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Approach for fatigue damage assessment of welded structure considering coupling effect between stress and corrosion
International Journal of Fatigue 88 (2016) 88–95
Contents lists available at ScienceDirect
International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Approach for fatigue damage assessment of welded structure considering coupling effect between stress and corrosion Shuo Yang a,⇑, Hongqi Yang b, Gang Liu b, Yi Huang b, Lidong Wang b a b
Technical Center, Department of Oil and Gas, Bureau Veritas, Shanghai, China School of Naval Architecture and Ocean Engineering, Dalian University of Technology, Dalian, China
a r t i c l e
i n f o
Article history: Received 8 January 2016 Received in revised form 17 March 2016 Accepted 18 March 2016 Available online 19 March 2016 Keywords: Coupling effect Mechanochemical experiment Nonuniform corrosion Welded joint Hot spot stress Fatigue damage
a b s t r a c t This paper presents a new approach to assess time-dependent corrosion fatigue damage of welded joint considering the coupling effect between mechanical factor and corrosion factor. The high stress region around weld will accelerate corrosion and be more likely to induce nonuniform corrosion of welded joint. And the effect of loading on corrosion behavior of the steel in NaCl solution was investigated. The synergistic effect between applied elastic stress and chemical attack on Q235 steel was evaluated by electrochemical experiments. A side longitudinal of ship structure is selected as a case study. Time-dependent stress concentration factor of welded joint as a function of corrosion deterioration was analyzed, and the iterative process of stress and corrosion degeneration of plate thickness was used to simulate coupling effect basing on the results of experiment. The hot spot stress approach was adopted to calculate the fatigue damage. It is revealed that the nonuniform corrosion could influence fatigue damage of welded joint, and that impact will be more and more significant with the growth of corrosion year. Ó 2016 Published by Elsevier Ltd.
1. Introduction Fatigue cracking may be the most important type of damage in welded structure [1,2], which is also a major requirement in design of marine structures. These requirements have been reflected in some design rules published by Classification Societies [3,4]. Compared with land structures, marine structures have a long term electrochemical reaction with seawater, and the surface of the structure may be subjected to more severe corrosion. Many experiments manifested [5,6] that fatigue life in corrosive environment is significantly lower than it in air. Therefore, the effects of mechanical and environmental factors on fatigue life are not a simple line relation but a complex one. The combined action of cyclic loading and aggressive environment often result in a significant reduction in fatigue performance compared with that obtained under cyclic loading in air. For a more accurate assessment of fatigue damage in corrosive environment, it is necessary to consider the coupling effects of corrosion and stress in some cases. Recently engineering methods accounting for corrosion had been introduced in some design rules [3,4]. The guidelines of several Classification Societies defined the values of corrosion addition in different local structures, and then reduced corrosion addition of
⇑ Corresponding author. E-mail address: [email protected] (S. Yang). http://dx.doi.org/10.1016/j.ijfatigue.2016.03.024 0142-1123/Ó 2016 Published by Elsevier Ltd.
ship structures in order to calculate the hot spot stress adjacent to critical joint such as weld toe, and finally evaluated fatigue damage according to S–N curve in air and Palmgren–Miner’s rule. And for those structures without corrosion protection, the guidelines used the S–N curve in corrosive environment which is more conservative. Engineering methods are simple and practical without considering the time effect on corrosion. In order to take into account the corrosion over time, timedependent corrosion wastage model has been used to calculate the fatigue damage in much research. Chakarov and Garbatov [7,8] studied the effect of general corrosion in decreasing the thickness of deck plate and found that the stress concentration factor is a function of hot spot stress and nominal stress is a nonlinear increasing with time function. Tran Nguyen et al. [9] applied the spectral fatigue damage approach to evaluate a main deck longitudinal stiffener which is considering the time-dependent corrosion effect, and found that the cumulative corrosion fatigue damage increases in all calculated cases after the failure of the corrosion protection system. However, the above calculating methods regard the corrosion reduction and fatigue as two separating processes without considering inherent coupling process between corrosion and stress, which is a limitation of these methods. Many authors studied the effect of stress on corrosion which is well known as mechanochemical interaction [10]. Gao et al. [11] reported the
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shown in Fig. 1. Fig. 1(a) and (b) shows the corrosion of welded joints in frame of No. 6 (BC6) and No. 2 (BC2) bulk carrier, it can be observed that the corrosion around fillet weld is more severe than any other place. Fig. 1(c) reveals that both the weld and the stiffeners of ship deck of No. 1 (SHT1) suffer serious corrosion in long term service for 22 years, and most of weld toe have been corroded. It can be seen from Fig. 1 that corrosion around welded joints are always more serious than any other place in ship structure sand should be paid more attention to these details. Moan [16] considered corrosion rates for steel in seawater may fluctuate between 0.04 and 1.2 mm/year, which exhibit a very large scatter depending upon the location in structure, and the investigations of Nakai et al. [15] also indicate that corrosion rates around welded joints scatter largely in different locations of ship structure, which are ranging from 0.04 to 0.77 mm/year as shown in Fig. 2. The corrosion of welded joints is not only affected by potential difference between weld and base metal, but the high stress also accelerates corrosion behavior of welded joint. The interactions between mechanical and chemical effects enhance surface reactions on materials, resulting in accelerated failure of welded joints. So the corrosion resistance of welded joints is affected by the stress distribution around welded joints. The region of high stress which is also called hot spot region will become more sensitive to corrosion, this region is vulnerable to suffer corrosion, and lead to nonuniform corrosion of welded joints over time. The combined effects of corrosion and stress may accelerate damage when welded joint is under the effect of external load.
