Effect of Pre-Corrosion Pits on Residual Fatigue Life for 42Crmo

materials

Article Eﬀect of Pre-Corrosion Pits on Residual Fatigue Life for 42CrMo Steel

Dezheng Liu 1,*, Yan Li 1, Xiangdong Xie 2,* and Jing Zhao 1

1 Hubei Key Laboratory of Power System Design and Test for Electrical Vehicle, Hubei University of Arts and Science; Xiangyang 441053, China 2 School of Urban Construction, Yangtze University, Jingzhou 201800, China * Correspondence: [email protected] (D.L.); [email protected] (X.X.)

Received: 13 June 2019; Accepted: 1 July 2019; Published: 2 July 2019

Abstract: The effect of pre-corrosion pits on residual fatigue life for the 42CrMo steel (American grade: AISI 4140) is investigated using the accelerated pre-corrosion specimen in the saline environment. Different pre-corroded times are used for the specimens, and fatigue tests with different loads are then carried out on specimens. The pre-corrosion fatigue life is studied, and the fatigue fracture surfaces are examined by a surface profiler and a scanning electron microscope (SEM) to identify the crack nucleation sites and to determine the size and geometry of corrosion pits. Moreover, the stress intensity factor varying with corrosion pits in different size parameters is analyzed based on finite element (FE) software ABAQUS to derive the regression formula of the stress intensity factor. Subsequently, by integrating the regression formula with the Paris formula, the residual fatigue life is predicted and compared with experimental results, and the relationship of the stress intensity factor, pit depth, and residual fatigue life are given under different corrosion degrees. The fatigue life predicted by the coupled formula agrees well with experiment results. It is observed from the SEM images that higher stress amplitude and longer pre-corroded time can significantly decrease the residual fatigue life of the steel. Additionally, the research work has brought about the discovery that the rate of crack extension accelerates when the crack length increases. The research in this paper also demonstrates that the corrosion pit size can be used as a damage index to assess the residual fatigue life.

Keywords: pre-corrosion pits; residual fatigue life; 42CrMo steel; stress intensity factor

1. Introduction Most engineering materials are subject to corrosion, and corrosion research has received much attention from different perspectives [1–7]. The 42CrMo (American grade: AISI 4140) is a commonly used ultrahigh-strength steel. Due to its high strength, toughness, and hardenability, 42CrMo steel is widely used in quenched and tempered heavy forgings to build components such as pressure vessels, gears, vehicle axles, and deep oil drilling rod subs [8,9]. However, their corrosion resistance is relatively poor and this material is prone to corrosion. Corrosion pits can weaken the strength of the structure and decrease its fatigue life [10,11], since the fatigue cracks are easy to nucleate at corrosion pits and propagate rapidly under dynamic loads [12]. Thus, to further understand corrosion effects on the strength and residual fatigue life of 42CrMo material, the stress state around corrosion pits should be reasonably estimated. In recent years, fatigue performance of pre-corroded metallic alloys has been studied extensively. For example, recent works [13–18] have reported the description of the stress concentration arising from corrosion pits based on the ﬁnite element (FE) method. Sharland [13] developed a mechanistic model of the propagation stage of an established pit or crevice to simulate the evolution of pit geometry and to describe the corrosion process. However, Wang [14] indicated that a detailed description of both the chemical reactions and the ionic transport was not included in it [13]. Through the use of interaction

