applied sciences

Article Corrosion-Fatigue Evaluation of Uncoated Weathering Steel Bridges

Yu Zhang, Kaifeng Zheng, Junlin Heng * and Jin Zhu Department of Bridge Engineering, School of Civil Engineering, Southwest Jiaotong University, Chengdu 610031, China * Correspondence: [email protected]; Tel.: +86-182-8017-6652



Received: 19 July 2019; Accepted: 19 August 2019; Published: 22 August 2019


Featured Application: The new findings highlight the enhancement in corrosion-fatigue performance of steel bridges by using the uncoated weathering steel. Besides, an innovative approach has been established to simulate the corrosion-fatigue process in uncoated weathering steel bridges, providing deep insights into the service life of the bridges. The approaches suggested in the article can be used (not limited to) as a reference for the research and design of uncoated weathering steel bridges.

Abstract: Uncoated weathering steel (UWS) bridges have been extensively used to reduce the lifecycle cost since they are maintenance-free and eco-friendly. However, the fatigue issue becomes significant in UWS bridges due to the intended corrosion process utilized to form the corrodent-proof rust layer instead of the coating process. In this paper, an innovative model is proposed to simulate the corrosion-fatigue (C-F) process in UWS bridges. Generally, the C-F process could be considered as two relatively independent stages in a time series, including the pitting process of flaw-initiation and the fatigue crack propagation of the critical pitting flaw. In the proposed C-F model, Faraday’s law has been employed at the critical flaw-initiation stage to describe the pitting process, in which the pitting current is applied to reflect the pitting rate in different corrosive environments. At the crack propagation stage, the influence of pitting corrosion is so small that it can be safely ignored. In simulating the crack propagation stage, the advanced NASGRO equation proposed by the NASA is employed instead of the classic Paris’ law, in which a modified fatigue limit is adopted. The fatigue limit is then used to determine the critical size of pitting flaws, above which the fatigue effect joins as a parallel driving force in crack propagation. The model is then validated through the experimental data from published articles at the initiation stage as well as the whole C-F process. Two types of structural steel, i.e., HPS 70W and 14MnNbq steel, have been selected to carry out a case study. The result shows that the C-F life can be notably prolonged in the HPS 70W due to the enhancement in fatigue strength and corrosion resistance. Besides, a sensitivity analysis has been made on the crucial parameters, including the stress range, stress ratio, corrosive environment and average daily truck traffic (ADTT). The result has revealed the different influence of the above parameters on the initiation life and propagation life.

Keywords: corrosion-fatigue; pitting corrosion; critical pitting size; fracture mechanics; uncoated weathering steel

1. Introduction Weathering steel has been widely used in bridge engineering in the U.S., Europe and Japan since half a century ago. Due to the excellent corrosion resistance of weathering steel, it can be applied in the corrosive environment without coating. Various grades of weathering steel have already been

Appl. Sci. 2019, 9, 3461; doi:10.3390/app9173461 www.mdpi.com/journal/applsci Appl. Sci. 2019, 9, x 3461 FOR PEER REVIEW 2 of 24 already been incorporated in the codes of practice, such as American grades A242, A588, A606 and incorporatedA709, Japanese in thegrades codes JIS of SMA practice, and suchthe British as American S355J2G1W grades [1,2]. A242, Since A588, 2017, A606 over and 50% A709, of highway Japanese gradessteel bridges JIS SMA in andthe theUS Britishwere constructed S355J2G1W with [1,2]. weathering Since 2017, oversteel. 50% In Japan, of highway 75% steelof the bridges weathering in the USsteels were were constructed used in with bridge weathering engineering steel. Inin Japan,2008, 75%and of80% the weatheringof newly built steels steel were usedbridges in bridgewere engineeringconstructed inwith 2008, weathering and 80% ofsteel newly in the built past steel 25 bridges years [3,4]. were constructedIn China, the with first weathering weathering steel steel in thebridge past was 25 yearsconstructed [3,4]. In in China, 1991 [5], the followed first weathering by the massive steel bridge application was constructed in the 2010s. in 1991 [5], followed by theA massivegreat advantage application of uncoated in the 2010s. weathering steel (UWS) bridges is the reduction of cost. Dolling et al. A[1] great claimed advantage that approximately of uncoated 5% weathering of the initial steel cost and (UWS) far in bridges excess isof the 5% reduction on capital of costs cost. Dollingcould be etsaved. al. [1 Moreover,] claimed thatHorii approximately et al. [6] indicate 5%d ofthat the weathering initial cost steels and could far in reduce excess about of the 25% 5% onlifecapital cycle cost costs according could be saved.to recently Moreover, under Horii construction et al. [6] indicatedbridges. In that addition, weathering Dolling steels also could listed reduce the aboutenvironmental 25% life cyclebenefits cost of according UWS bridges to recently arising under from construction avoiding painting bridges. [1]. In It addition, is also worth Dolling noting also listedthat the the fire environmental incident has benefits now become of UWS a bridges very critical arising issue from avoidingin steel bridges painting since [1]. Itit iscan also lead worth to notingextremely that detrimental the fire incident consequences has now become[7]. Wan a et very al. [8] critical claimed issue that in steelthe chemical bridges sinceelement it can Mo lead could to extremelynotably improve detrimental the fire-resistant consequences of steel. [7]. Wan Since et th al.e [element8] claimed Mo thatis generally the chemical included element in making Mo could the notablyhigh-performance improve the weathering fire-resistant steel, of a steel. much Since better the fi elementre-resistant Mo performance is generally included can be expected in making when the high-performancecompared with the weathering common steel,carbon a muchsteel. betterHowever, fire-resistant further performanceinvestigations can are be still expected required when to comparedreveal the actual with the fire common resistance carbon of weathering steel. However, steel. further investigations are still required to reveal the actualIn steel fire resistancebridges, ofthe weathering fatigue steel.issue is of particular concern due to the persistent loading-and-unloadingIn steel bridges, the process fatigue by issue the vehicles. is of particular Similar concernto the degradation due to the of persistent steel bridges loading-and- from the unloadingfire hazard process [7], theby corrosion the vehicles. effect Similar should to be the co degradationnsidered into of the steel design. bridges Nevertheless, from the fire the hazard fatigue [7], theissue corrosion of steel bridges effect should will be be further considered accelerated into the when design. exposed Nevertheless, to the corrosive the fatigue environment. issue of steelThe bridgescorrosion will process be further will accelerated lead to geometric when exposed irregulari to theties corrosive in components, environment. escalating The corrosion the local process stress willconcentration, lead to geometric which serves irregularities the fatigue in components, issue. In UWS escalating bridges, the the local problem stress is concentration, even more serious: which servesThe fatigue the fatigue crack issue.is hard In UWSto be bridges,detected the due problem to the isrust even layer more used serious: to proof The corrodents. fatigue crack Thus, is hard it tois becrucial detected to take due into to the consideration rust layer used the tocoupling proof corrodents. effect of corrosion-fatigue Thus, it is crucial (C-F) to take on intothe service consideration life of theUWS coupling bridges. e ffect of corrosion-fatigue (C-F) on the service life of UWS bridges. Figure1 1shows shows a typicala typical fatigue fatigue crack crack in a UWS in a bridge, UWS whichbridge, is which identified is byidentified the dye penetrationby the dye checkpenetration [9]. It check is worth [9]. statingIt is worth that, stating this type that, of this crack type is of very crack diffi iscult very to difficult be detected to be usingdetected common using approaches,common approaches, especially especially in its early in stage. its early Due stage. to the Due diffi toculty the indifficulty detection, in adetection, considerable a considerable number of unrecognizednumber of unrecognized fatigue cracks fatigue might cracks exist in might the aged exis UWSt in the bridges, agedimposing UWS bridges, high risks imposing on the high durability risks oron eventhe durability safety of the or bridgeeven safety consequently. of the bridge Therefore, consequently. a well-established Therefore, model a well-established is urgently required model for is theurgently evaluation required on thefor servicethe evaluation life of UWS on the bridges servic consideringe life of UWS the bridges C-F process. considering the C-F process.

Figure 1. TypicalTypical fatigue crack in uncoated weathering steel bridges.

The aim of the present study is to provide a deep insight into the corrosion-fatigue (C-F) performance ofof UWSUWS bridges, bridges, which which can can serve serve as as a usefula useful guidance guidance for for design design and and maintenance maintenance of this of typethis type of bridges. of bridges. On this On end, this an end, innovative an innova deteriorationtive deterioration model has model been established has been toestablished simulate theto coupledsimulate C-F the process.coupled In C-F the process. model, the In wholethe model, C-F process the whole has beenC-F process divided has into been two interrelated divided into stages, two i.e.,interrelated the corrosion-critical stages, i.e., the stage corrosi and fatigue-criticalon-critical stage stage. and Infatigue-critical the study, the C-Fstage. process In the is study, assumed the to C-F be startedprocess withis assumed the pitting to be corrosion, started with in which the pitting the crack-like corrosion, pitting in which flaw the will crack-like initiate [ 10pitting]. In modelingflaw will theinitiate pitting [10]. corrosion, In modeling the electrochemistry the pitting corrosion, theory isthe applied, electrochemistry and the pitting theory current is applied, is utilized and as the indexpitting reflecting current is the utilized influence as the of index different reflecting environments. the influence Meanwhile, of different the environments. critical pitting Meanwhile, flaw size is usedthe critical to connect pitting the flaw two size stages is used smoothly, to connect beyond the which two stages the fatigue smoothly, process beyond can come which into the eff ectfatigue as a drivingprocess forcecan income crack into propagation. effect as In a simulating driving theforce fatigue-induced in crack propagation. crack propagation, In simulating the fracture the fatigue-induced crack propagation, the fracture mechanics-based NASGRO equation, which is Appl. Sci. 2019, 9, 3461 3 of 24 mechanics-based NASGRO equation, which is proposed by the NASA [11,12], is applied to consider the propagation behavior of short cracks. In addition, a competition-based criterion has been introduced, in which the corrosion process and fatigue process are competing in terms of the propagation rate and the C-F process is controlled by the one with the higher rate. Based on the above method, the service life can be predicted at the two stages, respectively. Through combining the life at the two stages, the whole service life under the C-F process can be solved. The proposed model has been carefully verified through the experimental data collected from several publications. With the validated model, sensitivity analysis has been made on the crucial parameters, including the stress range, stress ratio, corrosive environment and average daily truck traffic (ADTT). The result reveals the influence of different factors on the C-F life of UWS bridges. Meanwhile, the proposed method can be referred to in the fatigue design of UWS bridges. Moreover, this study also highlights the advantage of UWS bridges in service life under corrosion and fatigue when compared with the traditional steel bridges.

