Fatigue life prediction for cyclically bent threaded connections

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1 ISSN 9-7. MECHNIK.. 7: -9 Fgue lfe predon for yllly en hreded onneons Ž. Juhnevus,. Krenevus Vlnus Gedns Tehnl Unversy, Suleko l., Vlnus, Lhun, Vlnus Gedns Tehnl Unversy, Suleko l., Vlnus, Lhun, E-l: hp://dx.do.org/.5755/j.eh.7... Inroduon Threded onneons ppled for hgh pressure vessel overng us hve deque ehnl srengh nd good lek ghness. Ofen n gskeed flnges he vrons of nernl pressure, eperure nd deforon of joned-up eleens use yl endng of hese eleens nd hreded onneons lso [-7]. Due o he hgh sress onenrons hred roos nd yl lodng hese onneons re prone o fgue flure. Low fgue srengh of porn hreded onneons s defned n ordne wh he SME ode [6] or Russn Federon sndrd [7]. These ehods requre he xu sress onenron n hred roo o e evlued nd hs n e done whou usng knowledge of he lod dsruon long he hred helx. More ex nll lulon of he sress he hred roos n e heved y dre usng of lod dsruon d. In he feld of hgh yle fgue severl ehods hve een suggesed o evlue he fgue l of ol y eployng ppropre heores or eprl lws o lule he lod long he hred helx followed y he xu sress onenron nd hen he fgue l. The nlyss of hese ehods s perfored n [8]. In he feld of low yle fgue.e. n [9], he nlyl ehod [] of lulon of lod dsruon eween urns whh seondly s used for he lulon of xu sresses he hred roos ws norpored no sndrd ehod [7] whh n [9] ws used for he predng of hreded onneon s fgue lfe. Unl now nlyl ehods for evlung fgue l or fgue lfee of hreded onneons usng lod dsruon d, were relle only n he se of hers xl yl lodng. Reenly he nlyl ehod o desre he lod dsruon n hred of en hreded onneon ws developed [], nd now he ove enoned evlung n e perfored for he yllly en hreded onneon lso. The oje of hs pper s o ssess poenl of he nlyl ehod [] n predng fgue lfe of yllly en hreded onneons y onng hs ehod wh sndrd [7]. For hs purpose lulon resuls hve een ssessed gns fgue es d whh re expressed n ers of nuers of lod yles fgue rk non n suds/ols of hreded onneons.. Posons of he segens nd hred helx n he hreded onneon In hs pper hreded onneon Fg.,, whh fer ghenng y fore F s loded y he endng oen s onsdered. Due o on of hese exernl lods he ppropre lods per un lengh q nd q rse n he sud nd nu hreds. Ths uses he proporonl urns pr defleons nd q, q where s urns pr plly nd s ross-seon loon oordne. Threded onneon s dvded n hree segens: I =,,. In he ddle segen he lengh of whh s H, he urns re engged over he full profle nd deph of urns enggeen s onsn. Therefor here plly of he urns pr = = ons does no hnge long ll lengh. In he oundry segens of he onneon,.e. on runous, where her lengh s H = H = P P s hred ph, due o he hngng deph of urns enggeen her plly s vryng eng ons nd ons. The orgn nd end of ny segen re found nd H respevelly. H H H H d F q q F f Fg. Lodng of he hreded onneon: - sud, - nu, ghenng, endng, lod fors use he sresses n suds urn roo, d segens of hreded onneon, e, f wo dfferen posons of he hred ph deer helx I n e seen n Fg., d h he orgn of oordne of ny ross-seon loon s reeded fro he free end of he nu on phse lengh f, whh s desgned o se poson of he hreded onneon wh respe o longudnl xs hus wh respe o endng plne lso. Poson for ny hred helx pon now n e expressed y urnng ngle = /P =. fer nsllon of he hreded onneon n o onsruon nd fer s ghenng he helx n our n ny poson wh respe H ; Rsn H ; H f e M Q R f q f q +q

