Influence of Micro-Structure on the Fatigue Crack Propagation in Bridge Steel

P oceedings 2018, 2, 470; doi:10.3390/ICEM18-05373 www.mdpi.com/jou nal/p oceedings P oceedings In luence o Mic o-S uc u e on he Fa igue C ack P opaga ion in B idge S eel † S anisla Sei l 1,2,*, Pe Mia ka 1,2, Pa el Poko ný 1, S anisla a Fin o á 1 and Jan Klusák 1 1 Ins i u e o Physics o Ma e ials, Academy o Science o he Czech Republic, Zizko a 22 B no 616 62, Czech Republic; pe .mia ka@ u .cz (P.M.); poko [email protected] (P.P.) in o [email protected] (S.F.); [email p o ec ed] (J.K.) 2 Facul y o Ci il Enginee ing, B no Uni e si y o Technology, Ve e i 331/95 B no 602 00, Czech Republic * Co espondence: [email p o ec ed]; Tel.: +420-532-290-361. † P esen ed a he 18 h In e na ional Con e ence on Expe imen al Mechanics (ICEM18), B ussels, Belgium, 1–5 July 2018. Published: 19 June 2018 Abs ac : The use o high s eng h s eels (HSS) allows designing ligh e , slende e and simple s uc u es wi h high s uc u al pe o mance. In gene al, he use o HSS leads o weigh educ ion o he whole s uc u e, which compensa es he highe cos o such a ma e ial compa ing o he con en ional cons uc ion s eels. Knowledge o he a igue esis ance o ma e ial plays he key ole du ing design and main enance o he b idge s uc u es. This con ibu ion b ings a compa ison o he a igue c ack g ow h esis ance o S355 J0 s eel. Di e ences in mic os uc u e and he ex u e o ma e ial s uc u e could gene ally play a ole in he a igue c ack g ow h. This s udy shows ha in he case o s udied s eel ex u e o ma e ial s uc u e has an in luence on ma e ial a igue beha io in Pa is’ law egime. Keywo ds: b idge s eel; Pa is’ law; mic os uc u e; s ess in ensi y ac o ; a igue p ope ies; S355 J0 1. In oduc ion Fa igue c ack p opaga ion, an impo an pa o he a igue li e o a b idge componen , is con olled by he local p ope ies a he c ack ip. The e o e, in he case o b idge s eels wi h a he e ogeneous mic os uc u e, i is di icul o cha ac e ize hei a igue p ope ies since he c ack p opaga es h ough di e en mic os uc u al egions wi h di e en mechanical p ope ies. By inding he e ec o each phase on a igue c ack p opaga ion, a igue p ope ies o b idge s eels can be well unde s ood and consequen ly op imized. The aim o his con ibu ion is o compa e expe imen ally ob ained a igue g ow h a es o long c acks in wo di e en mic os uc u es o S355 J0 s eel g ade and o de e mine he in luence o chemical composi ion and s uc u e ex u e on he beha iou o long a igue c acks in his s eel g ade. The a igue c ack p opaga ion is cha ac e ized by means o c ack g ow h cu es expe imen ally de e mined on compac ension (CT) specimens by using ASTM E647 [1] s anda d. The expe imen ally ob ained esul s a e discussed wi h esul s al eady published in [2,3]. This con ibu ion aims o ex end he expe imen al s udy done by Sei l e al. published in [4]. 2. Theo e ical Backg ound The ac u e mechanics-based app oach is used o he li e ime p edic ion o s uc u es wi h exis ing c acks. The ma e ial cha ac e is ic, i.e., he c ack g ow h cu e, is expe imen ally de e mined on no ched specimens, mos o en on CT specimens. The e exis wo basic es ing app oaches o c ack g ow h a e de e mina ion which a e based ei he on K-dec easing o on K-inc easing P oceedings 2018, 2, 470 2 o 6 p ocedu e (K is he s ess in ensi y ac o ) [1]. The a igue c ack g ow h a e o applied loading is de ined by he c ack leng h inc emen o gi en numbe o loading cycles. Pa is’ law [5], exp essed by he Equa ion (1)   =(∆)  (1) is o en used o he desc ip ion o he a igue c ack g ow h. C and m a e ma e ial cons an s, da/dN is he a igue c ack g ow h a e (da—c ack leng h inc emen , dN—co esponding numbe o cycles) and ΔK is he s ess in ensi y ac o ange. The numbe o load cycles o ailu e (N ) can be calcula ed by in eg a ing he c ack p opaga ion be ween an ini ial c ack leng h (ai) and c i ical c ack leng h (ac), Equa