mass loss of metal under different stress, concluded that applied stress can accelerate the corrosion, and determined the degradation of mechanical properties of steel induced by corrosion. Zhang et al. [12] investigated the effect of loading conditions on the corrosion behavior of a low carbon and low alloy steel with different microstructures in NaCl solution and results indicate that the elastic stress accelerated corrosion process of the steel significantly. The coupling effect of structures in seawater is that the thickness of structure decreased due to corrosion which increased the stress level under external load, and the higher stress in turn accelerated the corrosion so that the failure of structure happens sooner. In this study, we improve the traditional approaches of fatigue damage assessment by considering the coupling effect between corrosion and stress. The nonuniform distributed general corrosion of welded joint and the interaction between corrosion and stress are studied here. Electrochemical experiments are performed here to investigate the interaction between loading and corrosion rate. A finite element analysis (FEA) simulation procedure considering the coupling process between corrosion and stress is proposed in this paper, using a structural detail of ship structure as a case study. Time-dependent cumulative fatigue damage analysis is also performed. The aim of this work is to study the effect between stress and corrosion rate according to electrochemical experiment, and understand how nonuniform corrosion influences fatigue damage with respect to single uniform corrosion based on FEA. 2. Corrosion characteristic of welded joint The welded joints are commonly used in marine structures, and the failure around weld toe has been an area of particular concern in engineering. Kang and Kim [13,14] performed experiments for high performance steel to validate that corrosion fatigue life of the heat affected zone (HAZ) is shorter than base metal and weld metal, and HAZ exhibits a much higher stress sensitive characteristic than the others. The stress concentration around HAZ may have any influence on the corrosion and then affect the fatigue life of welded joints. To know the corrosion damage of welded joints in engineering, Nakai et al. [15] investigated the corrosion state around welded joints of eight ships include seven bulk carriers and one single hull oil tank, the service time of these ships ranges from 6 to 22 years, and the cross sections of fillet weld of ships are
3. Laboratory testing 3.1. Experimental procedures Many researchers [17–20] studied coupling effect between mechanical factor and corrosion factor by the mechanochemical tests which are made up of the mechanical tensile or bending test and electrochemical test. The present paper adopts similar method to study the coupling effect between stress and corrosion. The specimen used in this study is Q235 steel plate, which are widely used for marine structures. Mechanical properties are as follows: yield strength 235 ± 3 MPa, tensile strength 476 ± 1 MPa,
BC2-Frame (14 years)
BC6-Frame (12 years)
(a)
(b) Fig. 1. Corrosion of welded joint. (a) BC6-Frame; (b) BC2-Frame; (c) SHT1-Deck.
SHT1-Deck (22 years)
(c)
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reaction energy of corrosion. The exponential curve fitting (red trend line) is shown in Fig. 5 and it can be found from the experimental results that about a 37% increase in corrosion rate under about 80% of yield strength compare to that of no applied stress.
Corrosion thickness of welded joints (mm)
12 BC1 (10 years) BC2 (14 years) BC3 (12 years) BC4 (14 years) BC5 (6 years) BC6 (12 years) BC7 (13 years) SHT1-1 (22 years) SHT1-2 (22 years)
10
8
0.77mm/year
4. Time-dependent fatigue analysis Finite element method (FEM) is used here for analyzing the hot spot stress concentration factor of the case study, fatigue damage of welded joint can be estimated based on the calculations of hot spot stress, and nonuniform corrosion of welded joint will be considered in the calculation of FEM.
6
4
0.135mm/year 2
0.04mm/year 0
0
5
10
15
20
4.1. Finite element model 25
Time (year) Fig. 2. Corrosion data around welded joints of eight ships.
elongation 26 ± 1% and Young’s modulus (E) 206 ± 5 GPa, and the chemical composition of Q235 steel is shown in Table 1. To investigate the interaction between mechanics and corrosion during elastic deformation process, uniaxial tensile tests are performed in the 3.5 wt.% NaCl solution by using hydraulic servo fatigue testing machine (Shimadzu, Model: EHF-UM200KN). The microstructures of Q235 steel are shown in Fig. 3 and dimensions of this tensile specimen are 450 mm 50 mm 5 mm (Fig. 4(a)). The specimens are ground by emery paper to grit 1500 and then rinsed with ethanol. To obtain the stress state around the corrosion position of specimen, strain gages are pasted at critical location and the stress can be measured by the strain indicator. The constant temperature water bath is used to maintain the temperature of corrosion environment at about 24 °C, and the oxygen pump can keep dissolved oxygen in 3.5 wt.% NaCl solution ranges from 5 to 7 ppm. The PH of the Nacl solution is 7.826 in this test and the total volume of aqueous NaCl in the water bath is about 1.5-litre. The schematic diagrams are shown in Fig. 4(a)–(d). The electrochemical properties were analyzed by Princeton Model-263A electrochemical workstation, and linear polarization technique was used to measure corrosion rates of steel. A saturated silver/silver chloride electrode was used as the reference electrode, and the electrode potential of the test 0.594 VAg/AgCl. It was measured in the potential range from 10 mV to +10 mV (vs. open circuit potential) at a scanning rate of 0.1 mV/s and the tests started after immersion in solution for 0.5 h. The measurements were carried out 12 times in different load condition. The fitting curve of average corrosion rate was adopted for analysis. 3.2. General corrosion rate under various loading Fig. 5 shows the variations of general corrosion rate with time under different loading, which the measured corrosion rate is applied by a log scale. It can be seen that the general corrosion rates increase with growth of elastic stress and it is obvious that applied load can accelerate the corrosion process of steel. This behavior can be attributed to the applied load and deformation of the metal, which increased surface activity of metal and reduced
This case study is a side longitudinal of a ship structure, and the welded connection between side longitudinal and transverse frame is used for fatigue analysis. Numerical simulation is performed by commercial software ANSYS, and dimensions of the structure detail are shown in Fig. 6. The finite element analysis is influenced by mesh density and element types, and the selection of them is summarized in the guidelines [3,4] which already consider the sensibility of influenced factor above. In this study, the material used is a kind of common shipbuilding steel with typical values of mechanical properties, the modulus of elasticity and the Poisson’s ratio is 206 GPa and 0.3 respectively. Shell93 element is used for the FEA, and a function of variable thickness is used here to simulate the nonuniform corrosion around welded joint. As shown in Fig. 7(a), finer meshes are generated around welded connection, and a relatively coarse mesh is chosen far away from welded joint while the finer mesh leads to the time-consuming solution procedure. This structure is axially loaded and fatigue loads acting on the structure are selected as 4427:52 kN. The boundary condition and applied load are shown in Fig. 7(b). 4.2. Reduction of corrosion considering coupling effect It is commonly accepted that general corrosion rate of steel in seawater is about 0.1 mm/year [21], and coupon experimental results [22] of Q235 steel in different sea area of china also indicate that general corrosion rate of this steel in seawater is about 0.1 mm/year as shown in Fig. 8(a) and (b). So in this case study, the general corrosion rate 0.1 mm/year is adopted for analysis, and nonuniform corrosion caused by the acceleration of applied load on corrosion of welded joint need to be considered. The decreasing plate thickness due to corrosion will increase the stress levels adjacent to welded connection which in turn increase probability of crack initiation. According to the fitting curve between corrosion rates and loading as shown in Fig. 5, it can be assumed that relationship between corrosion rates and stress takes on an exponential function changing law, and the corrosion rate around weld joints can reach 0.137–0.14 mm/year while the stress around weld is close to yield strength. It is reasonable and in accordance with the corrosion rate of welded joints in BC6Frame which is the red trend line as shown in Fig. 2. Thickness reduction of accelerated corrosion is calculated according to exponential function changing law in Fig. 5 for 2 year intervals: from 0 to 20 years of corrosion. Corrosion around the
Table 1 Chemical composition of Q235 steel. Element Content (wt.%)
Fe 0.4978
C 0.182
Si 0.06
Mn 0.2
P 0.016
S 0.0063
Cu 0.029
Ni 0.008
Cr 0.027
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Fig. 3. Microstructure of Q235 steel in this test. (a) 150 lm; (b) 30 lm.
