. Singapore: Springer Nature Singapore Pte Ltd.; 2018. [10] Poutiainen I, Tanskanen P, Marquis G. Finite element methods for structural hot
[33] [34]
[35] [36] [37] [38] [39] [40] [41] [42] [43]
385
spot stress determination – a comparison of procedures. Int J Fatigue 2004;26(11):1147–57. Xiao Z, Yamada K. A method of determining geometric stress for fatigue strength evaluation of steel welded joints. Int J Fatigue 2004;26(12):1277–93. Dong P. A structural stress definition and numerical implementation for fatigue analysis of welded joints. Int J Fatigue 2001;23(10):865–76. Savaidis G, Vormwald M. Hot-spot stress evaluation of fatigue in welded structural connections supported by finite element analysis. Int J Fatigue 2000;22(2):85–91. Miner MA. Cumulative Damage in Fatigue. J Appl Mech 1945;12:A159–64. Zhou H, Liu K, Shi G, Wang YQ, Shi YJ, De Roeck G. Fatigue assessment of a composite railway bridge for high speed trains. Part I: Modeling and fatigue critical details. J Const Steel Res 2013;82:234–45. Shen W, Yan R, He F, Wang S. Multiaxial fatigue analysis of complex welded joints in notch stress approach. Eng Fract Mech 2018;204:344–60. Sonsino CM, Fricke W, de Bruyne F, Hoppe A, Ahmadi A, Zhang G. Notch stress concepts for the fatigue assessment of welded joints – Background and applications. Int J Fatigue 2012;34(1):2–16. Park W, Miki C. Fatigue assessment of large-size welded joints based on the effective notch stress approach. Int J Fatigue 2008;30(9):1556–68. Hobbacher AF. Recommendations for Fatigue Design of Welded Joints and Components. Cham: Springer International Publishing Switzerland; 2016. Zong L, Shi G, Wang Y, Li Z, Ding Y. Experimental and numerical investigation on fatigue performance of non-load-carrying fillet welded joints. J Constr Steel Res 2017;130:193–201. Anderson TL. Fracture Mechanics: Fundamentals and Applications. Boca Raton, FL: CRC Press; 2017. Hobbacher A. The use of fracture mechanics in the fatigue analysis of welded joints. In: Macdonald KA, editor. Fracture and Fatigue of Welded Joints and Structures. Cambridge: Woodhead Publishing Limited; 2011. p. 91–112. Zehnder AT. Fracture Mechanics. New York: Springer; 2011. Newman Jr JC, Raju IS. An empirical stress-intensity factor equation for the surface crack. Eng Fract Mech 1981;15(1–2):185–92. Bowness D, Lee M. Prediction of weld toe magnification factors for semi-elliptical cracks in T–butt joints. Int J Fatigue 2000;22(5):369–87. Lie ST, Vipin SP, Li T. New weld toe magnification factors for semi-elliptical cracks in double-sided T-butt joints and cruciform X-joints. Int J Fatigue 2015;80:178–91. Lie ST, Zhao HS, Vipin SP. New weld toe magnification factors for semi-elliptical cracks in plate-to-plate butt-welded joints. Fatigue Fract Eng Mater Struct 2017;40(2):207–20. Barsoum Z, Jonsson B. Fatigue assessment and LEFM analysis of cruciform joints fabricated with different welding processes. Weld World 2008;52(7–8):93–105. Zong L, Shi G, Wang Y, Yan J, Ding Y. Investigation on fatigue behaviour of loadcarrying fillet welded joints based on mix-mode crack propagation analysis. Arch Civ Mech Eng 2017;17(3):677–86. Zong L, Shi G, Wang Y, Zhou H. Fatigue assessment on butt welded splices in plates of different thicknesses. J Constr Steel Res 2017;129:93–100. Rozumek D, Faszynka S. Fatigue crack growth in 2017A–T4 alloy subjected to proportional bending with torsion. Fract Struct Integrity 2017;11(42):23–9. Lee SB. Fatigue failure of welded vertical members of a steel truss bridge. Eng Fail Anal 1996;3(2):103–8. Xiao ZG, Yamada K, Inoue J, Yamaguchi K. Fatigue cracks in longitudinal ribs of steel orthotropic deck. Int J Fatigue 2006;28(4):409–16. Kaufmann H, Sonsino CM, Demofonti G, Riscifuli S. High-Strength Steels in Welded State for Light-Weight Constructions under High and Variable Stress Peaks. Steel Res Int 2008;79(5):382–9. Akyel A, Kolstein MH, Bijlaard FSK. Fatigue strength of repaired welded connections made of very high strength steels. Eng Struct 2018;161:28–40. ABAQUS, ABAQUS User’s Manual Version 6.14-4, Dassault Systèmes Simulia Corp, Providence, 2014. Franc3D, Reference Manual for Version 7.3, Fracture Analysis Consultants Inc., 2019. Su H, Wang J, Du JS. Experimental and numerical study of fatigue behavior of bridge weathering steel Q345qDNH. J Constr Steel Res 2019;161:86–97. AASHTO/AWS D1.5M/D1.5. Bridge Welding Code, American Welding Society, Miami, 2015. Paris P, Erdogan F. A critical analysis of crack propagation laws. J Basic Eng 1963;85(4):528–33. Ibsø JB, Agerskov H. An analytical model for fatigue life prediction based on fracture mechanics and crack closure. J Constr Steel Res 1996;37(3):229–61. Bowness D, Lee MMK. Stress intensity factor solutions for semi-elliptical weld-toe cracks in T-butt geometries. Fatigue Fract Eng Mater Struct 1996;19(6):787–97. The British Standards Institution. BS7910 Guide to Methods for Assessing the Acceptability of Flaws in Metallic Structures. London: BSI Standards Limited; 2013.
