Prediction of Corrosive Fatigue Life of Submarine Pipelines of API 5L X56 Steel Materials

materials

Article Prediction of Corrosive Fatigue Life of Submarine Pipelines of API 5L X56 Steel Materials

Xudong Gao 1, Yongbo Shao 1,*, Liyuan Xie 1, Yamin Wang 2 and Dongping Yang 3

1 School of Mechatronic Engineering, Southwest Petroleum University, Chengdu 610500, China; [email protected] (X.G.); [email protected] (L.X.) 2 Centre for Infrastructure Engineering, Western Sydney University, Penrith, NSW 2751, Australia; [email protected] 3 Technology Inspection Center, China Petroleum & Chemical Corporation, Dongying 257062, China; [email protected] * Correspondence: [email protected]; Tel.: +86-28-83037601

Received: 28 January 2019; Accepted: 22 March 2019; Published: 28 March 2019

Abstract: Corrosive fatigue failure of submarine pipelines is very common because the pipeline is immersed in a sea environment. In Bohai sea, many old pipelines are made of API 5L X56 steel materials, and it is necessary to provide an accurate method for predicting the residual life of these pipelines. As Paris law has been proven to be reliable in predicting the fatigue crack growth in metal materials, the two constants in Paris law for API 5L X56 steel materials are obtained by using a new proposed shape factor based on the analysis of experimental data measured from fatigue tests on compact tension specimens immersed in the water of Bohai sea. The results of the newly proposed shape factor show that, for a given stress intensity factor range (∆K), the fatigue crack growth rate (da/dN) in seawater is 1.6 times of that that in air. With the increase of fatigue crack growth rate, the inﬂuence of seawater on corrosive fatigue decreases gradually. Thereafter, a ﬁnite element model for analyzing the stress intensity factor of fatigue crack in pipelines is built, and the corrosive fatigue life of a submarine pipeline is then predicted according to the Paris law. To verify the presented method, the fatigue crack growth (FCG) behavior of an API 5L X56 pipeline with an initial crack under cyclic load is tested. Comparison between the prediction and the tested result indicates that the presented method is effective in evaluating the corrosive fatigue life of API 5L X56 pipelines.

Keywords: API 5L X56 steel material; submarine pipelines; corrosive fatigue crack growth; Paris law constants; stress intensity factor

1. Introduction Submarine pipeline is regarded as the lifeline of offshore oil and gas transportation. As the offshore oil industry boomed, the frequency of pipeline leaks increased. The submarine pipeline is used in a harsh marine environment for a long time. It is vulnerable to failure due to complex alternating stress and external factors [1–3]. The phenomenon of submarine pipeline hanging is inevitable due to the scouring of sea water, and the hanging pipeline is subjected to alternating load under the action of sea wave and it is, hence, sensitive to fatigue failure [4]. Therefore, it is of great signiﬁcance to study the corrosive fatigue of submarine pipelines in service to prevent the failure. The crack growth rate under a given load depends on several factors, including crack length and geometry, temperature, environment, test frequency, and the microstructure of the material. Petit et al. [5,6] have investigated the detrimental effects of atmospheric conditions on fatigue crack propagation in steel, Al and Ti-based alloys. The deleterious effects of water vapor were analyzed based on experiments in a controlled partial pressure atmosphere, and modeling of intrinsic and

Materials 2019, 12, 1031; doi:10.3390/ma12071031 www.mdpi.com/journal/materials Materials 2019, 12, 1031 2 of 19 environmentally assisted crack growth is proposed. At present, many researchers have studied the influence of different environmental conditions on fatigue crack growth rate for different pipelines. Javidi et al. [7] studied the stress corrosion cracking behavior of API 5L X52 steel under the near-neutral and high pH conditions using slow strain rate tests and electrochemical methods. The results revealed that the anodic dissolution at a crack tip was the dominant mechanism at near-neutral pH condition. While at high pH medium, the hydrogen-based mechanism was dominant. Cheng et al. [8] established a two-component model considering anode dissolution and hydrogen embrittlement based on the fracture mechanics theory, and they applied the model for API 5L X65 pipeline steel. The results showed that the model can control the shape of the simulated crack growth curve and the fatigue crack growth (FCG) rate. As the global sustainable development strategy becomes the mainstream, offshore natural gas, which is considered as a clean energy, has attracted the attention of various countries. Therefore, many researchers have studied the FCG rate and the cracking behavior of pipeline steels in different gas environments [9–14]. Wang et al. [9] studied the FCG rate of the base metal and the heat affected zone of API 5L X70 pipeline steel under a hydrogen sulphide environment, and they found that the existence of H2S greatly accelerated the FCG rate. Zheng et al. [10] also obtained a similar law in the study of API 5L X56 pipeline steel under an H2S environment. In addition, it is found that the presence of gaseous hydrogen also has a great impact on the FCG rate of steel, which exceeded an order of magnitude larger than that of the FCG rate under laboratory air environment [11–14]. Amaro et al. [11] studied API 5L X100 pipeline steel in high-pressure gaseous hydrogen environments, and they found that the FCG response in hydrogen at da/dN < 3 × 10−4 mm/cycle is primarily affected by the hydrogen concentration within the fatigue process zone, resulting in a hydrogen-dominated mechanism, and the FCG response in hydrogen at da/dN < 3 × 10−4 mm/cycle results from fatigue-dominated mechanisms. API 5L X56 pipeline steel is now used in the submarine pipelines in the Bohai sea of China. Corresponding studies on X56 submarine pipeline steel have also been carried out in the literature [10,15,16]. Yi et al. [15] simulated stress corrosion cracking and hydrogen permeation behavior of X56 pipeline steel under atmospheric environment containing SO2, and the results show that hydrogen ion concentration decreases with time, indicating that the hydrogen concentration on the surface decreases with the formation of corrosion rust. As the passivation film dissolves, the hydrogen permeation rate increases and the stress corrosion cracking sensitivity of API 5L X56 increases with the increase of SO2 concentration. Zhu et al. [16] studied the permeation action of API 5L X56 steel in the sea mud with and without sulfate-reducing bacteria at corrosion and cathodic potential were studied with an improved Devanathan–Stachurski electrolytic cell. The above studies on the API 5L X56 submarine pipeline are all influenced by a single factor, and the fatigue remaining life of the pipeline with initial cracks in service is not analyzed. Structural cracking is a major problem for large infrastructures including dams, bridges, submarine pipelines and offshore wind turbine foundations. At the same time, reliability analysis has become a concern of researchers. Based on the probability theory, reliability analysis of fatigue fracture for engineering structures and components has been conducted, and proposed several analysis models. Commonly used techniques include Monte Carlo simulation method and first-order reliability method [17]. In Monte Carlo simulation, the random variable is formed by its distribution function. For each Monte Carlo simulation sample, the sensitivity of each stress intensity factor (SIF) to the random variable is calculated and compared with the obtained SIF to evaluate whether failure will occur. Based on the above method, the fatigue life of the pipeline is analyzed [18–20]. An S-N curve based on damage mechanics is another way to predict fatigue life. The S-N curve is used to predict the fatigue life of crack in suspended pipeline. Wormsen et al. [21] carried out tests on low alloy machined steel forgings and analyzed S-N curves in air and seawater environments with cathodic protection measures. They provided specific plans for fatigue tests of submarine pipelines. Cunha et al. [22] introduced an S-N curve from tensile test material properties, and they proposed a new algorithm to evaluate the fatigue life of dented pipelines. Hong et al. [23] collected ASTM standard specimens from the API 5L X42 gas pipeline, and FCG tests were subsequently performed. Additionally, S-N curve of Materials 2019, 12, 1031 3 of 19 each specimen was estimated to verify the accuracy of the prediction model. Dong et al. [24] analyzed the weld data recorded in a large number of literatures from 1947 to present by means of the new mesh-insensitive structural stress method and the associated master S-N curve approach. According to the characteristics of fracture mechanic materials, Lukács et al. [25,26] evaluated and calculated the reliability of different pipeline structural unit models, during which different crack geometries were assumed. Meanwhile, the stress intensity factors and safety factors were also determined for all cases. Both methods are based on empirical formulas, model analysis and finite element simulation to obtain the fatigue life. It is difficult to verify the accuracy of the predicted results in practical application. The methods for predicting fatigue life of metal materials or structures can be divided into S-N curves based on damage mechanics and Paris law based on fracture mechanics. At present, Paris law-based on fracture mechanics is used to predict the corrosion fatigue life of cracked parts. The main reason is that S-N curve based on damage mechanics is obtained by applying alternating loads on smooth and non-cracked specimens. In fact, defects are inevitable when metal is processed, and so the predicted life from S-N curve is dangerous. Paris law based on linear elastic fracture mechanics analyzes the remaining life of cracked components, which is more instructive for practical engineering. Moreover, Paris law can reflect the relationship between fatigue crack growth rate (da/dN) and stress intensity factor range (∆K). It is only necessary to measure the Paris law constants (C and m) in a certain environment through FCG tests. In this study, finite element analysis is carried out to analyze the stress intensity factors under different crack depths in API 5L X56 submarine pipelines. The fatigue crack growth life is then predicted from Paris law. To verify the accuracy of the prediction method, a full-scale size API 5L X56 pipeline was tested in a fatigue loading condition. The effect of seawater on the crack growth rate of API 5L X56 steel was also studied under a laboratory environment, and a new method for predicting the fatigue life of API 5L X56 pipeline life was proposed.

2. Test on Fatigue Crack Propagation of API 5L X56 Steel Material

2.1. Mechanical Properties of API 5L X56 Steel Material Fatigue crack growth test is based on Paris law to establish the relationship between the FCG rate (da/dN) and the stress intensity factor range (∆K). For a linear elastic steel specimen, the SIF is linearly related to the load and depends on the geometry and size of the steel specimen and the crack. Coupons test and Charpy pendulum impact test are both carried out to obtain the mechanical properties of API 5L X56 steel materials including the elastic modulus (E), the yield strength (σy), Poisson’s ratio (ν), and the fracture toughness (KIC). The impact energy is measured according to GB/T229-2007 standard for “Metallic materials—Charpy pendulum impact test method” [27], and the experimental results are listed in Table1.

