ࡱ> UWTjU@bjbj -,.    $22 vvvvQ_\1111111$3R6@1QQ1vvP2vv11"$-Y.v @rA -i1f202-Z7pZ7(Y.Z7Y.k>,$kkk11d   Prvi susret Hrvatskog druatva za mehaniku Rijeka, 29. lipanj 2007. GRANI NO OPTEREENJE HETEROGENOG ZAVARA S PUKOTINOM OPTEREENOG NA SAVIJANJE Kozak, D., Konjati, P., Serti, J., Gubeljak, N. & Mateji ek, F. Sa~etak: Danas se postupak reparaturnog zavarivanja koristi kao jedan od naj eaih postupaka popravljanja zavarenih komponenti strojarskih konstrukcija. Pri tome je dodatni materijal razli itih mehani kih svojstava od osnovnog materijala zavara. Zbog toga se ovaj lanak bazira na istra~ivanju lomnog ponaaanja zavarenog spoja sa prisutnom heterogenoau u zavaru. Kao primjer odabran je standardan uzorak mehanike loma za savijanje u tri to ke kod kojih su prisutna tri razli ita materijala s pukotinom u sredini zavarenog spoja. Osnovni materijal konstrukcije je su eono zavaren materijalom koji ima viau granicu te enja, te reparaturno zavaren materijalom sa ni~om granicom te enja od granice te enja osnovnog materijala. U materijalu s viaom granicom te enja prisutna je pukotina ija se duljina, kao i airina samog zavara sistemati no varirala. Ukoliko zavar iskazuje plasti no ponaaanje, uobi ajeno se kao provjera nosivosti konstrukcije izra unava grani no optereenje koje uvjetuje te enje materijala po cijelom presjeku zavara i time dovodi do otkaza konstrukcije. Za odabrani uzorak numeri ki je odreeno grani no optereenje za plastifikaciju preostalog ligamenta zavara. Materijali su modelirani kao elasti ni-idealno plasti ni. Postojea rjeaenja u SINTAP proceduri ne obuhvaaju rjeaenja za grani no optereenje s prisutnom heterogenoau materijala zavara. U ovom radu dana su rjeaenja za grani no optereenje zavarene komponente s greakom u heterogenom zavaru u ovisnosti o geometrijskim parametrima u obliku dijagrama. Klju ne rije i: Heterogeni zavar, epruveta za savijanje u tri to ke, pukotina, grani no optereenje 1 UVOD Procjena cjelovitosti konstrukcija temelji se na rjeaenjima za grani no optereenje i faktor intenzivnosti naprezanja. Danas postoji kompendij s izvedenim rjeaenjima za razli ite konstrukcijske komponente [3, 4]. Rjeaenja za grani no optereenje ovakvih komponenti naj eae se odreuju uz pomo metode kona nih elemenata (MKE) ili eksperimentalno [1]. Ipak, nijedno od tih rjeaenja ne predvia heterogenost materijala prilikom propagacije inicijalne pukotine iz jednog materijala u drugi. Takav slu aj je mogu kod raznorodnih materijala u zavarenom spoju, gdje je jedan materijal viae, a drugi ni~e vrstoe u odnosu na osnovni materijal. U ovom radu je uz pomo MKE odreeno grani no optereenje za 30 moguih slu ajeva geometrije lomno-mehani ke SE(B) epruvete optereene na savijanje s prisutnim su eono zavarenim I - spojem, izvedenim jednom polovinom od visoko vrstog, a drugom polovinom od nisko vrstog materijala. Geometrijski parametri poput omjera duljine pukotine i visine zavara a/W, vitkosti zavara W/2H (gdje H predstavlja airinu zavara) i udaljenosti vraka pukotine od linije staljivanja materijala zavara L sistematski su varirani [2]. Mogue oja avanje materijala nije uzeto u obzir u MKE izra unima, kako bi se rezultati mogli usporediti s onima iz literature. 