Materials 2019, 12, 2130; doi:10.3390/ma12132130 www.mdpi.com/journal/materials Materials 2019, 12, x FOR PEER REVIEW 2 of 13 Materials 2019, 12, 2130 2 of 13 that a detailed description of both the chemical reactions and the ionic transport was not included in it [13]. Through the use of interaction function to simulate the effect of the corrosion potential and functioncorrosion to current simulate density the effect on of thethe corrosioncorrosion potential process, and Xu corrosion [15] developed current densityan FE onmodel the corrosion for the process,simulation Xu of [15 the] developed mechanoelectrochemical an FE model for effect the simulation of pipeline of corrosion. the mechanoelectrochemical Because the fatigue estrengthffect of pipelineof the metallic corrosion. alloys Because decreases the fatigue differently strength ofunder the metallicthe different alloys decreasescorrosion di ffdepthserently and under stress the diamplitudesfferent corrosion [16], Pidaparti depths and [17] stress established amplitudes a new [16 FE], Pidapartimodel to [17inve] establishedstigate the astress new state FE model around to investigatecorrosion pits. the stressHowever, state aroundthe proposed corrosion FE pits. model However, in [17] the cannot proposed be used FE model to depict in [17 the] cannot growth be usedprocess to depict of corrosion the growth pits processwith time. of corrosion Through pits the withuse of time. the Throughdamage tolerance the use of method the damage to predict tolerance the methodcorrosion to fatigue predict life the for corrosion 7075-T6 fatigue stainless life steel, for 7075-T6Huang [18] stainless indicted steel, that Huang the nucleation [18] indicted time that of pits the nucleationand the material time of constant pits and of the crack material propagation constant can of crack affect propagation the residual can fatigue affect life the of residual stainless fatigue steel lifesignificantly. of stainless On steel the significantly. basis of [16–18], On theZheng basis [19] of proposed [16–18], Zheng that the [19 decrease] proposed of thatfatigue the life decrease depends of fatigueon the pre-corroded life depends ontime the and pre-corroded the size of timepre-corrosion and the size pits. of Most pre-corrosion recent studies pits. Moston the recent fatigue studies life of onsteel the in fatigue corrosion life ofenvironments steel in corrosion only environmentsconsider the factors only consider such as themass factors loss suchrate and as mass corrosion loss rate pit anddepth, corrosion and rarely pit depth, involve and the rarely stress involve intensity the stressfactor intensityvarying factorwith corrosion varying with pits corrosionin different pits size in diparameters.fferent size The parameters. stress concentration The stress concentration caused by corr causedosion by pits corrosion can dramatically pits can dramatically influence influencethe basic themacroscopic basic macroscopic mechanical mechanical properties properties of a steel [20]. of a Despite steel [20 the]. Despite extensive the research extensive on researchthe corrosion on the of corrosionmetallic alloys of metallic [21–24], alloys there [21 are–24 ],few there detailed are few studies detailed of studiesthe effect of theof pre-corrosion effect of pre-corrosion pits on residual pits on residualfatigue life fatigue for 42CrMo life for 42CrMosteel. steel. InIn thisthis study,study, thethe eeffectffectof ofstress stressdistribution distribution aroundaround corrosioncorrosion pitspits onon thethe stressstress intensityintensity factorfactor isis firstlyfirstly investigated.investigated. The The crack crack nucleation nucleation sites sites and and the the geometry geometry of ofcorrosion corrosion pits pits are are examined examined by bya surface a surface profiler profiler and and a scanning a scanning electron electron microsco microscopepe (SEM), (SEM), and and then then the therelationship relationship between between the thefatigue fatigue life life and and the the maximum maximum applied applied stress stress is is ob obtainedtained by by fatigue fatigue tests tests of of different different pre-corrodedpre-corroded specimens.specimens. BasedBased onon experimentexperiment results,results, anan FEFE modelmodel isis conductedconducted toto investigateinvestigate stressstress distributiondistribution aroundaround corrosioncorrosion pits, pits, and and regression regression formula formula of theof the stress stress intensity intensity factor factor varying varying with with corrosion corrosion pits inpits di ffinerent different size parameters size parameters is then is derived. then derived. Subsequently, Subsequently, by coupling by coupling the regression the regression formula withformula the Pariswith formulathe Paris [25 formula], the fatigue [25], performancethe fatigue performa is predictednce byis thepredicted FE method by the and FE then method compared and withthen experimentalcompared with tests. experimental Under the ditests.fferent Under stress the amplitudes different andstress pre-corroded amplitudes times,and pre-corroded the FE predictions times, arethe finallyFE predictions validated are by finally comparison validated with by the comparison experiment with results. the experiment results. 2. Materials and Methods 2. Materials and Methods 2.1. Material and Specimen Preparation 2.1. Material and Specimen Preparation To better understand the stress intensity factor varying with corrosion pits in different size parametersTo better and understand to accurately the depict stress the intensity residual factor fatigue varying life of 42CrMo with corrosion steel subject pits toin corrosion,different itsize is necessaryparameters to and quantitatively to accurately investigate depict the the residual effects fati of pre-corrosiongue life of 42CrMo levels steel on the subject fatigue to behaviorcorrosion, of it 42CrMois necessary steel. to Experimental quantitatively specimens investigate were the fabricated effects of using pre-corrosion the 42CrMo levels steel on (American the fatigue grade: behavior AISI 4140),of 42CrMo which steel. was providedExperimental by Baowu specimens Steel Companywere fabricated (Wuhan, using China). the 42CrMo Specimens steel were (American manufactured grade: inAISI the 4140), form ofwhich flat barewas sheetsprovided with by a Baowu thickness Stee ofl 6Company mm by wire(Wuhan, cutting China). machine, Specimens the sizes were of specimensmanufactured are providedin the form in Figureof flat 1bare. The sheets chemical with compositiona thickness of was 6 mm measured by wire using cutting an FLS980-stmmachine, the Edinburghsizes of specimens fluorescence are spectrometerprovided in Figure (Edinburgh 1. The Instruments chemical composition Ltd., Livingston, was UK).measured A comparison using an ofFLS980-stm the measured Edinburgh chemical fluorescence composition spectrometer of 42CrMo (E specimensdinburgh Instruments and the standard Ltd., Livingston, of GB/T3077-2015 UK). A (thecomparison national standardof the measured of the People’s chemical Republic compositio of Chinan of for 42CrMo alloy structural specimens steel) and for the 42CrMo standard steel isof presentedGB/T3077-2015 in Table (the1. Itnational can be seenstandard from Tableof the1 People’sthat the chemicalRepublic composition of China for of alloy the specimens structural used steel) infor this 42CrMo study steel meets is the presented requirement in Table of the 1. It national can be standard.seen from Table 1 that the chemical composition of the specimens used in this study meets the requirement of the national standard.

FigureFigure 1.1. SchematicSchematic diagramdiagram ofof specimenspecimen sizessizes (mm).(mm).

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Table 1. A comparison of the measured chemical composition of 42CrMo specimens and the standard Table 1. A comparison of the measured chemical composition of 42CrMo specimens and the of GB/T3077-2015 for 42CrMo steel (wt.%). standard of GB/T3077-2015 for 42CrMo steel (wt.%). wt.% C S P Cr Ni Mn Si Cu Mo wt.% C S P Cr Ni Mn Si Cu Mo 42CrMo42CrMo 0.42 0.42 0.0020.002 0.0220.022 1.081.08 0.020.02 0.690.69 0.28 0.28 0.020.02 0.180.18 GB/T3077-2015 0.38–0.45 0.035 0.90–1.20 0.30 0.50–0.80 0.17–0.37 0.25 0.15–0.25 GB/T3077-2015 0.38–0.45 ≤ ≤0.035 0.90–1.20 ≤ ≤0.30 0.50–0.80 0.17–0.37≤ ≤0.25 0.15–0.25

