COMBINED HIGH AND LOW CYCLE FATIGUE MODEL FOR PREDICTION OF STEEL BRIDGE LIVES

Transcription

1 505 COMBINED HIGH AND LOW CYCLE FATIGUE MODEL FOR PREDICTION OF STEEL BRIDGE LIVES M. OHGA *, K. KARUNANANDA, P.B.R. DISSANAYAKE 2 and S.A.S.C. SIRIWARDANE 3 Department of Cvl and Envronmental Engneerng, Ehme Unverst, Matsama, Japan 2 Department of Cvl Engneerng, Unverst of Peradena, Peradena, Sr Lanka 3 Department of Cvl and Envronment Engneerng, Unverst of Rhna, Galle, Sr Lanka ABSTRACT A new fatge model s presented to predct lfe of steel brdges for combned hgh and low ccle fatge. It conssts of a modfed stran-lfe crve and a new stran based damage ndex. The damage varable s based on a modfed von Mses valent stran to accont for effects of loadng non-proportonalt and stran path orentaton n mltaxal stress state. The proposed model was verfed wth expermental test reslts of two materals, avalable n the lteratre. Then, the proposed model was appled to a wroght ron ralwa brdge to estmate the fatge lfe de to sal traffc and earthqake loadngs. The obtaned reslts confrm the mportance and effectveness of the proposed model over commonl sed Mner s rle based lfe predcton of steel brdges. Kewords: Hgh ccle fatge, Low ccle fatge, Steel brdges, Lfe predcton, Earthqake loadng.. Introdcton Brdges are generall sbjected to hgh ccle fatge (HCF) de to low ampltde loadng b sal traffc drng ther servce lfe. However, the ma be sbjected to low ccle fatge (LCF) de to hgh ampltde loadngs sch as earthqake loadngs. The combned damage of HCF and LCF ma be a reason for a mch redced lfe (Kondo and Oka 2007). Most of fatge lfe estmaton of brdges s concentrated on mltaxal hgh ccle fatge. There s almost no lteratre consderng the combned damage of HCF and LCF of brdges. In other felds sch as arcraft engneerng, von Mses valent stran and Coffn-Manson stran-lfe crve are sed wth the Mner s rle as the general method to estmate the lfe for combned damage of HCF and LCF (Sresh 998). However, von Mses valent stran cannot captre the effects de to non-proportonal loadng and orentaton of stran path (Borod and Strzhalo 2000). The Mner s rle s the smplest and the most wdel sed fatge lfe predcton technqe. However nder man varable ampltde loadng condtons, Mner s rle based lfe predctons have been fond to be nrelable snce t cannot captre loadng sence effect (Srwardane et al. 2008). These reasons rase the qeston abot accrac of the Mner s rle based lfe estmaton for combned damage of HCF and LCF n brdges whch are generall sbjected varable ampltde * Correspondng athor, Tel/Fax: , E-mal: ohga@cee.ehme-.ac.jp

2 506 loadng and mltaxal stress state. Therefore, t s necessar to have a dfferent model, whch s based on commonl avalable materal propertes, to estmate more accratel the lfe for combned damage of HCF and LCF de to varable ampltde loadng. The objectve of ths paper s to propose a new model to accratel estmate the fatge lfe (crack ntaton lfe) when a brdge s sbjected to combned damage of HCF and LCF. Intall, the proposed combned HCF and LCF s presented. Then, verfcaton of the model s dscssed. Fnall, the proposed model s appled to an exstng ralwa brdge to estmate fatge lfe. 2. Proposed fatge model Ths secton proposes the new fatge model to estmate lfe of steel strctres. Intall, the detals relevant to proposed damage varable, modfed stran-lfe fatge crve are dscssed. Then, the proposed damage ndcator s explaned. 2.. Damage varable The damage varable for combned HCF and LCF s gven as (Borod and Strzhalo 2000), ( + αφ)( + ksnϕ) VM () where s the valent stran ampltde, α s the materal parameter for loadng non-proportonalt, φ s the ccle non-proportonalt parameter, k s the materal parameter for stran path orentaton, ϕ s the angle from the prncpal drecton to the appled stran path and VM s the von Mses stran as gven, VM ( xx ) + ( zz ) + ( zz xx ) + ( γ x + γ z + γ zx ) ( 2 ( )) 2 (2) + ν where ν s the Posson s rato. and γ are the axal and shear stran ampltdes n respectve planes. / Stran-lfe crve It s necessar to modf the stran-lfe fatge crve n HCF regme n order to consder the combned damage of HCF and LCF. The proposed crve conssts of two parts as shown n Fgre. The frst part of the crve descrbes fatge lfe of plastc stran ccles whch sall affect LCF. To descrbe ths part, Coffn-Manson stran-lfe crve s tlzed as shown below. σ + E f b c (2N) f (2N) (3) where s the valent stran ampltde, N s the nmber of ccles to falre, σ s the fatge strength coeffcent, b s the fatge strength exponent, s the fatge dctlt coeffcent, c s the fatge f dctlt exponent and E s the elastc modls of the materal. f * Correspondng athor, Tel/Fax: , E-mal: ohga@cee.ehme-.ac.jp