Table 1. Impact energy for API 5L X56 steel material.

Test ID Test Materials Test Temperature (◦C) Impact Energy (J) 1 API 5L X56 20 158.27 2 API 5L X56 20 69.76 3 API 5L X56 20 124.66 4 API 5L X56 20 97.08 Mean Value - - 112.44

The fracture toughness of API 5L X56 steel material is estimated according to Equation (1) provided in BS7910-2013 standard for “Guide to methods for assessing the acceptability of ﬂaws in metallic structures” [28] as follow

p 0.25 KIC= [(12 CV −20)(25/B) ] + 20, (1) Materials 2019, 12, x FOR PEER REVIEW 4 of 18

Table 2. Mechanical properties of API 5L X56 steel material. Materials 2019, 12, 1031 4 of 19 Material Elastic Modulus (GPa) Yield Strength (MPa) Poisson's Ratio 푲ΙC (퐌퐏퐚 ⋅ √퐦) API 5L X56 200 340 0.3 188

where CV is the Charpy impact energy, B is the thickness of the specimens. Based on the data in Table1, 2.2.the Design fracture of C(T) toughness Specimens of API 5L X56 steel material can be calculated. Combined with the tensile test of metalThe fatigue materials, crack the growth basic mechanical test is the propertiesmost commonly of API 5Lused X56 method steel material to study are the listed FCG in rates Table of2. various homogeneous metal materials. The material used in the C(T) specimens is API 5L X56 steel Table 2. Mechanical properties of API 5L X56 steel material. material which is obtained from the submarine pipelines in Bohai sea. Standard compact tension, √ C(T), specimensMaterial are Elastic extracted Modulus from (GPa) submarine Yield Strength pipeline (MPa) with a diameter Poisson’s Ratio of 219 mmKIC (MPa and · a wallm) thicknessAPI 5Lof 14 X56 mm. Figure 1a 200 shows that the plane direction 340 of the crack is 0.3 perpendicular to 188 the axial direction and parallel to the axial direction respectively. Li et al. [29] carried out a load-controlled three2.2.- Designpoint bending of C(T) Specimens test on API 5L X80 steel material. The results show that the FCG rate of the specimens from different directions are basically the same. In this study, the sampling direction of The fatigue crack growth test is the most commonly used method to study the FCG rates of C(T) specimens is no longer distinguished. various homogeneous metal materials. The material used in the C(T) specimens is API 5L X56 steel C(T) specimens are designed according to GB/T 6398-2000 standard for “Metallic material which is obtained from the submarine pipelines in Bohai sea. Standard compact tension, C(T), materials―Fatigue testing―Fatigue crack growth method” [30] and ASTM E647-13 [31]. The wall specimens are extracted from submarine pipeline with a diameter of 219 mm and a wall thickness of thickness of API 5L X56 pipeline is 14mm. Under the premise of guaranteeing the machining allowance,14 mm. Figure the thickness1a shows of that C(T) the specimens plane direction is selected of the as crackB=10mm is perpendicular and the width to is theselected axial as direction W=40 mm.and Fig parallelure 1bto is thea standard axial direction C(T) specimen respectively. used in Li fatigue et al. [ 29crack] carried growth out test. a load-controlled Overall, three specimens three-point arebending tested on test the on STM793 API 5L X80fatigue steel testing material. machine, The results and the show specimen that the marked FCG rate with of X56 the-A specimens-1 represents from thedifferent one tes directionsted in an air are environment basically the same.while Inthe this other study, two the specimens sampling (marked direction with of C(T) X56 specimens-S-1 and X56 is no- S-longer2) are tested distinguished. in Bohai sea environment.

(a) (b)

FigureFigure 1. 1.ExtractionExtraction location location and and dimensional dimensional drawing drawing of ofC(T) C(T) specimens: specimens: (a) ( aCrack) Crack plane plane orientation; orientation; (b()b C(T)) C(T) specimen specimen..

TheC(T) FCG specimens tests are arecarried designed out on according the STM793 to GB/T fatigue 6398-2000 testing machine, standard which for “Metallic is composed materials— of a loadingFatigue device testing—Fatigue and control crack system. growth The loading method” device [30] and is used ASTM to provide E647-13 [cyclic31]. The load, wall while thickness the control of API system5L X56 is pipeline used for is 14mm. control Underling loading the premise process of guaranteeing and collecting the machiningtesting data. allowance, All specimens the thickness are fabricatedof C(T) specimens to produce is a selected sharp crack as B with= 10 a mm certain and length the width of approximately is selected as W3 mm= 40 from mm. the Figure machined1b is a Vstandard-notch using C(T) the specimen K-decreasing used in technique fatigue crack to ensure growth that test. the Overall, K equation three is specimensnot affected are by tested the initial on the notchSTM793 shape. fatigue The testingstress-intensity machine, factor and the range specimen is step markedped down with at X56-A-1 a constant represents rate as the oneprecracked tested in lengthan air increases, environment and while the final the other ΔK twoequals specimens to the minimum (marked with ΔK X56-S-1at the end and X56-S-2)of the precracking. are tested in PrecrackingBohai sea environment. in air at a frequency of 10 Hz at room temperature, and the crack length at the end is The FCG tests are carried out on the STM793 fatigue testing machine, which is composed of a recorded as the initial crack length, a0. Thereafter, the constant amplitude loading stage for fatigue crackloading growth device test and is followed control system.. The test The is terminated loading device when is usedthe FCG to provide rate exceeded cyclic load, 0.01 whilemm/cycle the control, and system is used for controlling loading process and collecting testing data. All specimens are fabricated the crack length at this time is called the final crack length, af. to produce a sharp crack with a certain length of approximately 3 mm from the machined V-notch 2.3.using Parameter the K-decreasing Selection in F techniqueatigue Testto ensure that the K equation is not affected by the initial notch shape. The stress-intensity factor range is stepped down at a constant rate as the precracked length increases, and the ﬁnal ∆K equals to the minimum ∆K at the end of the precracking. Precracking in air at a frequency of 10 Hz at room temperature, and the crack length at the end is recorded as the initial crack length, a0. Thereafter, the constant amplitude loading stage for fatigue crack growth test is Materials 2019, 12, 1031 5 of 19 followed. The test is terminated when the FCG rate exceeded 0.01 mm/cycle, and the crack length at this time is called the ﬁnal crack length, af.

2.3. Parameter Selection in Fatigue Test The tests are carried out in both air and seawater conditions, and the seawater used in the test is taken from Bohai sea of China where the submarine pipeline is located. C(T) specimens tested in a seawater environment are soaked in seawater for more than 24 hours before precracking. All FCG tests in air and in seawater environments are loaded in a sinusoidal wave form with a stress ratio of 0.1 and a constant amplitude. It is noted here that, even though the applied load ratio experienced by the submarine pipeline may be negative, a previous study in the literatures [32–34] has found that the FCG rates at R-ratio of −1.0 is similar or lower than that at R = 0.1 for steel in air and in seawater environments. Therefore, the R-ratio of 0.1 used in this study to characterize the FCG rate is relatively conservative. Previous study indicated that the effect of loading frequency, f , on the fatigue crack growth tests varies from environment to environment [35]. To simulate the actual seawater environment as much as possible and to consider the efﬁciency problem, the loading frequency in this seawater test environment is 0.5 Hz. Previous studies found that the inﬂuence of loading frequency on the FCG rate of steel in the air environment is negligible [34,36,37]. Therefore, FCG test in the air is performed at a frequency of 10 Hz at room temperature. When selecting the maximum load, Pmax, the load should not be too large to guarantee that the crack tip is in the small yielding range to meet the requirements of Linear and Elastic Fracture Mechanics (LEFM). Simultaneously, the load should not be too small to ensure that ∆K is greater than the stress intensity factor threshold, 4Kth. In addition, the selection of the load is also within the effective control range of the fatigue testing machine. Testing parameters such as loading frequency, f , maximum loading load, Pmax and load ratio, R, are shown in Table3.

Table 3. Parameters in fatigue crack propagation test.

Test ID Environment a0 (mm) af (mm) f (Hz) RPmax (kN) X56-A-1(CT) Air 12.98 25.03 10 0.1 11 X56-S-1(CT) Seawater 13.02 24.98 0.5 0.1 11 X56-S-2(CT) Seawater 12.95 22.51 0.5 0.1 9.5 Submarine Pipeline Specimen Seawater 5.5/52.1 13.9/60.2 0.5 0.1 235

2.4. Crack Growth Monitoring In the FCG tests, a flexible method is used to measure the crack length development. Different monitoring methods are used in different environments. In the air environment, the crack propagation is monitored by using the Crack Opening Displacement (COD) gauge and the Back Face Strain (BFS) method. Figure2a shows the position of the COD gauge and strain gauge. Previous study in the literature [35] verified the accuracy of the COD and BFS method for monitoring crack growth, and the results showed that the BFS method can be used to replace the COD method. In this study, the test data of API 5L X56 pipeline steel collected from two monitoring methods are compared to verify the reliability of those two methods. Due to the difficulty in installing COD gauges in a seawater environment, only the BFS method is used to monitor FCG in this condition. For the fatigue test in seawater, the strain gauge surfaces are coated with a layer of AZ-710 anti-corrosive glue to protect the strain gauge from the effect of corrosion. After the glue is solidified, a layer of waterproof tape is applied to achieve double protection, as shown in Figure2b. In addition, it should be noted that the load frequency is up to 10 Hz. Therefore, the TST5912 dynamic signal test and analysis system is used for data acquisition. During the cyclic loading process, the acquisition frequency of the dynamic strain gauge in seawater is set to 100 Hz. Materials 2019, 12, 1031 6 of 19

Materials 2019, 12, x FOR PEER REVIEW 6 of 18

(a) (b)

FigureFigure 2. Fatigue 2. Fatigue crack crack propagation propagation monitoring monitoring method: method (a): Monitoring (a) Monitoring of crack of crack growth growth in air in air environment;environment; (b) Monitoring (b) Monitoring of crack of crack growth growth in seawater in seawater environment. environment.