TwelveTwelve smoothsmooth samplessamples werewere numberednumbered andand divideddivided intointo fourfour groups.groups. TheThe acceleratedaccelerated neutralneutral saltsalt sprayspray corrosioncorrosion experiment experiment was was established established to to achieve achieve the the pre-corroded pre-corroded steel steel plates plates based based on theon standardthe standard of JIS of H 8502.5JIS H [8502.526]. A schematic[26]. A schematic drawing ofdrawing the sample of the preparation sample andpreparation the pre-corroded and the experimentpre-corroded procedure experiment is shownprocedure in Figure is shown2. The in sampleFigure 2. preparation The sample was preparation carried out was in carried ﬁve steps: out (1)in five samples steps: were 1) samples manufactured were manufactured in the form ofin ﬂatthe bareform sheets of flat withbare thesheets dimensions with the indimensions Figure1 by in wireFigure cutting 1 by machine;wire cutting (2) the machine; surface 2) of eachthe surfac samplee of was each burnished sample bywas the burnished 1000 grit abrasiveby the 1000 paper grit to dispelabrasive burrs; paper (3) to samples dispel wereburrs; rinsed 3) samples in distilled were water;rinsed (4)in distilled samples werewater; degreased 4) samples through were degreased the use of acetonethrough solvent; the use (5)of allacetone surfaces solvent; of samples 5) all surfaces were rinsed of samples with deionized were rinsed water with and drieddeionized by a blowerwater and for thedried pre-corroded by a blower experiment. for the pre-corroded experiment.

Figure 2. Schematic drawing of the sample preparation and the pre-corroded experiment procedure. Figure 2. Schematic drawing of the sample preparation and the pre-corroded experiment procedure. In this study, the pre-corroded experiment procedure can be devised as four main steps: (1) the pure NaClIn this crystals study, ofthe 50 pre-corroded g were weighed experiment by an electronic procedure balance can andbe devise pouredd as into four one main liter ofsteps: deionized 1) the waterpure NaCl and stirred crystals with of glass50 g rodwere at weighed an ambient by temperaturean electronic of balance (25 1 andC) forpoured 5 min; into (2) fourone groupsliter of ± ◦ ofdeionized numbered water samples and stirred were alternatelywith glass immersedrod at an ambient in 5% NaCl temperature solution atof an(25 ambient ± 1 °C) for temperature 5 min; 2) offour (25 groups1 C )of for numbered 0 h, 24 h, samples 48 h, and were 96 h,alternately respectively; immersed (3) the in corrosion 5% NaCl products solution were at an removed ambient ± ◦ bytemperature membrane of removal(25 ± 1 °C) solution for 0 h, (prepared 24 h, 48 h, with and 10096 h, mL respectively; HCl, 100mL 3) the deionized corrosion water products and 0.6were g C6H12N4);removed by (4) membrane all surfaces removal of samples solution were (prepared rinsed with with deionized 100 mL waterHCl, 100 and mL dried deionized by a blower water for and pit depth0.6 g C6H12N4); measurement. 4) all surfaces of samples were rinsed with deionized water and dried by a blower for pit depth measurement. 2.2. Pre-Corrosion Pit Measurements and Fatigue Test 2.2. Pre-Corrosion Pit Measurements and Fatigue Test To achieve the morphology of the corrosion surface and to determine the size and geometry of pre-corrosionTo achieve pits, the a morphology non-contact of Dektak150 the corrosion surface surface proﬁler and (Veeco to determine Instruments the size Shanghai and geometry Co., Ltd., of Shanghai,pre-corrosion China) pits, and a non-contact an S-4800 scanning Dektak150 electron surface microscope profiler (Hitachi,(Veeco Instruments Tokyo, Japan) Shanghai were used Co., in Ltd., this study.Shanghai, A region China) of and 30 mm an S-480020 mm scanning (along theelectron directions microscope of longitude (Hitachi, and Tokyo, transverse, Japan) respectively) were used for in × eachthis specimenstudy. A wasregion approximately of 30 mm arranged × 20 mm at the(along area ofthe pre-estimated directions fatigueof longitude fracture. and It istransverse, noted that therespectively) rate of corrosion for each changes specimen steadily was with approximately the increase arranged of pre-corroded at the timearea [of27 ],pre-estimated thus the relationship fatigue betweenfracture. theIt is corrosion noted that time the and rate the of depthcorrosion of pre-corroded changes steadily pits can with be the expressed increase by of an pre-corroded exponential time [27], thus the relationship between the corrosion time and the depth of pre-corroded pits can be expressed by an exponential function. Based on reference [28], the coefficient of exponential function can be determined by fitting the measured data, and exponential function expression can be described as:

Materials 2019, 12, 2130 4 of 13 function. Based on reference [28], the coeﬃcient of exponential function can be determined by ﬁtting Materialsthe measured 2019, 12, data, x FORand PEER exponential REVIEW function expression can be described as: 4 of 13