2 o endng plne. Herewh n every new hred helx poson he onsdered helx pon on he hred ph deer R where s he ppropre urn lod q wll e dfferenly reoe fro he neurl lne suppose s lone. Here here s no roule o noe h urn lod q hen rees dfferen lol oens = q R sn n he se ross-seon of onneon. Two exples of hs dsne vron.e. R sn whh n e oned y usng wo dfferen vlues f re shown n Fg., e, f. In Fg., nernl xl fore Q, nernl endng oen M nd urn lods q + q whh n he suds ross seon oordne nd produe lol sresses n he hred roo re shown. They ll us e luled prrly when fgue lfe of he hreded onneon s preded.. Equons for hred lods nd sresses due o ghenng of hreded onneon The urn lod q nd nernl xl fore Q used y ghenng hve een luled y usng he ehod gven n []. These lods for every segen re expressed hrough urns defleon n he followng wy q, Q where = /E s s + /E n n ; E s, E n re Young s odul of he sud nd nu; s, n re ross-seonl res of he sud ore nd nu wll. For he seond segen where urns plles re = = ons he urns defleon nd s dervve re expressed y usng rgers heory snh osh osh snh where /. Expresson for he urns plles n runous where = or = hs he followng for [] 5 C n e n C e n C where n e. n To ese he sx unknowns fors nd of equons,, 6 nd 7 s used he syse of equons, whh express oundry ondons of segens Q, Q H Q, Q H Q, Q H F, H, H 8 In srengh lulon nor for nuler equpens [7] he fgue durly s esng ordng he lol lernng els sresses. These sresses for xl loded sud hred whh rse ghenng were luled y usng he followng forul [] q P Q K K 9,, f s here K,, K, re onenron fors of sresses due o he xl fore Q nd he sud urn lod q respevely; s s ross-seonl re of he sud ore; f s he urns on surfe projeon no he plne, perpendulr o he sud xs; P s he hred ph. The vlues of els sresses onenron fors, defned n work [] re: K, nd K,, 95, he urns roo roundngup rdus eng R =.P.. Equons for hred lods nd sresses due o endng of hreded onneon The urn lod q nd nernl endng oen M whh rse he endng of he hreded onneon hve een luled y usng he ehod gven n []. For every segens of onneon here re used he relons q, y sn where y s he funon of urns xu defleons. For he seond segen where urns plles re = = ons he ove enoned funon s he followng where for C nd power exponen n n e defned ordng o he es resuls of he urns prs, engged over he noplee profle for every segen - hey hve een luled y usng he known urns plly n one edge of segen H or H where H =, nd lso he experenl urns plly for n he ddle of hese segens +P/ =.67 or +P/ =.67. The urns pr defleon nd s dervve for he runous,.e. for segens =, re e e ln... n!! n e / e ln e!! / /... 6 y snh osh where, =R /, =/E s I s + /E n I n re onsn fors nd I s, I n re oens of ner of he ross-seonl re for he sud ore nd he nu wll respevely. The equon oned n [] for he lulon of nernl endng oen whh s n sud ore of he segen H hs he followng for R M osh sn / snh sn osh R 7 snh sn

3 5 osh sn / snh For hel purposes he vron of he urn s pr plly n lengh of ny runou n he en hreded onneon n [] s desred y oher forul hn n he se of enson onneon. Ths forul hs he followng expresson u Ve 5 where V nd u = or = re onsn for nd power exponen whh hve een defned n he se wy s n he se of gh hreded onneon,.e. y usng wo experenll urns pr plly vlues known for hese segens. The nlyl expresson of he funon for he runous urn xu defleon n [] ws oned n he followng for n n y e n W e -n W f f 6 where n, W, n nd W re he fors whh need o e found, f nd f re desgnons, = or =. The equon for he lulon of nernl endng oen whh s on he sud ore n segens = or = s M F F 7 where F nd F re desgnons whh re expressed n he followng oon for Re n os F n V p p sn W os sn p p p W 8 where ndex = or =, = = n u, V = V, p = p = +, =, = or = ; where re dul sgns he upper sgn s vld = nd he under sgn s vld n he se of =. The fors n, W nd n, W for ny runou us e solved fro he wo equon syses f / R F, f / R F 9 f / R F, f / R F The unknowns fors nd of Eqs.,, 6, 7 furher us e