70
30
50
Specimen Reference Electrode In Corrosion Region
450
Corrosion Region
Pt Electrode Oxygen Pump Out
Strain Gauge
Circulator Bath
3.5% NaCl
Applied Stress
(a)
(b)
(c) Fig. 4. (a) Size and shape of specimens; (b) schematic diagram of mechanochemical experiment; (c) photos of experimental set-up.
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fatigue damage in different year could be calculated in each cyclic procedure. The extrapolation can be used for obtaining hot spot stress. The relation between hot spot stress range to be used together with S–N curve and nominal stress range is hot spot stress concentration factor (SCF):
Experimental data Fing curve of corrosion rate
-0.60
SCF ¼ -0.65
-0.70
Model
Exp2PMod1
Equation
y = a*exp(b*x)
Reduced Chi-Sqr
2.81324E-4 0.90041
Adj. R-Square
Value
0.2
-0.69455
0.00441
?$OP:F=1
b
-0.27111
0.01308
0.4
0.6
σ /σ y
0.8
1.0
Fig. 5. Relationship curve between load and corrosion rate.
welded joint are reduced as 0.137–0.14 mm/year, and the other area of model are reduced as 0.1–0.137 mm/year. Nonuniform corrosion around the hot spot region for 20 years is shown in Fig.9(a). 4.3. Hot spot stress analysis In marine structures design, most of recent guidelines published by Classification Societies are using structural hot spot stress approach for fatigue assessment of welded joints. The aim of hot spot stress analysis is to evaluate the peak stress at structural detail weld toe. The element size of mesh generated in the hot spot is t t (thickness thickness) according to fatigue guidelines [3,4]. Location of hot spot is shown in Fig. 9(b) and the principal stresses obtained at points which is 0.5t and 1.5t away from weld toe are used for extrapolation based on rHS ¼ 1:5r0:5t 0:5r1:5t : For each instant of time, residual plate thickness is obtained by subtracting accelerated corrosion wastage from the initial plate thickness (uncorroded). Being different form uniform corrosion, the accelerated corrosion wastages are diverse in different zones of welded joint which could lead to nonuniform corrosion. The calculating flow of fatigue damage accounting for coupling effect is shown in Fig. 10. External load is applied to the initial finite element model (uncorroded) and corresponding stress response is obtained from the results of solution. The stress response is used for calculating accelerated corrosion of plate thickness and a new finite element is built after reduction of corrosion wastage for the next cycle of calculating process. Coupling process of corrosion and stress is simulated by the iterative process of stress response and corrosion reduction of plate thickness, and
where DrHS is hot spot stress amplitude, and Drnom is nominal stress amplitude. The SCF as a function of time in uniform corrosion and nonuniform corrosion are shown in Fig. 11, it can be seen that SCF smoothly increases with deterioration of plate thickness during the service life of ship, and the SCF of nonuniform corrosion around welded joint increase faster than a single uniform corrosion from the begining of corrosion, which is the outcome of interaction between environment and cyclic load. Therefore, nonuniform corrosion around the welded joint has much more influence on hot spot stress range than uniform corrosion. In this case, the SCF under the influence of coupling effect is larger than uniform corrosion because of more severe localized corrosion caused by stressdependent corrosion. With the increase of corrosion time, the SCF range under the influence of the coupling effect will become more and more significant. 4.4. Time-dependent fatigue assessment The fatigue damage under nonuniform corrosion is a coupling process which is demonstrated in Fig. 10. Fatigue assessment is generally based on the S–N approach, and a two-slope S–N curve of welded joint for air is selected in this case study which a reduction of plate thickness is regarded as the influence of corrosion. The design S–N curves are shown as:
mlog Dr0 log N ¼ log a
ð2Þ
where N is predicted number of cycles to failure for stress range is the interDr0 , m is the negative inverse slope of S–N curve, log a cept of log N-axis of the S–N curve. For marine structures, the long term distribution of stress ranges at local detail may be described by the two-parameter Weibull distribution, and fatigue damage is caculated as: m0 T d m m ð3Þ D¼ q C 1þ h a With
q¼
Dr 0
ð4Þ
lnðn0 Þ1=h
200 18 R=50
10
10
R=40
-PL12-
20
R=30
8 TYP R=40 TYP
212
R=50
B 72
312
155
HP 340×12
340
312
212
12
200
0.0
a
ð1Þ
100
(a)
B
30
16
12 12 A-A
B-B
(b)
Fig. 6. (a) Schematic diagram of side longitudinal; (b) dimensions of the structure detail.
65
-0.75
Standard Error
?$OP:F=1
DrHS Drnom
30
-0.55
30
Corrosion rate, lg(r)/(mm/year)
-0.50
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0.8 Coupon Experiment In Xiamen Sea Fing Curve of Q235 Steel
0.6
0.4 Model Equation
0.2
Allometric1 b y = a*x 0.00226
Reduced Chi-Sqr
0.96835
Adj. R-Square
Value
0.0 0
2
Standard Error
a
0.15142
0.02752
b
0.76438
0.09934
4
6
8
The average corrosion thickness (mm)
The average corrosion thickness (mm)
Fig. 7. Model of side longitudinal. (a) Finite element model; (b) boundary condition and applied load.