2.5.2.5. Fatigue Fatigue Crack Crack Propagation Propagation ParisParis law law is commonly is commonly used used to describe to describe the fatigue the fatigue crack crack propagation propagation relationship, relationship, i.e., i.e. the, the relationshiprelationship between between the theFCG FCG rate rate (da/dN (da/dN) and) and the stressthe stress intensity intensity factor factor range range (∆K ).(Δ TheK). The stress stress intensityintensity factor factor range range can becan deﬁned be defined as follows: as follows:

∆K = K∆Kmax = K−maxKmin - K,min, (2) (2) where K is the stress intensity factor, which is a parameter in linear and elastic fracture mechanics where K is the stress intensity factor, which is a parameter in linear and elastic fracture mechanics and and it is defined as follows: it is deﬁned as follows: √ K = FKσ = πFσa,√πa, (3) (3) wherewhereσ is theσ is nominal the nominal stress stress (the applied (the applied stress), stress),a is the cracka is the length, crack and length,F is aand dimensionless F is a dimensionless shape function.shape It function. is indicated It is clearly indicated in the clearly GB/T 6398-2000in the GB/T standard 6398-2000 that the standard SIF range that of the C(T) SIF specimens range of is C(T) calculatedspecimens from is the calculated following from equation: the following equation: ΔP a (4) ΔK∆ =P a g( ), ∆K = g(1/2 ),W (4) BW1/2BW W where P is the applied load at both ends of the C(T) specimen, B is the specimen’s thickness, and W where P is the applied load at both ends of the C(T) specimen, B is the specimen’s thickness, and W is the specimen’s width. The solution of the shape function for a standard C(T) specimen is given in is the specimen’s width. The solution of the shape function for a standard C(T) specimen is given in References [30,31] as follows: References [30,31] as follows: a (2 + α)(0.886 + 4.64α -13.32α2 + 14.72α3 - 5.6α4) (5) g( ) = 2 3 4 , a (2 W+ α)(0.886 + 4.64α − 13.32α3/2+ 14.72α − 5.6α g( ) = (1-α) , (5) W (1 − α)3/2 where α=a/W. Equations (2) and (4) derive the equation of the SIF range as follows: where α = a/W. Equations (2) and (4) derive the equation of the SIF1 rangea as follows: (6) ∆K = K -K = (P -P ) g( ), max min max min 1/2 W B1W a ∆K = Kmax−Kmin = (P −Pmin) g( ), (6) where da/dN is plotted against ΔK in log–log axes,max and generalBW1/2 threeW regions can be observed in FCG trend. The three regions are named as the fatigue crack initiation (region Ⅰ), the stable crack growth wherestage da/d (regionN is plotted Ⅱ), and against the unstable∆K in log–log fracture axes, stage and (region general Ⅲ three). In regionsregion Ⅰ can, the be observedSIF is lower in FCGthan the trend. The three regions are named as the fatigue crack initiation (region I), the stable crack growth stress intensity factor threshold, △Kth , and there is no crack growth. When ΔK exceeds stress stageintensity (region II),factor and threshold, the unstable it is fracture in region stage II and (region the crack III). In begins region to I, grow. the SIF It isis lowerworth than pointing the stress out that intensitythe crack factor growth threshold, follows∆Kth a, andpower there law, is nonamely crack growth.the so-called When Paris∆K exceeds law, as stressgiven intensityin Equation factor (7) in threshold, it is in region II and the crack begins to grow. It is worth pointing out that the crack growth region II. When ΔK increases to a certain value, it enters region III, where KImaxis close to the KIc of followsthe material, a power law,and namelythe FCG the rate so-called increases Paris sharply law, until as given the fracture. in Equation (7) in region II. When ∆K increases to a certain value, it enters region III, where KImax is close to the KIc of the material, and the da (7) FCG rate increases sharply until the fracture. = C(ΔK)m, dN da where C and m are material constants related= C (to∆K the)m, test conditions, and they can be obtained (7) by regression analysis of FCG test data. dN

Materials 2019, 12, 1031 7 of 19 where C and m are material constants related to the test conditions, and they can be obtained by regression analysis of FCG test data. Two methods for calculating the FCG rate (da/dN) are recommended in GB/T 6398-2000. One is the secant method and the other is the seven-point incremental polynomial method. Considering that the secant method is relatively simple to operate, it is used to calculate the FCG rate in this study.

3. Analysis of Fatigue Crack Growth According to the test conditions given in Table3, fatigue tests are carried out in air and seawater corrosive environments to obtain the crack propagation process. It is worth noting that the dynamic strain gauge output is the relationship between time and strain when using the BFS measurement method in the fatigue tests. Therefore, it is necessary to obtain the relationship between the strains and the corresponding crack lengths of C(T) specimen. Such relationship is obtained through finite element analysis by using ABAQUS software, and the calculation results are listed in Table4. The convergence analysis is carried out to analyze a C(T) specimen with a crack length of 13 mm, and it is found that the result converges when the element size is 0.7 mm. Based on the numerical results of the crack length and the back strain listed in Table4, a fifth-order polynomial, which is presented through a curve fitting technique by using DataFit software, is used to derive the relationship between the crack length and the strain, and the detailed expression of the polynomial is listed as follows [34]:

2 3 4 5 a = C0 + C1(µε ) + C2(µε) + C3(µε) + C4(µε) + C5(µε) , (8) where C0 to C5 are the regression coefficients. The curve fitting results are shown in Table5, and its fitting accuracy can be assessed from the value of R2 (much close to 1.0).

Table 4. Relationship between crack length and back face strain.

Model ID Crack Length/mm Strain Value/µε X56-13 13 668 X56-14 14 763 X56-15 15 870 X56-16 16 992 X56-17 17 1131 X56-18 18 1290 X56-19 19 1472 X56-20 20 1684 X56-21 21 1930 X56-22 22 2218 X56-23 23 2558 X56-24 24 2965 X56-25 25 3456 X56-26 26 4055 X56-27 27 4803

Table 5. Stress-strain relation coefﬁcient.

2 Equation C0 C1 C2 C3 C4 C5 R Equation (8) 2.938 −2.060 × 10−2 −1.001 × 10−5 −2.935 × 10−9 −4.526 × 10−13 −2.802 × 10−17 0.99998 Equation (9) 0.973 −1685.761 −1.644 × 106 8.214 × 109 −7.381 × 1012 1 0.99999

In addition, Adedipe et al. [35] established a relation between crack length and strain considering such factors as specimen’s material (elastic modulus E), specimen’s thickness B, specimen’s width W, and the applied load P, which mathematical expression is represented by the polynomial as follows:

2 3 4 5 a/W = C0 + C1U + C2U + C3U + C4U + C5U , (9) Materials 2019,, 12,, xx FORFOR PEERPEER REVIEWREVIEW 8 of 18

Equation (9), respectively, are plotted in the same coordinate system for comparison, as shown in Figure 4. It can be seen that the crack lengths calculated by the two formulas are almost the same. From the data analysis, the results calculated from Equation (8) are relatively bigger, i.e., the predicted life is safe. Therefore, Equation (8) is used to predict the crack propagation in this study.

Table 5. Stress-strain relation coefficient..

0 1 2 3 4 5 2 Equation C0 C1 C2 C3 C4 C5 R2 Materials 2019, 12, 1031 8 of 19 Equation (8) 2.938 -2.060E-02 -1.001E-05 -2.935E-09 -4.526E-13 -2.802E-17 0.99998 Equation (9) 0.973 -1685.761 -1.644E6 8.214E9 -7.381E12 1 0.99999 where a/W is the aspect ratio of the C(T) specimen and C0 to C5 are the regression coefﬁcients related to theThe crack purpose length of to FCG width tests ratio. is to obtain the material constants C and m of the API 5L X56 pipeline from Paris law and, thus, the relationship between the stress intensity factor range ΔK and the FCG 1/2 −1 rate da/dN can be determined. The GB/TU = 6398[( |EB-2000εW| [/30P]) and+ ASTM1] E647-2013 [31] standards indicate(10) that the shape function can be calculated using Equation (5) for a standard C(T) specimen | | withwhere a/WEB ≥ ε0.2W. /However,P is a back previous surface studies strain parameter. in the literature Compare [38,3 the9] pointed data calculated out that the from shape Equations function (8) solutionand (9); theof the method standard with C(T) higher specimen precision does to determinenot follow thethe crack equation length provided can be selected.by standards [30,31] for shallowFigure 3cracks shows with the a/W ﬁtting ≤ 0.4 results. To reduce of the the crack error length caused and by the the strain shape value factor, of the C(T)shape specimen factor of theusing standard Equations C(T) (8) specimen and (9), i respectively.s evaluated by The numerical crack lengths simulation calculated before from test Equation data processing. (8) and fromThe SIFsEquation of cracks (9), respectively,with different are lengths plotted in inthe the standard same coordinate C(T) specimens system are for calculated comparison, numerically as shown by in usingFigure the4. Itcontour can be integral seen that technique. the crack The lengths numerical calculated values by of the the two shape formulas function are are almost compared the same. with theFrom results the data from analysis, Equation the (5) results and the calculated new shape from factor Equation proposed (8) are in [3 relatively8] as shown bigger, in Figure i.e., the 5. predicted A shape functionlife is safe. calculation Therefore, equation Equation suitable (8) is used for this to predict test is proposed. the crack propagation in this study.