Contents lists available at ScienceDirect
Structures journal homepage: www.elsevier.com/locate/structures
Fatigue behavior of uncorroded butt welded joints made of bridge weathering steel
T
⁎
Han Su, Jian Wang, Jinsheng Du
School of Civil Engineering, Beijing Jiaotong University, Beijing 100044, China
A R T I C LE I N FO
A B S T R A C T
Keywords: Uncorroded bridge weathering steel Butt welded joint Fatigue behavior Fracture mechanics Mixed-mode fatigue crack propagation simulation
Bridge weathering steel produced in China has been employed in bridges worldwide, among them Q345qNH is the most commonly used steel grade. Fatigue behavior of uncorroded butt welded joints made of bridge weathering steel Q345qNH was explored in this paper. Fatigue tests were conducted on 13 specimens involving 9 stress ranges, S-N curve and its lower bound of 95% survival probability were established. It was observed that the design S-N curve for butt welded joint in Eurocode 3 is suitable for fatigue assessment of this batch of specimens and provides a considerable safety margin. Numerical simulation of mixed-mode fatigue crack propagation and analytical investigation of fatigue crack propagation were conducted, it was found that numerical simulation is preferred since it considers the variation in stress due to crack propagation. The influences of initial crack size, initial crack shape, initial crack location and angular misalignment of plates on fatigue behavior of butt welded joints were investigated, the expression between fatigue life and initial crack size was derived. Additionally, it is recommended that a semi-elliptical crack with initial crack depth of 0.2 mm and initial aspect ratio of 1/4 to be adopted when information on initial crack is unavailable. The fatigue test results provide reference for fatigue design of steel bridges made of coated weathering steel and serve as control for analysis of deterioration of fatigue behavior due to corrosion for corroded butt welded joints made of uncoated weathering steel.
1. Introduction Addition of alloy elements including Copper, Nickle, Chrome and others gives weathering steel better corrosion resistance than normal carbon steel [1,2]. Weathering steel can be used as coated, uncoated and rust layer stabilized [3]. When weathering steel is uncoated, dense and protective rust layer is formed on top of substrate base metal which protects itself from further corrosion; when weathering steel is coated in severely corrosive environments, it provides extended coating service life since the dense and protective rust layer prevents the coating from falling off [4,5]. It is gaining increasing popularity in China and worldwide due to its reduced overall costs of steel structures in their lifecycles [6]. In design codes such as Eurocode 3 [7] and AASHTO [8], S-N curves which are derived from nominal stress and hot spot stress [9–13] and the Palmgren-Miner accumulative damage rule [14] are adopted to assess fatigue damage, however this approach becomes ineffective when fatigue details are not covered in design codes or fatigue details experience multiaxial stresses [15]. Notch stress method [16–18] has been proposed as an alternative to assess fatigue performance, IIW [19]
⁎
proposes the universal design S-N curve derived from notch stress, which is applicable to all types of fatigue details. However, the aforementioned approaches are based entirely on S-N curves which are time and capital consuming to establish, and these approaches become difficult to use when the loading history is unknown [20]. Due to the limitations of S-N curve based approaches, fracture mechanics method [21–23] which focuses on crack initiation and crack propagation has been applied in fatigue assessment. Since welding inevitably introduces initial cracks in steel bridges, and steel bridges are mostly in a fully elastic static when they are under the actions of vehicle loads, linear elastic fracture mechanics (LEFM) is especially suitable for fatigue assessment of steel bridges. Analytical stress intensity factor solutions for plates have been developed by Newman and Raju [24], these factors can be revised by modification factors to account for stress concentration caused by the presence of weld or attachment [25–27], thereafter fatigue assessment of welds can be conducted. Numerical simulations of 3D mixed-mode crack propagation were performed by Barsoum [28] and Zong [20,29,30], and simulation results agreed well with experimental results. Since steel bridges undergo long-term repeated traffic loads, they
Corresponding author. E-mail address: [email protected] (J. Du).
https://doi.org/10.1016/j.istruc.2020.01.032 Received 30 September 2019; Received in revised form 20 January 2020; Accepted 23 January 2020 2352-0124/ © 2020 Institution of Structural Engineers. Published by Elsevier Ltd. All rights reserved.