3 507 ULCF Log ( ) ( +) f σ b (2N ) + f (2N ) E c ( ) () e N ) ( + R N N ( N n ) Log (N) N ( + ) R N N e Fgre : Schematc representaton of the proposed stran-lfe crve N e N + + b N N e The ltmate stran of low ccle fatge ( ) whch s the valent stran ampltde correspondng to ULCF falre n half reversal (a qarter of a ccle) s obtaned from Eq. (3) as, ) (4) ( ULCF f The second part of the crve descrbes the fatge lfe of elastc stran ccles whch sall affects HCF. Ths part of crve represents hpothetcal fll known crve. The shape of the crve s obtaned b drectl transformng the prevos fll known stress-lfe crve (Srwardane et al. 2008) to elastc stran-lfe crve as shown below. b N + N (5) e N N + e where e s the stran ampltde of the fatge lmt, N e s the correspondng nmber of ccles to falre. The and N are the eld stran and the correspondng nmber of ccles to falre. The b s the slope of the fnte lfe regon of the crve. The correspondng to half reversal (a qarter of a ccle) s expressed as, ( ) s the ltmate stran of HCF whch s the elastc stran ampltde σ ( ) (6) E where σ s the ltmate tensle strength of the materal. The N s the nmber ccles correspondng to the ntersecton of the tangent lne of the fnte lfe regon and the horzontal asmptote of the ltmate elastc stran ampltde ( ) as shown n Fgre. * Correspondng athor, Tel/Fax: , E-mal: ohga@cee.ehme-.ac.jp

4 Damage ndcator A new damage ndcator The proposed damage ndcator consders combned damage of HCF and LCF de to varable ampltde loadng. Sppose a component s sbjected to a certan valent stran ampltde ( ) of n nmber of ccles at load level. N s the fatge lfe (nmber of ccles to falre) correspondng to ( ) (Fgre ). Therefore, the redced lfe at the load level s obtaned as (N n ). The damage valent stran ( ) () (Fgre ), correspondng to the falre lfe (N n ) s defned as th level damage valent stran. Then, the new damage ndcator, D s stated as, D (7) ( )( ) ( ) where the ( ) ( ) ( ) s n nmber of ccles at If If ) ( ) ( > ( + N nmber of ccles at ( ) ) e ) ULCF ( ( ) (from Fg : stran-lfe crve) N R N n : Resdal lfe ( ) () : Eqvalent stran (from Fg : stran-lfe crve) D ( )( ) ( ) ( ) ( ) D D If D < No No ( ) ( ) ULCF ( ) ( ) < (8) n : nmber of ccles at If ( ) No Fatge falre ( ) At the end of th loadng level ( ), damage D has been accmlated (occrred) de to the effect of loadng ccles, the damage s transformed to load level as below. D (9) ( ) ( ) ( ) ( ) ( ) ( ) Damage transformaton from prevos step to next step ( ) ULCF ( ) ( ) D D ( )( ) ( ) ( ) If ( ) ( + ) > ( ) e No and ( ) s expressed, N ( + : nmber of ccles ) R ( ) ( ) (from Fg : stran-lfe crve) ( ) Then, ULCF s the damage valent stran at loadng level ( ) ( ) and t s calclated as, D ( ) [( ) ( ) ] + ( ) ( ) + () ( ) ( ) < (0) N ( ) R N( ) R n : Resdal lfe ( ) ( + ) : Eqvalent stran for N ( + ) R nmber of ccles (from Fg : stran-lfe crve) D ( + ) ( ) ( ) ( + ) ( ) ( ) Fgre 2: Flow chart of the proposed damage + + ndcator + The correspondng valent nmber of ccles to falre s obtaned from the stran-lfe crve as N ( +) R * Correspondng athor, Tel/Fax: , E-mal: ohga@cee.ehme-.ac.jp