30 30

25 25

20 20

Back strian from FE Back strian from FE Back strain from FE 15 15 Back strain from FE 15 Equation（8） 15 （） Equation 8 Crack Length(mm) Crack Length(mm) Equation （9）

Crack Length(mm) Crack Length(mm) Equation （9） 10 10 10 -5000 -4000 -3000 -2000 -1000 0 10 -5000 -4000 -3000 -2000 -1000 0 -5000 -4000 -3000 -2000 -1000 0 Strain(με) Strain(με) Strain(με) Strain(με) (a) (b)

FigFigureure 3 3... RRelationelation between between crack crack length length and and strain strain value value measured measured by by the the BFS BFS ( (BackBack Face Face Strain Strain)) compliancecompliance method method::: (( (aa)) Fitting Fitting results results from from Equation Equation (8); (8); ( (bb)) Fitting Fitting results results from from Equation Equation (9). (9).

30 The results from Eqation (8) 16.5 The results from Eqation (8) The results from Eqation (8) The results from Eqation (9) The results from Eqation (9) 16.0 25 The results from Eqation (9) (mm) 16.0 25 (mm)

(mm)

(mm) 15.5 20 15.0 14.5 15 14.5

Crack Length

Crack Length 14.0

Crack Length 14.0 10 0 4000 8000 12000 16000 20000 5500 6000 6500 7000 7500 8000 0 4000 8000 12000 16000 20000 Cycle (N) Cycle (N) Cycle (N) Cycle (N) (a) (b) Figure 4. Relation between crack length and strain value measured by the BFS compliance method: FigFigureure 4 4.. RRelationelation between between crack crack length length and and strain strain value value measured measured by by the the BFS BFS compliance compliance method method:: ((aa)) Comparison Comparison of of the the results results from from Equation Equationss (8) (8) and and (9); (9); ( (b)) Enlarged view of Figure 4 4aa...

The purpose of FCG tests is to obtain the material constants C and m of the API 5L X56 pipeline from Paris law and, thus, the relationship between the stress intensity factor range ∆K and the FCG rate da/dN can be determined. The GB/T 6398-2000 [30] and ASTM E647-2013 [31] standards indicate that the shape function can be calculated using Equation (5) for a standard C(T) specimen with a/W ≥ 0.2. However, previous studies in the literature [38,39] pointed out that the shape function solution of the standard C(T) specimen does not follow the equation provided by standards [30,31] for shallow cracks with a/W ≤ 0.4. To reduce the error caused by the shape factor, the shape factor of the Materials 2019, 12, 1031 9 of 19 standard C(T) specimen is evaluated by numerical simulation before test data processing. The SIFs of cracks with different lengths in the standard C(T) specimens are calculated numerically by using the contour integral technique. The numerical values of the shape function are compared with the results from Equation (5) and the new shape factor proposed in [38] as shown in Figure5. A shape function calculation equation suitable for this test is proposed. Materials 2019, 12, x FOR PEER REVIEW 9 of 18

24 Shape factor from References [38] 24 Equation from References [38] 22 Equation (5) 22 Equation (5)

Y 20 The results from FE 20 Equation (11) 18 18 The results from FE 16 16 14 14

shape factor Shape factor Shape 12 12 10 10 0.3 0.4 0.5 0.6 0.7 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 Aspect ratio of crack (a/W) Aspect ratio of crack (a/W) (a) (b)

FigFigureure 5 5.. ShapeShape factor factor error error analysis analysis:: (a (a) )Numerical Numerical simulation simulation compared compared with with recommended recommended shape shape factorfactor in in the the standard; standard; (b (b) )Comparison Comparison of of new new shape shape factor factor equation equation and and old old equation. equation.

FigureFigure 55aa analyzes analyzes the the shape shape factor factor of the of standard the standard C(T) specimen C(T) specimen made of made API 5L of X56 API submarine 5L X56 submarinepipeline material. pipeline The material. results The show results that show the ABAQUS that the ABAQUS simulation simulation is higher than is higher the results than the calculated results calculatedfrom Equation from Equation (5) and from (5) and the from new equationthe new equation proposed proposed in Reference in Reference [38]. It [3 can8]. beIt can found be found clearly clearlythat the that shallow the shallow crack withcracka with/W ≤ a/W0.4≤ has0.4 h aas larger a larger error. error Hence,. Hence, the the equation equation recommended recommended in thein thestandard standard cannot cannot be usedbe used in this in this study. study The. T datahe data obtained obtained from from numerical numerical simulation simulation is ﬁtted is fitted by using by usinga polynomial, a polynomial, and a and new a shapenew shape factor factor equation equation suitable suitable for calculating for calculating the stress the stress intensity intensity factor factor range, 2 range,∆K, of Δ theK, of material the material is presented is present ased expressed as expressed in Equationin Equation (11). (11). The The ﬁtting fitting degree degree ofof R2 isis 0.9983. 0.9983. FigureFigure 5b shows the comparison of the results calculated from different equations.equations.

5 4 3 2 Y =Y =− -1562.078α5+ 4225.5674225.567αα4- −4294.6024294.602α α+3 2164.728+ 2164.728α -α 538.762α+2− 538.762 63.495α + 63.495,, (11) (11)

3.1.4. FCGFCG BehaviorBehavior of of API API 5L 5L X56 X56 M Materialaterial in inAir Air TheThe fatigue fatigue crack crack growth growth tested tested in in the the air air is is monitored monitored by by the the COD COD gauge gauge method method and and the the BFS BFS method,method, both both of of which which belong belong to to the the flexible ﬂexible method. method. T Too verify verify the the accuracy accuracy of of the the two two measurement measurement methods,methods, the the collected collected data data of of specimen specimen X56 X56-A-1-A-1 a arere analyzed analyzed and and compared. compared. The The data data collected collected from from thethe COD COD gauge gauge is processed byby thethe STM793 STM793 control control system, system, and and the the relationship relationship between between the the FCG FCG rate, rate,da/dN da/, anddN, and the SIFthe range,SIF range,∆K, Δ isK ﬁnally, is finally displayed displayed on the on log–logthe log– axes.log axes The. T datahe data collected collected from from BFS method needs to be transferred. The threshold stress intensity factor range value (∆Kth) is used for BFS method needs to be transferred. The threshold stress intensity factor range value (훥퐾푡ℎ) is used forthe the assessment assessment of theof the used used initial initial stress stress intensity intensity factor factor range range values values [40, 41[40].,41]. After After processing processing the datathe data(contains (contains the datathe data of region of region I), it I), can it becan seen be seen in Figure in Figure6 that 6 thethat FCG the FCG trends trends observed observed in X56-S-1 in X56 and-S- 1X56-S-2 and X56 specimens-S-2 specimens suggest suggest that√ the that threshold the threshold stress intensity stress intensity factor range factor for range X56 steel for in X56 seawater steel in is approximately ∆Kth = 27 MPa · m. In addition, the threshold stress intensity factor range of X56 steel seawater is approximately 훥퐾푡ℎ=27 MPa ⋅ √m. In addition, the threshold stress intensity factor range√ · ofin X56the air steel environment in the air was environment directly inquired was directly from the inquired fatigue testing from machine, the fatigue∆K th testing= 28 MPa machine,m.

훥퐾푡ℎ=28 MPa ⋅ √m.

0.1 0.1 BFS test data of X56-S-1 BFS test data of X56-S-2

0.01 0.01

0.001 0.001

(mm/cycle)

(mm/cycle) Region II 1E-4 1E-4 Region II

da/dN

1E-5 1E-5 30 40 50 60 70 80 90100 30 40 50 60 70 80 90100 1/2 1/2 △K(MPa·mm ) △K(MPa·mm ) (a) (b)

Figure 6. Tested data points in log–log axes (contains the data of region I): (a) Specimen X56-S-1; (b) Specimen X56-S-2

Materials 2019, 12, x FOR PEER REVIEW 9 of 18

24 Shape factor from References [38] 24 Equation from References [38] 22 Equation (5) 22 Equation (5)

Y 20 The results from FE 20 Equation (11) 18 18 The results from FE 16 16 14 14

shape factor Shape factor Shape 12 12 10 10 0.3 0.4 0.5 0.6 0.7 0.30 0.35 0.40 0.45 0.50 0.55 0.60 0.65 0.70 Aspect ratio of crack (a/W) Aspect ratio of crack (a/W) (a) (b)

Figure 5. Shape factor error analysis: (a) Numerical simulation compared with recommended shape factor in the standard; (b) Comparison of new shape factor equation and old equation.

Figure 5a analyzes the shape factor of the standard C(T) specimen made of API 5L X56 submarine pipeline material. The results show that the ABAQUS simulation is higher than the results calculated from Equation (5) and from the new equation proposed in Reference [38]. It can be found clearly that the shallow crack with a/W≤ 0.4 has a larger error. Hence, the equation recommended in the standard cannot be used in this study. The data obtained from numerical simulation is fitted by using a polynomial, and a new shape factor equation suitable for calculating the stress intensity factor range, ΔK, of the material is presented as expressed in Equation (11). The fitting degree of R2 is 0.9983. Figure 5b shows the comparison of the results calculated from different equations. Y = -1562.078α5+ 4225.567α4- 4294.602α3+ 2164.728α2- 538.762α+ 63.495, (11)

3.1. FCG Behavior of API 5L X56 Material in Air The fatigue crack growth tested in the air is monitored by the COD gauge method and the BFS method, both of which belong to the flexible method. To verify the accuracy of the two measurement methods, the collected data of specimen X56-A-1 are analyzed and compared. The data collected from the COD gauge is processed by the STM793 control system, and the relationship between the FCG rate, da/dN, and the SIF range, ΔK, is finally displayed on the log–log axes. The data collected from

BFS method needs to be transferred. The threshold stress intensity factor range value (훥퐾푡ℎ) is used for the assessment of the used initial stress intensity factor range values [40,41]. After processing the data (contains the data of region I), it can be seen in Figure 6 that the FCG trends observed in X56-S- 1 and X56-S-2 specimens suggest that the threshold stress intensity factor range for X56 steel in seawater is approximately 훥퐾푡ℎ=27 MPa ⋅ √m. In addition, the threshold stress intensity factor range ofMaterials X56 steel2019, 12 in, 1031 the air environment was directly inquired from the fatigue testing machine,10 of 19

훥퐾푡ℎ=28 MPa ⋅ √m.