0.775 ϕ𝜑= 1.235 = 1.235t 𝑡. (1) where ϕφ isis thethe depthdepth ofof aa pre-corrodedpre-corroded pitpit ((µμm)m) andand tt isis thethe pre-corrodedpre-corroded timetime (h).(h). Based on the standard of ASTM E468-90 [[29],29], the fatigue performance of corroded specimens (24 h,h, 48 48 h, h, and and 96 h)96 wereh) were evaluated evaluated by a hydraulicby a hydraulic universal universal testing machine testing (Instron-8803,machine (Instron-8803, Norwood, Norwood,MA, USA) underMA, USA) a cyclic under load amplitudea cyclic load with amplitude a frequency with of 10 a Hz.frequency The loading of 10 operation Hz. The was loading force operationcontrolled was with force a proportional controlled with error a of proportional1%. A group error of un-corrodedof ±1%. A group specimens of un-corroded were also specimens tested as ± werea control also for tested fatigue as a studies. control Thefor fatigue stress ratio studies. was takenThe stress as 0.1, ratio and was the maximumtaken as 0.1, applied and the stresses maximum were 100applied MPa, stresses 200 MPa, were and 100 300 MPa, MPa, 200 respectively. MPa, and After 300 testing,MPa, respectively. the fractured After specimens testing, were the processedfractured specimensby cutting machinewere processed and the morphologyby cutting machine of the corrosion and the surface morphology was observed of the corrosion by surface surface proﬁler was and observedscanning electronby surface microscope. profiler and scanning electron microscope. The pre-corrosion pit reduced the fatigue life subs substantially,tantially, particularly the interacting pits and sharp pitspits [[30].30]. InIn thisthis study,study, the the Paris Paris theory theory [25 [2]5] was was applied applied to to analyze analyze the the relationship relationship between between the themorphology morphology of fatigue of fatigue cracks cracks and the and stress the state stress around state corrosionaround corrosion pits. According pits. According to Paris theory to Paris [25], theorythe stress [25], intensity the stress factor intensity of cracks factor can of be cracks described can be as: described as:

𝐾Ⅰ =𝜎√ 𝜋𝑎𝑓(𝛽) (2) KI = σ √πa f (β) (2) a 𝑎 β 𝛽== (3) b 𝑏 where KI1 isis thethe stressstress intensityintensity factorfactor ofof thethe crack,crack, σσ isis the e externalxternal stress stress under under the the plane plane stress stress state, state, and a is the crack length and b is the specimen width.width.

2.3. FE FE Model The FE analysis modelmodel ofof thethe 42CrMo42CrMo steel steel in in the the form form of of a a corroded corroded flat flat sheet sheet with with a thicknessa thickness of of6 mm 6 mm was was created created using using the HyperWorksthe HyperWorks software softwa (HyperWorksre (HyperWorks 11.0, 11.0, Altair Altair Corp., Corp., Troy, MI,Troy, USA). MI, USA).On the On basis the of basis the experiment of the experiment test, a single test, semi-ellipticala single semi-elliptical pit model pit was model conducted, was conducted, and the symmetry and the planesymmetry of the plane flatsheet of the and flatrefined sheet and mesh refined around mesh the around pit are shownthe pit inare Figure shown3. in Figure 3.

Figure 3. The FE analysis model. Figure 3. The FE analysis model. The CPS8 quadrilateral element type was adopted in the FE model and cracks were prefabricated on theThe surface CPS8 throughquadrilateral the use elemen of ant assigned type was seam adopted function inthat the wasFE providedmodel and by HyperWorks.cracks were Theprefabricated sweeping methodon the surface [31] was through used to generatethe use theof an mesh assigned in the integral seam function region and that the was singularity provided of theby HyperWorks.mesh was controlled The sweeping by the mesh method regeneration [31] was techniqueused to generate [32]. The the use mesh of the in abovethe integral techniques region [31 and,32] withthe singularity local reﬁnement of the andmesh appropriate was controlled local meshby the density mesh regeneration can improve thetechnique precision [32]. of theThe calculation. use of the above techniques [31,32] with local refinement and appropriate local mesh density can improve the precision of the calculation. Subsequently, the FE analysis model with a preset corrosion pit was imported into the ABAQUS software (ABAQUS 6.10, Dassault Systemes Simulia Corp., Johnston, RI, USA) to analyze the stress and fatigue performance of the specimens.

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Subsequently, the FE analysis model with a preset corrosion pit was imported into the ABAQUS software (ABAQUS 6.10, Dassault Systemes Simulia Corp., Johnston, RI, USA) to analyze the stress Materialsand fatigue 2019, 12 performance, x FOR PEER REVIEW of the specimens. 5 of 13

3.3. Results Results and and Discussion Discussion

3.1.3.1. Corrosion Corrosion Surface Surface Characterization Characterization WhenWhen the the 42CrMo 42CrMo specimens specimens were were immersed immersed in in Na NaClCl solution, solution, the the Cl Cl element element in in the the solution solution 2+ adheredadhered to thethe surfacesurface of of specimens specimens and and reacted reacted with with the Fethe inFe the2+ in metal the tometal form to a solubleform a clathrate,soluble clathrate,which resulted which inresulted the anodic in the dissolution anodic dissolution of the metal of surface the metal and thesurface formation and the of corrosionformation pits.of corrosionWith the increasepits. With of pre-corrodedthe increase of time, pre-corroded more metal time, dissolved more in metal the anode dissolved and thein the size anode of corrosion and the pit sizebecame of corrosion larger and pit larger became [33 ].larger The specimensand larger pre-corroded [33]. The specimens for 0 h, 24 pre-corroded h, 48 h, and 96for h 0 were h, 24 examined h, 48 h, andby an96 S-4800 h were scanning examined electron by an microscope S-4800 scanning and the morphologieselectron microscope of corrosion and surface the morphologies characterization of corrosionare shown surface in Figure characterization4. are shown in Figure 4.

(a) (b)

FigureFigure 4. 4. CorrosionCorrosion surface surface characterization: characterization: (a) (pre-corrodeda) pre-corroded for for0 h; 0 (b h;) pre-corroded (b) pre-corroded for 24 for h; 24 (c) h; pre-corroded(c) pre-corroded for 48 for h; 48 and h; and(d) pre-corroded (d) pre-corroded for 96 for h. 96 h.

