9.6 Blend-Out Repairs

Transcription

1 9.6 Bled-Out Repirs Oe of the ccepted procedures for removig smll mout of crck dmge i the field is through the use of bled-out repirs. These repirs re efficietly ccomplished d for the most prt, retur the structure close to its origil sttic stregth d desig crck growth life itervl. This subsectio ddresses the type of ftigue crck growth life lysis oe might coduct to esure tht bled-out repir hs ot sigifictly degrded the ticipted service life of the structure. There re two bsic coditios tht might degrde the life of the structure s result of bledout: () the ccidetl gougig, scrpig, or otherwise dmgig of the mteril durig the repir d () the developmet of stress cocetrtio site. Both coditios must be ctively voided sice both ted to ccelerte the developmet of ew crcks which could cuse sfetyof-flight problems. As discussed i Sectio 9.5, oe of the more difficult spects of repir lysis is the defiitio of iitil crck size utilized for life clcultios. If the iitil crck size ssumed fter repir is greter th or equl to the iitil crck size ssumed durig desig, the the structure life fter repir is less th or equl to the iitil desig life. To determie the frctiol loss (FL) i structurl life, egieer could utilize the rtio Life (Repir) FL (9.6.) Life (Blueprit) Altertely, the egieer could evlute the loss i blueprit life by formig the life rtio: Life (Repir) LR (9.6.) Life (Blueprit) For compriso purposes, it would probbly be dvisble to clculte both the repir life d blueprit life bsed o the sme iitil crck legth d thereby ssess the effects of stress cocetrtio itroduced by the bled-out opertio. To estblish the crck growth life of the repir i bsolute sese would require tht the choice of iitil crck legth be give creful egieerig cosidertio. Two exmples hve bee prepred to illustrte the types of lyses tht could be coducted to evlute the dmge tolerce of bled-out type repirs. Exmple 9.6. presets the clcultios where the iitil crck size for the repir is ssumed to be equl to the crck size i smufctured structure. A sesitivity study is preseted to demostrte the impct tht bled-out shpe hs o repir life. I Exmple 9.6., the crck size fter repir is ssumed to be smller th tht i the s-mufctured structure, d sesitivity study is preseted to illustrte the effect of crck size. 9.6.

2 EXAMPLE 9.6. Bled-Out Repir - Effect of Shpe The gle trsitio compoet show below periodiclly exhibits evidece of crckig i the loctio idetified d the egieer hs recommeded bled-out repir to remove ll evidece of crckig. Bsed o the mufcturer s stress report, the tesile stress i the gle trsitio compoet is 7 ksi for the criticl lod coditio. Evlute the dmge tolerce of the compoet ssumig tht the iitil crck size i the repir d the s-mufctured structure re the sme ( o ich) T6 Alumium Thickess Geometry of Structure with Smll Crck R Iitil σ Repir σ SOLUTION: Geometry of Bled-Out Repir Assumed for Alysis The dmge tolerce evlutio will be bsed o ssessmet of both the chge i crck growth lives d the chge i criticl crck size. Bsed o lck of both stress history d wide re crck growth rte equtio (discussed i prgrph 9.3.3), egieer might choose worst cse lodig eviromet to coduct the evlutio. Sice the stress coditio is kow (σ mx 7 ksi), the egieer could pproximte the lodig with oce per flight mximum stress of 7 ksi pplied i costt mplitude mer. For simplicity, the miimum stress per flight is presumed to be zero so tht the ssumed lodig is zero-tesio (R 0) costt mplitude with stress mximum of 7 ksi. 9.6.