2. Literature Review Extensive efforts were made by researchers on the C-F process of weathering steel. Hyun et al. [13] predicted the fatigue life of the aged car-body. In the analysis, the effect of corrosion on the car-body was simulated by proportionally reducing the plate thickness with the time. As a result, when considering corrosion, the fatigue life of the car-body was decreased by 20% and 40% for the 23-years old car and 40-years old car, respectively. Ludvík Kunz et al. [14] studied the fatigue performance of weathering steel Atmofix 52 in corroded and non-corroded situations. The result was expressed by the fatigue strength at 1 107 cycles under two stress ratios, i.e., R = 1 and R = 0. When the × − stress ratio equals to 1, the fatigue strength of non-corroded steel and corroded steel was 240 MPa − and 140 MPa, respectively. Under the stress ratio of zero, the two values were respectively 190 MPa and 120 MPa. Overall, the fatigue strength of corroded steel could be significantly lower than that of uncorroded steel. Albrecht et al. [15] investigated the fatigue performance of weathering steel A588 in two corrosive environments, including pure water and salt spray. The result indicated a significant increase in the fatigue notched factor, which reflects the degradation in fatigue strength. According to the result, the fatigue notched factors of sheltered welded steel beam were 1.52 and 3.07 in pure water and salt spray, respectively. At the same time, the fatigue notched factors of the sheltered plate steel beam were respectively 2.56 and 3.01 in pure water and salt spray. Several similar studies also demonstrated the degradation in fatigue performance under the corrosion, especially in the chlorine-rich environment [10,16]. Zampieri [17] studied the fatigue strength of bolted connections, which indicates that corrosion can influence the fatigue life of the joint. Moreover, extended studies were done by Zampieri et al. [18,19] that showed the degradation of the corroded bolted joint due to pitting corrosion. Besides, relevant studies suggested that the pitting flaw initiated by corrosion could be regarded as the source of fatigue cracking [14,16,20]. However, since the C-F process is a highly complicated issue, few models can be yet found on the C-F issue of steel bridges. As a matter of fact, the most reliable way to investigate the C-F process is the fatigue test under the corrosive environment. However, the corrosion is such a long-term process that it is difficult to be incorporated in the fatigue test employing a relatively high loading frequency (from 5 to 50 Hz). Alternatively, pre-corroded specimens were commonly used in the fatigue test [7,10]. Garbatov et al. [21] made specimens with corroded ship building steel in seawater, and the result showed that the fatigue strength decreases from FAT 86 to 64.95 MPa. In this case, the whole C-F process cannot be revealed comprehensively since the two interactive processes are artificially separated in the test. Generally, Kondo [16] claimed that the pitting corrosion is believed as the dominating effect at the early stage of the C-F process. On this end, the electrochemistry theory has been applied to evaluate the pitting corrosion process, which has been validated by the experimental data on aluminum alloy, stainless steel and crude steel [22,23]. Under this content, the electrochemistry theory is employed to describe the time-dependent development of pitting flaws, which can be regarded as the initial flaw in the crack propagation. Nevertheless, it is still difficult to find a way to couple the two processes systematically. Appl. Sci. 2019, 9, 3461 4 of 24

Thus, efforts are now gradually made to combine the electrochemistry theory and fracture mechanics in describing the C-F process of metal materials [10,23,24]. For instance, according to the article [10], under the pitting corrosion the initial flaws will be generated on the exposed material surface at the beginning of the C-F process. Then, when the stress intensity factor (SIF) reaches the fatigue limit, the process will be dominated by the fatigue-induced crack propagation. Similarly, in the article [24], the corrosion-fatigue performance of carbon steel in the corrosive solution was experimentally studied. In the test, the cyclic bending loads were applied to the specimens. According to the study, the C-F process can be divided into the pitting growth stage, small crack growth stage and long crack growth stage. Besides, the pitting growth stage can be evaluated by Faraday’s law, while the Paris law can be utilized to evaluate the small crack growth stage and long crack growth stage. In addition, it is also claimed in the study that the moment when the SIF reached the fatigue limit can be considered as the end of the pitting growth stage. Some recent studies worked on the C-F issue on steel. Zampieri et al. [19] studied the fatigue life of corroded bolted connections by a certain scale of tests and numerical analyses, in which pitting corrosion was taken into consideration. In this study, the Smith–Watson–Topper strain-life method was utilized to evaluate the fatigue life of corroded joints. Meanwhile, the result indicated that corrosion was not the only influence factor on the fatigue life of bolted connections. Xu et al. [20] also studied the fatigue behavior of corroded steel, which indicated that the fatigue life of corroded steel decreased rapidly due to the increasing rough surface. Peng et al. [25,26] combined the uniform corrosion and NASGRO equation to determine the remaining life of structures, the result indicated that the C-F life of the structure was decreased with the assumed initial flaw size increasing.

3. Corrosion Pitting Evaluation

3.1. Mechanism of Pitting Corrosion In UWS bridges, corrosion is always a big challenge to durability [27]. Generally, the corrosion process can be classified into two types, i.e., uniform corrosion and pitting corrosion. The two types of corrosion usually occur simultaneously in steel bridges, both of which can degrade the performance of the bridge. Under the uniform corrosion, the thickness of structural members will be reduced with time, which raises the stress level in the members. However, the effect of uniform corrosion in UWS bridges can be almost ignored due to the corrodent-proof rust film. Thus, the pitting corrosion is of particular concerns in UWS bridges. The pitting corrosion is an autocatalytic process inducing local corrosion interspersing on the material surface. The interspersing could be regarded as a kind of local irregularity, which in turns escalates the local stress concentration. Generally, the pitting corrosion is believed as the most detrimental form of corrosion, which could even cause structural failure [28]. In a C-F analysis, pitting flaw can be regarded as an equivalent initial flaw, from which the final critical fatigue crack can be formed under cyclic stress [29,30]. Based on the mechanism of corrosion, Zaya [31] divided the post-rust pitting corrosion into four different stages as the following: (1) The rupture of the stable rust layer; (2) the achievement of the critical condition that the pit begins to grow; (3) the dissolution of the substrate and (4) the formation of visible pitting irregularity. Referring to the above classification, the pitting process in the UWS bridges can be defined in a similar way, as shown in Figure2. It is shown that the rupture of the protective film occurs at first, followed by the initiation of the pitting flaw with weakened protective film. Finally, the pitting flaw grows without a protective film. However, some researchers [32–34] indicated that the rupture of the protective film occurred very rapidly. Besides, Melchers reported that the initiation of the pitting process only costs as short as several microseconds [32]. On this end, it is assumed in the following analysis that the C-F life is roughly equal to the time cost by the latter two stages, i.e., the initiation of pitting flaws and the propagation of the flaw. Appl. Sci. 2019, 9, x FOR PEER REVIEW 5 of 24

The pitting corrosion process can be accelerated by both the mechanical (e.g., cyclic loads) and chemical factors (e.g., corrosive environment), as suggested by studies [23,35]. In the presence of cyclic loads, the protective film is prone to rupture because of the reduced strength. At the same time, the pitting corrosion rate could be notably increased under the high-level stress range induced by the cyclic loads [23,35]. Besides the mechanical factor, the pitting process can also escalate the corrosive environment, especially the concentration of chlorine (Cl). Albercht et al. [36] claimed that pitting flaw could appear to the surface of the steel in high Cl ions concentration. For instance, the pitting corrosion rate of bridges in the marine environment, where the Cl ions concentration is high, is significantly higher than those in the non-marine environment. Meanwhile, the structural member will experience serious pitting corrosion when located in the sheltered position of UWS Appl. Sci. 2019, 9, 3461 5 of 24 bridges, since the Cl ions attached on the surface cannot be washed directly by the rain [37].

Figure 2. Illustration of the pitting corrosion.

3.2. ProposedThe pitting Model corrosion for Pitting process Corrosion can be accelerated by both the mechanical (e.g., cyclic loads) and chemical factors (e.g., corrosive environment), as suggested by studies [23,35]. In the presence of cyclic loads,Kondo the protective [16] proposed film is that prone the to pitting rupture flaw because depth of has the a reducedpower relation strength. with At the sametime based time, theon pittingthe test corrosion data, in ratewhich could the be power notably index increased is 1/3. under The thesimilar high-level relation stress is also range reflected induced by by the cyclicwell-known loads [Faraday’s23,35]. Besides law established the mechanical through factor, electroc the pittinghemistry process [38,39], can as also shown escalate in Equation the corrosive (1): environment, especially the concentration of chlorine (Cl). Albercht et al. [36] claimed that pitting flaw = , (1) could appear to the surface of the steel in high Cl ions concentration. For instance, the pitting corrosion ratewhere of bridges𝑉 is the involume the marine of the environment, pit; 𝑡 is the corrosion where the time; Cl ions 𝑀 concentration is the atomic mass is high, of the is significantly material; 𝑛 higheris the number than those of electrons in the non-marine released environment.during corrosion Meanwhile, of the metal; the structural 𝐹 is the memberFaraday willconstant; experience 𝜌 is seriousthe density pitting of the corrosion material when and 𝐼 located is the inpitting the sheltered current related position to ofthe UWS corrosive bridges, environment. since the Cl ions attachedThe onpitting the surfacecurrent cannotcould be be solved washed using directly Equation by the (2): rain [37]. ∆ 3.2. Proposed Model for Pitting Corrosion 𝐼 =𝐼 exp(− ) , (2) whereKondo 𝐼 is [16 the] proposed pitting thatcurrent the pittingcoefficient; flaw depth𝑅 is the has universal a power relation gas constant; with the 𝑇 time is the based absolute on the testtemperature data, in whichand ∆𝐻 the is power the activation index is enthalpy. 1/3. The similar relation is also reflected by the well-known Faraday’sObviously, law established the pitting through volume electrochemistry is a natural inde [38x, 39describing], as shown the in degree Equation of (1):pitting corrosion. Thus, as shown in Equations (1) and (2), the degree is determined by factors such as the time dV MIp exposed to corrosion, corrosive environment, temper= ature, and activation enthalpy. In this study, (1) dt nFρ the pitting flaw is idealized as a semi-ellipsoid with the round projection on the material surface, as wherea commonV is practice the volume [10]. of The the pitting pit; t is volume the corrosion could time;be calculatedM is the as atomic shown mass in Equation of the material; (3): n is the number of electrons released during corrosion of the metal; F is the Faraday constant; ρ is the density of the material and Ip is the pitting current related to the corrosive environment. The pitting current could be solved using Equation (2):

∆H Ip = Ip exp ( ), (2) 0 − RT where Ip0 is the pitting current coefficient; R is the universal gas constant; T is the absolute temperature and ∆H is the activation enthalpy. Obviously, the pitting volume is a natural index describing the degree of pitting corrosion. Thus, as shown in Equations (1) and (2), the degree is determined by factors such as the time exposed to corrosion, corrosive environment, temperature and activation enthalpy. In this study, the pitting Appl. Sci. 2019, 9, 3461 6 of 24

flaw is idealized as a semi-ellipsoid with the round projection on the material surface, as a common practice [10]. The pitting volume could be calculated as shown in Equation (3):

2 V = πab2, (3) 3 where a is the pitting depth and b is the radius of the round on the project surface. Since the pitting depth is believed as the major index reflecting the pitting process [28], it can be solved by combining Equations (1) and (3), as shown in Equation (4):

2/3 1/3 1/3 a = Bmasp Ip t , (4) where masp is the aspect ratio of the pitting flaw lateral section, i.e., a/b; B is a material-related constant and t stands for the time exposed to corrosion. Studies show that the aspect ratio of pitting flaws is close to 1.0 [10,40]. On this end, the aspect ratio in this study was determined as 1.0. Meanwhile, the constant B can be determined by the aforementioned material properties, as shown in Equation (5): s 3M B = 3 , (5) 2πnFρ where the parameters could be applied as M = 56 10 3 kg/mol, n = 2, F = 96,500 C/mol and × − ρ = 7850 kg/m3, respectively.

3.3. Degree of Pitting Corrosion It is important to find an index reflecting the corrosive environment. On this end, the pitting current Ip could be utilized since it only dependents on the corrosive environment. Thus, the pitting current has been explicitly expressed by rewriting Equation (4), as shown in Equation (6):

a3 Ip = . (6) 3 3 2 t B masp

The code ISO 9223 [41] classified the corrosive environment into six categories, named C1, C2, C3, C4, C5 and CX. A series of experiments has been carried out on the corrosion of weathering steel at various places representing different corrosive environment categories in China [42]. Five key indices are adopted to reflect various corrosive environments, and the value of each index corresponding to five corrosive environment categories are statistically obtained based on 8 years of data (from 2006 to 2014), as listed in Table1.

Table 1. Pitting corrosion data of weathering steel collected for 8 years.

Average Average Maximal Average Pit Maximal Pit Location (Category) Corrosion Rate Pitting Pitting Depth (µm) Depth (µm) (µm/a) Current (C/s) Current (C/s) Wuhan (C4) 9 130 150 4.93 10 10 7.58 10 10 × − × − Beijing (C3) 8 140 180 6.16 10 10 1.31 10 9 × − × − Jiangjin (C5) 18 280 390 4.93 10 9 1.33 10 8 × − × − Lhasa (C1) 1 20 30 1.80 10 12 6.06 10 12 × − × − Mohe (C2) 3.5 20 40 1.80 10 12 1.44 10 11 × − × − Xishuangbanna (C2) 9 70 110 7.70 10 11 5.48 10 9 × − × − Shenyang (C2) 8 100 180 2.25 10 10 3.51 10 9 × − × − Qingdao (C4) 18 240 360 3.10 10 9 1.05 10 8 × − × − Guangzhou (C4) 15.5 230 290 2.73 10 9 5.48 10 9 × − × − Qionghai (C3) 10 210 250 2.08 10 9 3.51 10 9 × − × − Appl. Sci. 2019, 9, x FOR PEER REVIEW 7 of 24

the ratio of the max value to average value was highly scattered in different places, ranging from Appl.53.6%–700%. Sci. 2019, 9, 3461It is worth noting that, the most critical place Jiangjin (C5) was not in the marine7 of 24 location. However, this place is a historic industrial area with heavy pollution of sulfur dioxide (SO2),The which pitting accelerates current in Tablethe corrosion1 is plotted significantly. against the corrosivityIn sum, the category rate of in Figurepitting3 ,corrosion along with was a briefdependent description on both of thethe geographiccorrosivity feature,category i.e., and the chem marineical factor, or non-marine. while the The latter following could have letters a larger “-M” andinfluence. “-A” stand for the maximal and average value of pitting current, respectively.