Structures 24 (2020) 377–385
H. Su, et al.
are prone to have fatigue problems, and fatigue of materials could cause abrupt destruction of steel bridges which results in disasters [31], as evidenced by the sudden collapse of Seongsu Bridge in Korea in 1994 which was caused by fatigue crack initiated from a welded vertical member [32]. Butt welded joint is among the most widely used types of connections in practical fabrication of bridges [15,30]. Since bridges experience cyclic fatigue loads and butt welded joints are vulnerable to fatigue damage [33], fatigue behavior of butt welded joints should be investigated. Fatigue behavior of butt welded joints have been investigated by many researchers. Kaufmann et al. [34] investigated fatigue behavior of butt welded joints made of S355N, S355M, S690Q and S960Q, it was found that butt welded joints made of S960Q performed better under variable amplitude loading and in the case of overloads. Zong et al. [30] assessed fatigue behavior of butt welded joints connecting plates with different thicknesses made of normal carbon steel Q345qD, and found that all specimens satisfied the fatigue requirements of Eurocode 3. Akyel et al. [35] tested fatigue strength of repaired butt welded joints made of S690 and S890, and found that repair procedure recovered fatigue strength of damaged butt welded joints. However, there are scarce researches regarding the fatigue behavior of butt welded joints made of weathering steel. This paper investigates the fatigue behavior of uncorroded butt welded joints made of bridge weathering steel Q345qDNH. Fatigue tests were conducted on 13 butt welded joint specimens which were under 9 stress ranges, S-N curve and its lower bound of 95% survival probability were established. Mixed-mode crack propagation was then simulated by ABAQUS [36] and FRANC3D [37] and then compared with analytical solution. The influences of initial crack size, initial crack shape, initial crack location and angular misalignment of plates on fatigue behavior of butt welded joints were analyzed and discussed, and suitable initial crack was recommended. The results provide reference for fatigue design of steel bridges made of coated weathering steel and for comparison with corroded butt welded joints made of uncoated weathering steel, and they could serve as control to analyze deterioration of fatigue behavior due to corrosion in the future study.
Fig. 2. Design geometry of butt welded joint.
2. Experimental details 2.1. Specimen preparation Fatigue detail of butt welded joint with temporary ceramic backing in Eurocode 3 [7] with a fatigue strength of 71 MPa was chosen to investigate the fatigue behavior of butt welded joint, as indicated in Fig. 1. The design geometry of butt welded joint specimen is illustrated in Fig. 2, and a typical finished butt welded joint is illustrated in Fig. 3. The butt welded joints were made from the same batch of steel plates and welding wires as in [38], the mechanical properties are included in Table 1. The butt welded joint specimens were fabricated by CO2 arc welding with welding current of 240 ± 20 A and welding voltage of 30 ± 2 V. The design geometry of the weld is shown in Fig. 4, the groove was welded from the top by seven weld beads with a temporary ceramic backing on the bottom. The butt welded joints were proved to be of good quality by non-destructive testing. The variations in straightness of specimens were checked and the requirements of American Standard AASHTO/AWS D1.5M/D1.5 “Bridge Welding Code” were met [39]. Before fatigue tests, geometric dimensions of butt welded joints
Fig. 3. A typical finished butt welded joint. Table 1 Mechanical properties of Q345qDNH base metal and CHT71NHQ welding wire. Content
fy (MPa)
fu (MPa)
A (%)
Yield strength ratio
E (GPa)
Base metal Welding wire
413 485
550 561
30 24.5
0.75 0.86
206 –
Fig. 4. Design geometry of butt welds.
were measured by image processing approach to facilitate establishment of finite element model, as shown in Fig. 5, Measured geometric dimensions are tabulated in Table 2. Fig. 1. Typical butt welded joint with temporary ceramic backing. 378
Structures 24 (2020) 377–385
H. Su, et al.
Fig. 5. Geometric profile of butt welded joints.
2.2. Experimental details The tests were carried out at room temperature. The specimens were loaded on QBG-250 High Frequency Fatigue Tester with constant amplitude, the experimental setup was shown in Fig. 6. The loading capacity of the machine is ± 25 tons. The stiffness of the specimen determines the loading frequency, the stiffness of the specimen decreases as the crack propagates, leading to a decrease in loading frequency. The specimens were tested under initial loading frequency of 101.4–114.9 Hz. The boundary conditions were that the bottom plate was fixed while the axial tensile stress was applied on the top plate. The stress ratio was set to be 0.1 for all specimens. The maximum number of loading cycles was set to be 5 million. The fatigue test would terminate if either the loading frequency decreases by 10 Hz or the number of loading cycles reaches 5 million. If the latter case happens, the specimen will be labelled as run out. The maximum stress was set to be 100 MPa for the first specimen, which corresponds to a stress range of 90 MPa. If the specimen fails, the maximum stress would increase by 10 MPa for the next test, otherwise the maximum stress would increase by 20 MPa. 13 specimens were tested and results for 9 stress ranges were obtained. For each test, the loading machine was momentarily paused when loading frequency decreases by 2 Hz, which indicated that the crack might have propagated to a visible size. The location of the visible crack was measured and recorded, and the location was deemed to be the location of crack initiation.
Fig. 6. Experimental setup.