2 GRANI NO OPTEREENJE ZA SE(B) LOMNO-MEHANI KU EPRUVETU S HOMOGENIM MATERIJALOM ZAVARA U kompendiju rjeaenja za grani no optereenje komponenti, temelj predstavlja izraz za silu te enja materijala u primjeru kad je cijela SE(B) epruveta izraena od osnovnog materijala [1]:  EMBED Equation.3  (1) gdje su:  EMBED Equation.3  sYB  granica te enja osnovnog materijala, B  airina epruvete, W  visina epruvete, a  duljina pukotine, S = 4W  duljina epruvete izmeu oslonaca pri savijanju. Svojstva osnovnog materijala se uzimaju kao konstantna, dok svojstva dodatnog materijala (zavara) variraju o koriatenoj elektrodi. Omjer granice te enja dodatnog materijala u odnosu na osnovni materijal epruvete opisuje se uz pomo faktora M (engl. yield strength mis-match factor):  EMBED Equation.3  (2) gdje je sYW  granica te enja dodatnog materijala. Zavariva ki kodeks nala~e uporabu elektrode sa materijalom jednake ili viae granice te enja od materijala plo e (engl. overmatching - OM), pri emu je M > 1. Rjeaenja za silu te enja u tom primjeru dana su u bezdimenzijskom obliku, kao odnos prema sili te enja u primjeru kad bi cijela epruveta bila napravljena iz osnovnog materijala [1]:  EMBED Equation.3  (3) gdje je:  EMBED Equation.3  Ipak, poveana uporaba visoko vrstih elika natjerala je proizvoa e na koriatenje elektroda s ni~om vrstoom, kako bi se osigurala dovoljno visoka ~ilavost materijala. U tom slu aju prisutan je efekt ni~e granice te enja zavara (engl. undermatching - UM), gdje je M < 1. Tada se sila te enja materijala definira kao [1]:  EMBED Equation.3  (4) gdje je:  EMBED Equation.3 . 3 MKE ANALIZA ZA SE(B) LOMNO-MEHANI KU EPRUVETU S HETEROGENIM MATERIJALOM ZAVARA U praksi se nehomogeni zavari izvedeni u viae prolaza s jednom polovinom izvedenom od materijala viae (OM), a drugom polovinom od materijala ni~e vrstoe u odnosu na materijal plo e (UM) koriste kod reparaturnog zavarivanja, gdje materijal ni~e vrstoe osigurava dostatnu ~ilavost, a materijal viae vrstoe atiti od pojave pukotina. U tom slu aju se gore navedeni izrazi ne mogu koristiti, buduu su oni izvedeni za zavare koji su homogenog sastava. Konzervativan pristup bi bio izra unati silu te enja kao da je cijeli zavar izveden kao UM. Taj pristup je blizak realnosti samo za omjer a/W=0,5, gdje je podru je ispred pukotine od UM materijala, ali za pretpostavku kratke pukotine, sila te enja epruvete bila bi podcijenjena. Takav pristup postaje sve viae nerealan, kako se airina zavara 2H smanjuje. Naime, kako zavar postaje u~i, njegov utjecaj na kompletno lomno ponaaanje epruvete opada. U tom slu aju se mo~e o ekivati konvergencija rjeaenja onima koja su dobivena kad je cijela epruveta izvedena iz osnovnog metala. U ovom radu je analiza fokusirana na 2D MKE analizu (pretpostavljeno stanje ravninske deformacije) SE(B) epruvete s pukotinom smjeatenom u sredini visoko vrstog materijala zavara (OM). 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Sve kombinacije dane su na slici 1, gdje se svaka nazna ena to ka mo~e povezati s odgovarajuim MKE modelom. Zbog prisutne simetrije modelirana je samo 1/2 epruvete.  