FigureFigure 3.3. Pitting current in didifferentfferent corrosivitycorrosivity categories.categories.

4. ModelIt can of be Corrosion-Fatigue observed from Figure 3 that the corrosivity category was directly proportional to the pitting current. Meanwhile, the result also indicates that the average pitting current was remarkably higher4.1. Corrosion-Fatigue in the marine locationProgress than in the non-marine location, i.e., 3.38–5.92 times higher. Besides, the ratio of the max value to average value was highly scattered in different places, ranging from Since UWS bridges are exposed to the corrosion and fatigue action simultaneously, it is critical 53.6%–700%. It is worth noting that, the most critical place Jiangjin (C5) was not in the marine location. to incorporate the coupling effect of the two processes in solving the service life. At the early stage, However, this place is a historic industrial area with heavy pollution of sulfur dioxide (SO ), which pitting flaws will be generated on the surface of components by the corrosion. The size2 of these accelerates the corrosion significantly. In sum, the rate of pitting corrosion was dependent on both the flaws increases with the time, as suggested by the Faraday’s law [22,39]. Meanwhile, the pitting corrosivity category and chemical factor, while the latter could have a larger influence. process could be further escalated by the load-induced stress range [23,35]. Once the pitting flaw 4.reaches Model the of Corrosion-Fatiguecritical size, the fatigue process becomes the major driving force in the crack propagation while the chemical effect could be ignored [11]. Generally, the range of SIF could be 4.1.used Corrosion-Fatigue to determine the Progress propagation rate of cracks [43]. Meanwhile, failure of members could be assumed when the crack penetrated through the thickness of any plate in the member. Based on the Since UWS bridges are exposed to the corrosion and fatigue action simultaneously, it is critical above analysis, C-F life can be divided into two stages, the C-F crack initiation and the C-F crack to incorporate the coupling effect of the two processes in solving the service life. At the early stage, propagation, which is also suggested in [44]. Figure 4 illustrates the whole C-F process. pitting flaws will be generated on the surface of components by the corrosion. The size of these flaws According to the above discussion, the C-F model can be established. At the beginning of the increases with the time, as suggested by the Faraday’s law [22,39]. Meanwhile, the pitting process C-F process, the pitting flaw keeps growing under the corrosion only, as described by Faraday’s could be further escalated by the load-induced stress range [23,35]. Once the pitting flaw reaches law. The corrosion process could be further accelerated by the vehicle-induced cyclic stress [23,35]. the critical size, the fatigue process becomes the major driving force in the crack propagation while Thus, modification has been made in Equation (4) to incorporate the influence of cyclic stress, as the chemical effect could be ignored [11]. Generally, the range of SIF could be used to determine the shown in Equation (7): propagation rate of cracks [43]. Meanwhile, failure of members could be assumed when the crack 2/3 1/3 1/3 𝜎𝑎 penetrated through the thickness of any𝑎 plate=𝐵𝑚 in𝑎𝑠𝑝 the𝐼𝑝 member.𝑡 𝐶𝑝 ,Based on the above analysis, C-F life(7) can be divided into two stages, the C-F crack initiation and the C-F crack propagation, which is also 𝐶 𝜎 suggestedwhere in is [the44]. constant Figure4 relatedillustrates to the the material whole C-F and process. is the stress range. AccordingAs aforementioned, to the above the discussion,pitting flaw thecould C-F be model regarded can beas an established. equivalent At crack. the beginningAs suggested of the by C-FNewman process, et theal. [40], pitting the flaw stress keeps intensity growing factor under (SIF the) could corrosion be solved only, for as describedthe equivalent by Faraday’s crack based law. Theon the corrosion stress range, process pitting could flaw be further property accelerated and geometry by the of vehicle-induced plates, as shown cyclic in Equation stress [23 (8):,35 ]. Thus, modification has been made in Equation (4) to incorporate the influence of cyclic stress, as shown in ∆𝐾 = (𝑆 +𝐻𝑆 )𝜋 𝐹( , , ,∅) , (8) Equation (7): 2/3 1/3 1/3 σa a = Bmasp Ip t Cp , (7) where Cp is the constant related to the material and σa is the stress range. Appl. Sci. 2019, 9, x FOR PEER REVIEW 8 of 24 where 𝑎 is the pitting depth; 𝑐 is the pitting width; 𝑡 it the thickness of the plate; 𝑏 is the width of the whole plate; ∅ is the angle of crack boundary; 𝑆 and 𝑆 are uniform-tension stress and bending stress; 𝐻 is boundary-correction factor and 𝑄 and 𝐹 are functions associated with 𝑎, 𝑐, 𝑡, 𝑏 and ∅. Due to the fatigue limit that exists in metals, the fatigue effect has little influence on the crack propagation when the crack size is under a specific critical size. Once the pitting flaw grows to the critical size, the fatigue effect will join as a parallel driving force in the crack propagation. The fatigue-induced propagation could be solved according to the fracture mechanics. For instance, the well-known Paris law [43] can be applied, as shown in Equation (9): =𝐶(∆𝐾) , (9) where 𝑎 is the crack size; 𝑁 is the numbers of loading cycles; 𝐶 and 𝑚 are the material-related constant and power index, respectively and ∆𝐾 is the range of the SIF. As proposed in [39], the competition criterion is introduced that the two effects, i.e., corrosion and fatigue, will compete in terms of the crack growth rate. As a result, the C-F process will be dominated by the driving force with the higher rate. It can be found from Equations (7)–(9) that, with the time passing, the growth rate of pitting corrosion is decreasing while that of the fatigue is increasing. As a result, the fatigue will gradually replace the corrosion as the major driving force in Appl.the propagation Sci. 2019, 9, 3461 as aforementioned. 8 of 24

Figure 4. Schematic stages of corrosion-fatigue (C-F).

AsBased aforementioned, on the above analysis, the pitting the flaw time could period be before regarded the asgrowth an equivalent rate of fatigue crack. surpasses As suggested that byof Newmanpitting corrosion et al. [40 could], the stressbe regarded intensity as factorthe C-F (SIF) crack could initiation be solved stage, for thein which equivalent the crack crack growth based onis theonly stress determined range, pittingby the flawcorrosion property process. and geometryAfter that, of the plates, influence as shown of corrosion in Equation can (8):be ignored, and the corresponding stage can be regarded as ther C-F crack propagation stage. At this stage, the a a a c fatigue process becomes the only∆ Kdriving= (St +forceHS bin) crπack Fpropagation,( , , , ∅), in which the SIF can be used (8)to Q t c b calculate the propagation rate. whereIt aisis worth the pitting noting depth; that, caccordingis the pitting to Equation width; t it(8), the the thickness larger flaw of the size plate; leadsb is to the the width higher of SIF the under the same stress state. As a result, fatigue crack is more likely to initiate from the larger pitting whole plate; ∅ is the angle of crack boundary; St and Sb are uniform-tension stress and bending stress; H is boundary-correction factor and Q and F are functions associated with a, c, t, b and ∅. Due to the fatigue limit that exists in metals, the fatigue effect has little influence on the crack propagation when the crack size is under a specific critical size. Once the pitting flaw grows to the critical size, the fatigue effect will join as a parallel driving force in the crack propagation. The fatigue-induced propagation could be solved according to the fracture mechanics. For instance, the well-known Paris law [43] can be applied, as shown in Equation (9):

da = C(∆K)m, (9) dN where a is the crack size; N is the numbers of loading cycles; C and m are the material-related constant and power index, respectively and ∆K is the range of the SIF. As proposed in [39], the competition criterion is introduced that the two effects, i.e., corrosion and fatigue, will compete in terms of the crack growth rate. As a result, the C-F process will be dominated by the driving force with the higher rate. It can be found from Equations (7)–(9) that, with the time passing, the growth rate of pitting corrosion is decreasing while that of the fatigue is increasing. As a result, the fatigue will gradually replace the corrosion as the major driving force in the propagation as aforementioned. Appl. Sci. 2019, 9, 3461 9 of 24

Based on the above analysis, the time period before the growth rate of fatigue surpasses that of pitting corrosion could be regarded as the C-F crack initiation stage, in which the crack growth is only determined by the corrosion process. After that, the influence of corrosion can be ignored, and the corresponding stage can be regarded as the C-F crack propagation stage. At this stage, the fatigue process becomes the only driving force in crack propagation, in which the SIF can be used to calculate the propagation rate. It is worth noting that, according to Equation (8), the larger flaw size leads to the higher SIF under the same stress state. As a result, fatigue crack is more likely to initiate from the larger pitting flaw. Since the maximal pitting current can represent the highest degree of pitting corrosion, it has been employed in Equation (7) for conservativeness.

4.2. Service Life of Corrosion-Fatigue Crack Initiation In solving the service life of C-F crack initiation it is crucial to determine the critical flaw size, beyond which the fatigue can become the major driving force. There are generally two approaches proposed to determine the critical size: (1) The equal rate method, assuming that the critical size reaches at the time when the growth rates of corrosion equals to the one of fatigue [16,45] and (2) the fatigue limit method, which determines the critical size based on the fatigue limit in terms of SIFs [10,46]. In the type (1) method, the growth rate of fatigue should be solved at the beginning of the C-F process when the flaw is extremely small. However, the propagation behavior of small cracks is still a controversial issue that can hardly be illustrated. Alternatively, the type (2) method only requires the solution on the well-initiated flaws, which is more concise and practical but may compromise the accuracy to a small extent. To determine the critical size with appreciable accuracy, the above two types of methods were combined in determining the crack initiation life in the present study. By setting the SIF same as the fatigue limit, the critical size could be solved using Equation (8). It is worth stating that the fatigue limit here is not the threshold value for the long crack, which will be discussed in detail later. Based on Equation (7), the service life of initiation could be solved, as shown in Equation (10): 3 ac ti = + tc, (10) 3 2 3σa 3σa B maspIpC Cp where ti is the service life of the C-F crack initiation; ac stands for the critical depth and tc is the service life spent during the competition, which is calculated from the moment when critical depth is reached to the moment when the growth rate of the fatigue effect exceeds that of pitting corrosion. Verification has been carried out using two typical materials [35], including the 2024-T3 aluminum alloy and the 12% Cr stainless steel. The material properties are listed in Table2.

Table 2. Parameters for the selected aluminum alloy and stainless steel.

Material BCp Ip (C/s) masp ∆Kth (MPa √m) Aluminum alloy 2.55 10 4 1.001–1.02 1.83 10 9 1.0 2.32 × − × − Stainless steel 2.61 10 4 1.005–1.01 1.51 10 10 1.0 8.14 × − × −

The prediction value is plotted against the test data [22,23] under various stress ranges, as shown in Figure5. In the prediction, the critical depth was solved by the fatigue limit listed in Table2, while the Paris’ law was employed to determine the crack growth rate induced by the fatigue effect. The result shows that the prediction curve matched well with the test data, indicating the effectiveness of the proposed method in solving the C-F crack initiation life. It is worth noting that a similar verification was done by Mao et al. [47]. Appl. Sci. 2019, 9, 3461 10 of 24 Appl. Sci. 2019, 9, x FOR PEER REVIEW 10 of 24

(a) (b)

FigureFigure 5. 5.C-F C-F initiation initiation life life of of selected selected materialsmaterials under various stress stress ranges: ranges: (a ()a 2014-T3) 2014-T3 aluminum aluminum alloyalloy and and (b ()b 12%) 12% Cr Cr stainless stainless steel. steel.