Fig. 7. Fatigue test results and S-N curve from Eurocode 3.
3. Experimental observations and results
130.4 MPa, the computed fatigue strength according to lower bound of 95% survival probability is 111.4 MPa, which are both considerably larger than the design fatigue strength of 71 MPa. It is observed that the S-N curve in Eurocode 3 safely covers all the test results for this batch of specimens and also offers a considerable safety margin.
3.1. Fatigue test results Among the test results of 13 specimens, 9 specimens failed, and 4 specimens were run outs. The test results along with the S-N curve corresponding to this specific fatigue detail in Eurocode 3 [7] were plotted in logarithmic coordinates in Fig. 7. The 9 valid test results were linearly fitted with a fixed slope of m = 3, the lower bound of 95% survival probability was also derived according to the test data evaluation approach recommended by Hobbacher [19]. The average ratio between the recorded fatigue life and the computed fatigue life according to the lower bound of 95% survival probability is 2.16, the average ratio between the recorded fatigue life and the computed fatigue life according to design S-N curve from Eurocode 3 is 8.36, the average ratio between the computed fatigue life according to lower bound of 95% survival probability and the computed fatigue life according to design S-N curve from Eurocode 3 is 3.86. The computed fatigue strength according to linearly fitted S-N curve of test results is
3.2. Initial crack location and critical crack depth Locations of crack initiation of every failed specimens were observed and recorded. It was found that all cracks initiated from the intersection line between butt weld and base metal, as shown in Fig. 8. A local measuring coordinate was established to facilitate measurement and recording of crack initiation locations, as illustrated in Fig. 9(a). The average measured location of crack initiation was found to be 5.44 mm away from the longitudinal edge of the specimen and is illustrated in Fig. 9(b). When the fatigue tests finished, the cracked specimens were loaded to complete fracture to facilitate observing the depth of the crack, it was observed that the crack occupied
Table 2 Average geometric dimensions of butt welded joints. Category
t/mm
B1/mm
C1/mm
B2/mm
C2/mm
α/degrees
θ/degrees
Mean value
16.24
32.62
2.97
17.43
2.15
0.04
19.98
379
Structures 24 (2020) 377–385
H. Su, et al.
b) Critical crack size acr, c) Appropriate fatigue crack growth rate parameters C and m, d) Stress intensity factor ΔK.
4.2. Simulation details The finite element model of the butt welded joint was established according to the geometric dimensions tabulated in Table 2. The bottom plate was fixed, the axial stress was applied on the end of the top plate, which were in line with actual experimental boundary conditions. The applied stresses were also consistent with fatigue tests. The material was assumed to be perfectly elastic. Element type C3D20 was chosen. Ibsø and Agerskov [41] investigated the initial crack geometry and determined that the initial aspect ratio a0/c0 to be 1/4, the initial crack depth a0 scatters from 0.075 mm to 0.4 mm. Thus, different initial crack depths which are 0.075 mm, 0.1 mm, 0.2 mm, 0.3 mm and 0.4 mm were considered, and initial aspect ratio was taken as 1/4. When the fatigue tester stopped due to a drop in loading frequency of 10 Hz caused by rapid propagation of fatigue crack, the crack depth occupied approximately half of the plate depth, therefore the critical crack size acr is determined to be 8 mm to be consistent with experimental observations. The fatigue crack growth rate parameters of the same batch of Q345qDNH have been measured in [38], the results derived from group specimen method were adopted in this analysis, where logC is taken as −10.37 and m is taken as 2.38. Fatigue crack growth threshold is assumed to be non-existent, which results in a conservative prediction of fatigue life, and the Paris Law becomes applicable to propagation of tiny cracks under this assumption. After the crack was inserted in FRANC3D, the model was re-meshed, as shown in Fig. 10. The stress intensity factor was calculated by the interaction integral method. Due to angular misalignment of plates and geometric asymmetry after insertion of crack, the crack is a mixedmode crack, thus the maximum tensile stress (MTS) criterion was applied to account for mixed-mode crack, and the corresponding effective stress intensity factor range was calculated by [42]:
Fig. 8. Location of crack initiation and crack propagation.
approximately half of the plate depth. 4. Numerical simulation 4.1. Fatigue crack simulation First of all, the finite element model is established and boundary conditions are applied in ABAQUS. Secondly, the model is exported to FRANC3D for inserting the crack. Thereafter, the model is being remeshed by wedge and hex elements near the crack tip, while remaining areas will be re-meshed by tet elements, and displacements will be calculated. Finally, the crack front will be repeatedly updated by using the calculated displacements, and the model will be iteratively re-meshed accordingly. Crack propagation direction, which is also called kink angle, and the equivalent stress intensity range model are two criteria which need to be determined for numerical simulation to progress. The size of crack extension is predetermined in FRANC3D, the number of loading cycles is calculated by Paris Law [40]:
Ni =
∫a
ai + 1
i
da C (ΔK )m
(i = 1, 2, 3, ...,n)
(1)
where Ni is the number of loading cycles, ai is the initial crack size of the ith step, ai+1 is the predetermined size of crack extension, C and m are fatigue crack growth rate parameters. The fatigue life can be calculated by n
N=
acr
∑ Ni = ∫a0 1
da C (ΔK )m
(2)
where N is the fatigue life, a0 is the initial crack size, acr is the critical crack size. As can be seen from Eq. (2), to predict the fatigue life accurately, four sets of parameters need to be determined:
ΔK eff =
a) Initial crack size a0,
ΔK eff =
KI2 + KII2 +
2 KIII (1 − ν )
(3)
where ν is Poisson’s ratio, which is 0.3 for steel, thus 2 KI2 + KII2 + 1.429KIII
Fig. 9. Measurement of initial crack location. 380
(4)