AccordingAccording to FigureFigure4 ,4, corrosion corrosion surface surface characterization characterization can becan clearly be clearly observed observed and the and obvious the obviouscorrosion corrosion pits after pre-corrosionpits after pre-corrosion can be found can within be found the crack within source the area crack in each source diagram. area Asin showneach diagram.in Figure As4a, thereshown was in noFigure corrosion 4a, there pit onwas the no surface corrosion of specimens pit on the without surface pre-corrosion. of specimens Withwithout the pre-corrosion.pre-corrosion treatment,With the pre-corrosion Figure4b shows treatment, that there Fi weregure local4b shows micro-pits that there and pits were distributed local micro-pits densely. andWith pits the increasedistributed of pre-corrodeddensely. With time, the Figure increase4c,d showsof pre-corroded that corrosion time, pits Figure became 4c,d larger shows since that the corrosionsmall pits pits were became interconnected larger since to the form small larger pits corrosion were interconnected pits. A series to of form electrochemical larger corrosion corrosion pits. Aprocesses series of occurred electrochemical when the corrosion specimen processes was immersed occurred in the when NaCl the solution. specimen In this was study, immersed the corrosion in the NaClprocess solution. can be In generally this study, divided the corrosion into two proce stages:ss can 1) thebe generally initiation divided of the pits into stage two andstages: 2) the1) the pit initiationdevelopment of the stage. pits Instage the and ﬁrst stage,2) the adsorptionpit development and agglomeration stage. In the offirst chloride stage, ions adsorption took place and at agglomerationcertain weak sites of chloride and the ions corrosion took place pits formed. at certain In weak the second sites and stage, the the corrosion pits developed pits formed. as a result In the of secondthe anodic stage, dissolution the pits developed of the metal as a [ 34result–36]. of Thus, the anodic the small dissolution pits were of interconnected the metal [34–36]. to form Thus, larger the smallcorrosion pits were pits. interconnected to form larger corrosion pits. ToTo obtain obtain the effect eﬀect ofof thethe stressstress distribution distribution around around corrosion corrosion pits pits on on the the stress stress intensity intensity factor factor and andthe residualthe residual fatigue fatigue life of life corroded of corroded steel, thesteel, size the of size pre-corroded of pre-corroded pits should pits beshould accurately be accurately assessed assessed and the depth of pre-corroded pits can be measured by a surface profiler. The schematic diagram of pre-corrosion pits under the pre-corroded times 24 h, 48 h, and 96 h is shown in Figure 5. From Figure 5, one can see that the depth of the maximum corrosion pit can be regarded as the radius of a semi-circular surface crack. The depth of the maximum corrosion pit was measured by a surface profiler and an SEM.

Materials 2019, 12, 2130 6 of 13 and the depth of pre-corroded pits can be measured by a surface proﬁler. The schematic diagram of pre-corrosion pits under the pre-corroded times 24 h, 48 h, and 96 h is shown in Figure5. From Figure5, one can see that the depth of the maximum corrosion pit can be regarded as the radius of a semi-circular Materialssurface 2019 crack., 12, Thex FOR depth PEER ofREVIEW the maximum corrosion pit was measured by a surface proﬁler and an6 SEM. of 13

(a)

(b)

(c)

Figure 5. 5. TheThe schematic schematic diagram diagram of ofpre-corrosion pre-corrosion pits pits under under the thedifferent diﬀerent pre-corroded pre-corroded times: times: (a) pre-corroded(a) pre-corroded for for24 h; 24 ( h;b) (pre-corrodedb) pre-corroded for for48 h; 48 and h; and (c) (pre-corrodedc) pre-corroded for for96 96h. h.

3.2. Fatigue Fatigue Test Test Results and Discussion Pre-corrosionPre-corrosion not not only only reduces reduces residual residual fatigue fatigue li life,fe, but but also also leads leads to to the the change change of of the stress intensityintensity factor.factor. UnderUnder the the cyclic cyclic load load with with a frequency a frequency of 10 of Hz, 10 theHz, local the stresslocal concentrationstress concentration around aroundthe corrosion the corrosion pits accelerated pits accelerated the process the of process fatigue of damage fatigue and damage resulted and in resulted the reduced in the fatigue reduced life fatigueof the specimen. life of the Three specimen. constant Three stress constant levels st (100ress MPa, levels 200 (100 MPa, MPa, and 200 300 MPa, MPa) and were 300 carried MPa) outwere to carriedpre-corroded out to specimenspre-corroded for specimens 0 h, 24 h, 48 for h, 0 and h, 24 96 h, h. 48 The h, fatigueand 96 testingh. The resultsfatigue of testing specimens results with of specimensdifferent exposure with different times areexposure shown times in Table are2 .shown in Table 2. Table2 shows that the fatigue life decreased obviously with the increase of pre-corroded time under the same constantTable stress 2. The level. fatigue Furthermore, testing results the of fatigue specimens life decreasedwith different approximately exposure times. by more than 12% when the pre-corroded time was doubled, and the fatigue life decreased approximately by more than Fatigue Life (×105 Cycles) 11% when the appliedPre-Corroded stress level was Time doubled, (h) indicating that both pre-corroded time and applied 100 MPa 200 MPa 300 MPa stress level can significantly affect the fatigue life of specimens, which shows a good agreement with 0 11.26 9.95 7.29 the previous works [37,38]. Although the external load is normally invariant in practical engineering 24 9.81 7.91 5.47 structures and residual fatigue life usually depends on corrosion surface condition and the nominal 48 7.52 6.21 4.09 96 5.03 3.91 2.61