4.3.4.3. Service Service Life Life of of Corrosion-Fatigue Corrosion-Fatigue CrackCrack PropagationPropagation AsAs aforementioned, aforementioned, once once the the critical critical flaw flaw size size is achieved, is achieved, the fatigue the fatigue effects effects as well as as well the corrosionas the effectscorrosion are the effects two major are the driving two major forces driving in crack forces propagation. in crack Accordingly, propagation. the Accordingly, fatigue process the competesfatigue withprocess the corrosion competes process with the in corrosion terms of theprocess crack in growth terms of rate, the andcrack the growth propagation rate, and is the dominated propagation by the oneis withdominated a higher bygrowth the one rate.with Ita canhigher be inferredgrowth rate. from It Equationscan be inferred (7) and from (9) Equations that, with (7) the and development (9) that, ofwith the crack, the development the growth rateof the is crack, decreasing the growth for the rate corrosion is decreasing process for while the corrosion increasing process for the while fatigue process.increasing Once for the the growth fatigue rateprocess. induced Once bythe the growth fatigue rate process induced exceeds by the fatigue that caused process by exceeds the corrosion that process,caused the by fatiguethe corrosion effect becomesprocess, thethe dominatedfatigue effect driving becomes force the and dominated the influence driving of corrosionforce and couldthe beinfluence ignored. of Therefore, corrosionit could is crucial be ignored. to determine Therefore, the it crack is crucial growth to determine rate induced the bycrack the growth fatigue rate effect. induced by the fatigue effect. Studies [48] show that the fatigue crack can be divided into small Studies [48] show that the fatigue crack can be divided into small (short) cracks and long cracks during (short) cracks and long cracks during the propagation. For small cracks, the fatigue limit is the propagation. For small cracks, the fatigue limit is significantly lower than that of long cracks, while significantly lower than that of long cracks, while the propagation rate is much faster [48]. the propagation rate is much faster [48]. Obviously, the behavior of small cracks cannot be reflected by Obviously, the behavior of small cracks cannot be reflected by the crude Paris law since the the crude Paris law since the difference is not considered. difference is not considered. Thus,Thus, the the advanced advanced NASGRO NASGRO equation equation has beenhas been applied, applied, in which in thewhich small the crack small is considered,crack is asconsidered, shown in Equation as shown (11): in Equation (11): h p im da =𝐷(∆𝐾−∆𝐾)/1−𝐾/𝐴 , (11) = D (∆K ∆K )/ 1 Kmax/A , (11) dN − thr − where ∆𝐾 is the decreased fatigue limit in terms of the SIF range, which will be discussed later; where𝐾∆ Kisthr theis themaximal decreased SIF; fatigue 𝑅 is limitthe instress terms ratio; of the 𝐴 SIF is range,the fracture which willtoughness be discussed and later;𝐷 is K amax is thematerial-related maximal SIF; constant.R is the stress ratio; A is the fracture toughness and D is a material-related constant. TheThe maximal maximal SIF SIF can can be be calculated calculated basedbased onon thethe stress ratio, ratio, as as shown shown in in Equation Equation (12): (12): ∆ 𝐾 = . ∆()K (12) Kmax = . (12) (1 R) Based on Equation (11), the service life of propagation− could be solved, as shown in Equation (13):Based on Equation (11), the service life of propagation could be solved, as shown in Equation (13): ℎ 𝑚 𝑡Z= h 𝑑𝑎/ 𝐷(∆𝐾 − ∆𝐾𝑡ℎ𝑟)/1−𝐾𝑚𝑎𝑥/𝐴 , (13) 1 𝑎𝑖  h p im tp = da/ D (∆K ∆Kthr)/ 1 Kmax/A , (13) where 𝑓 is the frequency of thef appliedai cyclic loads− and 𝑎 is− the crack initiation depth. where4.4. Corrosion-Fatiguef is the frequency Model of the applied cyclic loads and ai is the crack initiation depth.

4.4. Corrosion-FatigueIn the C-F crack Model initiation stage, Faraday’s law is more suitable for this process, which considers many factors such as the material property, temperature, corrosion system and time. In theIn C-F the crack C-F crack propagation initiation stage, stage, Paris Faraday’s law needs law isdifferent more suitable propagation for this parameters process, whichC, m and considers the many factors such as the material property, temperature, corrosion system and time. In the C-F crack Appl. Sci. 2019, 9, 3461 11 of 24 propagation stage, Paris law needs different propagation parameters C, m and the threshold value for a short crack and long crack respectively, which makes the evaluation rather complicated. Thus, the NASGRO equation requiring only a few parameters is preferable for the evaluation on this process, while it can describe both a short crack and long crack within the same pattern effectively. Based on the above analysis, the whole C-F life of the structural steel for bridges could be solved by combining the initiation life and propagation life, as shown in Equation (14):

3 Z h   ac 1 h p im tC F = + tc + da/ D (∆K ∆Kthr)/ 1 Kmax/A , (14) − 3 2 3σa f − − B maspIpCp ai where tC F is the C-F life of the material. − As shown in Equation (14), the whole C-F life consists of three parts. In the first part, the pitting corrosion is the only driving force since the condition is not met for the fatigue-induced propagation. The material constant B is similar in different kinds of steel so that its influence on the C-F life of different steel is not significant. Meanwhile, the constant Cp is highly dependent on the category of steel that a small variation in the constant can lead to a great difference in the initiation life. Besides, with the increase in the environment-related pitting current, the initiation life can be remarkably decreased. It is also indicated by Equation (14) that, the higher stress range further accelerates the pitting process described in the first part. In the last part, the fatigue effect outcompetes the corrosion effect and becomes the major driving force in crack propagation. Fatigue limit and fracture toughness are dependent on the fracture mechanical property of the material. Meanwhile, a higher frequency of cyclic loads can reduce the propagation life directly. Within the integral operation, the parameters ∆K and Kmax related to the stress range and stress ratio can also influence the propagation. Besides, the constants D and m are almost the same for structural steel, as given in [12]. For the geometric factor ai, it depends on the stress range, stress ratio, plate thickness, the rate of pitting corrosion and the rate of fatigue crack propagation. In the middle part, it is assumed that during the time period tc, both the pitting corrosion and the fatigue effect serve as the driving force in crack propagation parallelly and compete with each other. Thus, the time period tc at this part will be affected by the above factors in both the corrosion and fatigue process. In sum, the C-F life of steel is a highly complicated process, which is affected by many crucial factors. Further verification has been carried out for the whole C-F life, through the experimental data of a type of precipitation hardening steel [10]. The material properties of the steel are listed in Table3, with the fatigue limit recommended by Kondo [16]. The experiment data has been obtained under three different temperatures, i.e., 25 ◦C, 75 ◦C and 150 ◦C. Based on that, the pitting current can be respectively calculated under the three testing temperature based on Equation (14). As a result, the pitting currents are determined as, 1.8065 10 8 C/s, 1.8991 10 11 C/s and 8.7407 10 11 C/s × − × − × − under 25 ◦C, 75 ◦C and 150 ◦C, respectively.

Table 3. Parameters for the selected steel material.

BCp masp ∆Kth (MPa √m) 2.60 10 4 1.01 1.0 1.2 × −

The prediction curve is plotted against the experimental data, as shown in Figure6. In the prediction, the specimens were in the round section. For this reason, the expression for the SIF range can be written as follows: 2.2 ∆K = ( )Kt ∆σ √π a, (15) π · · where Kt is the stress concentration factor in the location, however, the Kt = 1 for the location with regular geometry. Appl. Sci. 2019, 9, x FOR PEER REVIEW 12 of 24 the prediction curve under 25 °C. Further analysis suggests that this deviation could be attributed to the relative large scatter in the data under 25 °C However, the trend was still highly similar betweenAppl. Sci. 2019 the, 9 ,test 3461 data and prediction curve under 25 °C Thus, it was proved that the proposed12 of 24 model could predict the whole C-F life effectively.

Figure 6. C-FC-F life life of of the the selected selected precipitation precipitation hardening steel.

5. AnalysisThe result on Corrosion-Fatigue exhibited that the experimental of Structural data Steel under for Bridges 25 ◦C and 75 ◦C were similar, which shows the minor influence of the pitting current on C-F life in relatively low temperatures. Generally, the 5.1.prediction Material curves match well with the experimental data, especially under 75 ◦C and 150 ◦C. It is also worth noting that a notable deviation existed between the experimental data and the prediction curve Based on the proposed model, a case study was carried out to investigate the C-F process in under 25 C. Further analysis suggests that this deviation could be attributed to the relative large steel bridges.◦ The typical weathering steel HPS 70W [49] was selected while the normal carbon steel scatter in the data under 25 C However, the trend was still highly similar between the test data and 14MnNbq (named Q370q at ◦the same time) was also investigated for comparison. The HPS 70W is a prediction curve under 25 C Thus, it was proved that the proposed model could predict the whole kind of high performance steel◦ widely used in bridge engineering, which has higher strength, better C-F life effectively. corrosion resistance and better weldability compared to traditional weathering steel. The yield strength5. Analysis of onthe Corrosion-FatigueHPS 70W and the of 14MnNbq Structural steel Steel are for 485 Bridges MPa and 370 MPa, respectively. The chemical compositions and mechanical properties [49–52] are listed in Tables 4 and 5, respectively.

It5.1. is worth Material stating that the fatigue limit ∆𝐾 in Table 5 was the value for the long crack. Based on the proposed model, a case study was carried out to investigate the C-F process in Table 4. Chemical composition of the selected steel. steel bridges. The typical weathering steel HPS 70W [49] was selected while the normal carbon steel 14MnNbq (named Q370q at the sameElement time) HPS was 70 alsoW investigated14MnNbq for comparison. The HPS 70W is a kind of high performance steel widelyC used0.11 max in bridge 0.11–0.17 engineering, which has higher strength, better corrosion resistance and betterMn weldability 1.10–1.50 compared 1.20–1.60 to traditional weathering steel. The yield P 0.020 max 0.025 max strength of the HPS 70W and the 14MnNbq steel are 485 MPa and 370 MPa, respectively. The chemical S 0.006 max 0.015 max compositions and mechanical properties [49–52] are listed in Tables4 and5, respectively. It is worth Si 0.30–0.50 0.20–0.60 stating that the fatigue limit ∆Kth in TableCu 5 was0.25–0.40 the value for the- long crack. Ni 0.25–0.40 - Table 4. ChemicalCr composition0.45–0.70 of the selected- steel. Mo 0.02–0.08 - Element HPS 70W 14MnNbq V 0.04–0.08 - CAl 0.010–0.040 0.11 max - 0.11–0.17 MnN 0.015 1.10–1.50 max - 1.20–1.60 P 0.020 max 0.025 max S 0.006 max 0.015 max As suggested by the NASGROSi equation, 0.30–0.50 instead of the 0.20–0.60 original fatigue limit, a decreased fatigue value should be used inCu accordance with 0.25–0.40 fracture toughness, - to consider the behavior of small cracks. Table 5 shows the twoNi parameters 0.25–0.40 of the selected steel - under different stress ratios. Cr 0.45–0.70 - Mo 0.02–0.08 - V 0.04–0.08 - Al 0.010–0.040 - N 0.015 max - Appl. Sci. 2019, 9, 3461 13 of 24

Table 5. Fatigue limit for long cracks in the selected steel.

Steel Stress Ratio ∆Kth (MPa √m) HPS 70W 0.10 7.22 0.05 6.67 14MnNbq 0.25 5.14 0.50 3.32

As suggested by the NASGRO equation, instead of the original fatigue limit, a decreased fatigue value should be used in accordance with fracture toughness, to consider the behavior of small cracks. Table5 shows the two parameters of the selected steel under di fferent stress ratios. The parameters of the selected steel [12] are shown in Table6.

Table 6. Decreased fatigue limits and fracture toughness of the selected steel.

Steel Stress Ratio ∆Kthr (MPa √m) A (MPa √m) 0.0 5.5 120 HPS 70W 0.8 3.8 120 14MnNbq 0.05 5.5 100

5.2. Fatigue Limit As fatigue cracks can be divided into long cracks and small cracks, Phillips et al. [53] claimed that different fatigue limits should be applied for the large-crack and small-crack, respectively [53]. Meanwhile, Kondo [16] proposed that the threshold value for crack initiation is smaller than that of the fatigue limit for long cracks. In another world, the crack can also initiate and propagate when the SIF range is between the fatigue limit for a long crack and the threshold for crack initiation. On this end, the decreased fatigue limit recommended in [12] was utilized as shown in Equation (11). Studies [54,55] indicate that the fatigue limit of steel is affected by the stress ratio, as shown in Equation (16):

∆K = ∆K (1 αR), (16) th th,0 − where ∆Kth is the decreased fatigue limit; R stands for the stress ratio; ∆Kth,0 is the fatigue limit when R = 0 and α is a material-related parameter. According to Equation (16), the threshold value of the two selected materials can be obtained under different stress ratios, as shown in Table7.