3 To coduct the life lysis, the life equtio bsed o cotiuous crck growth (cosistet with the costt mplitude lodig ssumptio) will be utilized, i.e., life will be clculted usig Life f o d f ( K ) The fuctio f(k) describes the crck growth rte for the mteril d lodig coditio; o d f re the iitil d criticl crck sizes, respectively. Three elemets re ecessry for the life clcultio: () the fuctio f(k), () the stress-itesity fctor reltioship for the geometry, d (3) the criticl crck size ( f ). Ech elemet will be seprted determied i the prgrphs below; subsequetly, LIFE will be determied. Fuctio f(k) Estblished The fuctio f(k) describes crck growth rte s fuctio of stress-itesity fctor prmeter (such s K). As result of the costt mplitude lodig coditio, the egieer would cosult the Dmge Tolert Desig (Dt) Hdbook [Ski, et l., 994] to fid dt cosistet with the mteril d stress rtio coditios. The dt i Figure of the DTDH re cosidered represettive of the 7079-T6 lumium lloy. While it is possible to utilize the me tred dt give i tbulr form, s preseted i the figure, i cojuctio with computer codes tht employ tble look-up schemes, it is istructive to plot the me tred dt d determie if simple (power lw) crck growth rte equtio, i.e. d dn C K describes the behvior. Both the me tred dt for the R 0.05 dt set d power lw equtio tht describes these dt re preseted. The power lw equtio ws determied (grphiclly evluted) to be d dn 584. x0-0 K 409. Becuse the stress rtio (R) for the ssumed lodig (R 0) d the dt set (R 0.05) re reltively close, o stress rtio correctio fctor is pplied to Equtio If stress rtio correctio must be pplied to hdbook dt set, it is suggested tht Wlker type correctio be cosidered. The suggested Wlker correctio fctor for lumium lloys is give by d dn R Rdesired C dtset R R dtset desired K where R dt set d R desired re the stress rtios ssocited with the Hdbook dt set d the ssumed lodig, respectively, d where is the power lw expoet for the dt set ( 4.09 for the 7079-T6 lumium dt set). A quick evlutio of the Wlker equtio with the pproprite costts shows tht the crck growth rte expressio give by the power lw equtio is pproximtely 0 percet higher th correspodig stress rtio corrected expressio, d thus ot overly coservtive for first order pproximtio

4 Dt Pge From the Dmge Tolert Desig (Dt) Hdbook [Ski, et l., 994] Used i Exmple

5 7079-T6 AL.E-04 d/dn (i/cycle).e-05.e-06 me tred power lw.e Delt K (ksi i^.5) Dt From Dmge Tolert Desig (Dt) Hdbook Plotted d Compred to Grphiclly Estblished Power Lw Equtio Stress-Itesity Fctor Estblishmet The stress-itesity fctor for the bled-out crckig problem c be solved without ccess to exct fiite elemet stress lyses through the use of some work of Dowlig [979]. For the purpose of providig methodology for estimtig totl ftigue life (crck iititio plus crck propgtio lives) of otched structures, Dowlig eeded trsitio crck legth tht seprted the iititio life lysis from the crck propgtio life lysis. His studies of the coditios cotrollig smll crck growth behvior led him to the stress-itesity fctor evlutio show below. The poit M idetifies the coditio where the short crck stress-itesity fctor (K s ) is equl to the log crck solutio (K l ). Dowlig oted tht these two crck solutios provided resobly ccurte estimtes of the fiite elemet solutio i their respective crck legth regios. For crck iititio life lysis, Dowlig restricted crck legth size mesured i smooth ftigue smples to sizes less th the crck legth ssocited with the poit M i the figure. This is becuse the stress cocetrtio effect domites i this regio

6 Short d Log Limitig Cses d Numericl Solutio, for Crck Growig from Circulr Hole i Ifiite Plte (Newm) For the purpose of lysis, the egieer could estimte the stress-itesity fctor for the bledout repir usig Dowlig type pproch where for smll crcks, short crck stress-itesity fctor would pply, d for loger crcks, log crck stress-itesity fctor would pply. Thus, for the bled-out repir, the egieer could describe the stress-itesity fctor s: K K s K K l if if > M M with the short d log crck stress-itesity fctors give by: d K s. k σ t π K. σ π( + d ) l where k t is the stress cocetrtio fctor ssocited with the bled-out shpe. The equtios re writte i form slightly differet th those preseted i the figure becuse () the geometry of the bled-out is more i lie with edge crck rther th cetrl crck (Dowlig s solutio) d () the crck legth is mesured from the surfce of the bled-out (see the figure for defiitio of d d)