esed y usng he syse of equons, whh express segens oundry ondons M, M H M, M H M, M H, H, H The lernng els sresses n he sud hred due o endng were luled on he nlogy of Eq. 9 q P MRsn K f K 9,, Is where K, kr K, nd K, K, re onenron fors of he sresses due o endng oen M nd due he sud urn lod q respevely; k r s he for whh eses he dfferene eween lol sresses n he sud endng nd s enson; here ws ssued k r Lod nd sresses dsruons long he hred helx Fgs. -7 presened n hs Seon refle he lulon sequene for he sresses yle preers whh re used furher for he suds fgue lfe predon. Clulons hve een perfored for he onneons M6 hegh of he nu H =.8d =.8 de fro seel 5ChMF. The se sud-nu onneons hve een used n he fgue ess he resuls of whh re presened n he nex seon. verge ndes of ehnl properes of onneons seel 5ChF: proof srenghs R p. = 86 MP nd R p. = 89 MP, ensle srengh R = MP, perenge re of reduon Z = 6. %, odule of elsy E GP. Indes for one urn pr M6 were eslshed experenlly y he ehnque desred n []: plly =.78 - /kn/ nd yeld urns lod.e. lod per un lengh whh pls deforon of he urn pr egns q y = kn/. Threded onneon n e yllly loded y one-sde or wo-sde endng oen. one-sde yl lodng he endng oen n he perod of yle nreses nd dereses whou s dreon hnge. Then he preers of he lernng els sresses yle n he sud hred plude of sresses, en sresses, xu nd nu sresses re he followng.5,. 5,, x n wo-sde syerl yl lodng he dreon of he endng oen hnges fer every seyle of he lodng. Then he preers of sress yle re he followng where P nd P /, y usng / n f n e n W n f n e n W H,, x, - n Furher he fgures presened n hs seon refle he lulon d for he onneon M6 whh hve een oned suh exernl lods F nd whh use he followng suds nonl sresses:

4 6,no /R p. =.57 ghenng nd,no,x /R p. =. endng. I ws ssued n he lulon h he helx of hreded onneon s se n he poson I. In hs se he suds hred lernng sresses due o endng nd lernng sresses due o ghenng hve xu vlues n he se ross-seon []. Ths ross-seon n he sud s found he oordne where R sn = R n hs se nd where runou he erng surfe of he nu egns. In Fgs. nd re shown dsruons of lods q, Q nd q, M whh hve een luled ordng o he ehods gven n seons nd. Verl dshed lne here nd furher rks orgn of he runou dsne - f =.8 fro he free end of he nu where dngerous ross-seon of he sud helx poson I s found. q ; q, kn/ f, Fg. Turn lods dsruons n he hred: q, q, q he seond seyle n he se of wo-sde endng 8 6 Q, kn; M, kn f, Fg. Inernl xl fore nd nernl endng oen of he sud ross-seons: nernl xl fore Q, nernl endng oen M lernng sresses n he hred roos due o ghenng nd sresses due o endng re shown n Fgs. nd 5. Sresses of he prry porne n he lulon of he fgue lfee re, euse hey gve nuerl vlues for he sresses yle - 6 8, MP f, Fg. lernng sresses n he sud s hred roos due o ghenng: sresses due o q, sresses due o Q, ol sresses due o ghenng: plude Eqs. nd. I s well known h fgue lfee s osly sensve nely o he sresses plude. In Fg. 5 re vsle hree pons where xu pludes of he lol sresses re prlly equl: wo lk pons nd one whe pon on he oppose lyers of he sud ll n he endng plne. Therefore n he se of wo-sde endng los sulneous nons of he fgue rk n e expeed n he sud ross-seons whh re rked y hese pons , MP, f, Fg. 5 lernng sresses n he sud hred roos due o endng: sresses due o q, sresses due o M, lol endng sresses:, funon y/, 5 he seond seyle n he se of wo-sde endng In Fgs. 6 nd 7 dsruons of he ol lernng sresses n he sud hred M6 re presened. I s seen n Fgs. 6 nd 7 h n he poson I of he hreded onneon n oh ses of he yl endng n he se of one or wo sde yl endng he xu en nd xu ol lernng sresses rse he orgn of runou,.e. he dsne - f =.8 fro he free end of he nu. he hgh level of ghenng,no /R p. >.85 ol lod of he urns pr q = q + q oned for he hred els se exeeds he yeld urns lod q y Fg. 8. Relly here due o he urns pls deforon n he regon of runou he erng surfe of he nu he ol urns pr lod wll e less hn oned. In suh ses he orreon of he plude of he urns lod, MP, MP f, Fg. 6 lernng sresses of he sud hred roos n he se of wo-sde yl endng: sresses fer ghenng, ol sresses, ol sresses he seond endng se-yle