Table 7. Stress intensity factor (SIF) threshold for fatigue crack propagation and initiation and their material parameter α.

Material Stage ∆Kth,0 (MPa √m) α Propagation 7.51 0.386 HPS 70W Initiation 5.50 0.386 Propagation 7.03 1.060 14MnNbq Initiation 5.80 1.060

5.3. Critical Pitting Depth of Steels As aforementioned, the pitting flaw can be treated as an equivalent crack. As suggested by Newman [40,56], the range of SIFs at the pitting flaw can be calculated as shown in Equations (17) and (18):  a 2 a 4 2 ∆K = 1.04 + 0.201( ) 0.106( ) ∆σ √πa, (17) b h − h π Appl. Sci. 2019, 9, 3461 14 of 24

 a 2 a 4 a 2 2 ∆Ks = 1.04 + 0.201( ) 0.106( ) 1.1 + 0.35( ) ∆σ √πa, (18) h − h h π where ∆Kb and ∆Ks are the ranges of SIFs at the crack tip and the crack edge, respectively; a is the pittingAppl. Sci. depth; 2019, 9, hx isFOR the PEER plate REVIEW thickness and ∆σ is the remote stress range. 14 of 24 As aforementioned, the critical size of pitting flaws is achieved when any of the SIFs reaches the fatiguethe remote limit. stress It can range, be found stress from ratio Equations and the plate (17) and thickness. (18) that Thus, the critical the critical size issize determined in the HPS by 70W the remoteand 14MnNbq stress range, was investigated stress ratio andunder the different plate thickness. combinations Thus, of the parameters, critical size as in shown the HPS in 70WFigures and 7 14MnNbqand 8. The was result investigated indicates underthat critical different pitting combinations depth of these of parameters, two types as of shown steel decreased in Figures 7with and the8. Theincrease result in indicates stress range that criticaland stress pitting ratio. depth For ofin thesestance, two when types the of stress steel decreasedrange increased with the from increase 50 MPa in stressto 200 range MPa, and the stresscritical ratio. pitting For depth instance, reduced when theroughly stress by range 93% increased in both types from 50of MPasteel. to Meanwhile, 200 MPa, the as criticalthe stress pitting ratio depth rose reducedfrom 0.01 roughly to 0.5, bythe 93% critical in both depth types reduced of steel. by Meanwhile, 33% in the asHPS the 70W stress and ratio 77% rose in fromthe 14MnNbq. 0.01 to 0.5, theMoreover, critical depth critical reduced pitting by depth 33% in was the HPSmuch 70W more and sensitive 77% in the to 14MnNbq. stress range Moreover, in low criticalstress range pitting state. depth It wascould much also more be found sensitive that tothe stress plate range thickness in low had stress little range impact state. on It critical could alsopitting be founddepth, that which the platewas less thickness than 3% had change little impact in the ondepth critical when pitting the thickness depth, which increased was less from than 20 3% mm change to 50 inmm. the Besides, depth when the result the thickness also suggests increased that from the crit 20 mmical depth to 50 mm. in the Besides, HPS 70W the resultwas not also sensitive suggests to that the thechange critical in depththe stress in the ratio HPS when 70W compared was not sensitive with th toe 14MnNbq. the change As in thea result, stress ratioa considerable when compared higher withcritical the depth 14MnNbq. could As be a expected result, a considerablein the HPS 70W higher under critical a high depth stress could ratio, be expected which in in turn the HPSindicates 70W underits better a high robustness stress ratio, in fatigue which performance. in turn indicates its better robustness in fatigue performance.

(a) (b)

(c) (d)

FigureFigure 7.7. Critical pitting pitting depth depth of of the the steel steel 14MnNbq 14MnNbq with with different different plate plate thicknesses: thicknesses: (a) (20a) mm; 20 mm; (b) (30b) 30mm; mm; (c) (40c) 40mm mm and and (d) ( d50) 50mm. mm.

(a) (b) Appl. Sci. 2019, 9, x FOR PEER REVIEW 14 of 24 the remote stress range, stress ratio and the plate thickness. Thus, the critical size in the HPS 70W and 14MnNbq was investigated under different combinations of parameters, as shown in Figures 7 and 8. The result indicates that critical pitting depth of these two types of steel decreased with the increase in stress range and stress ratio. For instance, when the stress range increased from 50 MPa to 200 MPa, the critical pitting depth reduced roughly by 93% in both types of steel. Meanwhile, as the stress ratio rose from 0.01 to 0.5, the critical depth reduced by 33% in the HPS 70W and 77% in the 14MnNbq. Moreover, critical pitting depth was much more sensitive to stress range in low stress range state. It could also be found that the plate thickness had little impact on critical pitting depth, which was less than 3% change in the depth when the thickness increased from 20 mm to 50 mm. Besides, the result also suggests that the critical depth in the HPS 70W was not sensitive to the change in the stress ratio when compared with the 14MnNbq. As a result, a considerable higher critical depth could be expected in the HPS 70W under a high stress ratio, which in turn indicates its better robustness in fatigue performance.

(a) (b)

(c) (d)

Appl. Sci.Figure2019, 7.9, 3461Critical pitting depth of the steel 14MnNbq with different plate thicknesses: (a) 20 mm; (15b) of 24 30 mm; (c) 40 mm and (d) 50 mm.

Appl. Sci. 2019, 9, x FOR PEER REVIEW 15 of 24 (a) (b)

(c) (d)

FigureFigure 8.8. Critical pitting pitting depth depth of of the the steel steel HPS HPS 70W 70W with with different different plate plate thicknesses: thicknesses: (a) (20a) mm; 20 mm; (b) (30b) 30mm; mm; (c) (40c) 40mm mm and and (d) ( d50) 50mm. mm. 5.4. Evaluation on the Corrosion-Fatigue Process 5.4. Evaluation on the Corrosion-Fatigue Process The C-F crack development in UWS bridges mainly depends on the category of environment, The C-F crack development in UWS bridges mainly depends on the category of environment, the fracture mechanics-related properties and the stress state under live loads. Meanwhile, there are the fracture mechanics-related properties and the stress state under live loads. Meanwhile, there are also some other conditions that lead to an accelerated C-F process under same corrosion environment also some other conditions that lead to an accelerated C-F process under same corrosion and material, e.g., the relatively huge pitting flaw size due to the uncertainty in pitting corrosion. environment and material, e.g., the relatively huge pitting flaw size due to the uncertainty in pitting As suggested by Albrecht [15,57], the fatigue strength will be reduced due to the corrosion corrosion. effect, and the degree of reduction increases with original fatigue strength. Since the base metal is As suggested by Albrecht [15,57], the fatigue strength will be reduced due to the corrosion believed with the highest fatigue strength, the reduction in the fatigue strength of the base metal is effect, and the degree of reduction increases with original fatigue strength. Since the base metal is correspondingly the most serious. Thus, investigations were made on the C-F performance of base believed with the highest fatigue strength, the reduction in the fatigue strength of the base metal is metal. The stress range used in the analysis was determined after the design fatigue strength at correspondingly the most serious. Thus, investigations were made on the C-F performance of base 2 million cycles in the Chinese code JTG D64 [58]. The ADTT was selected according to the number of metal. The stress range used in the analysis was determined after the design fatigue strength at 2 heavy vehicles in traffic category 2 stipulated in the Eurocode 1 [59]. In addition, the pitting current million cycles in the Chinese code JTG D64 [58]. The ADTT was selected according to the number of was used the same as the value from the corrosion test in Qingdao [42]. The main parameters were heavy vehicles in traffic category 2 stipulated in the Eurocode 1 [59]. In addition,8 the pitting current listed as the following: ∆σ = 140 MPa, R = 0.4, ADTT = 1370, Ip = 1.05 10 C/s, Cp = 1 and masp = 1. was used the same as the value from the corrosion test in Qingdao [42].× The− main parameters were Besides, it was assumed that each passing truck generated only one stress range. The results are shown listed as the following: 𝛥𝜎 = 140 MPa, 𝑅 = 0.4, ADTT = 1370, 𝐼 = 1.05 × 10−8 C/s, 𝐶 = 1 and 𝑚 in Figure9. = 1. Besides, it was assumed that each passing truck generated only one stress range. The results are The result indicates that crack development at the crack initiation stage was notably different shown in Figure 9. from that at the crack propagation stage. For instance, the crack growth rate was remarkably lower The result indicates that crack development at the crack initiation stage was notably different at the initiation stage than at the propagation stage. In addition, it could also be found that the from that at the crack propagation stage. For instance, the crack growth rate was remarkably lower initiation life accounted for the largest part of the whole C-F life in both types of steel, i.e., 80.3% in at the initiation stage than at the propagation stage. In addition, it could also be found that the the HPS 70W and 61.6% in the 14MnNbq. Similar conclusions can also be found in many relevant initiation life accounted for the largest part of the whole C-F life in both types of steel, i.e., 80.3% in studies [22,60]. At the same time, the crack initiation life in HPS 70W was much longer than in the the HPS 70W and 61.6% in the 14MnNbq. Similar conclusions can also be found in many relevant 14MnNbq, i.e., almost 5.3 times longer. On this end, the weathering steel HPS 70W steel exhibited studies [22,60]. At the same time, the crack initiation life in HPS 70W was much longer than in the much better C-F performance than the normal carbon steel 14MnNbq, even under the same pitting 14MnNbq, i.e., almost 5.3 times longer. On this end, the weathering steel HPS 70W steel exhibited current. This advantage of the HPS 70W could be attributed to the higher fatigue resistance and lower much better C-F performance than the normal carbon steel 14MnNbq, even under the same pitting decrease in fatigue limit with the increase in stress ratio. Besides, the corrosion resistance of HPS 70W current. This advantage of the HPS 70W could be attributed to the higher fatigue resistance and lower decrease in fatigue limit with the increase in stress ratio. Besides, the corrosion resistance of HPS 70W was far better than the normal carbon steel 14MnNbq, which led to a further enhancement in the C-F performance of the HPS 70W. Appl. Sci. 2019, 9, 3461 16 of 24

Appl. Sci. 2019, 9, x FOR PEER REVIEW 16 of 24 was far better than the normal carbon steel 14MnNbq, which led to a further enhancement in the C-F performanceAppl. Sci. 2019,of 9, x the FOR HPS PEER 70W. REVIEW 16 of 24

(a) (b) (a) (b) Figure 9. Crack development in the C-F process: (a) 20 mm and (b) 50 mm. FigureFigure 9. 9.Crack Crack developmentdevelopment in the C-F process: process: (a (a) )20 20 mm mm and and (b ()b 50) 50 mm. mm. 6. Sensitivity Analysis on Parameters 6.6. Sensitivity Sensitivity Analysis Analysis on on Parameters Parameters In this section, a sensitivity analysis was performed to investigate the influence of the C-F InIn this this section, section, a a sensitivity sensitivity analysisanalysis was performed performed to to investigate investigate the the influence influence of ofthe the C-F C-F life-critical factors, including the stress range, stress ratio, corrosive environment and ADTT on the life-criticallife-critical factors, factors, including including the the stress stress range, range, stress stress ratio, ratio, corrosive corrosive environment environment and and ADTT ADTT on on the the C-F C-F life of both two types of steel. For comparison purpose, the original sets of parameters were lifeC-F of bothlife of two both types two oftypes steel. of For steel. comparison For comparison purpose, purpose, the original the original sets of se parametersts of parameters were keptwere the kept the same as in Section 5.4. samekept as the in same Section as in5.4 Section. 5.4.

6.1.6.1. Influence Influence Influence of of the the Stress Stress Range Range TheThe stress stress range range varied varied from from 120120 MPaMPa toto 200200 MPa MPa in inin the thethe analysis. analysis.analysis. The The crack crack depth depth was was plotted plottedplotted againstagainst time, time, as as shown shown in in Figure Figure 10 10.10.. According According toto the the result, result, when when the the stress stress range rangerange increased increasedincreased from from 120120 MPa MPa to to 200 200 MPa, MPa, the the whole whole C-FC-F lifelife in the two two types types of of steel steel was was reduced reduced by by similar similar rates, rates, i.e., i.e., 92.4%92.4% in in the the HPS HPS 70W 70W and and 88.7% 88.7% inin thethe 14MnNbq.14MnNbq. However,However, it it should should be be noted noted that that the the C-F C-F life life of of HPSHPS 70W 70W was was far far longer longer thanthan than thatthat that ofofof 14MnNbq14MnNbq14MnNbq steelsteel due due to toto postponing postponingpostponing in inin the thethe crack crackcrack initiation. initiation.initiation.