Table 2 shows that the fatigue life decreased obviously with the increase of pre-corroded time under the same constant stress level. Furthermore, the fatigue life decreased approximately by more than 12% when the pre-corroded time was doubled, and the fatigue life decreased approximately by more than 11% when the applied stress level was doubled, indicating that both

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stress level, the raised nominal stress caused by the reduction of the cross-sectional area of components due to corrosion still decreases the fatigue life of steel [39]. After fatigue testing, the fracture surface of the corroded specimens under 100 MPa was observed by SEM, and the results are shown in Figure6. Materials 2019, 12, x FOR PEER REVIEW 7 of 13 Table 2. The fatigue testing results of specimens with diﬀerent exposure times. pre-corroded time and applied stress level can significantlyFatigue Life affect ( 105 Cycles)the fatigue life of specimens, which shows a goodPre-Corroded agreement Time with (h) the previous works [37,38].× Although the external load is 100 MPa 200 MPa 300 MPa normally invariant in practical engineering structures and residual fatigue life usually depends on corrosion surface condition 0and the nominal stress 11.26 level, the 9.95raised nominal 7.29 stress caused by the 24 9.81 7.91 5.47 reduction of the cross-sectional48 area of components 7.52 due to corrosion 6.21 still decreases 4.09 the fatigue life of steel [39]. After fatigue testing,96 the fracture 5.03surface of the 3.91corroded specimens 2.61 under 100 MPa was observed by SEM, and the results are shown in Figure 6.

(a) (b)

FigureFigure 6. The 6. The fracture fracture surface surface of the of thecorroded corroded specimens specimens under under 100 MPa: 100 MPa: (a) pre-corroded (a) pre-corroded for 0 forh; (b 0) h; pre-corroded(b) pre-corroded for 24 forh; ( 24c) h;pre-corroded (c) pre-corroded for 48 for h; and 48 h; (d and) pre-corroded (d) pre-corroded for 96 for h. 96 h.

FigureFigure 6a6 showsa shows the the fracture fracture surface surface of of the the non- non-corrodedcorroded specimen specimen under under the the constant constant stress stress of of 100100 MPa, MPa, and and it can it can be be seen seen that that the the crack crack propagated propagated along along grain grain boundaries. boundaries. Figures Figure 6b–d6b–d reveal reveal thatthat the the crack crack originated originated at atthe the tip tip of ofthe the corrosion corrosion pit pit and and propagated propagated along along the the grain grain boundaries, boundaries, andand the the white white highlight highlight area area phenomena phenomena was was caused caused by by the the deposition of corrosive elements.elements. DueDue to to thethe existenceexistence ofof corrosioncorrosion defects,defects, stress stress concentration concentration occurred occurred around around the the sharp sharp intrusion intrusion at at the the pit pitbottom bottom and and accelerated accelerated the the process process of of fatigue fatigue damage. damage.

3.3. FE Investigations 3.3. FE Investigations BasedBased on on Equations Equations (1)–(3), (1)–(3), ABAQUS ABAQUS was was app appliedlied to tocompute compute the the stress stress intensity intensity factor factor correspondingcorresponding to todifferent diﬀerent corrosion corrosion pit pit morphology morphology characteristics, characteristics, which which were were depicted depicted in inthe the previousprevious section. section. The The same same material material properties properties an andd loading loading conditions conditions in in Section 2.2 were appliedapplied to to thethe FEFE models,models, andand thethe computedcomputed stressstress distributionsdistributions aroundaround the the crack crack tip tip are are shown shown in in Figure Figure7 .7. TheThe ashy ashy area area in inFigure Figure 7 represents7 represents the the yielding yielding zone zone in specimens. in specimens. The The numbers numbers 1, 2, 1, and 2, and3 in 3 Figurein Figure 7 denomination7 denomination represent represent the theconstant constant stress stress level level of of100 100 MPa, MPa, 200 200 MPa, MPa, and and 300 300 MPa, MPa, respectively.respectively. From From Figure Figure 7,7 it, itcan can be be seen seen th that,at, under under the the same same pre-corroded pre-corroded time, time, the the yielding yielding zone increased with the increase of applied loads through the transverse comparison. Under the same applied loads, it can be seen that the yielding zone increased with the increase of the size of pre-corrosion pits. Moreover, the FEM investigations revealed that the rate of crack extension accelerated when the crack length increased.

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zone increased with the increase of applied loads through the transverse comparison. Under the same applied loads, it can be seen that the yielding zone increased with the increase of the size of pre-corrosion pits. Moreover, the FEM investigations revealed that the rate of crack extension accelerated when the crack length increased. Materials 2019, 12, x FOR PEER REVIEW 8 of 13

0 h, 100 MPa 0 h, 200 MPa 0 h, 300 MPa

(a1) (a2) (a3) 24 h, 100 MPa 24 h, 200 MPa 24 h, 300 MPa

(b1) (b2) (b3) 48 h, 100 MPa 48 h, 200 MPa 48 h, 300 MPa

(c1) (c2) (c3) 96 h, 100 MPa 96 h, 200 MPa 96 h, 300 MPa

(d1) (d2) (d3)

FigureFigure 7. 7.TheThe stress stress distributions distributions around around the the crack crack tip. tip. (a1), (a1 ),(a2), (a2 ),and and (a (3):a3 ):non-corroded non-corroded specimen specimen underunder the the different different cons constanttant stress stress levels; levels; (b (1),b1 (),b (2),b2 and), and (b (3):b3 ):24 24h pre-corroded h pre-corroded specimen specimen under under the the differentdifferent constant constant stress stress levels; levels; (c1), (c1 ),(c2), (c2 ),and and (c3): (c3 ):48 48h pre-corroded h pre-corroded specimen specimen under under the the different different constantconstant stress stress levels; levels; and ((d1d1),), (d2(d2),), and and (d3 (d):3): 96 96 h pre-corrodedh pre-corroded specimen specim underen under the di fftheerent different constant constantstress levels.stress levels.