Structures 24 (2020) 377–385
H. Su, et al.
Fig. 10. Crack insertion of butt welded joint by FRANC3D.
4.3. Simulation results and determination of initial crack
5. Discussion
The simulation results of different initial crack sizes are presented in Fig. 11. The test results, the design S-N curve corresponding to this specific fatigue detail in Eurocode 3, the fitted experimental S-N curve of test results and the lower bound of 95% survival probability are also presented. The fatigue strengths for initial crack sizes of 0.075 mm, 0.1 mm, 0.2 mm, 0.3 mm and 0.4 mm are 111.3 MPa, 106.5 MPa, 94.2 MPa, 86.8 MPa and 81.1 MPa respectively. It is found that when the initial semi-elliptical crack depth is 0.2 mm for this batch of specimens, the numerical simulation could cover all the test results and provide reasonably accurate predictions of fatigue lives.
5.1. Size of initial crack The initial crack size influences fatigue behavior significantly, thus its influence on fatigue behavior needs to be analyzed. The predicted fatigue lives of butt welded joint specimens when the stress range is 110 MPa with initial crack depths of 0.075 mm, 0.1 mm, 0.2 mm, 0.3 mm and 0.4 mm are derived and plotted in Fig. 12. Regression analysis was conducted and the expression between fatigue life and initial crack depth is derived as
N = (2.534 − 7.421a0 + 8.856a0 2)·106 (0.075 ⩽ a0 ⩽ 0.4)
(5)
It can be seen that as the initial crack depth increases, the predicted fatigue life decreases dramatically. The reason is that stress intensity factors correspond to tiny cracks are low, therefore cracks propagate at extraordinarily slow rates, consequently considerable number of
Fig. 11. Predicted S-N curves by numerical simulation. 381
Structures 24 (2020) 377–385
H. Su, et al.
However, for this batch of specimens, aspect ratio of 1/4 is still recommended as it better reflects their fatigue behavior. 5.3. Location of initial crack The aforementioned analyses assumed that the crack initiated from the average measured location of crack initiation. However, crack could initiate from various locations in reality, ranging from the center of the plate to the corner of the plate, as shown in Fig. 14. Thus, the influence of initial crack location on fatigue behavior of butt welded joints needs to be investigated. The S-N curves and a-N curves of center crack, average measured crack and corner with an initial crack size of 0.2 mm and initial aspect ratio of 1/4 are derived by numerical simulation and plotted in Fig. 15. The fatigue strengths for center crack, average measured crack and corner crack are 97.9 MPa, 97.3 MPa and 94.2 MPa respectively, the differences between fatigue strengths for center crack, corner crack and fatigue strength for average measured crack are 3.8%, and 3.2%, the differences between fatigue lives for center crack, corner crack and fatigue life for average measured crack are 9.2% and 7.8%. Therefore, it was found that the influence of initial crack location on fatigue behavior of butt welded joint is insignificant. The influence of initial crack location on fatigue behavior of butt welded joints can also be investigated analytically. Newman and Raju [24] have developed analytical stress intensity factor solutions for semielliptical center and corner surface flaws in plates, and these solutions are adopted by BS 7910 [43]. The stress intensity factor is calculated by:
Fig. 12. Influence of size of initial crack on fatigue behavior of butt welded joints.
loading cycles is required to propagate the crack a short distance. The importance of accurately measuring the initial crack size by non-destructive testing techniques is thus being stressed. 5.2. Shape of initial crack The aforementioned analyses were conducted under the assumption that the aspect ratio a0/c0 is 1/4. Although this assumption is supported by Ibsø and Agerskov [41], the exact aspect ratio may vary in reality. Thus, the influence of initial crack shape on fatigue behavior of butt welded joints needs to be investigated. The S-N curves and a-N curves with aspect ratio ranging from 1/1 to 1/4 and initial crack size of 0.2 mm are derived by numerical simulation and plotted in Fig. 13. The fatigue strengths for initial crack aspect ratio of 1/1, 1/2, 1/3 and 1/4 are 107.8 MPa, 101.3 MPa, 97.2 MPa and 94.2 MPa respectively, the differences between fatigue strengths for initial crack aspect ratio of 1/1, 1/2, 1/3 and fatigue strength for initial crack aspect ratio of 1/4 are 12.6%, 7.0% and 3.1%, the differences between fatigue lives for initial crack aspect ratio of 1/1, 1/2, 1/3 and fatigue life for initial crack aspect ratio of 1/4 are 38.5%, 15.9% and 7.7%. Therefore, it can be concluded that the influence of initial crack shape on fatigue behavior of butt welded joint is relatively significant.