(a) (a)

(b) (b) Figure 10. Crack development under various stress ranges: (a) HPS 70W and (b) 14MnNbq. Figure 10. Crack development under various stress ranges: ( a) HPS 70W and (b) 14MnNbq. For further comparison, the influence of the stress range on the initiation life and the propagationFor further life comparison,are shown in Figurethe influence 11a,b, respective of the ly.stress It can range be found on that,the dueinitiation to the increaselife and in the propagationthe stress range,life are the shown propagation in Figure life 11a,b, was respectivereduced byly. 83.9% It can inbe the found HPS that, 70W due and to 81.2%the increase in the in the14MnNbq. stress range, Meanwhile, the propagation the initiation life life was in theredu HPSced 70W by 83.9%steel was in reducedthe HPS by 70W 94.0% and while 81.2% that in in the 14MnNbq. Meanwhile, the initiation life in the HPS 70W steel was reduced by 94.0% while that in Appl. Sci. 2019, 9, 3461 17 of 24

For further comparison, the influence of the stress range on the initiation life and the propagation life are shown in Figure 11a,b, respectively. It can be found that, due to the increase in the stress range, theAppl. propagation Sci. 2019, 9, x FOR life PEER was REVIEW reduced by 83.9% in the HPS 70W and 81.2% in the 14MnNbq. Meanwhile,17 of 24 Appl. Sci. 2019, 9, x FOR PEER REVIEW 17 of 24 the initiation life in the HPS 70W steel was reduced by 94.0% while that in the 14MnNbq steel was the 14MnNbq steel was decreased by 92.2%. The result suggests that the stress range had a great decreased by 92.2%. The result suggests that the stress range had a great effect on the C-F life of both effectthe 14MnNbq on the C-F steel life wasof both decreased types of by steel 92.2%. at bo Theth the re sulttwo suggestsstages. Meanwhile that the stress, it also range could had be afound great types of steel at both the two stages. Meanwhile, it also could be found that the effect of the stress thateffect the on effect the C-F of the life stress of both range types on of the steel C-F at life bo ofth boththe two two stages. types ofMeanwhile steel was ,highly it also similar.could be found rangethat the on effect the C-F of lifethe ofstress both range two typeson the of C-F steel life was of both highly two similar. types of steel was highly similar.

(a) (b) (a) (b) Figure 11. Impact of stress range on the C-F life: (a) Initiation life and (b) propagation life. FigureFigure 11.11. ImpactImpact ofof stressstress rangerange onon thethe C-FC-F life:life: ((aa)) InitiationInitiation lifelife andand ((bb)) propagationpropagation life.life. 6.2. Influence Influence of the Stress Ratio 6.2. Influence of the Stress Ratio The stress ratio (R) variedvaried from 0.010.01 toto 0.50.5 inin thethe analysis.analysis. The crackcrack depthdepth waswas plottedplotted againstagainst The stress ratio (R) varied from 0.01 to 0.5 in the analysis. The crack depth was plotted against time, asas shownshown inin Figure Figure 12 12.. According According to to the the result, result, when when the the stress stress ratio ratio ranges ranges increased increased from from 0.01 time, as shown in Figure 12. According to the result, when the stress ratio ranges increased from to0.01 0.5, to the0.5, whole the whole C-F life C-F was life reducedwas reduced by 64.9% by 64.9% in the in HPS the 70W HPS and 70W 95.6% and in95.6% the 14MnNbq.in the 14MnNbq. It is also It 0.01 to 0.5, the whole C-F life was reduced by 64.9% in the HPS 70W and 95.6% in the 14MnNbq. It worthis alsonoting worth that noting the C-Fthat life the in C-F the 14MnNbqlife in the became14MnNbq longer became than thatlonger in the than HPS that 70W inwhen the HPS the stress70W is also worth noting that the C-F life in the 14MnNbq became longer than that in the HPS 70W ratiowhen was the belowstress ratio 0.05, was which below would 0.05, be which discussed would in thebe discussed following. in the following. when the stress ratio was below 0.05, which would be discussed in the following.

(a) (a)

(b) (b) Figure 12. Crack development under various stress ratios: ( a) HPS 70W and ( b) 14MnNbq. Figure 12. Crack development under various stress ratios: (a) HPS 70W and (b) 14MnNbq. The influenceinfluence of the stress range on the initiation life and the propagation life are also shown in FigureThe 1313a,b, a,b,influence respectively. respectively. of the stress It couldIt couldrange be found onbe thefound that initiation with that the lifewith increases and the the increases inpropagation the stress in ratio, thelife arestress the also propagation ratio, shown the in propagationFigure 13a,b, life respectively. steel was decreased It could by be 42.7% found in thethat HPS with and the 81.2% increases in the in14MnNbq. the stress Meanwhile, ratio, the thepropagation initiation lifelife steelwas wasreduced decreased by 68.3% by 42.7%in the in HPS the 70WHPS and 81.2%97.6% inin thethe 14MnNbq.14MnNbq. Meanwhile, The result suggeststhe initiation that thelife C-Fwas life reduced in the byHPS 68.3% 70W in was the less HPS sensitive 70W and to 97.6%the variation in the 14MnNbq.in the stress The ratio. result In anothersuggests word, that thethe C-FHPS life 70W in had the betterHPS 70W robustness was less unde sensitiver the change to the invariation the stress in ratiothe stressas previously ratio. In illustratedanother word, by the the analysis HPS 70W on hadthe criticalbetter robustnessdepth. It is undealso rworth the change noting in that the when stress the ratio stress as previously ratio was illustrated by the analysis on the critical depth. It is also worth noting that when the stress ratio was Appl. Sci. 2019, 9, 3461 18 of 24 life steel was decreased by 42.7% in the HPS and 81.2% in the 14MnNbq. Meanwhile, the initiation life was reduced by 68.3% in the HPS 70W and 97.6% in the 14MnNbq. The result suggests that the C-F life

Appl.in the Sci. HPS 2019 70W, 9, x FOR was PEER less sensitiveREVIEW to the variation in the stress ratio. In another word, the HPS 70W18 of had 24 betterAppl. Sci. robustness 2019, 9, x FOR under PEER theREVIEW change in the stress ratio as previously illustrated by the analysis on18 of the 24 lesscritical than depth. 0.05, Itboth is also the worthinitiation noting lifethat and when the prop theagation stress ratio life wasin the less HPS than 70W 0.05, were both shorter the initiation than that life inandless the thethan 14MnNbq. propagation 0.05, both On the life the initiation in contrary, the HPS life 70W once and were thethe shorterpropstressagation ratio than thatincreasedlife in the 14MnNbq.HPSbeyond 70W 0.05, were On a the shortertotally contrary, oppositethan once that trendthein the stress could 14MnNbq. ratio be increasedobserved. On the beyondThis contrary, phenomenon 0.05, once a totally the could stress opposite ex ratioplain trend increasedthe couldfact why bebeyond observed.the C-F 0.05, life Thisa in totally the phenomenon 14MnNbq opposite wascouldtrend higher explaincould under be the observed. facta stress why This ratio the phenomenon C-Fof 0.05, life inas theshown could 14MnNbq exin plainFigure was the 12. higherfact However, why under the itC-F a only stress life happened in ratio the of14MnNbq 0.05, under as someshownwas higher extremely in Figure under rare12 .a However, stresssituations ratio it that onlyof 0.05,the happened stressas shown ra undertio inwas Figure some under extremely12. 0.05 However, in steel rare situationsitbridges. only happened Thus, that the the under stress HPS 70Wratiosome could was extremely under be said 0.05rare to have insituations steel a much bridges. that better the Thus, stressC-F theperformance ra HPStio was 70W under under could 0.05 different be saidin steel to stress havebridges. ratios. a much Thus, better the HPS C-F performance70W could be under said to di ffhaveerent a stressmuch ratios.better C-F performance under different stress ratios.

(a) (b) (a) (b) Figure 13. Impact of the stress ratio on the C-F life: (a) Initiation life and (b) propagation life. Figure 13. Impact of the stress ratio on the C-F life: (a) Initiation life and (b) propagation life. Figure 13. Impact of the stress ratio on the C-F life: (a) Initiation life and (b) propagation life. 6.3. Influence Influence of the Corrosive Environment 6.3. Influence of the Corrosive Environment For better illustration,illustration, Ip𝐼can can be be written written in in the the form form of Iofp =𝐼k =I 𝑘where × 𝐼 whereI stands 𝐼 forstands the original for the × pi pi pittingoriginalFor current pittingbetter thatillustration,current is 1.05 that 𝐼 10is can 81.05C be/s, ×written and 10−8k C/s,is in the theand pitting form 𝑘 is of current the 𝐼 pitting= magnify 𝑘 ×current 𝐼 coewhereffi magnifycient 𝐼 rangingstands coefficient for from the × − ranging0.7original to 3.4. frompitting The 0.7 crack currentto 3.4. depth The that was crack is plotted 1.05 depth × against was10−8 plottedC/s, time, and asagainst shown𝑘 is thetime, in pitting Figure as shown 14current. in Figure magnify 14. coefficient ranging from 0.7 to 3.4. The crack depth was plotted against time, as shown in Figure 14.

(a) (a)

(b) (b) Figure 14. Crack development under various pitting currents: ( a)) HPS HPS 70W and ( b) 14MnNbq. Figure 14. Crack development under various pitting currents: (a) HPS 70W and (b) 14MnNbq. According to the result, when the pitting current magnify coefficient increased from 0.7 to 3.4, the wholeAccording C-F life to thewas result, reduced when by the70.2% pitting in th currente HPS 70Wmagnify steel coefficient and 59.6% increased in the 14MnNbq from 0.7 tosteel. 3.4, However,the whole even C-F underlife was the reduced higher reductionby 70.2% rate,in th thee HPS C-F 70W life in steel the HPSand 59.6%70W was in thestill 14MnNbq far longer steel.than thatHowever, in the 14MnNbqeven under under the higher various reduction pitting currents.rate, the C-F life in the HPS 70W was still far longer than that in the 14MnNbq under various pitting currents. Appl. Sci. 2019, 9, 3461 19 of 24

According to the result, when the pitting current magnify coefficient increased from 0.7 to 3.4, the whole C-F life was reduced by 70.2% in the HPS 70W steel and 59.6% in the 14MnNbq steel. However,Appl. Sci. 2019 even, 9, xunder FOR PEER the REVIEW higher reduction rate, the C-F life in the HPS 70W was still far longer19 than of 24 that in the 14MnNbq under various pitting currents. ForFor further further analysis, analysis, the the influence influence of of pitting pitting current curre onnt on the the initiation initiation life andlife and the propagationthe propagation life arelife shown are shown in Figure in Figure 15a,b, 15a,b, respectively. respectively.

(a) (b)

FigureFigure 15. 15.Impact Impact of of pitting pitting current current on on the the C-F C-F life: life: ( a(a)) Initiation Initiation life life and and ( b(b)) propagation propagation life. life.