0.1 0.1 BFS test data of X56-S-1 BFS test data of X56-S-2

0.01 0.01

0.001 0.001

(mm/cycle)

(mm/cycle) Region II 1E-4 1E-4 Region II

da/dN

1E-5 1E-5 30 40 50 60 70 80 90100 30 40 50 60 70 80 90100 1/2 1/2 △K(MPa·mm ) △K(MPa·mm ) (a) (b)

FigureFigure 6 6.. TestedTested data data points points in inlog log–log–log axes axes (contains (contains the thedata data of region of region I): (a I):) Specimen (a) Specimen X56-S X56-S-1;-1; (b) MaterialsSpecimen(b 2019) Specimen, 12 ,X56 x FOR- X56-S-2.S- 2PEER REVIEW 10 of 18

WhenWhen processing processing BFS BFS data, data, the the data data points points that that mainly mainly exhibit exhibit linear linear behavior behavior are are selected, selected, and and theythey are are used used to to draw draw the the average average curve curve and and the the upper upper and and the the lower lower limits limits on on the the log log–log–log axes axes (average(average curve curve ±± SD).SD). All All the the test test points are re-selectedre-selected byby using using FORTRAN FORTRAN compiler compiler software, software, and and the thedata data outside outside the the upper/lower upper/lower limit limit are are eliminated. eliminated. The The relationship relationship between between the the FCG FCG rate, rate,da/dN da/dN, and, andthe the stress stress intensity intensity factor factor range, range,∆K, isΔ shownK, is shown in Figure in Figure7a. The 7a. relationship The relationship between between the FCG the rate FCG and ratethe and stress the intensity stress int factorensity range factor obtained range obtained by the two by the ﬂexible two methodsflexible methods is shown is inshown Figure in7 b.Figure It shows 7b. Itthat shows the datathat the monitored data monitored by the COD by the method COD and method by the and BFS by method the BFS have method a high have degree a high of coincidence, degree of coincidence,indicating that indicating both methods that both can methods achieve the can purpose achieve ofthe monitoring purpose of crack monitoring length. Thiscrack result length. provides This resulta basis provides for monitoring a basis crack for monitoringlength using crack the BFS length method using alone the in BFS seawater method experimental alone in seawater tests. The experimentaldata are measured tests. The in data two waysare measured to calculate in two the ways material to calculate constants the Cmaterialand m constantsof Paris law, C and and m theof Pariscalculated law, and results the calculated are summarized results in are Table summ6. arized in Table 6.

0.1 0.1 X56-A-1 BFS test data of X56-A-1 COD test data of X56-A-1 0.01 Mean curve 0.01 Mean curve±SD Mean curve Mean curve±SD 0.001 0.001

(mm/cycle)

1E-4 1E-4

da/dN

da/dN(mm/cycle)

1E-5 1E-5 30 40 50 60 70 80 90 30 40 50 60 70 80 90 1/2 1/2 △K(MPa·mm ) △K(MPa·mm ) (a) (b)

FigureFigure 7. 7. ComparisonComparison of of different different crack crack growth growth monitoring monitoring methods: methods: (a ()a )FCG FCG test test data data obtained obtained by by BFSBFS method; method; (b (b) )Comparison Comparison of of test test results results of of COD COD and and BFS. BFS.

TableTable 6. 6. C(T)C(T) specimens specimens material material constants constants and and remaining remaining life. life.

Calculation from Equation Recommended by GB/T Calculation from Equation Recommended Calculation from Equation (11) Sample ID Test Count 6398-2000 Calculation from Equation (11) Sample ID Test Count Cby m GB/TR2 6398-Cycles2000 Error (%) C m R2 Cycles Error (%) X56-A-1 29156 9.95C× 10−9 m2.854 R2 0.95Cycles 26283 Error−9.85 (%) 6.60C× 10−9 m2.950 R2 0.95Cycles 27851 Error−4.48 (%) X56-S-1 15547 2.92 × 10−9 3.353 0.96 14159 −8.93 2.14 × 10−9 3.418 0.96 15273 −1.76 X56X56-S-2-A-1 29156 16394 9.95E3.76 ×-1009− 82.8542.636 0.95 0.95 26283 15358 -−9.856.32 6.60E3.26 ×-1009−8 2.9502.661 0.95 0.94 27851 16154 -4.48−1.46 X56Pipeline-S-1 15547 42079 2.92E3.76 ×-1009− 83.3532.636 0.96 0.95 1415938444/36651 -8.93- 2.14E3.26 ×-1009−8 3.4182.661 0.96 0.94 1527340935/39383 -1.76- X56-S-2 16394 3.76E-08 2.636 0.95 15358 -6.32 3.26E-08 2.661 0.94 16154 -1.46 Pipeline 42079 3.76E-08 2.636 0.95 38444/36651 - 3.26E-08 2.661 0.94 40935/39383 -

3.2. FCG Behavior of API 5L X56 Material in Seawater Since the presence of seawater increases the difficulty of the fatigue test, the crack length is monitored in the seawater environment by using only BFS method. Table 3 shows that fatigue tests on two specimens are conducted in seawater to verify the accuracy of the tested results. The two sets of data are preprocessed separately, and the processing method is the same as the BFS method data processing method in air. The relationship between the FCG rate, da/dN, and the stress intensity factor range, ΔK, is shown in Figure 8. Figure 8a,b show the trend between the FCG rate and the stress intensity factor range for specimens X56-S-1 and X56-S-2, respectively. As seen in Figure 8, the relationship between da/dN and ΔK exhibits a linear change in log–log axes. According to this relationship, the two sets of tested data are fitted linearly to obtain the Paris law constants (C and m) of the API 5L X56 pipeline steel under free corrosion conditions, as shown in Table 6. The Paris law constants obtained from the two sets of data are used for fatigue life prediction of the standard C(T) specimen, and then the prediction results are compared with the tested results in Table 6 to judge the accuracy of the prediction method. The results show that both sets of data can be used to predict fatigue life of a standard C(T) specimen. Since the predicted results of specimen X56-S-2 are closer to

Materials 2019, 12, 1031 11 of 19

5. FCG Behavior of API 5L X56 Material in Seawater Since the presence of seawater increases the difﬁculty of the fatigue test, the crack length is monitored in the seawater environment by using only BFS method. Table3 shows that fatigue tests on two specimens are conducted in seawater to verify the accuracy of the tested results. The two sets of data are preprocessed separately, and the processing method is the same as the BFS method data processing method in air. The relationship between the FCG rate, da/dN, and the stress intensity factor range, ∆K, is shown in Figure8. Figure8a,b show the trend between the FCG rate and the stress intensity factor range for specimens X56-S-1 and X56-S-2, respectively. As seen in Figure8, the relationship between da/dN and ∆K exhibits a linear change in log–log axes. According to this relationship, the two sets of tested data are ﬁtted linearly to obtain the Paris law constants (C and m) of the API 5L X56 pipeline steel under free corrosion conditions, as shown in Table6. The Paris law constants obtained from the two sets of data are used for fatigue life prediction of the standard C(T) specimen, and then the prediction results are compared with the tested results in Table6 to judge the accuracy of the prediction method. The results show that both sets of data can be used to predict Materialsfatigue 2019 life, of12, a x standardFOR PEER REVIEW C(T) specimen. Since the predicted results of specimen X56-S-2 are closer11 of 18 to thethe experimental value,value, thethe ParisParis law law constants constants measured measured by by X56-S-2 X56-S- specimen2 specimen are are used used to predictto predict the thecorrosion corrosion fatigue fatigue life life of the of the submarine submarine pipeline. pipeline.

0.1 0.1 BFS test data of X56-S-1 BFS test data of X56-S-2 0.01 Mean curve 0.01 Mean curve Mean curve±SD Mean curve± SD

0.001 0.001

(mm/cycle) (mm/cycle)

1E-4 1E-4

da/dN da/dN

1E-5 1E-5 30 40 50 60 70 80 90 30 40 50 60 70 80 90 1/2 1/2 △K(MPa·mm ) △K(MPa·m ) (a) (b)

FigureFigure 8. Tested 8. Tested data points data pointsin log– inlog log–log axes: ( axes:a) Specimen (a) Specimen X56-S- X56-S-1;1; (b) Specimen (b) Specimen X56-S- X56-S-2.2

3.36. Comparison. Comparison of of FCG FCG B Behaviorehavior in inAir Air and and in S ineawater Seawater TheThe FCG datadata testedtested in in air air and and in seawaterin seawater are are plotted plotted together together in the in same the same log–log log axes–log as axes shown as shownin Figure in9 .Figure Figure 9a. showsFigure a9 comparisona shows a comparison of the tested of data, the andtest Figureed data,9b showsand Figure a comparison 9b shows of a comparisonﬁtting curves of (withfitting standard curves (with deviation). standard It indicatesdeviation). that It indicate the da/dNs that− ∆theK curveda/dN- inΔK air curve is consistent in air is consistentwith the trend with of the steady trend fatigue of steady crack fatigue growth crack in region growth II, i.e.,in region the FCG II, ratesi.e., the increases FCG rates linearly increases when linearlythe stress when intensity the stress factor intensity range increases. factor range After increases calculation,√ . After the calculat FCG rate,ion, da/dN the FCG, corresponding rate, da/dN, correspondingto the stress intensity to the stress factor intensity range factor∆K = range 29.64 MPaΔK =· 29.64m (theMPa initial⋅ √m (the crack initial length crack of length the X56-A-1 of the − × 4 −4 X56specimen-A-1 specimen is 12.98 mm) is 12.98 is 1.53 mm)10 is mm/cycle. 1.53×10 mm/cycle At√ the end. A oft the test, end the of FCG the test, rate corresponding the FCG rate · correspondingto the stress intensity to the stress factor intensity range ∆K factor= 75.06 rangeMPa ΔK =m 75.06(crack MPa termination⋅ √m (crack length terminationaf = 25.03 length mm) a isf −3 =2.4 25.03× 10 mm)mm/cycle. is 2.4 × 10−3 mm/cycle. For API 5L X56 pipeline material, there are similar laws in seawater as in air. The difference from the air environment is that the FCC rate of the specimen in the seawater is increased faster, and the slope of the da/dN-ΔK logarithmic curve in the seawater is small. This indicates that the influence of seawater corrosion on the FCG rate is greater in the initial stage of fatigue crack growth. With the increase of ΔK, the influence of seawater corrosion is reduced gradually, and the FCG rate in the seawater is closer to the FCG rate in the air. −4 According to Table 6, da/dN = 2.57 × 10 mm/cycle corresponding to a0 = 12.98 mm in seawater is obtained, which is about 1.68-times the FCG rate in air. The corresponding da/dN =3.63×10−3 mm/cycle at af = 25.03 mm is about 1.52-times the FCG rate in air. From the whole test process, the FCG rate of API 5L X56 pipeline material in seawater is about 1.6-times that in air. However, the influence of seawater on corrosion fatigue is reduced gradually with the increase of FCG rate.