1.0 Coupon Experiment In Qingdao sea Fing Curve of Q235 steel
0.8 0.6 0.4
Allometric1 Model b y = a*x Equation 0.00388 Reduced Chi-Sqr 0.96529 Adj. R-Square
0.2
Value
0.0 0
Corrosion years
2
Standard Error
a
0.17059
0.03517
b
0.79935
0.11188
4
6
8
Corrosion years
(b)
(a) Fig. 8. The coupon experiments in (a) Xiamen and (b) Qingdao.
Corrosion For 20 years 9.37mm
PL 12mm PL 12mm
9.42mm
9.11mm 9.47mm
9.55mm
9.4mm
(a)
(b)
Fig. 9. (a) The nonuniform corrosion model around; (b) the hot spot region.
where D is the accumulated fatigue damage, m0 is the average zerocrossing frequency, T d is the design life of ship, C is the Gamma function, the Weibull shape parameter h depends on the length of ship, q is the Weibull scale parameter. Fig. 12 shows the variation of cumulative fatigue damage of uniform and nonuniform corrosion over time.The difference of cumulative fatigue damage between them is not significant at the
initiation of corrosion year, but the gap become more and more large over corrosion time, it means that the coupling effect of corrosion and stress has a significant influence on fatigue damage with respect to the single uniform corrosion in long term immersion. It can be seen from Fig. 12 that the time-dependent SCF as a result of nonuniform corrosion reflect to a significant difference
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Reducon of Corrosion
Finite Element Model
External Load
Accelerated Corrosion Of Thickness Solve Relaonship Curve Between Load And Corrosion Rate Element Stress Results Corrosion Experiment
Fague Damage Calculaons Fig. 10. Flowchart of fatigue damage assessment.
corrosion and stress. The nonuniform corrosion of welded joints is investigated according to the corrosion data which are shown in Fig. 2. The synergistic effect between elastic stress and corrosion is verified by electrochemical experiment, and the relationship curve between load and corrosion rate of Q235 steel is given in this study based on the experimental results. The comparisons of numerical examples have been made between uniform corrosion and nonuniform corrosion which are caused by stress-dependent corrosion. From the study in this work, following conclusions can be drawn:
1.60
SCF of Hot spot
1.55
Uniform corrosion Nonuniform corrsion
1.50
1.45
1.40
1.35
1.30
0
4
8
12
16
20
Time (year) Fig. 11. SCF of hot spot as a function of time.
2.4
Uniform corrosion Nonuniform corrsion
Cumulave fague damage
2.0
1.6
1.2
0.8
0.4
0.0
(1) It can be observed from the investigation of the ships in service that the corrosion of welded joints are more severe than the other places in ship, which is the combine effect of macro corrosion cell and acceleration caused by high stress area around weld. And furthermore, the hot spot region in weld toe may initiate crack, so it is very important to pay attention to the coupling effect of corrosion and stress of welded joints. (2) The stress can affect corrosion by altering activation energy of metal, and a rise of corrosion rate is observed with the growth of stress level. An exponential function changing law between corrosion rate and loading can be established by experimental results of Q235 steel. (3) The results of FEA indicate that the effect of coupling interaction has a significant influence on fatigue damage with respect to the uniform corrosion for long term immersion in seawater. The new approach is more reasonable for corrosion fatigue damage assessment of welded joints.
Acknowledgements 0
4
8
12
16
20
Time (year) Fig. 12. Time-dependent total cumulative fatigue damage of hot spot.
in fatigue damage, the effect of the stress-dependent corrosion leads to a 17% growth of fatigue damage for the 20 years of service life with respect to uniform corrosion. 5. Conclusion The detailed procedures of a FEA approach for calculating the fatigue damage of welded joint under nonuniform corrosion are outlined in this paper, which consider the coupling effect of
This work is supported by the Major State Basic Research Development Program (‘‘973”Program) of China (Project No. 2011CB013704), and the National Natural Science Foundation of China (No. 51379031). References [1] Xu T. Fatigue of ship structural details: technical development and problems. J Ship Res 1997;41(4):318–31. [2] Akpan UO, Koko TS, Ayyub B, et al. Risk assessment of aging ship hull structures in the presence of corrosion and fatigue. Mar Struct 2002;15 (3):211–31. [3] DNV. Fatigue assessment of ship structures. In: Det Norske Veritas; 2010. [4] ABS. Guide for the fatigue assessment of offshore structures-section 3 S–N curves. Houston: American Bureau of Shipping; 2003. [5] Li Y, Hou B. Corrosion fatigue of welded joints of steel for marine platform. Ind J Eng Mater Sci 2006;13(5):467–70.
S. Yang et al. / International Journal of Fatigue 88 (2016) 88–95 [6] Palin-Luc T, Pérez-Mora R, Bathias C, et al. Fatigue crack initiation and growth on a steel in the very high cycle regime with sea water corrosion. Eng Fract Mech 2010;77(11):1953–62. [7] Chakarov K, Garbatov Y, Guedes Soares C. Hot-spot stress analysis of deck structures subjected to corrosion and fatigue. In: Guedes Soares C, Kolev, editors. Maritime industry, ocean engineering and coastal resources. London, UK: Taylor & Francis Group; 2008. [8] Garbatov Y, Rudan S, Soares C Guedes. Fatigue damage of structural joints accounting for non-linear corrosion. J Ship Res 2002;46:289–98. [9] Tran Nguyen K, Garbatov Y, Soares C Guedes. Fatigue damage assessment of corroded oil tanker details based on global and local stress approaches. Int J Fatigue 2012;43:197–206. [10] Gutman EM. Mechanochemistry of solid surfaces. Singapore: World Scientific; 1994. [11] Gao K, Li D, Pang X, Yang S. Corrosion behaviour of low-carbon bainitic steel under a constant elastic load. Corros Sci 2010;52:3428–34. [12] Ren RK, Zhang S, Pang XL, Gao KW. A novel observation of the interaction between the macroelastic stress and electrochemical corrosion of low carbon steel in 3.5 wt% NaCl solution. Electrochim Acta 2012;85:283–94. [13] Kim Seong-Jong, Okido Masazumi. The electrochemical study on mechanical and hydrogen embrittlement properties of HAZ part as a function of post-weld heat treatment in SMAW. Surf Coat Technol 2003; 169–170:163–7.