5 7,, MP f, Fg. 7 lernng sresses of he sud hred roos n he se of one-sde yl endng: - n, -, - x 8 6 q, kn/ q y q f, Fg. 8 Shee of he urn pr lod plude orreon q - q y / hs een perfored n he followng wy: q = q - -[q -q y ]/. Then he oned q s eeng used n Eq. 9 nsed q. Fnlly n hs seon s usefull shorly o nlyse he gnudes of lernng sresses plude n he sud hred oned y usng els odel for he ses of helx poson dfferen fro he poson I.,, MP f, Fg. 9 pludes of lernng sresses n he sud hred vrous posons of hred helx: helx poson I, oher helx posons I hve een defned h n he ses of oher helx poson he xu of lol sresses plude n he sud hred re whn he regon of he runou nd her vlues re los equl very slgh lower o he vlue oned n he se of helx poson I. Suh four ses re shown n Fg. 9, where lk rngle pons rk he ppropre ross-seons of he sud. Due o he lower en q q sresses ghenng sresses whn hs regon Fg. he nuers of lod yles up o rk non n he sud hred luled y he ehods presened n he nex seon n ove enoned ses re lso lower hn n he se of helx poson I, u jus very slghly. 6. Fgue lfe predon In order o ese fgue lfe of he yllly en hreded onneons he possles o upply sndrd ehod [7] nd odfed sndrd ehod [9] re onsdered. Conrry o he sndrd ehod n s odfon he d of sresses dsruon long hred of he sud re used edely. In he se of yl enson of hreded onneons hs hs gven lulon resuls of he onneons lfee noly lose o he experenl d [9]. Two Coffn-Mnson-Lnger ype forule re presened n sndrd [7]. The sller vlue of he nuer of lod yles up o rk non n he sud hred N us e fnlly hosen ou of wo ssessed vlues. These forule, ppled o he sud, no sfey fors onsdered, re s follows Ee s R N R / R r/ r Ese R N N e r / r where R - s fgue l sress of he erl, e s erl plsy ndex, nd e re exponens of power, r s syery for of he lol sresses yle, R s erl srengh ndex reln on ensle srengh R nd s plude of lernng lol sresses n hred roos of he sud whh s luled y usng only one sress onenron for ordng o he followng foruls: K K,no nd K. 57 P / R r where,no s plude of xu nonl sresses of sud nd R r s urns roo roundng rdus. y usng dsruon of he sress n roos of he sud hred, defned under he ehods presened n seons nd, s possle o lule he nuer of yles N unl he rk ppers for ny urn of he sud, s well s N C = N for he sud s dngerous rossseon C hereof. Here expresson C oned for suds he hred helx poson I ws used. To prove hs he followng forul djused n [9] hs een used E e s C [N C r ] e [N C ] r where e.78 Z.6 R s he power exponen, djused n [9] on he ss of he experenl d oned xl yl lodng n sndrd [7],.e. n R

6 8 forul ppropre power exponen s e. lg[ R / R. Z]. The possles o pply foruls, or for yllly en hreded onneon hve een nlysed y usng oprson of he luled yle lfe N,l, wh he experenl d N,exp. Tess preers of he sud-nu onneons M6 de fro seel 5 re gven n Tle. In every speen roundng rdus of he sud hred roo ws R r =.P nd he oher densons of er hred were s spefed y ISO 7. Tle Speen No.,no,no Rp. R p. r n,no x,no endng sdes.7.. wo.7.8. wo wo wo one one wo wo wo wo wo wo.57.. wo Cyl lfe ess of he hreded onneons hve een rred ou under endng yl lods where he dspleen s proporonl o he ngulr dspleen of he wsed suppor of he nu s eng onored Fg.. Two prs of guges 6 Fg. hve een used n order o onrol he xu nonl endng sresses n ousde lyers