ItIt could could be be found found that that with with the the increases increases in in the the pitting pitting current, current, the the initiation initiation life life was was reduced reduced by 74.9%by 74.9% in the in HPS the HPS 70W 70W and 69.2% and 69.2% in the in 14MnNbq the 14MnNbq steel. Meanwhile,steel. Meanwhile, with the with same the change same change in the pitting in the current,pitting thecurrent, propagation the propagation life was reduced life was by reduce 47.7% ind by the 47.7% HPS 70W in the and HPS 41.5% 70W in the and 14MnNbq 41.5% in steel. the It14MnNbq could also steel. be found It could that also the dibeff erencefound inthat the the initiation difference life in between the initiation two types life ofbetween steel was two extremely types of highsteel underwas extremely the low pitting high under current. the As low the pitting current curr increased,ent. As thethe di currentfference increased, gradually the reduced difference to a relativegradually stable reduced value afterto a therelative magnify stable coe ffivaluecient after reached the 3.0. magnify A similar coefficient trend could reached also be3.0. observed A similar in termstrend ofcould the propagation also be observed life. Meanwhile, in terms of it isthe worth prop notingagation that life. pitting Meanwhile, corrosion it is could worth still noting dominate that thepitting C-F processcorrosion for could a while still after dominate the pitting the C-F depth proc reachedess for a the while critical after size, the especiallypitting depth under reached the high the pittingcriticalcurrent. size, especially Therefore, under it indicates the high that pitting the highcurrent. pitting Therefore, current it could indicates lead tothat the the result high that pitting the corrosion-inducedcurrent could lead growth to the rate result was higherthat the than corro thesion-induced fatigue-induced growth rate when rate crackwas sizehigher was than small. the fatigue-induced rate when crack size was small. 6.4. Influence of ADTT

6.4. TheInfluence average of ADTT daily truck traffic (ADTT) varied from 500 to 5000 in the analysis. The crack development was plotted against time, as shown in Figure 16. According to the result, when the ADTT increased The average daily truck traffic (ADTT) varied from 500 to 5000 in the analysis. The crack from 500 to 5000, the whole C-F life was reduced by 35.5% in the HPS 70W and 57.3% in the 14MnNbq. development was plotted against time, as shown in Figure 16. According to the result, when the However, even under the extremely high ADTT (i.e., 5000), the whole C-F life in the HPS 70W was still ADTT increased from 500 to 5000, the whole C-F life was reduced by 35.5% in the HPS 70W and significantly higher than that in the 14MnNbq. 57.3% in the 14MnNbq. However, even under the extremely high ADTT (i.e., 5000), the whole C-F For further analysis, the influence of ADTT on the initiation life and the propagation life are life in the HPS 70W was still significantly higher than that in the 14MnNbq. shown in Figure 17a,b, respectively. It could be found that with the increases in the ADTT, the propagation life was reduced by 73.4% in the HPS 70W and 77.1% in the 14MnMbq steel. Meanwhile, the initiation life was reduced by 20.7% in the HPS 70W and 38.7% in the 14MnMbq steel. Consequently, in addition to the notable impact on the propagation life, the ADTT also had a secondary effect on the initiation life in both types of steel. In this case, with the increase in the ADTT, the fatigue-related crack growth rate was increased. As a result, the competition time period tc was reduced, which in turn affected the initiation life.

(a) Appl. Sci. 2019, 9, x FOR PEER REVIEW 19 of 24

For further analysis, the influence of pitting current on the initiation life and the propagation life are shown in Figure 15a,b, respectively.

(a) (b)

Figure 15. Impact of pitting current on the C-F life: (a) Initiation life and (b) propagation life.

It could be found that with the increases in the pitting current, the initiation life was reduced by 74.9% in the HPS 70W and 69.2% in the 14MnNbq steel. Meanwhile, with the same change in the pitting current, the propagation life was reduced by 47.7% in the HPS 70W and 41.5% in the 14MnNbq steel. It could also be found that the difference in the initiation life between two types of steel was extremely high under the low pitting current. As the current increased, the difference gradually reduced to a relative stable value after the magnify coefficient reached 3.0. A similar trend could also be observed in terms of the propagation life. Meanwhile, it is worth noting that pitting corrosion could still dominate the C-F process for a while after the pitting depth reached the critical size, especially under the high pitting current. Therefore, it indicates that the high pitting current could lead to the result that the corrosion-induced growth rate was higher than the fatigue-induced rate when crack size was small.

6.4. Influence of ADTT The average daily truck traffic (ADTT) varied from 500 to 5000 in the analysis. The crack development was plotted against time, as shown in Figure 16. According to the result, when the ADTT increased from 500 to 5000, the whole C-F life was reduced by 35.5% in the HPS 70W and 57.3% in the 14MnNbq. However, even under the extremely high ADTT (i.e., 5000), the whole C-F Appl. Sci. 2019, 9, 3461 20 of 24 life in the HPS 70W was still significantly higher than that in the 14MnNbq.

Appl. Sci. 2019, 9, x FOR PEER REVIEW 20 of 24

Appl. Sci. 2019, 9, x FOR PEER REVIEW 20 of 24 (a)

(b)

Figure 16. Crack development under different average daily truck traffic (ADTT): (a) HPS 70W and (b) 14MnNbq. (b) For further analysis, the influence of ADTT on the initiation life and the propagation life are Figure 16.16. Crack development under didifferentfferent averageaverage daily truck tratrafficffic (ADTT):(ADTT): (a) HPSHPS 70W70W andand shown in Figure 17a,b, respectively. ((b)) 14MnNbq.14MnNbq.

For further analysis, the influence of ADTT on the initiation life and the propagation life are shown in Figure 17a,b, respectively.

(a) (b)

FigureFigure 17. 17.Impact Impact of of stress stress ADTT ADTT on on C-F C-F life: life: ((aa)) InitiationInitiation life life and and ( b(b)) propagation propagation life. life.

7. Conclusions It could be found( athat) with the increases in the ADTT, the propagation(b) life was reduced by 73.4% in theThe HPS uncoated 70W and weathering 77.1% insteel the 14MnMbq (UWS) bridges steel. become Meanwhile, increasingly the initiation popular life due was to their reduced advantages by 20.7% Figure 17. Impact of stress ADTT on C-F life: (a) Initiation life and (b) propagation life. inin both the HPS the lifetime 70W and cost 38.7% and environmentin the 14MnMbq protection. steel. Consequently, However, the C-Fin addition issue is ofto particularthe notable concern impact inon UWS the propagation bridges, which life, is the further ADTT escalated also had by a thesecondary designated effect corrosion on the initiation process. Onlife thisin both end, types a solid of It could be found that with the increases in the ADTT, the propagation life was reduced by 73.4% evaluationsteel. In this method case, iswith urgently the increase required in for the the ADTT, C-F process the fatigue-related in UWS bridges crack to ensure growth the rate lifetime was in the HPS 70W and 77.1% in the 14MnMbq steel. Meanwhile, the initiation life was reduced by 20.7% serviceabilityincreased. As and, a result, more important,the competition safety. Intime this period paper, an𝑡 innovativewas reduced, model which was in established turn affected through the in the HPS 70W and 38.7% in the 14MnMbq steel. Consequently, in addition to the notable impact combininginitiation life. the electrochemistry theory and fracture mechanics. The proposed model for C-F crack on the propagation life, the ADTT also had a secondary effect on the initiation life in both types of initiation was then validated using the experimental data in existing literatures. Based on the verified steel. In this case, with the increase in the ADTT, the fatigue-related crack growth rate was model,7. Conclusions the case study was carried out on two typical types of structural steel, i.e., HPS 70W and increased. As a result, the competition time period 𝑡 was reduced, which in turn affected the 14MnNbq steel. Besides, investigations were also made on the effect of crucial C-F parameters, initiationThe life.uncoated weathering steel (UWS) bridges become increasingly popular due to their includingadvantages the in stress both range, the lifetime stress ratio, cost corrosiveand enviro environmentnment protection. and average However, daily truck the C-F traffi issuec (ADTT). is of 7.particular ConclusionsBased onconcern the above in UWS analysis, bridges, the which following is further conclusions escalated could by be the drawn: designated corrosion process. On this(1) Analysis end, a solid was evaluation made to find method out a suitableis urgently index required to reflect for the the degree C-F process of corrosion, in UWS based bridges on the to The uncoated weathering steel (UWS) bridges become increasingly popular due to their experimentensure the datalifetime collected serviceability at various and, places more with import differentant, corrosionsafety. In categoriesthis paper, in an China. innovative As a result, model a advantages in both the lifetime cost and environment protection. However, the C-F issue is of clearwas relationestablished could through be observed combining between the the electroche degree ofmistry corrosion theory and theand pitting fracture current, mechanics. which were The particular concern in UWS bridges, which is further escalated by the designated corrosion process. proposed model for C-F crack initiation was then validated using the experimental data in existing On this end, a solid evaluation method is urgently required for the C-F process in UWS bridges to literatures. Based on the verified model, the case study was carried out on two typical types of ensure the lifetime serviceability and, more important, safety. In this paper, an innovative model structural steel, i.e., HPS 70W and 14MnNbq steel. Besides, investigations were also made on the was established through combining the electrochemistry theory and fracture mechanics. The effect of crucial C-F parameters, including the stress range, stress ratio, corrosive environment and proposed model for C-F crack initiation was then validated using the experimental data in existing average daily truck traffic (ADTT). literatures. Based on the verified model, the case study was carried out on two typical types of Based on the above analysis, the following conclusions could be drawn: structural steel, i.e., HPS 70W and 14MnNbq steel. Besides, investigations were also made on the effect of crucial C-F parameters, including the stress range, stress ratio, corrosive environment and average daily truck traffic (ADTT). Based on the above analysis, the following conclusions could be drawn: Appl. Sci. 2019, 9, 3461 21 of 24 only related to the corrosion environment. Thus, the pitting current was utilized to reflect the degree of pitting corrosion in this study. (2) An innovative model was established to simulate the C-F process in UWS bridges. The two stages in the C-F process were independently treated in series, i.e., the C-F crack initiation stage and the C-F crack propagation stage. Meanwhile, the critical pitting depth could serve as an indicator of the fatigue effect, which competed against the corrosion effect. At the C-F crack initiation stage, the pit could be regarded as an equivalent initial flaw that only grew under the corrosion. Once the flaw reached the critical size, the fatigue effect joined as a parallel driving force in crack propagation. The two effects then competed with each other, and the C-F process was dominated by the one with the higher growth rate. As a result, the fatigue effect gradually replaced the corrosion as the major driving force, which was the symbol of the C-F crack propagation stage, and the crack then grew under the cyclic stress until the final failure. In the study, the pitting corrosion process was considered through Faraday’s law, while fracture mechanics was employed to describe the propagation of fatigue cracks. (3) The model proposed for the initiation stage and the whole C-F process was validated using the experimental data in the existing literatures. The result shows that the prediction curve matched well with the test data, indicating the effectiveness of the proposed method in predicting the C-F life. (4) A case study was carried out on the bridge respectively constructed of two brands of steel, i.e., the normal steel 14MnNbq and the high-performance weathering steel HPS 70W. The result shows that when considering the coupled C-F process, the bridge with the HPS 70W had a remarkably higher service life than the one with the 14MnNbq. Besides, it also suggests that the C-F crack initiation stage accounted for the largest part in the whole C-F life, i.e., around 61.6%–80.3%. (5) A sensitive analysis was conducted on various C-F parameters, including the stress range, stress ratio, corrosive environment and ADTT, on the C-F life of normal steel 14MnNbq and HPS 70W. The investigation was performed with respect to the influence on both the initiation life and propagation life. The result shows that stress range and stress ratio both had dramatic impacts on C-F life. Moreover, the C-F life decreased with the increase in the stress range and stress ratio. As an index of the corrosive environment, the pitting current only affected the C-F crack initiation life. Besides, the ADTT had a significant impact on the propagation life while its effect on the initiation life was just limited.

Author Contributions: Data collection, simulation, methodology, and writing—Original draft preparation, Y.Z.; supervision, project administration and funding acquisition, K.Z.; conceptualization, methodology and writing—Review and editing, J.H; writing—Review and editing, J.Z. Funding: The research was funded by the National Natural Science Foundation of China (grant number: 51778536, 51908472), Doctoral Innovation Fund Program of Southwest Jiaotong University (grant number: D-CX201701), the Zhejiang Department of Transportation (grant number: 10115066), China postdoctoral science foundation (2019TQ0271). Acknowledgments: The corresponding author gratefully acknowledges financial support from China Scholarship Council and British Council during studying in the UK. Special thanks to Sakdirat at the University of Birmingham, and European Commission for H2020-MSCA-RISE Project No. 691135 “RISEN: Rail Infrastructure Systems Engineering Net-work” (www.risen2rail.eu). Conflicts of Interest: The authors declare no conflict of interest.