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[14] Kang Dong-Hwan, Kim Sanghoon, Lee Changhee. Corrosion fatigue behaviors of HSB800 and its HAZs in air and seawater environments. Mater Sci Eng, A 2013;559:751–8. [15] Nakai Tatsuro, Matsushita Hisao, Yamamoto Norio, Arai Hironori. Effect of corrosion on static strength of hull structural members (2nd report). J Soc Naval Archit Jpn 2004;195:221–31 [in Japanese]. [16] Moan T. Reliability-based management of inspection, maintenance and repair of offshore structures. Struct Infrastruct Eng 2005;1(1):33–62. [17] Ma J, Zhang B, Wang J, et al. Anisotropic 3D growth of corrosion pits initiated at MnS inclusions for A537 steel during corrosion fatigue. Corros Sci 2010;52 (9):2867–77. [18] Xu LY, Cheng YF. Corrosion of X100 pipeline steel under plastic strain in a neutral pH bicarbonate solution. Corros Sci 2012;64:145–52. [19] Wang Y, Zhao W, Ai H, et al. Effects of strain on the corrosion behaviour of X80 steel. Corros Sci 2011;53(9):2761–6. [20] Xu LY, Cheng YF. An experimental investigation of corrosion of X100 pipeline steel under uniaxial elastic stress in a near-neutral pH solution. Corros Sci 2012;59:103–9. [21] Dong W, Moan T, Gao Z. Fatigue reliability analysis of the jacket support structure for offshore wind turbine considering the effect of corrosion and inspection. Reliab Eng Syst Saf 2012;106:11–27. [22] Cao C. Natural environmental corrosion of material in China; 2005 [in Chinese].
Contents lists available at ScienceDirect
International Journal of Fatigue journal homepage: www.elsevier.com/locate/ijfatigue
Approach for fatigue damage assessment of welded structure considering coupling effect between stress and corrosion Shuo Yang a,⇑, Hongqi Yang b, Gang Liu b, Yi Huang b, Lidong Wang b a b
Technical Center, Department of Oil and Gas, Bureau Veritas, Shanghai, China School of Naval Architecture and Ocean Engineering, Dalian University of Technology, Dalian, China
a r t i c l e
i n f o
Article history: Received 8 January 2016 Received in revised form 17 March 2016 Accepted 18 March 2016 Available online 19 March 2016 Keywords: Coupling effect Mechanochemical experiment Nonuniform corrosion Welded joint Hot spot stress Fatigue damage
a b s t r a c t This paper presents a new approach to assess time-dependent corrosion fatigue damage of welded joint considering the coupling effect between mechanical factor and corrosion factor. The high stress region around weld will accelerate corrosion and be more likely to induce nonuniform corrosion of welded joint. And the effect of loading on corrosion behavior of the steel in NaCl solution was investigated. The synergistic effect between applied elastic stress and chemical attack on Q235 steel was evaluated by electrochemical experiments. A side longitudinal of ship structure is selected as a case study. Time-dependent stress concentration factor of welded joint as a function of corrosion deterioration was analyzed, and the iterative process of stress and corrosion degeneration of plate thickness was used to simulate coupling effect basing on the results of experiment. The hot spot stress approach was adopted to calculate the fatigue damage. It is revealed that the nonuniform corrosion could influence fatigue damage of welded joint, and that impact will be more and more significant with the growth of corrosion year. Ó 2016 Published by Elsevier Ltd.
1. Introduction Fatigue cracking may be the most important type of damage in welded structure [1,2], which is also a major requirement in design of marine structures. These requirements have been reflected in some design rules published by Classification Societies [3,4]. Compared with land structures, marine structures have a long term electrochemical reaction with seawater, and the surface of the structure may be subjected to more severe corrosion. Many experiments manifested [5,6] that fatigue life in corrosive environment is significantly lower than it in air. Therefore, the effects of mechanical and environmental factors on fatigue life are not a simple line relation but a complex one. The combined action of cyclic loading and aggressive environment often result in a significant reduction in fatigue performance compared with that obtained under cyclic loading in air. For a more accurate assessment of fatigue damage in corrosive environment, it is necessary to consider the coupling effects of corrosion and stress in some cases. Recently engineering methods accounting for corrosion had been introduced in some design rules [3,4]. The guidelines of several Classification Societies defined the values of corrosion addition in different local structures, and then reduced corrosion addition of
⇑ Corresponding author. E-mail address: [email protected] (S. Yang). http://dx.doi.org/10.1016/j.ijfatigue.2016.03.024 0142-1123/Ó 2016 Published by Elsevier Ltd.
ship structures in order to calculate the hot spot stress adjacent to critical joint such as weld toe, and finally evaluated fatigue damage according to S–N curve in air and Palmgren–Miner’s rule. And for those structures without corrosion protection, the guidelines used the S–N curve in corrosive environment which is more conservative. Engineering methods are simple and practical without considering the time effect on corrosion. In order to take into account the corrosion over time, timedependent corrosion wastage model has been used to calculate the fatigue damage in much research. Chakarov and Garbatov [7,8] studied the effect of general corrosion in decreasing the thickness of deck plate and found that the stress concentration factor is a function of hot spot stress and nominal stress is a nonlinear increasing with time function. Tran Nguyen et al. [9] applied the spectral fatigue damage approach to evaluate a main deck longitudinal stiffener which is considering the time-dependent corrosion effect, and found that the cumulative corrosion fatigue damage increases in all calculated cases after the failure of the corrosion protection system. However, the above calculating methods regard the corrosion reduction and fatigue as two separating processes without considering inherent coupling process between corrosion and stress, which is a limitation of these methods. Many authors studied the effect of stress on corrosion which is well known as mechanochemical interaction [10]. Gao et al. [11] reported the
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shown in Fig. 1. Fig. 1(a) and (b) shows the corrosion of welded joints in frame of No. 6 (BC6) and No. 2 (BC2) bulk carrier, it can be observed that the corrosion around fillet weld is more severe than any other place. Fig. 1(c) reveals that both the weld and the stiffeners of ship deck of No. 1 (SHT1) suffer serious corrosion in long term service for 22 years, and most of weld toe have been corroded. It can be seen from Fig. 1 that corrosion around welded joints are always more serious than any other place in ship structure sand should be paid more attention to these details. Moan [16] considered corrosion rates for steel in seawater may fluctuate between 0.04 and 1.2 mm/year, which exhibit a very large scatter depending upon the location in structure, and the investigations of Nakai et al. [15] also indicate that corrosion rates around welded joints scatter largely in different locations of ship structure, which are ranging from 0.04 to 0.77 mm/year as shown in Fig. 2. The corrosion of welded joints is not only affected by potential difference between weld and base metal, but the high stress also accelerates corrosion behavior of welded joint. The interactions between mechanical and chemical effects enhance surface reactions on materials, resulting in accelerated failure of welded joints. So the corrosion resistance of welded joints is affected by the stress distribution around welded joints. The region of high stress which is also called hot spot region will become more sensitive to corrosion, this region is vulnerable to suffer corrosion, and lead to nonuniform corrosion of welded joints over time. The combined effects of corrosion and stress may accelerate damage when welded joint is under the effect of external load.