K = (Mkt St + Mkb HSb) π
a a a c F ⎛ , , , ϕ⎞ Q ⎝t c b ⎠
(6)
where St and Sb are the tension and bending stresses respectively. Mkt and Mkb are the magnification factors for applied tension and bending stresses respectively, which are functions of a/t, c/a, B1/t and θ [25], where θ is the weld angle and θ is taken as 0.349 for this batch of specimens. H is a function of H1, H2 and p that can be calculated by Eq. (7). Q is the shape factor for elliptical crack that can be calculated by Eq. (8). F is the stress intensity boundary correction factor which is a function of a/t, a/c, c/b and ϕ that can be calculated by Eq. (9).
H = H1 + (H2 − H1)sinp ϕ
(7)
where H1 and H2 are functions of a/t. p is a function of a/c and a/t.
Fig. 13. Influence of shape of initial crack on fatigue behavior of butt welded joints. 382
Structures 24 (2020) 377–385
H. Su, et al.
Fig. 14. Center crack and corner crack.
Fig. 15. Influence of location of initial crack on fatigue behavior of butt welded joints by numerical simulation.
Fig. 16. Influence of location of initial crack on fatigue behavior of butt welded joints by analytical approach.
383
Structures 24 (2020) 377–385
H. Su, et al.
Fig. 17. Influence of misalignment of plates on fatigue behavior of butt welded joints by analytical approach.
a 1.65 Q = 1 + 1.464 ⎛ ⎞ ⎝c⎠
a ⎛ ⩽ 1⎞ ⎝c ⎠
2
straightness to be up to 1 mm/m. Since angular misalignment in plates introduces stress concentration, it could be extraordinarily harmful for fatigue behavior, hence the influence of angular misalignment on fatigue behavior of butt welded joints needs to be investigated. The effectiveness of analytical method to explore the influence of parameters on fatigue behavior has been illustrated in Section 5.3, therefore the influence of angular misalignment on fatigue behavior of butt welded joints are also investigated by analytical method. When the stress range is 110 MPa, the K-a curves and a-N curves of different variations in straightness with an initial center crack whose size is 0.2 mm and initial aspect ratio of 1/4 are derived analytically and plotted in Fig. 17. It can be seen that as the variation in straightness increases, the stress intensity factor also increases, resulting in decrease in fatigue life. The difference of stress intensity factors at fracture between 0 and 1 mm/m variation in straightness is 2.1%, the difference of fatigue life between 0 and 1 mm/m variation in straightness is 9.4%. Therefore, it can be concluded that as long as welding meets the fabrication requirements prescribed in AASHTO/AWS D1.5 M/D1.5, the influence of angular misalignment on fatigue behavior of butt welded joints can be regarded as relatively insignificant.
(8)
4
a a F = ⎡M1 + M2 ⎛ ⎞ + M3 ⎛ ⎞ ⎤ fϕ gfw ⎢ ⎝t ⎠ ⎥ ⎝t ⎠ ⎣ ⎦
(9)
where M1, M2 and M3 are functions of a/c. f ϕ is a function of a/c and ϕ. g is a function of a/t and ϕ. fw is a finite width correction factor which is a function of c/b and a/t. The bending stress Sb is caused by misalignment in butt welds. For the butt welded joints which have fixed ends, Sb can be calculated by [43]:
Sb = St
3α l ⎛ tanh(β /2) ⎞ ⎜ ⎟ t ⎝ β /2 ⎠
(10)
where l is half the length of the butt welded joint specimen. β is calculated by
β=
2 l ⎛ 3σmax, m ⎞0.5 t ⎝ E ⎠
(11)
where σmax,m is the membrane component of the maximum applied tensile stress which can be calculated with the assistance of the finite element model in Section 4. Consequently, when the stress range is 110 MPa, the K-a curves and a-N curves of center crack and corner with an initial crack size of 0.2 mm and initial aspect ratio of 1/4 are derived analytically and plotted in Fig. 16. The difference of stress intensity factors at fracture between center crack and corner crack is 10.4%, the difference of fatigue life between center crack and corner crack is 12.1%. Therefore, the finding is consistent with the conclusion drawn from numerical simulation that the influence of initial crack location on fatigue behavior of butt welded joint is insignificant. However, fatigue lives obtained analytically are considerably lower than those obtained numerically, the reason is that the local bending stress caused by misalignment decreases as crack propagates, however the decrease in local bending stress cannot be taken into account by analytical approach.