References

1. Dolling, C.N.; Hudson, R.M. Weathering steel bridges. Proc. Inst. Civ. Eng. Bridge Eng. 2003, 156, 39–44. [CrossRef] 2. Yamashita, M. Structure of protective rust layers formed on weathering steels by long-term exposure in the industrial atmospheres of America. ISIJ Int. 1998, 38, 285–290. [CrossRef] 3. Yamaguchi, E. Assessment method for atmospheric corrosiveness and durability design of weathering steel bridges. In Proceedings of the 23rd US-Japan Bridge Engineering Workshop, Tsukuba, Japan, 5–7 November 2007. Appl. Sci. 2019, 9, 3461 22 of 24

4. Yasumori, F.; Mutsuto, T.; Hiroshi, K.; Kazumi, M. Corrosion risk management methods to realize long-term durability of weathering steel bridges. Nippon Steel Tech. Rep. 2008, 387, 53. (In Japanese) 5. Liu, Q.; Wang, B.; Wang, X. Research, application and prospect of weathering steel. In China Steel Structure Association Building Steel Structure Branch; Steel Construction: Guiyang, China, 2011; pp. 110–118. 6. Horii, S.; Mishima, Y.; Hashimoto, M. Steel bridge quality management and weathering steel application technologies in Japan. In Proceedings of the IABSE-JSCE Joint Conference on Advances in Bridge Engineering-II, At Dhaka, Bangladesh, 21–22 August 2015; pp. 476–484. 7. Kodur, V.K.R.; Naser, M.Z. Designing steel bridges for fire safety. J. Constr. Steel Res. 2019, 156, 46–53. [CrossRef] 8. Wan, R.; Feng, S.; Zhang, L.; Shan, A. Effects of Mo on high-temperature strength of fire-resistant steel. Mater. Des. 2012, 35, 335–341. [CrossRef] 9. Katherine, K.B. Performance of Weathering Steel in Highway Bridges; A Third Phase Report; American Iron and Steel Institute: Pittsburgh, PA, USA, 1995. 10. Wu, Q.; Chen, X.; Fan, Z.; Nie, D.; Wei, R. Corrosion fatigue behavior of FV520B steel in water and salt-spray environments. Eng. Fail. Anal. 2017, 79, 422–430. [CrossRef] 11. Jones, R. Fatigue crack growth and damage tolerance. Fatigue Fract. Eng. Mater. Struct. 2014, 37, 463–483. [CrossRef] 12. Ali, K.; Peng, D.; Jones, R.; Singh, R.R.K.; Zhao, X.; Mcmillan, A.J.; Berto, F. Crack growth in a naturally corroded bridge steel. Fatigue Fract. Eng. Mater. Struct. 2017, 40, 1117–1127. [CrossRef] 13. Jun, H.K.; Seo, J.W.; Kwon, S.J.; Lee, D.H.; Park, S.H. Effect of corrosion on the fatigue life of aged EMU under fatigue loading. Int. J. Precis. Eng. Manuf. 2016, 17, 73–79. [CrossRef] 14. Kunz, L.; Luká, P.; Klusák, J. Fatigue Strength of Weathering steel. Mater. Sci. 2012, 18, 18–22. [CrossRef] 15. Albrecht, P.; Lenwari, A. Fatigue strength of weathered A588 steel beams. J. Bridge Eng. 2009, 14, 436–443. [CrossRef] 16. Kondo, Y. Prediction of fatigue crack initiation life based on pit growth. Corrosion 1989, 45, 7–11. [CrossRef] 17. Zampieri, P.; Curtarello, A.; Maiorana, E.; Pellegrino, C. A Review of the Fatigue Strength of Shear Bolted Connections. Int. J. Steel Struct. 2019, 19, 1084–1098. [CrossRef] 18. Zampieri, P.; Curtarello, A.; Maiorana, E.; Pellegrino, C. Fatigue strength of corrode bolted connection. Frat. Integrità Strutt. 2018, 43, 90–95. 19. Zampieri, P.; Curtarello, A.; Maiorana, E.; Pellegrino, C. Numerical analyses of corroded bolted connections. Procedia Struct. Integr. 2017, 5, 592–599. [CrossRef] 20. Xu, S.H.; Qiu, B. Experimental study on fatigue behavior of corroded steel. Mater. Sci. Eng. A 2013, 584, 163–169. [CrossRef] 21. Garbatov, Y.; Guedes, S.C.; Parunov, J. Fatigue strength experiments of corroded small scale steel specimens. Int. J. Fatigue 2014, 59, 137–144. [CrossRef] 22. Ebara, R. Corrosion fatigue crack initiation in 12% chromium stainless steel. Mater. Sci. Eng. A 2007, 468, 109–113. [CrossRef] 23. Ishihara, S.; Saka, S.; Nan, Z.; Goshima, T.; Sunada, S. Prediction of corrosion fatigue lives of aluminium alloy on the basis of corrosion pit growth law. Fatigue Fract. Eng. Mater. Struct. 2010, 29, 472–480. [CrossRef] 24. Li, S.; Akid, R. Corrosion fatigue life prediction of a steel shaft material in seawater. Eng. Fail. Anal. 2013, 34, 324–334. [CrossRef] 25. Peng, D.; Jones, R. Effect of corrosion and fatigue on the remaining life of structure and its implication to additive manufacturing. Frat. Integrità Strutt. 2018, 45, 33–44. 26. Peng, D.; Jones, R.; Singh, R.R.K.; Berto, F.; McMillan, A.J. On the interaction between corrosion and fatigue which determines the remaining life of bridges. Fatigue Fract. Eng. Mater. Struct. 2017, 41, 314–322. [CrossRef] 27. Tamaki, Y.; Shimozato, T.; Arizumi, Y. Evaluation of corrosion deterioration of weathering steel bridge under the environment corrosiveness. In Proceedings of the 5th International Conference on Bridge. Maintenance, Safety, Management and Life-Cycle Optimization, Philadelphia, PA, USA, 11–15 July 2010; pp. 3563–3569. 28. Jyoti, B.; Faisal, K.; Rouzbeh, A.; Vikram, G.; Roberto, O. Modelling of pitting corrosion in marine and offshore steel structures—A technical review. J. Loss Prev. Process Ind. 2015, 37, 39–62. 29. Mazánová, V.; Polák, J. Initiation and growth of short fatigue cracks in austenitic sanicro 25 steel. Fatigue Fract. Eng. Mater. Struct. 2018, 26, 1529–1545. [CrossRef] Appl. Sci. 2019, 9, 3461 23 of 24

30. Polak, J.; Liskutin, P. Nucleation and short crack growth in fatigued polycrystalline copper. Fatigue Fract. Eng. Mater. Struct. 1990, 13, 119–133. [CrossRef] 31. Zaya, P.G.R. Evaluation of Theiores for the Initial Stages of Pitting Corrosion. Ph.D. Thesis, McMaster University, Hamilton, ON, Canada, 1984. 32. Melchers, R.E. Pitting Corrosion in Marine Environments: A Review; Department of Civil Engineering and Surveying, University of Newcastle, Australia: Newcastle, Australia, 1994. 33. Abood, T.H. The Influence of Various Parameters on Pitting Corrosion of 316L and 202 Stainless Steel; Department of Chemical Engineering of the University of Technology: Baghdad, Iraq, 2008. 34. Agar, J.N.; Hoar, T.P. The influence of change of size in electrochemical systems. Discuss. Faraday Soc. 1947, 1, 158–162. [CrossRef] 35. Sriraman, M.R.; Pidaparti, R.M. Crack initiation life of materials under combined pitting corrosion and cyclic loading. J. Mater. Eng. Perform. 2010, 19, 7–12. [CrossRef] 36. Albrecht, P.; Naeemi, A.H. Performance of Weathering Steel in Bridges; NCHRP Report; NCHRP: Washington, DC, USA, 1984. 37. McKenzie, M. The corrosion performance of weathering steel in highway bridges. In Atmospheric Corrosion, The Electrochemical Society; Ailor, W.H., Ed.; John Wiley and Sons: New York, NY, USA, 1982; pp. 717–736. 38. Huang, X.-G.; Xu, J.-Q. Pit morphology characterization and corrosion fatigue crack nucleation analysis based on energy principle. Fatigue Fract. Eng. Mater. Struct. 2012, 35, 606–613. 39. Harlow, D.G.; Wei, R.P.Probabilities of occurrence and detection of damage in airframe materials. Fatigue Fract. Eng. Mater. Struct. 2010, 22, 427–436. [CrossRef] 40. Newman, J.C.; Raju, I.S. An empirical stress-intensity factor equation for the surface crack. Eng. Fract. Mech. 1976, 15, 185–192. [CrossRef] 41. ISO 9223. Corrosion of Metals and Alloys-Corrosion of Atmospheres-Classification, Determination and Estimation; International Organization for Standardization: Geneva, Switzerland, 2012. 42. China Gateway to Corrosion and Protection. Available online: http://www.ecorr.org/ (accessed on 10 April 2019). 43. Paris, P.; Erdogan, F. A Critical analysis of crack propagation laws. Trans. ASME 1963, 85, 528–533. [CrossRef] 44. Chen, H.; Grondin, G.; Driver, R.G. Fatigue Resistance of High Performance Steel; University of Alberta Department of Civil Environmental Engineering: Edmonton, AB, Canada, 2005. 45. Chen, G.; Wan, K.; Gao, M.; Wei, R.; Flournoy, T.H. Transition from pitting to fatigue crack growth—Modeling of corrosion fatigue crack nucleation in a 2024-T3 aluminum alloy. Mater. Sci. Eng. A 1996, 219, 126–132. [CrossRef] 46. Harlow, D.G.; Wei, R.P. Probability approach for prediction of corrosion and corrosion fatigue life. AIAA J. 1994, 32, 2073–2079. 47. Mao, M.; Zhang, X.; Tu, S.; Xuan, F. Prediction of crack initiation life due to corrosion pits. J. Aircr. 2014, 51, 805–810. [CrossRef] 48. Kaynak, C.; Ankara, A.; Baker, T.J. A comparison of short and long fatigue crack growth in steel. Int. J. Fatigue 1996, 18, 17–23. [CrossRef] 49. American Society for Testing Materials. Standard Specification for Structural Steel for Bridges; Designation: A709/A709M; American Society for Testing Materials: West Conshohocken, PA, USA, 2013. 50. Liu, Y.; Chen, C.; Li, G.Q. Fatigue crack growth and control of 14MnNbq welding plates used for bridges. J. Eng. Mech. 2012, 138, 30–35. [CrossRef] 51. Wang, C.; Duan, L.; Li, Z.; Hu, J. Fatigue crack growth rate tests of high performance steel HPS 485W for bridges. Eng. Mech. 2013, 30, 212–216. 52. Liu, Y.; Chen, C.; Li, G. Study on the surface crack growth behavior in 14MnNbq bridge steel. Acta Mech. Solida Sin. 2010, 23, 361–369. [CrossRef] 53. Phillips, E.P.; Newman, J.C. Impact of small-crack effects on design life calculations. Exp. Mech. 1989, 29, 221–225. [CrossRef] 54. Ahmed, T.M.; Tromans, D. Fatigue threshold behavior of α-phase copper alloys in desiccated air: Modulus effects. Int. J. Fatigue 2004, 26, 641–649. [CrossRef] 55. Sobieck, T.; Atadero, R.A.; Mahmoud, H.N. Fatigue crack propagation of notched steel rebar in RC beams repaired with externally bonded CFRP. J. Compos. Constr. 2015, 19, 04014076. [CrossRef] Appl. Sci. 2019, 9, 3461 24 of 24

56. Newman, J.C., Jr.; Raju, I.S. Analyses of Surface Cracks in Finite Plates Under Tension or Bending Loads; NASA TP-1578; NASA: Washington, DC, USA, 1979. 57. Albrecht, P. Fatigue Strength of A588 Steel Beams; Department of Civil Engineering, University of Maryland: College Park, MD, USA, 1988. 58. Standardization Administration of the People’s Republic of China (SAC). Specifications for Design of Highway Steel Bridge; JTG D64-2015; Standards Press of China: Beijing, China, 2015. (In Chinese) 59. European Committee for Standardization (CEN). Eurocode 1: Actions on Structures—Part2: Traffic Loads on Bridges; BS EN 1991-2:2003; CEN: Brussels, Belgium, 2003. 60. Thierry, P.L.; Rubén, P.M.; Claude, B.; Gonzalo, D. Fatigue crack initiation and growth on a steel in the very high cycle regime with sea water corrosion. Eng. Fract. Mech. 2010, 77, 1953–1962.

© 2019 by the authors. Licensee MDPI, Basel, Switzerland. This article is an open access article distributed under the terms and conditions of the Creative Commons Attribution (CC BY) license (http://creativecommons.org/licenses/by/4.0/).