mass loss of metal under different stress, concluded that applied stress can accelerate the corrosion, and determined the degradation of mechanical properties of steel induced by corrosion. Zhang et al. [12] investigated the effect of loading conditions on the corrosion behavior of a low carbon and low alloy steel with different microstructures in NaCl solution and results indicate that the elastic stress accelerated corrosion process of the steel significantly. The coupling effect of structures in seawater is that the thickness of structure decreased due to corrosion which increased the stress level under external load, and the higher stress in turn accelerated the corrosion so that the failure of structure happens sooner. In this study, we improve the traditional approaches of fatigue damage assessment by considering the coupling effect between corrosion and stress. The nonuniform distributed general corrosion of welded joint and the interaction between corrosion and stress are studied here. Electrochemical experiments are performed here to investigate the interaction between loading and corrosion rate. A finite element analysis (FEA) simulation procedure considering the coupling process between corrosion and stress is proposed in this paper, using a structural detail of ship structure as a case study. Time-dependent cumulative fatigue damage analysis is also performed. The aim of this work is to study the effect between stress and corrosion rate according to electrochemical experiment, and understand how nonuniform corrosion influences fatigue damage with respect to single uniform corrosion based on FEA. 2. Corrosion characteristic of welded joint The welded joints are commonly used in marine structures, and the failure around weld toe has been an area of particular concern in engineering. Kang and Kim [13,14] performed experiments for high performance steel to validate that corrosion fatigue life of the heat affected zone (HAZ) is shorter than base metal and weld metal, and HAZ exhibits a much higher stress sensitive characteristic than the others. The stress concentration around HAZ may have any influence on the corrosion and then affect the fatigue life of welded joints. To know the corrosion damage of welded joints in engineering, Nakai et al. [15] investigated the corrosion state around welded joints of eight ships include seven bulk carriers and one single hull oil tank, the service time of these ships ranges from 6 to 22 years, and the cross sections of fillet weld of ships are
3. Laboratory testing 3.1. Experimental procedures Many researchers [17–20] studied coupling effect between mechanical factor and corrosion factor by the mechanochemical tests which are made up of the mechanical tensile or bending test and electrochemical test. The present paper adopts similar method to study the coupling effect between stress and corrosion. The specimen used in this study is Q235 steel plate, which are widely used for marine structures. Mechanical properties are as follows: yield strength 235 ± 3 MPa, tensile strength 476 ± 1 MPa,
BC2-Frame (14 years)
BC6-Frame (12 years)
(a)
(b) Fig. 1. Corrosion of welded joint. (a) BC6-Frame; (b) BC2-Frame; (c) SHT1-Deck.
SHT1-Deck (22 years)
(c)
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reaction energy of corrosion. The exponential curve fitting (red trend line) is shown in Fig. 5 and it can be found from the experimental results that about a 37% increase in corrosion rate under about 80% of yield strength compare to that of no applied stress.
Corrosion thickness of welded joints (mm)
12 BC1 (10 years) BC2 (14 years) BC3 (12 years) BC4 (14 years) BC5 (6 years) BC6 (12 years) BC7 (13 years) SHT1-1 (22 years) SHT1-2 (22 years)
10
8
0.77mm/year
4. Time-dependent fatigue analysis Finite element method (FEM) is used here for analyzing the hot spot stress concentration factor of the case study, fatigue damage of welded joint can be estimated based on the calculations of hot spot stress, and nonuniform corrosion of welded joint will be considered in the calculation of FEM.
6
4
0.135mm/year 2
0.04mm/year 0
0
5
10
15
20
4.1. Finite element model 25
Time (year) Fig. 2. Corrosion data around welded joints of eight ships.