ion (2). = (∆)   , (2) The s ess in ensi y ac o anges o c acks in CT specimens can be compu ed using Equa ion (3) acco ding o ASTM E647 S anda d [1]. ∆ = ∆ √ () ()  (0.886 + 4.64 − 13.32+ 14.72−5.6 ), (3) whe e α = a/W, a is he c ack leng h, W is he wid h o he specimen, B is he hickness o he specimen and ΔF is he applied load ange. The c ack leng h inc emen is calcula ed as an a e age alue o wo c ack leng h measu emen s pe o med on bo h sides o he CT specimen du ing he expe imen . In his s udy he K-dec easing me hod acco ding o he ASTM E647 [1] was used o ob ain he alues nea he h eshold alues. F om his poin , he cons an load alue was used o he es ima ion o he c ack g ow h a e o he es ed specimens in he Pa is’ egion. CT Specimen The es ed CT specimens (see Figu e 1-le ) had dimensions: L = 62.5 mm, W = 50 mm, B = 10 mm, D =13 mm, an = 12.5 mm, H/2 = 30 mm and he angle β 1 = 60°. (a) (b) Figu e 1. CT es specimen—geome y (a) and ac ual es se up (b). The a igue c ack g ow h expe imen s we e ca ied ou a a compu e -con olled es ing machine (Amsle —20 kN, see Figu e 1 igh ). Tes s we e conduc ed unde load con ol. The s ess a io R = P oceedings 2018, 2, 470 3 o 6 Fmin/Fmax = 0.1, whe e Fmin and Fmax e e o he minimum and maximum load o a sinusoidal wa e in each cycle. The load equency used o he es s a ied om 96 ( o he sho es c acks) o 42 Hz ( o he longes c acks). The con olled alues o empe a u e and ela i e humidi y we e 23 ± 2 °C and 50%, espec i ely. 3. Ma e ial The chemical composi ion o he in es iga ed s eel g ade is speci ied in EN 10025-2:2004 s anda d [6] and is p esen ed in Table 1. Chemical composi ion o he expe imen al ma e ial was e i ied by p oduce and i is in ag eemen wi h he s anda d p esen ed in his pape . Table 1. Chemical composi ion in pe cen age by weigh (max. w .%) o he used s eel g ades acco ding o EN 10025-2:2004 s anda d [6]. S eel G ade C Mn Si P S N Cu CEV S355 J0 0.2 1.6 0.55 0.035 0.035 0.012 0.55 0.47 The mic os uc u e o he es ed ma e ial was c ea ed wi h polyhed al g ains o e i e and pea li e, while he pea li ic colonies a e elonga ed in he olling di ec ion, Figu e 2. The a e age g ain size es ima ed wi h linea in e sec ion me hod was 13.6 ± 1.9 μm o he S355 J0 s eel. Small pa icles p esen in he g ains and on he g ain bounda ies we e obse ed in in es iga ed specimen. (a) (b) Figu e 2. S uc u e o specimen S355_J0_FM (a) and S355_J0_RM (b) made om he HS S355 J0 g ade, he c ack was p opaga ing in he ho izon al di ec ion; e ched wi h 2% Ni al, ligh op ical mic oscope 4. Resul s and Discussion The expe imen al measu emen s we e done on wo di e en specimens made om S355 J0 ma e ial. These specimens had di e en su ace s uc u e. One specimen showed ine su ace s uc u e and he o he one showed ough su ace s uc u e, he e o e specimens we e ma ked as “S355_J0_FM”, “S355_J0_RM” espec i ely. The ma e ial cons an s C and m measu ed om he Pa is’ law egion o hese wo specimens we e compa ed o he da a published by de Jesus [2]. Values o he exponen m can ange om 2.0 o 7.0 wi h mos alues being be ween 3.0 and 4.0 [7]. The measu ed ma e ial cons an m shows good ag eemen wi h da a om li e a u e S355 J0 s eel g ade, compa ison o he expe imen al da a a e s a ed in he Table 2. To quan i y he in luence o he mic os uc u e on he a igue c ack g ow a e o he S355 J0 s eel a c ack g ow a es unde he cons an alue o ΔKI we e measu ed. The same alue o ΔKI was chosen as 20 MPam1/2 hen c ack g ow h a es da/dN we e measu ed. The e alua ed c ack g ow h a e da/dN o S355_J0_FM is 4.2 × 10−5 mm/cycle and o S355_J0_RM specimen is 2.5 × 10−5 mm/cycle. This di e ence can be seen (ma ked by dash line) in Figu e 3. P oceedings 2018, 2, 470 4 o 6 Table 2. The Compa ison o ma e ial cons an s C and m, om expe imen al measu emen and li e a u e de Jesus e al. [2]. Ma e ial C [mm/(cycle⋅MPa⋅m0.5)] m [-] de Jesus 6.0 × 10−10 3.561 S355_J0_FM 1.0 × 10−8 2.697 