3.4.3.4. Regression Regression Formula Formula of ofthe the Stress Stress Intensity Intensity Factor Factor ByBy the the adoption adoption of ofEquations Equations (2) (2) and and (3), (3), the the stress stress intensity intensity factor factor around around the the crack crack tip tip in inthe the processprocess of ofcrack crack propagation propagation for for non-corroded non-corroded spec specimensimens can can be be calculated calculated and and compared compared with with the the stressstress intensity intensity factor factor that that was was computed computed by by ABAQUS ABAQUS software software to tovalidate validate the the accuracy accuracy of ofthe the FE FE simulationsimulation results. results. A Acomparison comparison of ofthe the stress stress intensity intensity factor factor by by theoretical theoretical Paris Paris formula formula and and FE FE simulationsimulation is isshown shown in inFigure Figure 8.8 .

Materials 2019, 12, 2130 9 of 13 Materials 2019, 12, x FOR PEER REVIEW 9 of 13

FigureFigure 8. 8.Comparison Comparison of of the the stress stress intensity intensity factor factor by by theoretical theoretical Paris Paris formula formula and and FE FE simulation. simulation. The maximum percentage error of the calculated stress intensity factor between the theoretical The maximum percentage error of the calculated stress intensity factor between the theoretical Paris formula and the FEM is 4.7%, which indicates that the theoretical calculation agreed well with the Paris formula and the FEM is 4.7%, which indicates that the theoretical calculation agreed well with simulated results. Through the integration of the ashy area around the crack tip in Figure7, the stress the simulated results. Through the integration of the ashy area around the crack tip in Figure 7, the intensity factor of the crack tip for pre-corroded specimens can be obtained and the relationship between stress intensity factor of the crack tip for pre-corroded specimens can be obtained and the the stress intensity factor at the crack tip and the depth of the pre-corrosion pits can be established. relationship between the stress intensity factor at the crack tip and the depth of the pre-corrosion Figure9 shows the relationship between the stress intensity factor at the crack tip and the size pits can be established. of pre-corrosion pits. By using the numerical fitting method, the regression formula to represent the Figure 9 shows the relationship between the stress intensity factor at the crack tip and the size relationship between the stress intensity factor and the depth of the pre-corrosion pits is derived as: of pre-corrosion pits. By using the numerical fitting method, the regression formula to represent the relationship between the stress intensityK factor and the depth of the pre-corrosion pits is derived as: IS = 0.273e3.378ϕ + 0.731 (4) KI0𝐾 = 0.273𝑒. 0.731 (4) 𝐾 where KIS is the pre-corroded stress intensity factor, KI0 is the non-corroded stress intensity factor, and ϕwhereis the depthKIS is the of corrosion pre-corroded pits. stress The fatigue intensity life factor, can be estimatedKI0 is the non-corroded according to the stress Paris intensity formula factor, [25]. Theand Paris φ is formulathe depth is of shown corrosion as follows: pits. The fatigue life can be estimated according to the Paris formula da [25]. The Paris formula is shown as follows: = C∆Km (5) dN 𝑑𝑎 where da/dN is the fatigue crack propagation, ∆K is the=𝐶∆𝐾 stress intensity factor at the tip of cracks, and C(5) 𝑑𝑁 and m are the equation coefficients, respectively. For the 42CrMo steel, the coefficients of C and m are takenwhere as da/dN 4.349 is 10the12 fatigueand 3.07, crack respectively propagation, [40]. Δ ThroughK is the thestress integration intensity of factor Equation at the (5), tip the of fatigue cracks, × − lifeand of C 42CrMo and m steelare the can equation be estimated coefficients, as: respectively. For the 42CrMo steel, the coefficients of C −12 and m are taken as 4.349 × 10 and 3.07, respectivelyZ [40]. Through the integration of Equation (5), da the fatigue life of 42CrMo steel can be estimatedN = as: (6) ( )3.07 C ∆K𝑑𝑎 𝑁= . (6) By combining Equations (4) and (6), the relationship𝐶(∆𝐾) between the fatigue life of pre-corroded and non-corrodedBy combining specimens Equations can be (4) written and (6), as: the relationship between the fatigue life of pre-corroded

and non-corroded specimens can be written as: 3.07 N = e3.378ϕ + − N C 0.273 .0.731 .0 (7) 𝑁 = (0.273𝑒 0.731) 𝑁 (7) wherewhere NNCC isis the the fatigue fatigue life lifeof pre-corroded of pre-corroded specimens specimens and N0 andis theN fatigue0 is the life fatigueof non-corroded life of non-corrodedspecimens. specimens.

MaterialsMaterials 20192019,, 1212,, 2130x FOR PEER REVIEW 1010 ofof 1313

Figure 9. The relationship between the stress intensity factorfactor andand thethe depthdepth ofof pre-corrosionpre-corrosion pits.pits. Under diﬀerent stress ranges and corrosion degrees, the residual fatigue life of pre-corrosion Under different stress ranges and corrosion degrees, the residual fatigue life of pre-corrosion specimens is predicted through the use of Equation (7). The comparison of predicted fatigue life and specimens is predicted through the use of Equation (7). The comparison of predicted fatigue life experimental fatigue life is summarized in Table3. and experimental fatigue life is summarized in Table 3.