of he sud found n endng plne nd nonl ghenng sresses n lyers neurl plne. G f G f onneon. fer eh proof nspeon, y usng uxlry nus wh pns, no lod ppled, he jon s sseled n suh wy, h n he ourse of furher esng, poson of he nu relve o he sud rens unhnged. Now, suh dngerous se of he sud s hred roos, when he lengh of rork round he perphery hereof reh - 6, s onsdered o e he rk non. N,exp,yle Eq. Eq. N,l, yle N,exp,yle Eq. N,l, yle Fg. Coprson of lfees for sud-nu onneons M6 : lulons s per sndrd s foruls nd, lulon s per forul ; nd pons for wo-sde nd one-sde yl endng;,,, lnes N,exp /N,l =,, 5, F s F 5 6 s In Fg. re shown h ll pons whh rk luled rk non lfees of he suds les n he sfe pr of lfe e rnge over he lne. The experenl vlues N,exp exeed lfees N,l oned y usng foruls nd up nd 5 es respevely nd ou -5 es n he se of usng forul. G f 7 G f 7. Conlusons Fg. Shee of yl endng of he sud-nu onneon: sud, nu, wsed suppor, nerede del, 5 roll, 6 four srn guges, 7 uxlry nu; G fore vryng durng lodng yle e The nonl ghenng sresses of he sud,no yl lodng unll rk non hve deresed ou -5% u s nonl endng sresses,no,x prlly rened unhnged. Mgne lunesen powder ehod hs een eployed o defne he sr pon of rk non n he sud. Deeon of foron of he rk n he sud s eng perfored on roune ss y knokng down he. To norpore he hreds lod dsruon d no he lulon of fgue durly of yllly en hreded onneons he odfed forule ould e used.. Low yle durly up o yles of he yllly en hreded onneons se ordng o odfed ehod for yl srengh s noly hgher ou -5 es hn he luled vlues se ordng o he Nor of Rusn Federon Nor RF [7]. They re lose o experenl vlues, howerer do no exeed he.

7 9 Referenes. rger, I..; Ioslevh, G ol nd Flnge Conneons. Mosow: Mshnosroenje. 65p. n Russn.. Mhuov, N..; Sekolnkov, V.V.; Frolov, K.V.; Prgorovskj, N.I Consruons nd Mehods of Clulon of Wer-Wer Power Reors. Mosow: Nuk. p. n Russn.. Tuons, L.; Shneder, M.; Knusks, R.; Kenusks,. 9. Coprson of dyn ehvor of EM- rlgun under dfferenly ndued lodngs, Mehnk 78: -7.. Venskus,.; Kln S.; kons, J.; Ulns, T.. Inegred lod opon of els-pls xsyer ples shkedown, Journl of Cvl Engneerng nd Mngeen 6: Dunys, M.; esnvus, R. 9. Low yle sress srn urves nd fgue under enson-opresson nd orson, Mehnk 68: SME oler nd Pessure Vessel Code, Se. III. Rules for onsruon of Nuler Power Pln Coponens, Dv. I., Suse. N, Nor for lulon of nuler power equpens nd ppelnes srengh. Mosow: Energood, p. n Russn. 8. Person, E Coprve sudy of ehods for esng ol fgue ls, Fgue nd Frure of Engneerng Merls nd Sruures : Krenevus,.; Leonvus, M. 8. Fgue lfe predon for hreded jodn, Mehnk 7: 5-.. Selvone, J.; Krenevus,.. Dsruon of Lod n he Threds, Mehnk 6: -6.. Krenevus,.; Juhnevus, Ž.; Leonvus, M.. The odel of en hreded onneon n hree segens, Mehnk 8: 5-. Ž. Juhnevus,. Krenevus CIKLIŠKI LENKIM SRIEGINI JUNGI ILGMŽIŠKUMO PROGNOZVIMS R e u Srpsnyje prody, kd odfkuos norns eods, vernns pkrovos psskrsy srego vjose, yr nks kron lenk sregn jung klno lgžškuo prognovu. Pnudos pkrovos r ep psskrsyo vjose odels, kurs spnd vsu r ne vsu proflu sukus vj por projo deforvo svyes. Gu jung M6 klno lgžškuo skvo reul r eksperenns rekšs r j nevršj. Ž. Juhnevus,. Krenevus FTIGUE LIFE PREDICTION FOR CYCLICLLY ENT THREDED CONNECTIONS S u r y In hs pper s shown h he odfed norve ehod proved y norporng n he lulon he d of lod dsruon n hreds s fed for he fgue lfe predon of yllly en hreded onneons. The odel for lulon of lod nd sress dsruon long he hred sed on els deforon properes of he full nd prl profle urns prs s used. Resuls of fgue lfe predon oned for he yllly en hreded onneons M6 re lose o he experenl vlues, howerer do no exeed he..,. e - -,, -. -,. - - M6 -. Reeved Ooer, eped prl 7,