0.1 0.1 Test data of X56-A-1 Mean curve of X56-A-1 0.01 Test data of X56-S-2 0.01 Mean curve ± SD of X56-A-1

0.001 0.001

(mm/cycle)

1E-4 1E-4

da/dN Mean curve ± SD of X56-S-2

da/dN Mean curve of X56-S-2 1E-5 1E-5 30 40 50 60 70 80 90 30 40 50 60 70 80 90 △K(MPa·mm1/2) △K(MPa·mm1/2) (b) (a)

Materials 2019, 12, x FOR PEER REVIEW 11 of 18 the experimental value, the Paris law constants measured by X56-S-2 specimen are used to predict the corrosion fatigue life of the submarine pipeline.

0.1 0.1 BFS test data of X56-S-1 BFS test data of X56-S-2 0.01 Mean curve 0.01 Mean curve Mean curve±SD Mean curve± SD

0.001 0.001

(mm/cycle) (mm/cycle)

1E-4 1E-4

da/dN da/dN

1E-5 1E-5 30 40 50 60 70 80 90 30 40 50 60 70 80 90 1/2 1/2 △K(MPa·mm ) △K(MPa·m ) (a) (b)

Figure 8. Tested data points in log–log axes: (a) Specimen X56-S-1; (b) Specimen X56-S-2

3.3. Comparison of FCG Behavior in Air and in Seawater The FCG data tested in air and in seawater are plotted together in the same log–log axes as shown in Figure 9. Figure 9a shows a comparison of the tested data, and Figure 9b shows a comparison of fitting curves (with standard deviation). It indicates that the da/dN-ΔK curve in air is consistent with the trend of steady fatigue crack growth in region II, i.e., the FCG rates increases linearly when the stress intensity factor range increases. After calculation, the FCG rate, da/dN, corresponding to the stress intensity factor range ΔK = 29.64 MPa ⋅ √m (the initial crack length of the X56-A-1 specimen is 12.98 mm) is 1.53×10−4 mm/cycle. At the end of the test, the FCG rate corresponding to the stress intensity factor range ΔK = 75.06 MPa ⋅ √m (crack termination length af = 25.03 mm) is 2.4 × 10−3 mm/cycle. For API 5L X56 pipeline material, there are similar laws in seawater as in air. The difference from the air environment is that the FCC rate of the specimen in the seawater is increased faster, and the slope of the da/dN-ΔK logarithmic curve in the seawater is small. This indicates that the influence of seawater corrosion on the FCG rate is greater in the initial stage of fatigue crack growth. With the increase of ΔK, the influence of seawater corrosion is reduced gradually, and the FCG rate in the seawater is closer to the FCG rate in the air. −4 According to Table 6, da/dN = 2.57 × 10 mm/cycle corresponding to a0 = 12.98 mm in seawater is obtained, which is about 1.68-times the FCG rate in air. The corresponding da/dN =3.63×10−3 mm/cycle at af = 25.03 mm is about 1.52-times the FCG rate in air. From the whole test process, the FCGMaterials rate2019 of, 12API, 1031 5L X56 pipeline material in seawater is about 1.6-times that in air. However,12 ofthe 19 influence of seawater on corrosion fatigue is reduced gradually with the increase of FCG rate.

0.1 0.1 Test data of X56-A-1 Mean curve of X56-A-1 0.01 Test data of X56-S-2 0.01 Mean curve ± SD of X56-A-1

0.001 0.001

(mm/cycle)

1E-4 1E-4

da/dN Mean curve ± SD of X56-S-2

da/dN Mean curve of X56-S-2 1E-5 1E-5 30 40 50 60 70 80 90 30 40 50 60 70 80 90 △K(MPa·mm1/2) △K(MPa·mm1/2) (b) (a)

Figure 9. Comparison of FCG rates of API 5L X56 steel in seawater and in air: (a) Comparison of tested data on log–log axes; (b) Comparison of ﬁtting curves on log–log axes.

For API 5L X56 pipeline material, there are similar laws in seawater as in air. The difference from the air environment is that the FCC rate of the specimen in the seawater is increased faster, and the slope of the da/dN − ∆K logarithmic curve in the seawater is small. This indicates that the influence of seawater corrosion on the FCG rate is greater in the initial stage of fatigue crack growth. With the increase of ∆K, the influence of seawater corrosion is reduced gradually, and the FCG rate in the seawater is closer to the FCG rate in the air. −4 According to Table6, da/dN = 2.57 × 10 mm/cycle corresponding to a0 = 12.98 mm in seawater is obtained, which is about 1.68-times the FCG rate in air. The corresponding −3 da/dN = 3.63 × 10 mm/cycle at af = 25.03 mm is about 1.52-times the FCG rate in air. From the whole test process, the FCG rate of API 5L X56 pipeline material in seawater is about 1.6-times that in air. However, the influence of seawater on corrosion fatigue is reduced gradually with the increase of FCG rate.

7. Prediction of Corrosion Fatigue Life of Submarine Pipeline with Initial Crack Defect Based on Paris law and the ﬁnite element analysis for SIF, an approximate integration method is presented for predicting the fatigue life of a submarine pipeline with an initial crack defect. To verify the effectiveness of the presented method, a corresponding experimental test on a full-scale API 5L X56 pipeline is carried out in laboratory.

7.1. Experimental Test on Corrosion Crack Growth of a Full-Scale Submarine Pipeline The corrosion fatigue crack propagation test on a full-scale API 5L X56 submarine pipeline is carried out to provide an actual basis for the prediction of corrosion fatigue life. The API 5L X56 submarine pipeline used in the test is fabricated in accordance with API SPEC 5L [42] issued by the American National Standards Institute. The structure of the fatigue testing machine and the clamping of the specimen are shown in Figure 10. In addition, the prefabricated surface crack shown in the ﬁgure is located on the bottom surface of the specimen at the mid-span, and it is prefabricated by a circular abrasive cutting wheel to produce a surface crack with a width of 1.5 mm, a length of 52.1 mm and a depth of 5.5 mm. The pipeline is pinned at both ends on the supports, and a pressure in the sinusoidal wave is applied at the mid-span. To ensure that the crack can expand during the fatigue loading process, the amplitude of the cyclic loading must make the crack tip has a certain stress intensity factor to drive the crack propagation and ensure that the pipeline does not produce a wide range of yield. The amplitude of the cyclic load in the fatigue test is 235 kN. The loading frequency, waveform, stress ratio, and other parameter settings are consistent with the FCG tests of the API 5L X56 C(T) specimens. The speciﬁc experimental parameters are shown in Table3. Materials 2019, 12, x FOR PEER REVIEW 12 of 18

Figure 9. Comparison of FCG rates of API 5L X56 steel in seawater and in air: (a) Comparison of tested data on log–log axes; (b) Comparison of fitting curves on log–log axes.

4. Prediction of Corrosion Fatigue Life of Submarine Pipeline with Initial Crack Defect Based on Paris law and the finite element analysis for SIF, an approximate integration method is presented for predicting the fatigue life of a submarine pipeline with an initial crack defect. To verify the effectiveness of the presented method, a corresponding experimental test on a full-scale API 5L X56 pipeline is carried out in laboratory.

4.1. Experimental Test on Corrosion Crack Growth of a Full-Scale Submarine Pipeline The corrosion fatigue crack propagation test on a full-scale API 5L X56 submarine pipeline is carried out to provide an actual basis for the prediction of corrosion fatigue life. The API 5L X56 submarine pipeline used in the test is fabricated in accordance with API SPEC 5L [42] issued by the American National Standards Institute. The structure of the fatigue testing machine and the clamping of the specimen are shown in Figure 10. In addition, the prefabricated surface crack shown in the figure is located on the bottom surface of the specimen at the mid-span, and it is prefabricated by a circular abrasive cutting wheel to produce a surface crack with a width of 1.5 mm, a length of 52.1 mm and a depth of 5.5 mm. The pipeline is pinned at both ends on the supports, and a pressure in the sinusoidal wave is applied at the mid-span. To ensure that the crack can expand during the fatigue loading process, the amplitude of the cyclic loading must make the crack tip has a certain stress intensity factor to drive the crack propagation and ensure that the pipeline does not produce a wide range of yield. The amplitude of the cyclic load in the fatigue test is 235 kN. The loading frequency, waveform,Materials stress2019, 12 ratio, 1031, and other parameter settings are consistent with the FCG tests of the API 5L13 of 19 X56 C(T) specimens. The specific experimental parameters are shown in Table 3.

(a) (b)

FigureFigure 10. Fatigue 10. Fatigue test on test a full on a-scale full-scale submarine submarine pipeline pipeline:: (a) Fatigue (a) Fatigue test equipment test equipment for full for-scale full-scale pipelinepipeline;; (b) Schematic (b) Schematic view viewand details and details of fatigue of fatigue crack cracktest test.