elongation 26 ± 1% and Young’s modulus (E) 206 ± 5 GPa, and the chemical composition of Q235 steel is shown in Table 1. To investigate the interaction between mechanics and corrosion during elastic deformation process, uniaxial tensile tests are performed in the 3.5 wt.% NaCl solution by using hydraulic servo fatigue testing machine (Shimadzu, Model: EHF-UM200KN). The microstructures of Q235 steel are shown in Fig. 3 and dimensions of this tensile specimen are 450 mm 50 mm 5 mm (Fig. 4(a)). The specimens are ground by emery paper to grit 1500 and then rinsed with ethanol. To obtain the stress state around the corrosion position of specimen, strain gages are pasted at critical location and the stress can be measured by the strain indicator. The constant temperature water bath is used to maintain the temperature of corrosion environment at about 24 °C, and the oxygen pump can keep dissolved oxygen in 3.5 wt.% NaCl solution ranges from 5 to 7 ppm. The PH of the Nacl solution is 7.826 in this test and the total volume of aqueous NaCl in the water bath is about 1.5-litre. The schematic diagrams are shown in Fig. 4(a)–(d). The electrochemical properties were analyzed by Princeton Model-263A electrochemical workstation, and linear polarization technique was used to measure corrosion rates of steel. A saturated silver/silver chloride electrode was used as the reference electrode, and the electrode potential of the test 0.594 VAg/AgCl. It was measured in the potential range from 10 mV to +10 mV (vs. open circuit potential) at a scanning rate of 0.1 mV/s and the tests started after immersion in solution for 0.5 h. The measurements were carried out 12 times in different load condition. The fitting curve of average corrosion rate was adopted for analysis. 3.2. General corrosion rate under various loading Fig. 5 shows the variations of general corrosion rate with time under different loading, which the measured corrosion rate is applied by a log scale. It can be seen that the general corrosion rates increase with growth of elastic stress and it is obvious that applied load can accelerate the corrosion process of steel. This behavior can be attributed to the applied load and deformation of the metal, which increased surface activity of metal and reduced
This case study is a side longitudinal of a ship structure, and the welded connection between side longitudinal and transverse frame is used for fatigue analysis. Numerical simulation is performed by commercial software ANSYS, and dimensions of the structure detail are shown in Fig. 6. The finite element analysis is influenced by mesh density and element types, and the selection of them is summarized in the guidelines [3,4] which already consider the sensibility of influenced factor above. In this study, the material used is a kind of common shipbuilding steel with typical values of mechanical properties, the modulus of elasticity and the Poisson’s ratio is 206 GPa and 0.3 respectively. Shell93 element is used for the FEA, and a function of variable thickness is used here to simulate the nonuniform corrosion around welded joint. As shown in Fig. 7(a), finer meshes are generated around welded connection, and a relatively coarse mesh is chosen far away from welded joint while the finer mesh leads to the time-consuming solution procedure. This structure is axially loaded and fatigue loads acting on the structure are selected as 4427:52 kN. The boundary condition and applied load are shown in Fig. 7(b). 4.2. Reduction of corrosion considering coupling effect It is commonly accepted that general corrosion rate of steel in seawater is about 0.1 mm/year [21], and coupon experimental results [22] of Q235 steel in different sea area of china also indicate that general corrosion rate of this steel in seawater is about 0.1 mm/year as shown in Fig. 8(a) and (b). So in this case study, the general corrosion rate 0.1 mm/year is adopted for analysis, and nonuniform corrosion caused by the acceleration of applied load on corrosion of welded joint need to be considered. The decreasing plate thickness due to corrosion will increase the stress levels adjacent to welded connection which in turn increase probability of crack initiation. According to the fitting curve between corrosion rates and loading as shown in Fig. 5, it can be assumed that relationship between corrosion rates and stress takes on an exponential function changing law, and the corrosion rate around weld joints can reach 0.137–0.14 mm/year while the stress around weld is close to yield strength. It is reasonable and in accordance with the corrosion rate of welded joints in BC6Frame which is the red trend line as shown in Fig. 2. Thickness reduction of accelerated corrosion is calculated according to exponential function changing law in Fig. 5 for 2 year intervals: from 0 to 20 years of corrosion. Corrosion around the
Table 1 Chemical composition of Q235 steel. Element Content (wt.%)
Fe 0.4978
C 0.182
Si 0.06
Mn 0.2
P 0.016
S 0.0063
Cu 0.029
Ni 0.008
Cr 0.027
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Fig. 3. Microstructure of Q235 steel in this test. (a) 150 lm; (b) 30 lm.
70
30
50
Specimen Reference Electrode In Corrosion Region
450
Corrosion Region
Pt Electrode Oxygen Pump Out
Strain Gauge
Circulator Bath
3.5% NaCl
Applied Stress
(a)
(b)
(c) Fig. 4. (a) Size and shape of specimens; (b) schematic diagram of mechanochemical experiment; (c) photos of experimental set-up.
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fatigue damage in different year could be calculated in each cyclic procedure. The extrapolation can be used for obtaining hot spot stress. The relation between hot spot stress range to be used together with S–N curve and nominal stress range is hot spot stress concentration factor (SCF):
Experimental data Fing curve of corrosion rate
-0.60
SCF ¼ -0.65
-0.70
Model
Exp2PMod1
Equation
y = a*exp(b*x)
Reduced Chi-Sqr
2.81324E-4 0.90041
Adj. R-Square
Value
0.2
-0.69455
0.00441
?$OP:F=1
b
-0.27111
0.01308
0.4
0.6
σ /σ y
0.8
1.0
Fig. 5. Relationship curve between load and corrosion rate.
welded joint are reduced as 0.137–0.14 mm/year, and the other area of model are reduced as 0.1–0.137 mm/year. Nonuniform corrosion around the hot spot region for 20 years is shown in Fig.9(a). 4.3. Hot spot stress analysis In marine structures design, most of recent guidelines published by Classification Societies are using structural hot spot stress approach for fatigue assessment of welded joints. The aim of hot spot stress analysis is to evaluate the peak stress at structural detail weld toe. The element size of mesh generated in the hot spot is t t (thickness thickness) according to fatigue guidelines [3,4]. Location of hot spot is shown in Fig. 9(b) and the principal stresses obtained at points which is 0.5t and 1.5t away from weld toe are used for extrapolation based on rHS ¼ 1:5r0:5t 0:5r1:5t : For each instant of time, residual plate thickness is obtained by subtracting accelerated corrosion wastage from the initial plate thickness (uncorroded). Being different form uniform corrosion, the accelerated corrosion wastages are diverse in different zones of welded joint which could lead to nonuniform corrosion. The calculating flow of fatigue damage accounting for coupling effect is shown in Fig. 10. External load is applied to the initial finite element model (uncorroded) and corresponding stress response is obtained from the results of solution. The stress response is used for calculating accelerated corrosion of plate thickness and a new finite element is built after reduction of corrosion wastage for the next cycle of calculating process. Coupling process of corrosion and stress is simulated by the iterative process of stress response and corrosion reduction of plate thickness, and
where DrHS is hot spot stress amplitude, and Drnom is nominal stress amplitude. The SCF as a function of time in uniform corrosion and nonuniform corrosion are shown in Fig. 11, it can be seen that SCF smoothly increases with deterioration of plate thickness during the service life of ship, and the SCF of nonuniform corrosion around welded joint increase faster than a single uniform corrosion from the begining of corrosion, which is the outcome of interaction between environment and cyclic load. Therefore, nonuniform corrosion around the welded joint has much more influence on hot spot stress range than uniform corrosion. In this case, the SCF under the influence of coupling effect is larger than uniform corrosion because of more severe localized corrosion caused by stressdependent corrosion. With the increase of corrosion time, the SCF range under the influence of the coupling effect will become more and more significant. 4.4. Time-dependent fatigue assessment The fatigue damage under nonuniform corrosion is a coupling process which is demonstrated in Fig. 10. Fatigue assessment is generally based on the S–N approach, and a two-slope S–N curve of welded joint for air is selected in this case study which a reduction of plate thickness is regarded as the influence of corrosion. The design S–N curves are shown as:
mlog Dr0 log N ¼ log a
ð2Þ
where N is predicted number of cycles to failure for stress range is the interDr0 , m is the negative inverse slope of S–N curve, log a cept of log N-axis of the S–N curve. For marine structures, the long term distribution of stress ranges at local detail may be described by the two-parameter Weibull distribution, and fatigue damage is caculated as: m0 T d m m ð3Þ D¼ q C 1þ h a With
q¼
Dr 0
ð4Þ
lnðn0 Þ1=h
200 18 R=50
10
10
R=40
-PL12-
20
R=30
8 TYP R=40 TYP
212
R=50
B 72
312
155
HP 340×12
340
312
212
12
200
0.0
a
ð1Þ
100
(a)
B
30
16
12 12 A-A
B-B
(b)
Fig. 6. (a) Schematic diagram of side longitudinal; (b) dimensions of the structure detail.