Table 3. Comparison of predicted fatigue life and experimental fatigue life. Table 3. Comparison of predicted fatigue life and experimental fatigue life. Corrosion Pit Size Load Experimental Values Predicted Values Corrosion Pit Load Experimental5 Values Predicted5 Values Errors (%) (µm) (Stress/MPa) ( 10 Cycles) ( 10 Cycles) Errors (%) Size (μm) (Stress/MPa) (×10× 5 Cycles) (×10× 5 Cycles) 100 9.82 10.13 3.15 62 100200 9.82 7.53 10.13 7.85 3.15 4.08 62 200300 7.53 5.02 5.317.85 4.08 5.46 300100 5.02 8.24 8.735.31 5.46 5.61 147 100200 8.24 6.32 6.758.73 5.61 6.37 147 200300 6.32 4.21 4.536.75 6.37 7.06 300100 4.21 5.62 6.614.53 7.06 8.17 255 200 4.43 5.24 8.85 100 5.62 6.61 8.17 300 2.95 3.25 9.23 255 200 4.43 5.24 8.85 300 2.95 3.25 9.23 Table2 shows that the fatigue life predicted by the coupled formula agreed well with experiment results,Table and 2 the shows percentage that the errors fatigue between life predictedpredicted values by the and coupled experimental formula values agreed were well less thanwith 10%.experiment In the caseresults, of low and corrosion the percentage degrees errors and low between stress levels,predicted the percentagevalues and errorsexperimental were less values than 5%.were With less thethan increase 10%. In ofthe pre-corroded case of low corrosion time and degrees stress levels, and low the percentagestress levels, error the percentage was increased errors to approximatelywere less than 9.3%.5%. With The stressthe increase intensity of factorpre-corr at theoded tip time of cracks and stress was calculated levels, the on percentage the basis oferror the linearwas increased elastic model to approximately and the morphology 9.3%. The of stress the pre-corrosionintensity factor pits at simulatedthe tip of cracks by FEM was took calculated pre-set defectson the basis in the of middle the linear of the elastic specimen, model while and thethe practicalmorphology corrosion of the pits pre-corrosion had the characteristics pits simulated of theby unevenFEM took distribution pre-set defects and sizein the of themiddle specimen. of the sp Thus,ecimen, the while percentage the practical errors betweencorrosion the pits predicted had the valuescharacteristics and the experimentalof the uneven values distribution were slightly and increasedsize of the with specimen. the increase Thus, of pre-corrodedthe percentage time errors and stressbetween levels. the predicted values and the experimental values were slightly increased with the increase of pre-corroded time and stress levels. 4. Recommendation for Future Research 4. RecommendationIn this research, thefor eFutureﬀect of Research pre-corrosion pits on the residual fatigue life of the 42CrMo steel was experimentally and numerically studied. It was demonstrated in this paper that the corrosion pit size In this research, the effect of pre-corrosion pits on the residual fatigue life of the 42CrMo steel can be used as a damage index to assess the residual fatigue life. Therefore, the monitoring of corrosion was experimentally and numerically studied. It was demonstrated in this paper that the corrosion pit size is important not only to know the corrosion status, but also to predict the residual fatigue pit size can be used as a damage index to assess the residual fatigue life. Therefore, the monitoring life of the steel. With the recent development of structural health monitoring technology [41–44], of corrosion pit size is important not only to know the corrosion status, but also to predict the especially the piezoceramic-based active sensing method [45–47], electromechanical impedance (EMI) residual fatigue life of the steel. With the recent development of structural health monitoring approach [48–50], and imaging technology [51,52], it is now possible to monitor corrosion pit number technology [41–44], especially the piezoceramic-based active sensing method [45–47], electromechanical impedance (EMI) approach [48–50], and imaging technology [51,52], it is now

Materials 2019, 12, 2130 11 of 13 and size [10]. Future work should include the real-time monitoring of the onset and growth of the corrosion pit and the prediction of the residual fatigue life of the 42CrMo steel specimens. Future works should also focus on the quantitative analysis of corrosion pits to improve the predicted accuracy of the residual fatigue life for the corroded 42CrMo steel.

5. Conclusions In summary, this study investigated the eﬀect of pre-corrosion pits on the residual fatigue life of the 42CrMo steel. It was found that higher stress amplitude and longer pre-corroded time signiﬁcantly decreased the residual fatigue life of the steel. The investigation of the residual fatigue life of pre-corrosion specimens was conducted through the use the regression formula and experimental measures, and the fatigue life predicted by the regression formula agreed well with experiment results. Moreover, it was found that the rate of crack extension accelerated when the crack length increased. It is also demonstrated in this paper that the corrosion pit size can be used as a damage variable to assess the residual fatigue life. The recommendation for future research is to monitor corrosion pit characteristics and to predict the residual fatigue life of the 42CrMo steel.

Author Contributions: Conceptualization, D.L.; methodology, D.L. and J.Z.; software, D.L. and Y.L.; validation, Y.L.; formal analysis, X.X.; writing—original draft preparation, D.L.; writing—review and editing, X.X.; visualization, Y.L.; supervision, X.X.; project administration, D.L. Funding: This research was funded by Hubei Superior and Distinctive Discipline Group of “Mechatronics and Automobiles” (No. XKQ2019009). Conﬂicts of Interest: The authors declare no conﬂict of interest.

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