5 509 shown n Fgre. The ( ) s the stran at the level and spposng that t s sbjected to n nmber ( ) of ccles, then the correspondng resdal lfe at load level, N ( ) R N ( ) R n( ) N ) R ( + s calclated as, (2) Therefore, stran, ( ) ( + ) whch corresponds to N ( I + ) R at load level, s obtaned from the stran-lfe crve as shown n Fgre. Then the cmlatve damage at the end of load level s defned as, D( + ) (3) ( ) ( ) ( ) ( ) ( ) Ths s carred ot ntl D s al to. Flow chart of the damage ndcator s gven Fgre Verfcaton of the proposed model Ths secton explans the verfcaton of the proposed fatge model b comparng fatge test reslts avalable n the lteratre. Two expermental test reslts were sed: S45C steel and Hanes Verfcaton for S45C Steel Fatge tests performed b Chen et al were sed to verf the proposed fatge model. Axal (A) and torsonal (T) testng were performed n HCF and LCF regmes. The parameter, k, s estmated as 0.5 from the constant ampltde fatge tests (Km et al 999). Then, fatge lves of the proposed model and Mner s rle based prevos model are estmated as gven Table. Table Expermental smmar and predcted fatge lves of S45C steel Frst load level Second load level Predcted lfe Test Stran ampltde No of ccles (n ) Stran ampltde No of ccles (n 2 ) Expermental lfe (n +n 2 ) Prevos model Proposed model AT AT AT AT AT TA TA TA TA TA TA * Correspondng athor, Tel/Fax: , E-mal: ohga@cee.ehme-.ac.jp

6 50 The percentage varatons of the predctons are determned wth the expermental reslts. The prevos model gves a percentage varaton of 23.9 % whle the proposed model gves a vale of 6.2 %. Therefore, the proposed model based fatge lves are more accrate than prevos model predctons Verfcaton for Hanes 88 Fatge test performed b Kallr and Bonacse 2002 were sed verf the proposed fatge model. Axal (A) and torsonal (T) testngs have been performed n dfferent sences (AA, AT, TT and TA). The parameter, k was estmated as 0.7 from constant ampltde tests gven (Kallr and Bonacse 999). Expermental reslts were compared wth the predcted lves of the proposed fatge model. In addton, the prevos model sed wth the Mner s rle was also sed n ths case. The obtaned comparsons are gven n Table 2. Table 2 Expermental smmar and predcted fatge lves of Hanes 88 Frst load level Second load level Predcted lfe Test Stran ampltde No of ccles (n ) Stran ampltde No of ccles (n 2 ) Expermental lfe (n +n 2 ) Prevos model Proposed method AA AA AA AA TT TT TT TT TT AT AT AT AT TA TA TA TA The percentage varatons of prevos model predctons wth expermental reslts were estmated as 0.74 % whle the proposed model has a percentage varaton of 0.62 %. Therefore, the predcted fatge lves b the proposed fatge model are more accrate than prevos model predctons. * Correspondng athor, Tel/Fax: , E-mal: ohga@cee.ehme-.ac.jp