65
-0.75
Standard Error
?$OP:F=1
DrHS Drnom
30
-0.55
30
Corrosion rate, lg(r)/(mm/year)
-0.50
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0.8 Coupon Experiment In Xiamen Sea Fing Curve of Q235 Steel
0.6
0.4 Model Equation
0.2
Allometric1 b y = a*x 0.00226
Reduced Chi-Sqr
0.96835
Adj. R-Square
Value
0.0 0
2
Standard Error
a
0.15142
0.02752
b
0.76438
0.09934
4
6
8
The average corrosion thickness (mm)
The average corrosion thickness (mm)
Fig. 7. Model of side longitudinal. (a) Finite element model; (b) boundary condition and applied load.
1.0 Coupon Experiment In Qingdao sea Fing Curve of Q235 steel
0.8 0.6 0.4
Allometric1 Model b y = a*x Equation 0.00388 Reduced Chi-Sqr 0.96529 Adj. R-Square
0.2
Value
0.0 0
Corrosion years
2
Standard Error
a
0.17059
0.03517
b
0.79935
0.11188
4
6
8
Corrosion years
(b)
(a) Fig. 8. The coupon experiments in (a) Xiamen and (b) Qingdao.
Corrosion For 20 years 9.37mm
PL 12mm PL 12mm
9.42mm
9.11mm 9.47mm
9.55mm
9.4mm
(a)
(b)
Fig. 9. (a) The nonuniform corrosion model around; (b) the hot spot region.
where D is the accumulated fatigue damage, m0 is the average zerocrossing frequency, T d is the design life of ship, C is the Gamma function, the Weibull shape parameter h depends on the length of ship, q is the Weibull scale parameter. Fig. 12 shows the variation of cumulative fatigue damage of uniform and nonuniform corrosion over time.The difference of cumulative fatigue damage between them is not significant at the
initiation of corrosion year, but the gap become more and more large over corrosion time, it means that the coupling effect of corrosion and stress has a significant influence on fatigue damage with respect to the single uniform corrosion in long term immersion. It can be seen from Fig. 12 that the time-dependent SCF as a result of nonuniform corrosion reflect to a significant difference
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Reducon of Corrosion
Finite Element Model
External Load
Accelerated Corrosion Of Thickness Solve Relaonship Curve Between Load And Corrosion Rate Element Stress Results Corrosion Experiment
Fague Damage Calculaons Fig. 10. Flowchart of fatigue damage assessment.
corrosion and stress. The nonuniform corrosion of welded joints is investigated according to the corrosion data which are shown in Fig. 2. The synergistic effect between elastic stress and corrosion is verified by electrochemical experiment, and the relationship curve between load and corrosion rate of Q235 steel is given in this study based on the experimental results. The comparisons of numerical examples have been made between uniform corrosion and nonuniform corrosion which are caused by stress-dependent corrosion. From the study in this work, following conclusions can be drawn:
1.60
SCF of Hot spot
1.55
Uniform corrosion Nonuniform corrsion
1.50
1.45
1.40
1.35
1.30
0
4
8
12
16
20
Time (year) Fig. 11. SCF of hot spot as a function of time.
2.4
Uniform corrosion Nonuniform corrsion
Cumulave fague damage
2.0
1.6
1.2
0.8
0.4
0.0
(1) It can be observed from the investigation of the ships in service that the corrosion of welded joints are more severe than the other places in ship, which is the combine effect of macro corrosion cell and acceleration caused by high stress area around weld. And furthermore, the hot spot region in weld toe may initiate crack, so it is very important to pay attention to the coupling effect of corrosion and stress of welded joints. (2) The stress can affect corrosion by altering activation energy of metal, and a rise of corrosion rate is observed with the growth of stress level. An exponential function changing law between corrosion rate and loading can be established by experimental results of Q235 steel. (3) The results of FEA indicate that the effect of coupling interaction has a significant influence on fatigue damage with respect to the uniform corrosion for long term immersion in seawater. The new approach is more reasonable for corrosion fatigue damage assessment of welded joints.
Acknowledgements 0
4
8
12
16
20
Time (year) Fig. 12. Time-dependent total cumulative fatigue damage of hot spot.
in fatigue damage, the effect of the stress-dependent corrosion leads to a 17% growth of fatigue damage for the 20 years of service life with respect to uniform corrosion. 5. Conclusion The detailed procedures of a FEA approach for calculating the fatigue damage of welded joint under nonuniform corrosion are outlined in this paper, which consider the coupling effect of
This work is supported by the Major State Basic Research Development Program (‘‘973”Program) of China (Project No. 2011CB013704), and the National Natural Science Foundation of China (No. 51379031). References [1] Xu T. Fatigue of ship structural details: technical development and problems. J Ship Res 1997;41(4):318–31. [2] Akpan UO, Koko TS, Ayyub B, et al. Risk assessment of aging ship hull structures in the presence of corrosion and fatigue. Mar Struct 2002;15 (3):211–31. [3] DNV. Fatigue assessment of ship structures. In: Det Norske Veritas; 2010. [4] ABS. Guide for the fatigue assessment of offshore structures-section 3 S–N curves. Houston: American Bureau of Shipping; 2003. [5] Li Y, Hou B. Corrosion fatigue of welded joints of steel for marine platform. Ind J Eng Mater Sci 2006;13(5):467–70.
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