To simulateTo simulate the seawater the seawater conditions, conditions, natural naturalseawater seawater is continuously is continuously injected into injected the crack into- the containingcrack-containing part during part the during test. At the the test. same At the time, same non time,-corrosive non-corrosive clean water clean wateris injected is injected into the into the pipelinepipeline to monitor to monitor the penetration the penetration of the of fatigue the fatigue crack. crack. A large A largeamount amount of water of water leakage leakage occurs occurs when when the fattheigue fatigue crack crack is through is through the tube the tubewall. wall.At the At left the of left Figure of Figure 11, the 11 crack, the crack has been has beenpenetrated penetrated and and the waterthe water starts starts to drip. to drip.After Afterthe end the of end the offatigue the fatigue test, the test, crack the surface crack surface is visible is visiblein the cut in thepipe cut as pipe shownas in shown Figure in 11. Figure It can 11 .be It seen can befrom seen the from fatigu thee fatiguecrack surface crack surfacethat the that fatigue the fatiguecrack expands crack expands in both inlength both and length depth and direction. depth direction. However, However, the expansion the expansion rate does rate not does change not uniformly change uniformly during the during fatiguethe crack fatigue propagation. crack propagation. In the beginning, In the beginning, the initial the initialcrack propagatescrack propagates faster faster along along the depth the depth directiondirection of the of pipeline, the pipeline, while while the crack the crack propagates propagates relatively relatively slowly slowly along along the length. the length. As the As crack the crack depthdepth increases, increases, the FCG the FCGrate along rate along the circumferential the circumferential direction direction increases. increases. Materials 2019, 12, x FOR PEER REVIEW 13 of 18

Figure 11. Surface of fatigue crack.crack.

7.2.4.2. Prediction on FatigueFatigue LifeLife by UsingUsing ParisParis lawlaw When the safety evaluation of crack-containingcrack-containing components isis carried out, the material constants of Paris law are onlyonly relatedrelated toto thethe testtest environmentenvironment and materials, and they are widelywidely used for the predictionprediction ofof fatiguefatigue life.life. The life prediction can be performedperformed by integrating Paris law as shownshown inin Equation (12).(12). Z ai+1 da Z Ni+1 ai+1 da =Ni+1 dN, (12) ∫ mm= ∫ dN, (12) ai ai CC((∆ΔK)) Ni Ni

wherewhere aai iand anda i+ a1i+1are are the the crack crack depths depth ofs anyof any two two cracks cracks inthe in the stable stable crack crack growth growth region, region,Ni and Ni Nandi+1 areNi+1 theare numberthe number of cycles of cycles corresponding corresponding to the to crackthe crack length length is ai isand ai aandi+1. ai+1. Equation (12) shows that the fatigue life of the crack in region II can be predicted if the initial

crack length (a0) and the final crack length (a1) are known. The ΔK of the C(T) specimen can be calculated according to Equation (5). In this paper, the new shape factor, which is calculated from the presented equation based on finite element analysis, is used to calculate ΔK. The accuracy of the Paris law constants obtained in the FCG test directly affects the prediction of the corrosion fatigue life of the submarine pipeline. ΔK is calculated using two shape factor equations, and the corresponding Paris law constants are fitted based on this. Using Equation (12) to obtain the number of cycles of the C(T) specimen and comparing it with the test results, it was found that the error was within 10% as listed in Table 6. Using Equations (5) and (11), respectively, to calculate the Paris law constants, it is found that the power exponent constants calculated from Equation (5) are usually smaller than the calculated results from the new equation of shape factor. Table 6 shows that predicting the fatigue life of the C(T) specimen using Equation (5) recommended in the standard produces more conservative predictions. In contrast, the results calculated from Equation (11) can be used for expectations of the remaining life of the specimens with a better result.

4.3. Finite Element Analysis for K of Fatigue Crack in Submarine Pipeline In recent years, finite element analysis using commercial software has been favored by researchers because of its simple operation, low cost and strong applicability. ABAQUS is used here to carry out numerical analysis for the stress intensity factor range (ΔK) of the C(T) specimen, and the numerical results are compared with the experimental values. It is found that the finite element analysis can obtain better results. Therefore, ABAQUS is also used to carry out finite element analysis to analyze the cracked pipelines. When using finite element software to simulate the crack propagation process of submarine pipelines, the crack propagation process in the pipeline can be divided into several stages, and the crack propagation life at the end of a certain stage can be used to predict the crack propagation life at this stage. This method is called approximate integration method. In addition, there are growth behavior in both the radial direction and the circumferential direction during the fatigue crack growth process of the pipeline, and the FCG rates are different. The established finite element model for cracked pipeline needs to calculate the SIF values along the crack front. Such SIFs can be used in Pairs law to calculate the crack growth rate and rate ratio in different directions. According to the ratio of the circumferential direction to the radial direction, the circumferential fatigue crack direction of the pipeline can be matched. Depending on the ratio of the

Materials 2019, 12, 1031 14 of 19

Equation (12) shows that the fatigue life of the crack in region II can be predicted if the initial crack length (a0) and the final crack length (a1) are known. The ∆K of the C(T) specimen can be calculated according to Equation (5). In this paper, the new shape factor, which is calculated from the presented equation based on finite element analysis, is used to calculate ∆K. The accuracy of the Paris law constants obtained in the FCG test directly affects the prediction of the corrosion fatigue life of the submarine pipeline. ∆K is calculated using two shape factor equations, and the corresponding Paris law constants are fitted based on this. Using Equation (12) to obtain the number of cycles of the C(T) specimen and comparing it with the test results, it was found that the error was within 10% as listed in Table6. Using Equations (5) and (11), respectively, to calculate the Paris law constants, it is found that the power exponent constants calculated from Equation (5) are usually smaller than the calculated results from the new equation of shape factor. Table6 shows that predicting the fatigue life of the C(T) specimen using Equation (5) recommended in the standard produces more conservative predictions. In contrast, the results calculated from Equation (11) can be used for expectations of the remaining life of the specimens with a better result.

7.3. Finite Element Analysis for ∆K of Fatigue Crack in Submarine Pipeline In recent years, finite element analysis using commercial software has been favored by researchers because of its simple operation, low cost and strong applicability. ABAQUS is used here to carry out numerical analysis for the stress intensity factor range (∆K) of the C(T) specimen, and the numerical results are compared with the experimental values. It is found that the finite element analysis can obtain better results. Therefore, ABAQUS is also used to carry out finite element analysis to analyze the cracked pipelines. When using finite element software to simulate the crack propagation process of submarine pipelines, the crack propagation process in the pipeline can be divided into several stages, and the crack propagation life at the end of a certain stage can be used to predict the crack propagation life at this stage. This method is called approximate integration method. In addition, there are growth behavior in both the radial direction and the circumferential direction during the fatigue crack growth process of the pipeline, and the FCG rates are different. The established finite element model for cracked pipeline needs to calculate the SIF values along the crack front. Such SIFs can be used in Pairs law to calculate the crack growth rate and rate ratio in different directions. According to the ratio of the circumferential direction to the radial direction, the circumferential fatigue crack direction of the pipeline can be matched. Depending on the ratio of the radial and the circumferential FCG rates, the length of the cracks along the radial and the circumferential directions can be matched. Because of the stress singularity at the crack tip, a 15-node iso-parametric stress singular element is required for simulating the crack tip using the perimeter integral technique. Except for the crack front region, the other regions are meshed with a 20-node hexahedron. The reduced integration technique is introduced in the calculation process to improve the calculation efficiency. The loading and the boundary conditions in the finite element analysis are as consistent as possible with the testing conditions, and the finite element model of the pipeline are shown in Figure 12. Materials 2019, 12, x FOR PEER REVIEW 14 of 18

radial and the circumferential FCG rates, the length of the cracks along the radial and the circumferential directions can be matched. Because of the stress singularity at the crack tip, a 15-node iso-parametric stress singular element is required for simulating the crack tip using the perimeter integral technique. Except for the crack front region, the other regions are meshed with a 20-node hexahedron. The reduced integration technique is introduced in the calculation process to improve the calculation efficiency. The loading and the boundary conditions in the finite element analysis are Materialsas consistent2019, 12, 1031as possible with the testing conditions, and the finite element model of the pipeline15 of 19are shown in Figure 12.

(a) (b)

FigureFigure 12. 12.Finite Finite element element model model of of pipeline pipeline with with initial initial crack: crack (:a ()a Schematic) Schematic view view of of FE FE model; model; (b ()b) DetailsDetails of of the the FE FE model. model

DuringDuring the the propagation propagation process process of of the the corrosion corrosion fatigue fatigue crack, crack, the the crack crack propagates propagates along along the the radialradial and and the the circumferential circumferential directions directions of theof the pipeline pipeline and and the expansionthe expansion rate israte different. is different. Taking Taking the X56-S-2the X56 specimen-S-2 specimen as an example,as an example, the cracked the cracked pipeline pipeline needs needs to establish to establish a ﬁnite a element finite element model model with differentwith different crack lengths crack in lengths two directions in two for directions analysis. The for stress analysis. intensity The factorstress range intensity corresponding factor range to s differentcorresp crackonding lengths to different are shown crack in lengths Tables are7 and shown8, respectively. in Tables 7 and 8, respectively.