S355_J0_RM 6.0 × 10−10 3.553 Figu e 3. Compa ison o he a igue c ack g ow h a es o S355_J0_FM and S355_J0_RM specimens and es ima ion o he c ack g ow a es. (a) (b) (c) (d) Figu e 4. The compa ison o he mic os uc u es wi h wo magni ica ions 200 μm and 50 μm o he S355_J0_FM (a) 200 μm (b) 50 μm and S355_J0_RM (c) 200 μm and (d) 50 μm a same alue o s ess in ensi y ange ΔKI = 20 MPam1/2 wi h a ious c ack p opaga ion a e. 1.0E-06 1.0E-05 1.0E-04 1.0E-03 110100 da/dN [mm/cycle] ΔK I [MPam 1/2 ] S355_J0_FM S355_J0_RM 1×10 -3 1×10 -4 1×10 -5 1×10 -6 2.5×10 -5 4.2×10 -5 20 P oceedings 2018, 2, 470 5 o 6 Fo his cons an alue o ΔKI = 20 MPam1/2 om gi en posi ion om measu emen a mic os uc u e o he specimen was in es iga ed. The di e ence o mic os uc u e is show in Figu e 4. 5. Conclusions In his pape he in luence o he ma e ial mic os uc u e on he a igue c ack a es o he S355 J0 s eel g ade was in es iga ed. This e ec can be exp essed by means o changes o he ma e ial cons an s in he Pa is’ law. These changes o ma e ial cons an s due o mic os uc u e can lead o he signi ican educ ion o a igue li e ime o he s uc u e made om s eel wi h ine mic os uc u e. These a igue p ope ies o S355 J0 will be used in u he p obabilis ic e alua ion e.g., [8–10] and a igue modelling o calcula ion as p esen ed in e.g., [11–16]. Au ho Con ibu ions: S.S., P.M. and J.K. ha e p epa ed analyzes and ha e analyzed he measu ed expe imen al da a, P.P. has pe o med expe imen al measu emen s and S.F. has cap u ed mic os uc u e o he specimens. Acknowledgmen s: This pape has been w i en wi h inancial suppo om he p ojec No. 17-01589S suppo ed by he Czech Science Founda ion. The second au ho is B no Ph.D. Talen Schola ship Holde — Funded by he B no Ci y Municipali y. Con lic s o In e es : The au ho s decla e no con lic o in e es . Re e ences 1. ASTM E647. S anda d es me hod o measu emen o a igue c ack g ow h a es. In Annual book o as m s anda ds. Am. Soc. Tes . Ma e . 1991, 3, 591–629. 2. De Jesus, A.M.P.; Ma os, R.; Fon ou a, B.F.C.; Rebelo, C.; Simões da Sil a, L.; Veljko ic, M. A compa ison o he a igue beha io be ween s355 and s690 s eel g ades. J. Cons uc . S eel Res. 2012, 79, 140–150. 3. Adedipe, O.; B ennan, F.; Kolios, A. Re iew o co osion a igue in o sho e s uc u es: P esen s a us and challenges in he o sho e wind sec o . Renew. Sus ain. Ene gy Re . 2016, 61, 141–154. 4. Sei l, S.; Mia ka, P.; Klusák, J.; Fin o á, S.; Kunz, L. Compa ison o he a igue c ack p opaga ion a es in S355 J0 and S355 J2 s eel g ades. Key Eng. Ma e . 2018, a e e ision in p ess. 5. Pa is, P.; E dogan, F. A c i ical analysis o c ack p opaga ion laws. J. Basic Eng. 1963, 85, 528–533. 6. EN 10025—Pa 2: Technical Deli e y Condi ions o Non-Alloy S uc u al S eels. In Ho Rolled P oduc s o S uc u al S eels; Eu opian Comi ee o S anda iza ion: Gene a, Swi ze land, 2004; p. 33. 7. B anco, R.; An unes, F.V.; Fe ei a, J.M.; Sil a, J.M. De e mina ion o Pa is law cons a n s wi h a e e se enginee ing echnique. Eng. Fail. Anal. 2008, 16, 631–638 8. Fe nández Can eli, A.; P zybilla, C.; Nogal, M.; López Aenlle, M.; Cas illo, E. 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P obabilis ic p edic ion o a igue damage based on linea ac u e mechanics. F a u a ed In eg i a S u u ale 2017, 11, 143–159. 15. K ejsa, M.; Janas, P.; K ejsa, V.; Kala, Z.; Sei l, S. DOP oC-based eliabili y assessmen o s eel s uc u es exposed o a igue. Pe spec . Sci. 2016, 7, 228–235. P oceedings 2018, 2, 470 6 o 6 16. K ejsa, M.; Sei l, S.; B ozo sky, J.; Lehne , P. Fa igue damage p edic ion o sho edge c ack unde a ious load: Di ec Op imized P obabilis ic Calcula ion. P ocedia S uc . In eg . 2017, 5, 1283–1290. ©2018 by he au ho s. Licensee MDPI, Basel, Swi ze land. This a icle is an open access a icle dis ibu ed unde he e ms and condi ions o he C ea i e Commons A ibu ion (CC BY) license (h p://c ea i ecommons.o g/licenses/by/4.0/).