EMBED Word.Picture.8 Sl. 1. Klju ne to ke koje odgovaraju odreenim MKE modelima U ovom radu analiziran je slu aj u kojem visoko vrsti i nisko vrsti materijal zavara sa M=1,19 odnosno M=0,86, u odnosu na materijal plo e s granicom te enja od 545 MPa, imaju jednak udjel. Oja anje materijala, kao i promjene materijala u zoni utjecaja topline nisu uzeti u obzir. Detalj mre~e kona nih elemenata sa airinom zavara od H=W/8 i duljinom pukotine od 0,3W prikazan je na slici 2. Broj elemenata i vorova je 1847 odnosno 5690, pri emu prvi red elemenata ima veli inu od 100 mm. Svi materijali u spoju su modelirani kao elasti ni-idealno plasti ni, kako bi se dobiveni rezultati mogli usporediti s literaturom. Koriateni su izoparametrijski 8- vorni kona ni elementi s reduciranom integracijom, kako bi se izbjegli problemi nestialjivosti. Polje plasti ne deformacije je poprili no kompleksno kod ovako izvedenih zavara, ato mo~e ote~ati konvergenciju rjeaenja, naro ito kod plitkih pukotina.  EMBED Word.Picture.8  Sl. 2. Tipi na mre~a kona nih elemenata (H=W/8, a=0,3W) 4 RJE`ENJA ZA SILU TE ENJA ZA SE(B) EPRUVETU S HETEROGENIM ZAVAROM I DISKUSIJA REZULTATA Inkrement sile, koja uzrokuje kontinuirano te enje kroz preostali ligament, treba biti vrlo mali, kako bi se ato preciznije odredio trenutak te enja materijala. Grani no optereenje SE(B) epruveta s heterogenim zavarom za razli ite airine zavara 2H dano je u obliku FYM/FYB na slici 3, ovisno o udaljenosti vraka pukotine od linije spajanja dva materijala zavara L. Rezultati za vrijednost sile te enja se najviae razlikuju za SE(B) epruvetu s najduljom pukotinom a/W=0,5 (L = 0) - za oko 17%. Poveanje airine nehomogenog zavara H pri konstantnoj udaljenosti izmeu linije staljivanja i vraka pukotine L dovodi do smanjivanja vrijednosti sile te enja FYM, generalno.  Sl. 3. Utjecaj udaljenosti izmeu vraka pukotine i linije staljivanja L na vrijednost sile te enja heterogenog zavara (pukotina locirana u OM dijelu zavara)  Sl. 4. Utjecaj omjera duljine pukotine i visine zavara a/W na vrijednost sile te enja heterogenog zavara (pukotina locirana u OM dijelu zavara) 5 ZAKLJU AK U radu su dana rjeaenja za grani no optereenje SE(B) lomno-mehani ke epruvete, koja sadr~i pukotinu u sredini heterogenog zavara, u obliku dijagrama. Pri tome su varirani omjer duljine pukotine i visine zavara a/W, odnosno airina zavara 2H, kao najutjecajniji geometrijski parametri, uz zadr~avanje konstantnog udjela visoko vrstog i nisko vrstog materijala u zavaru. Rjeaenja za silu te enja za omjer a/W < 0,3 su sli na OM rjeaenjima, zato ato je ispred vraka pukotine joa uvijek dovoljno dominantnog visoko vrstog materijala, dok je kod a/W=0,5 (L=0) prisutno rasipanje rezultata za silu te enja (najviae oko 17%), ovisno o airini zavara. Tako je sila te enja 6% vea u odnosu na silu te enja za epruvetu od istog osnovnog materijala (za primjer uskog zavara), odnosno za 11% manja ukoliko je zavar airine W/2. To su ujedno i najvea odstupanja, ukoliko bi se u izra un ialo idealizirano, odnosno kao da je cijela epruveta izraena od osnovnog materijala. Literatura: [1] Kim, Y.-J., Schwalbe, K.-H.,  Compendium of yield load solutions for strength mis-matched DE(T), SE(B) and C(T) specimens , Engineering Fracture Mechanics, Vol. 68, 2001, str. 1137-1151. [2] Kozak, D., Vojvodi -Tuma, J., Gubeljak, N., Semenski, D.,  Factors influencing the yielding constraint for cracked welded components , Materials and Technology, Vol. 39 (1-2), 2005, str. 29-36. [3] R6:  Assessment of the integrity of structures containing defects , Nuclear Electric Procedure R/H/R6, Revision 3, 1998. [4] SINTAP:  Structural INTegrity Assessment Procedures for European Industry , Final