7 5 4. Case std: fatge lfe estmaton of a brdge member The proposed model was appled to a wroght ron ralwa brdge member to estmate the fatge lfe de to traffc and earthqake loadngs. The selected brdge s stated near Colombo n Sr Lanka and one of ts members was selected for lfe estmaton. The evalatons are especall based on secondar stresses and strans, whch are generated arond the rveted connecton of the member de to stress concentraton effect of prmar stresses cased b sal traffc and earthqake loadngs. The selected member s shown n Fgre 3 (a) and (b). Consdered member (a) (b) Fgre 3: Vews of (a) the brdge; (b) consdered member The combned damage of HCF and LCF s evalated consderng all sx rvets are actve whle all the rveted locatons have no clampng force. The clampng force s generall defned as the compressve force n the plates whch s ndced b the resdal tensle force n the rvet. Snce ths std assmes that the rveted locatons have no clampng force (vale of clampng force s zero), the connected members are consdered to sbject to the baxal stress state. Therefore, a crtcal member wthot rvets can be consdered to analze the baxal state of stress of a 2D fnte element analss. The nne node sopermetrc shell elements were sed for the FE analss. Earthqake was consdered to occr at dfferent tmes n the brdge lfe as shown n Table 3. It s assmed that sal traffc load s followed after the earthqake. The fatge lfe of the member was estmated sng approaches: () proposed model; (2) prevos model (Coffn-Manson crve wth the Mner s rle). The obtaned reslts are gven n Table 3. The reslts ndcate that combned damage of HCF and LCF cases an apprecable redcton of brdge lfe. For the proposed model, percentage redcton of lfe s the hghest when the earthqake occrs at 50 ears. If the earthqake ampltde s ncreased, the maxmm percentage redcton occrs before 50 ears. For the prevos model, the redcton of servce lfe s constant rrespectve of tme of earthqake occrrence snce Mner s rle cannot captre the loadng sence effect. Comparson of fatge lfe reveals that the proposed model predctons dffer from the prevos model predctons. Ths verfes that the proposed stran-lfe crve wth new damage ndcator better represent the combned HCF and LCF behavor than Coffn-Manson relatonshp wth Mner s rle. Table 3 Fatge lfe of the member for dfferent earthqake occrrences * Correspondng athor, Tel/Fax: , E-mal: ohga@cee.ehme-.ac.jp

8 52 Prevos model (Mner s rle) Proposed model Tme of Fatge lfe Percentage Fatge lfe Percentage earthqake* (ears) (ears) redcton of lfe (%) (ears) redcton of lfe (%) No earthqake *After constrcton The dfferences of case std reslts confrm the mportance of accrate combned HCF and LCF model to estmate the fatge lfe of exstng steel brdges. 5. Conclsons A new model for combned damage of HCF and LCF was proposed to estmate lfe of steel brdge. A verfcaton of the proposed model was condcted b comparng the predcted lves wth expermental lves of two materals. It was shown that the proposed fatge model gves an accrate fatge lfe for combned damage of HCF and LCF where detaled stress hstores are known. The proposed fatge model was appled to estmate the fatge lfe of a wroght ron ralwa brdge Case std realzed the mportance of consderaton of the earthqake ndced LCF damage n addton to HCF damage de to sal traffc loadng n steel brdges. The mportance and effectveness of accrate predcton of combned damage of HCF and LCF was also confrmed. References Bonacse P and Kallr S (2002). Senced axal and torsonal cmlatve fatge: low ampltde followed b hgh ampltde loadng, Baxal/Mltaxal Fatge and Fractre, Elsever. Borod MV and Strzhalo VA (2000). Analss of expermental data on a low ccle fatge nder nonproportonal stran hardenng, Internatonal Jornal of Fatge, 22(4), pp Chen X, Jn D and Km KS (2006). Fatge damage of medm carbon steel nder sental applcaton of axal and torsonal loadng, Fatge and Fractre of Engneerng Materals and Technolog, 29(3), pp Kallr S and Bonacse PJ (999). Cmlatve axal and torsonal fatge: an nvestgaton of load-tpe sencng effects, Smposm of mltaxal fatge and deformaton: testng and predcton, Seattle, USA. Km KS, Park JC and Lee JW (999). Mltaxal fatge nder varable ampltde loads, Jornal of Engneerng Materals and Technolog, 2(3), pp Kondo Y and Oka K (2007). The effect of sesmc loadng on the fatge strength of welded jonts. Materal Scence and Engneerng A , pp Srwardane S, Ohga M, Dssanaake R and Tanwak K (2008). Applcaton of new damage ndcator-based sental law for remanng fatge lfe estmaton of ralwa brdges. Jornal of Constrctonal Steel Research. 64(2), pp Sresh S (998). Fatge of Materals, UK: Cambrdge Unverst Press, Cambrdge. * Correspondng athor, Tel/Fax: , E-mal: ohga@cee.ehme-.ac.jp