6. Conclusions This paper investigated the fatigue behavior of uncorroded butt welded joints made of bridge weathering steel Q345qDNH, the results provide reference for fatigue design of steel bridges made of coated weathering steel and serve as control for analysis of deterioration of fatigue behavior due to corrosion for corroded butt welded joints made of uncoated weathering steel. Fatigue tests were conducted on 13 butt welded joint specimens which were under 9 stress ranges, mixed-mode crack propagation was numerically simulated by ABAQUS and FRANC3D, and analytical analyses were conducted. The influences of initial crack size, initial crack shape, initial crack location and angular misalignment of plates on fatigue behavior of butt welded joints were analyzed and discussed, and suitable initial crack was recommended. Main conclusions are as follows: 1. 9 effective fatigue test data which were under 9 stress ranges were obtained, S-N curve and its lower bound of 95% survival probability were established. It was found that the design S-N curve for butt welded joint in Eurocode 3 is suitable for fatigue assessment of this batch of specimens made of bridge weathering steel Q345qDNH and provides a considerable safety margin. 2. Numerical simulation of mix-mode fatigue crack propagation and
5.4. Angular misalignment of plates The average measured angular misalignment between the two plates of specimens tested in this research is 0.04 degrees, as shown in Table 2, which corresponds to a variation in straightness of 0.7 mm/m. However, AASHTO/AWS D1.5 M/D1.5 [39] allows for the variation in 384
Structures 24 (2020) 377–385
H. Su, et al.
analytical investigation of fatigue crack propagation were conducted. It was observed that numerical simulation gives more accurate prediction results as it is able to take into account the variation in stress due to crack propagation while analytical method cannot, therefore numerical simulation can better reflect the stress redistribution and crack propagation. 3. The initial crack assumption was investigated, it is recommended that when information on initial crack is not available, a semi-elliptical crack with initial crack size of 0.2 mm and initial aspect ratio of 1/4 can be used to obtain reasonably accurate predicted fatigue life. 4. The influences of initial crack size, initial crack shape, initial crack location and angular misalignment of plates on fatigue behavior of butt welded joints were investigated. The initial crack size influences fatigue behavior significantly, the expression between fatigue life and initial crack depth was derived; the influence of initial crack shape on fatigue behavior of butt welded joint is relatively significant; the influence of initial crack location on fatigue behavior of butt welded joint is insignificant, and influence of angular misalignment on fatigue behavior of butt welded joints can be regarded as relatively insignificant as long as welding meets the fabrication requirements prescribed in standards.
[11] [12] [13] [14] [15]
[16] [17]
[18] [19] [20]
[21] [22]
[23] [24]
Declaration of Competing Interest
[25]
The authors declare that they have no known competing financial interests or personal relationships that could have appeared to influence the work reported in this paper.
[26] [27]
Acknowledgments [28]
Funding: “Application Expressway” Construction
This work was sponsored by the research project of of High Performance Weathering Steel in Hai’an-Qidong from Jiangsu Provincial Transportation Engineering Bureau (No. C18L01160).
[29]
[30] [31]
References
[32]
[1] Diaz I, Cano H, de la Fuente D, Chico B, Vega JM, Morcillo M. Atmospheric corrosion of Ni-advanced weathering steels in marine atmospheres of moderate salinity. Corros Sci 2013;76:348–60. [2] Kamimura T, Hara S, Miyuki H, Yamashita M, Uchida H. Composition and protective ability of rust layer formed on weathering steel exposed to various environments. Corros Sci 2006;48(9):2799–812. [3] Guo XY, Kang JF, Zhu JS, Duan MH. Corrosion Behavior and Mechanical Property Degradation of Weathering Steel in Marine Atmosphere. J Mater Civ Eng 2019;31(9):04019181. [4] Qian Y, Ma C, Niu D, Xu J, Li M. Influence of alloyed chromium on the atmospheric corrosion resistance of weathering steels. Corros Sci 2013;74:424–9. [5] Damgaard N, Walbridge S, Hansson C, Yeung J. Corrosion protection and assessment of weathering steel highway structures. J Constr Steel Res 2010;66(10):1174–85. [6] McConnell J, Shenton III HW, Mertz DR, Kaur D. National Review on use and performance of uncoated weathering steel highway bridges. J Bridge Eng ASCE 2014;19(5):04014009. [7] European Committee for Standardization (CEN), EN 1993-1-9 Eurocode 3, Design of steel structures-part 1-9: fatigue, Brussels, 2009. [8] American Association of State Highway and Transportation Officials (AASHTO). LRFD Bridge Design Specifications. eighth ed. Washington, DC: AASHTO; 2017. [9] Niemi E, Fricke W, Maddox SJ. Structural Hot-Spot Stress Approach to Fatigue Analysis of Welded Components. 2nd ed. Singapore: Springer Nature Singapore Pte Ltd.; 2018. [10] Poutiainen I, Tanskanen P, Marquis G. Finite element methods for structural hot