Revision, EU-Project BE 95-1462, Brite Euram Programme, 1999. Autori: Dra~an Kozak, Sveu iliate Josipa Jurja Strossmayera u Osijeku, Strojarski fakultet u Slavonskom Brodu, Zavod za strojarske konstrukcije, Trg Ivane Brli-Ma~urani 2, HR-35000 Slavonski Brod, tel. 035 446 188, fax 035 446 446, e-mail: dkozak@sfsb.hr, web stranica: http://www.sfsb.hr/djel.php?ko=dkozak Pejo Konjati, Sveu iliate Josipa Jurja Strossmayera u Osijeku, Strojarski fakultet u Slavonskom Brodu, Zavod za strojarske konstrukcije, Trg Ivane Brli-Ma~urani 2, HR-35000 Slavonski Brod, tel. 035 446 188, fax 035 446 446, e-mail: pekon@sfsb.hr, web stranica: http://www.sfsb.hr/djel.php?ko=pekon Josip Serti, Sveu iliate Josipa Jurja Strossmayera u Osijeku, Strojarski fakultet u Slavonskom Brodu, Zavod za strojarske konstrukcije, Trg Ivane Brli-Ma~urani 2, HR-35000 Slavonski Brod, tel. 035 446 188, fax 035 446 446, e-mail: jsertic@sfsb.hr, web stranica: http://www.sfsb.hr/djel.php?ko=jsertic Nenad Gubeljak, Univerza v Mariboru, Fakulteta za strojniatvo, Inatitut za konstruiranje in oblikovanje, Smetanova 17, SI-2000 Maribor, Slovenija, tel. 00386 2 220 7660, fax 00386 2 220 7990, e-mail: nenad.gubeljak@uni-mb.si, web stranica: http://fs-server.uni-mb.si/si/inst/iko/lsek/ Franjo Mateji ek, Sveu iliate Josipa Jurja Strossmayera u Osijeku, Strojarski fakultet u Slavonskom Brodu, Zavod za strojarske konstrukcije, Trg Ivane Brli-Ma~urani 2, HR-35000 Slavonski Brod, tel. 035 446 188, fax 035 446 446, e-mail: fmatej@sfsb.hr, web stranica: http://www.sfsb.hr/djel.php?ko=fmatej V.W0W2W4W6W@WBWJWLWZWbWdWfWhWvWWWWWXXXXXXX$Y4Y6Y\Y`YZ Z"Z$ZTZVZxZ|Z~ZлۥzozogozogzozozozozozhmHsHh`Ph`PmHsHhp} mHsHh`PmHsHh:mHsHhLA\hmHsHhmHsHh\hmHsHj-hlhU!jwJ hCJUVmHsHhh|hmHsHjhUh\hCJmHsHhc5mHsHh+mHsH(0W2WWW^^0___T`V`eeffg $`a$gdqW $`a$gd4 @`gdqW`gda?Qgda?Q`gd: $`a$gd: `gd:gd:gd $`a$gd`gd~ZZZZZZZZZZZZZZZZ [ [[[[$[&[*[6[D[R[[[[[[[\\\]]]6]@]L]\]^]`]b]d]]]^^^^^^^(_ậh:jh:Uh:hXqCJaJmHsHhLA\h:CJmHsHh:mHsHhJ+mHsHhp} hp} OJQJmHsHhmHsHhp} mHsHhp} h`P6mHsHh`Ph`PmHsH8(_*_,_._0_8_:_>_____________________`"`R`T`V`l`ӴӴȕwwwobZhqWmHsHh\ha?QCJmHsHhcNmHsHhFha?QmHsHha?QmHsHh\ha?QmHsHhmHsHh:h:mHsHh:h:6mHsHhp} h:6mHsHh:mHsHh\h:mHsHh`Ph:mHsHjh:Ujh:U!j,|J h:CJUVmHsH!l`p`r`v``````aaaa b bDbFbjblbpbrbtbxbzbbb*c,c.c2cccccccccdd ddd d&d2dDdFdxdzd|d~ddddŹŹ𣗣𣋣h5bhqW6mHsHh{2YhqW6mHsHha?QhqWmHsHh{2Yh{2YmHsHh{2Yha?QH*mHsHh{2Yha?Q6mHsHh{2Yh{2Y6mHsHh{2YmHsHha?Qha?QmHsHhqWmHsHhZ"mHsH6dddddddd eeelenepeteeeeeeeeeef fffffffff g"ggȽwllddhmHsHh\hqWmHsHh\ha?QCJmHsHj{h6ha:UhLA\h4mHsHh8h86mHsHh8mHsHh\h4mHsHh4jhBmha:Uha?QhqWCJmHsHh5bhqWH*mHsHh5bhqW6mHsHhqWmHsHha?QhqWmHsH%>g@gBgDgggghh h$hii4i6iiiiiiijj2k4k6k8kFlHlJlLlXlZlbndnooooļį|qhhog5mHsHhch|i}mHsHh\hqjmHsHh]_h]_6mHsHh]_mHsHhh6mHsHhmHsHh\hogCJmHsHhogmHsHh\hogmHsHhLA\hqWmHsHhqWmHsHhh6mHsHhmHsHh6mHsH&gh hjooo*qrstttNwy|B~ ` gd |O ` gd~CI ` gd4& ^`gda: ^`gdKb ^`gdoggd|i}gdoggdoggdogoooooooooooooppppppqq*q,q.qqBqDqHqZqbqdqhqjq~qqqqqqqqqq:rrprrrrrrrrrrȼȳȳȼȼȼȪѪ hm{CJhm{hiCJhplhm{CJhm{hm{CJhplh"rCJ hiCJ h"rCJh"rh"rCJ ha:CJhKbh"rCJhogmHsHh:ChogmHsHh\hog5mHsH8rrrrrrrBsDssssssstLtNttttttttt@~B~b~*ĸĢh\h2YmHsHh~CImHsHh~CIh2YmHsHh~CIh~CImHsHhMNhMNmHsHh\hubN5mHsHh5mHsHh\hu5mHsHha:hubNCJhplha:CJ hiCJ ha:CJhKbha:CJ + 0&P 1A/R & _7!n"n#n$n%Dd ` b  c $A? ?3"`?2h4 Yi ?=DD`!<4 Yi ?=@@ xcdd``ndb``aaV d,FYzP1n:&~! 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