TableTable 7. 7.Radial Radial crack crack propagation propagation and and loading loading cycles. cycles. √ Model IDModel Crack ID DepthCrack Depth ∆KΔK(mm/cycle) (mm/cycle) da/dNda/dN (퐌퐏퐚(MPa⋅·√퐦m)) Cycles Cycles Model-1-RModel-1-R 5.55.5 20.84820.848 1.05381.0538E×-0410 −4 - - Model-2-RModel-2-R 66 21.35421.354 1.12201.1220E×-0410 −4 4457 4457 Model-3-RModel-3-R 77 23.00623.006 1.36951.3695E×-0410 −4 7302 7302 −4 Model-4-RModel-4-R 88 24.71524.715 1.66361.6636E×-0410 6011 6011 −4 Model-5-RModel-5-R 99 25.77625.776 1.85321.8532E×-0410 5396 5396 Model-6-R 10 27.180 2.1341 × 10−4 4686 Model-6-R 10 27.180 2.1341E-04 4686 Model-7-R 11 27.714 2.2475 × 10−4 4449 Model-7-R 11 27.714 2.2475E-04 4449 Model-8-R 12 28.302 2.3767 × 10−4 4208 Model-9-RModel-8-R 1312 29.56128.302 2.66842.3767E×-0410 −4 4208 3748 Model-10-RModel-9-R 13.213 30.69329.561 2.94902.6684E×-0410 −4 3748 678 Model-10-R 13.2 30.693 2.9490E-04 678 Table 8. Circumferential crack growth and loading cycles. Table 8. Circumferential crack growth and loading cycles√ Model ID Crack Length ∆K(mm/cycle) da/dN (MPa· m) Cycles Model ID Crack Length ΔK(mm/cycle) da/dN (퐌퐏퐚 ⋅ √퐦) Cycles Model-1-C 52.1 8.209 8.8265 × 10−6 - Model-1-C 52.1 8.209 8.8265E-06 - Model-2-C 52.2 9.522 1.3099 × 10−5 3817 Model-3-CModel-2-C 52.552.2 11.5399.522 2.18391.3099E×-1005 −5 3817 6868 Model-4-CModel-3-C 52.952.5 14.73311.539 4.18412.1839E×-1005 −5 6868 4780 Model-5-CModel-4-C 53.552.9 17.07314.733 6.19344.1841E×-1005 −5 4780 4844 −5 Model-6-CModel-5-C 54.353.5 20.29517.073 9.81056.1934E×-1005 4844 4077 −4 Model-7-CModel-6-C 55.354.3 22.69920.295 1.32149.8105E×-1005 4077 3784 Model-8-C 56.6 25.188 1.7429 × 10−4 3729 Model-7-C 55.3 22.699 1.3214E-04 3784 Model-9-C 58 27.199 2.1381 × 10−4 3274 Model-10-CModel-8-C 59.556.6 27.75525.188 2.25641.7429E×-1004 −4 3729 4210 Model-9-C 58 27.199 2.1381E-04 3274

Table 6 shows that the submarine pipeline experienced a total of 42079 loading cycles during the corrosion fatigue test. The final crack parameters corresponding to the number of loading cycles are as follows: the crack propagation in radial direction (crack depth) is 13.9 mm, and the crack propagation in circumferential direction (crack length) is 60.2 mm. The final crack parameters simulated from finite element analysis are as follows: the crack propagation in radial direction is 13.2 mm, and the crack propagation in circumferential direction is 59.5 mm. The numerical simulation produces an accurate Materials 2019, 12, x FOR PEER REVIEW 15 of 18

Model-10-C 59.5 27.755 2.2564E-04 4210

Table 6 shows that the submarine pipeline experienced a total of 42079 loading cycles during the corrosion fatigue test. The final crack parameters corresponding to the number of loading cycles are as follows: the crack propagation in radial direction (crack depth) is 13.9 mm, and the crack propagation in circumferential direction (crack length) is 60.2 mm. The final crack parameters Materials 2019, 12, 1031 16 of 19 simulated from finite element analysis are as follows: the crack propagation in radial direction is 13.2 mm, and the crack propagation in circumferential direction is 59.5 mm. The numerical simulation producesenough prediction an accurate on enough the fatigue prediction crack propagation, on the fatigue which crack indicates propagation, that the which presented indicates ﬁnite that element the presentedmodel is suitable finite element for analyzing model theis su SIFsitable of for the analyzing crack in a the pipeline. SIFs of the crack in a pipeline.

4.4.7.4. A Analysisnalysis of of C Corrosionorrosion F Fatigueatigue C Crackrack P Propagationropagation WhenWhen fatigue fatigue crack crack propagates propagates in the pipe pipeline,line, it i iss found found that that the the crack crack growth growth rate ratess in in the the radial radial directiondirection and and in in the the circumferential circumferential directi directionon are are not not the the same. same. T Too reflect reflect the the expansion rates rates of of the the crackcrack in in the the depth depth direction direction and and in in the the length length direction direction more more clearly clearly and and intuitively intuitively,, the the data data in in two two differentdifferent directions directions are are compared compared in in Figure Figure 13.. The The figure figure shows shows that that the the initial initial crack crack grow growss faster faster alongalong the the radial radial direction direction of of the the pipeline pipeline at at the the beginning beginning of of the the FCG FCG test test while while the the crack crack propagates propagates relativelyrelatively slowly slowly along along the the circumferential circumferential direction. direction. As As the the crack crack depth depth increases increases to to a a certain certain extent, extent, thethe growth growth of of the the crack crack along along the the circum circumferentialferential has has a a certain certain hindrance hindrance to to the the radial radial expansion, expansion, and and thethe rate rate of of crack crack propagation propagation along along the the circumferential circumferential increases, increases, i.e. i.e.,, the the slope slope of of the the curve curve becomes becomes largerlarger when when the the number number of of cycles cycles in in the the figure figure is is approximately approximately 15,000. 15,000. Subsequently, Subsequently, whe whenn the the crack crack growsgrows to to a a certain certain extent extent in in the the circumferential circumferential direction, direction, the the FCG FCG rate rate in in that that direction direction will will decrease. decrease. TheThe number of cycles perper stagestage isis accumulatedaccumulated to to calculate calculate the the fatigue fatigue life life of of the the pipeline pipeline extending extending in indifferent different directions. directions. Numerical Numerical analysis analysis of radial of crack radial propagation crack propagation revealed that revealed the crack that experiences the crack experiences40,935 loading 40,935 cycles loading when cycles it propagates when it frompropagates 5.5 mm from to 13mm 5.5 mm in depth, to 13mm which in depth, results which in an errorresult ofs in− 2.7%an error compared of −2.7% to thecompared experimental to the measurement.experimental measurement. The crack experiences The crack a totalexperience of 39,383s a loadingtotal of 39,cycles383 inloading circumferential cycles in direction circumferential from 52 mmdirection to 58 mm from based 52 onmm numerical to 58 mm simulation, based on which numerical has an simulationerror of −6.4%, which compared has an to error the experiment of −6.4% compared measurement. to the If experiment the life prediction measurement is carried. If out the from life predictionEquation (5), is carried the above out twofrom errors Equation are − (5),8.6% the and above−12.9%, two errors respectively. are −8.6% and −12.9%, respectively.

0.001

1E-4

(mm/cycle) 1E-5

da/dN Radial direction of crack Circumferential direction of crack 1E-6 0 10000 20000 30000 40000 Cycles(N) Figure 13 13.. FCGFCG rates rates in in the the radial radial and circumferential direction of the pipeline.pipeline

TheThe prediction predictionss show show that that the the predicted predicted values values from from two two equations equations are are smaller smaller than than the the experimentalexperimental values, values, indicating indicating that that the the predict predicteded results results are are within within the the safe safe life life of of the the cracked cracked pipeline,pipeline, and and the the predictions predictions have have guiding guiding significance signiﬁcance for for the the corrosion corrosion fatigue fatigue life life evaluation evaluation for for pipelinepipelines.s. In In addition, addition, it it is is fou foundnd that that the the results results predicted predicted by by the the new new equation equation with with the the shape shape factor factor prpresentedesented in this this study study are are closer closer to to the the experimental experimental values values while while the the predictions predictions based based on on the the shape shape factorfactor recommended recommended in in the the standard standard are are too too conservative. conservative. In Insummary, summary, through through the the combination combination of FCGof FCG test test and and the the finite ﬁnite element element simulation, simulation, fatigue fatigue crack crack growth growth in in a apipeline pipeline can can be be predicted accuratelyaccurately and and effectively effectively.. It It is is also also worth worth noting noting that that the the fatigue fatigue life life prediction prediction needs needs to to verify verify the the shapeshape factor factor equation equation recommended recommended in the standard to obtain more accurate prediction.

8. Conclusions Tests on corrosion fatigue propagation of the API 5L X56 pipeline in Bohai sea are carried out. To obtain the material constants in Paris law, the standard C(T) specimens made of API 5L X56 steel material in air and seawater are tested, respectively. The stress intensity factors in both C(T) specimens and in pipeline specimen are calculated from ﬁnite element analysis. Using Paris law, the fatigue life of Materials 2019, 12, 1031 17 of 19 submarine pipelines in Bohai sea is predicted. Based on the above studies, the following conclusions are drawn:

1. Based on finite element analysis to calculate the stress intensity factor of C(T) specimen, it is found that the recommended equation of shape factor in GB/T 6398-2000 produces relatively lower values. Especially for the shallow crack (a/W < 0.4), such shape factor provides prediction with a large error. 2. By comparing the Paris law constants obtained from equations in the standard and from the presented equation in this study, it is found that the Paris law constants calculated from the equation recommended in the standard are usually smaller than the results calculated from the new presented equation of the shape factor. When the fatigue life is predicted by using the equation recommended in the standard, the prediction is too conservative. 3. The datasets obtained from the FCG test show that for a given ∆K, the FCG rate (da/dN) in seawater is 1.6-times that in air and the effect of seawater on corrosion fatigue decreases with the increase of the FCG rate. 4. When using the finite element analysis to simulate the expansion of fatigue crack in the pipeline, the fatigue crack propagation starts to expand faster along the pipeline radial direction while the crack propagates relatively slowly along the circumferential direction in the early stage. When the crack depth increases to a certain extent, the expansion rate in the circumferential direction also increases. When the crack expands to a certain extent in the circumferential direction, the fatigue crack growth rate will decrease, which is in agreement with the experimental results. 5. Based on the combination of the FCG test and finite element simulation, Paris law can be used to predict fatigue crack growth of submarine pipeline accurately and effectively.

Author Contributions: X.G, L.X. and Y.S. designed the experiments; Y.W. conducted the experimental tests on full-scale pipeline; X.G. analyzed the data; D.Y. contributed materials for tests. Funding: This study is supported by Scientific Innovation Group for Youths of Sichuan Province (Fund No. 2019JDTD0017) and the National Key R&D Program of China (2016YFC0802305). Conflicts of Interest: The authors declare no conflict of interest.

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