[33] [34]
[35] [36] [37] [38] [39] [40] [41] [42] [43]
385
spot stress determination – a comparison of procedures. Int J Fatigue 2004;26(11):1147–57. Xiao Z, Yamada K. A method of determining geometric stress for fatigue strength evaluation of steel welded joints. Int J Fatigue 2004;26(12):1277–93. Dong P. A structural stress definition and numerical implementation for fatigue analysis of welded joints. Int J Fatigue 2001;23(10):865–76. Savaidis G, Vormwald M. Hot-spot stress evaluation of fatigue in welded structural connections supported by finite element analysis. Int J Fatigue 2000;22(2):85–91. Miner MA. Cumulative Damage in Fatigue. J Appl Mech 1945;12:A159–64. Zhou H, Liu K, Shi G, Wang YQ, Shi YJ, De Roeck G. Fatigue assessment of a composite railway bridge for high speed trains. Part I: Modeling and fatigue critical details. J Const Steel Res 2013;82:234–45. Shen W, Yan R, He F, Wang S. Multiaxial fatigue analysis of complex welded joints in notch stress approach. Eng Fract Mech 2018;204:344–60. Sonsino CM, Fricke W, de Bruyne F, Hoppe A, Ahmadi A, Zhang G. Notch stress concepts for the fatigue assessment of welded joints – Background and applications. Int J Fatigue 2012;34(1):2–16. Park W, Miki C. Fatigue assessment of large-size welded joints based on the effective notch stress approach. Int J Fatigue 2008;30(9):1556–68. Hobbacher AF. Recommendations for Fatigue Design of Welded Joints and Components. Cham: Springer International Publishing Switzerland; 2016. Zong L, Shi G, Wang Y, Li Z, Ding Y. Experimental and numerical investigation on fatigue performance of non-load-carrying fillet welded joints. J Constr Steel Res 2017;130:193–201. Anderson TL. Fracture Mechanics: Fundamentals and Applications. Boca Raton, FL: CRC Press; 2017. Hobbacher A. The use of fracture mechanics in the fatigue analysis of welded joints. In: Macdonald KA, editor. Fracture and Fatigue of Welded Joints and Structures. Cambridge: Woodhead Publishing Limited; 2011. p. 91–112. Zehnder AT. Fracture Mechanics. New York: Springer; 2011. Newman Jr JC, Raju IS. An empirical stress-intensity factor equation for the surface crack. Eng Fract Mech 1981;15(1–2):185–92. Bowness D, Lee M. Prediction of weld toe magnification factors for semi-elliptical cracks in T–butt joints. Int J Fatigue 2000;22(5):369–87. Lie ST, Vipin SP, Li T. New weld toe magnification factors for semi-elliptical cracks in double-sided T-butt joints and cruciform X-joints. Int J Fatigue 2015;80:178–91. Lie ST, Zhao HS, Vipin SP. New weld toe magnification factors for semi-elliptical cracks in plate-to-plate butt-welded joints. Fatigue Fract Eng Mater Struct 2017;40(2):207–20. Barsoum Z, Jonsson B. Fatigue assessment and LEFM analysis of cruciform joints fabricated with different welding processes. Weld World 2008;52(7–8):93–105. Zong L, Shi G, Wang Y, Yan J, Ding Y. Investigation on fatigue behaviour of loadcarrying fillet welded joints based on mix-mode crack propagation analysis. Arch Civ Mech Eng 2017;17(3):677–86. Zong L, Shi G, Wang Y, Zhou H. Fatigue assessment on butt welded splices in plates of different thicknesses. J Constr Steel Res 2017;129:93–100. Rozumek D, Faszynka S. Fatigue crack growth in 2017A–T4 alloy subjected to proportional bending with torsion. Fract Struct Integrity 2017;11(42):23–9. Lee SB. Fatigue failure of welded vertical members of a steel truss bridge. Eng Fail Anal 1996;3(2):103–8. Xiao ZG, Yamada K, Inoue J, Yamaguchi K. Fatigue cracks in longitudinal ribs of steel orthotropic deck. Int J Fatigue 2006;28(4):409–16. Kaufmann H, Sonsino CM, Demofonti G, Riscifuli S. High-Strength Steels in Welded State for Light-Weight Constructions under High and Variable Stress Peaks. Steel Res Int 2008;79(5):382–9. Akyel A, Kolstein MH, Bijlaard FSK. Fatigue strength of repaired welded connections made of very high strength steels. Eng Struct 2018;161:28–40. ABAQUS, ABAQUS User’s Manual Version 6.14-4, Dassault Systèmes Simulia Corp, Providence, 2014. Franc3D, Reference Manual for Version 7.3, Fracture Analysis Consultants Inc., 2019. Su H, Wang J, Du JS. Experimental and numerical study of fatigue behavior of bridge weathering steel Q345qDNH. J Constr Steel Res 2019;161:86–97. AASHTO/AWS D1.5M/D1.5. Bridge Welding Code, American Welding Society, Miami, 2015. Paris P, Erdogan F. A critical analysis of crack propagation laws. J Basic Eng 1963;85(4):528–33. Ibsø JB, Agerskov H. An analytical model for fatigue life prediction based on fracture mechanics and crack closure. J Constr Steel Res 1996;37(3):229–61. Bowness D, Lee MMK. Stress intensity factor solutions for semi-elliptical weld-toe cracks in T-butt geometries. Fatigue Fract Eng Mater Struct 1996;19(6):787–97. The British Standards Institution. BS7910 Guide to Methods for Assessing the Acceptability of Flaws in Metallic Structures. London: BSI Standards Limited; 2013.