7 R σ L d σ Geometry of Bled-Out with Edge Crck Preset Bsed o lysis of these equtios, oe c see tht the bled-out geometry ffects the stress-itesity fctor solutios through the stress cocetrtio fctor (k t ) d bled-out depth (d). A estimte of the stress cocetrtio k t for bled-out repir is mde usig the solutio of ellipticl cut out i plte. For ellipse orieted with the mjor xis i lie with the directio of the stress xis, the stress cocetrtio is give by [Mushhelishvili, 954; Peterso, 974]: 3 + M M k t + M + M where L d M L + d with L d d defied s the mjor d mior rdii of the ellipse. As c be oted from the figure, L d d defie segmet of circle tht we re pproximtig with semi-ellipse. Thus, if oe hs mesure of L d d for bled-out repir, oe c estimte k t d the correspodig short crck stress-itesity fctor usig the equtios bove. Criticl Crck Size, f The criticl crck size for both s-mufctured (blueprit) d repired structure will be bsed o the Irwi hypothesis for brupt filure, i.e., whe K K cr filure occurs. The criticl stress-itesity fctor is obtied by estimtig the stress-itesity fctor rge required to chieve growth rte of 000 microiches/cycle. Solvig the power lw equtio i iverse mer, i.e., solvig K yields K ksi i As lower boud to this estimte, oe might choose K cr 30 ksi i for coveiece. K cr 30 ksi i correspods to crck growth rte of 64 microiches/cycle. The stress-itesity fctor for the blueprit structure is give by K. π wheres tht for the repired structure is give by 9.6.7

8 K. σ π( + d ) (Note tht the log crck solutio is beig used for the repir). I both equtios, is mesured from the surfce. Solvig for K cr 30 ksi i d the bove stress-itesity fctor solutios yields f 0.35 ich for the blueprit criticl size d f (0.35-d) ich for the repir criticl size. Life Estimtig While the LIFE equtio could be used directly for life estimtes of the s-mufctured (blueprit) structure, the stress-itesity fctor lysis requires tht the itegrl equtio be broke ito two itervls. For this repir lysis, LIFE is clculted usig LIFE M o d f ( K s + ) f M d f ( K l ) where the crck size M is ssocited with the trsitio betwee the short d log crck stressitesity fctor solutios. This crck size is obtied by equtig the two solutios d solvig for M, thus K s K l i cojuctio with the stress itesity equtios results i m d k t Sice for bled-out repir k t would be greter th.0 d hopefully less th.4, M will be greter th d. Numericl Detils of Blueprit Life For edge crck problem with the mteril crck growth rte respose give by power lw expressio, i.e. the LIFE equtio c be writte s LIFE C(. σ π ) f o d Whe itegrted, this equtio becomes LIFE C(. σ f o π ) 9.6.8

9 Give the growth rte costts C d, the criticl crck size f, the give stress (σ 7 ksi) d the give iitil crck size ( o ich), the crck growth life for the blueprit coditios is determied to be LIFE 90 cycles of zero-tesio lodig. Numericl Detils of Repir Life For the bled-out repir with the mteril crck growth rte respose give by power lw expressio, the LIFE equtio c be expressed s: LIFE π ) kt M C(. σ Whe itegrted, this equtio becomes LIFE C(. σ o d + f M ( d + d ) M o ( f d ) ( M d ) π ) kt Give the growth rte costts C (5.84 x 0-0 ) d (4.09), the criticl crck size, the give stress (σ 7 ksi), d the give iitil crck size ( o ich), oe c estimte the LIFE for defied vlues of k t d d. For exmple, whe d d L re 0.08 ich d.0 ich, k t is.6, f 0.45 ich, M 0.3 ich, d LIFE 033 cycles of zero-tesio lodig. This is pproximtely 30 percet lower th tht give for the blueprit life. Comprtive Alysis of Shpe Effect To summrize the lysis for differet bled-out shpes, the LIFE equtio ws repetitively solved for severl differet legth (L) d depth (d) coditios for o ich. These results re preseted i the followig tble i the form of life rtios d utilize the blueprit life obtied bove. Focusig o three crck depths (0.050, 0.00 d 0.50 iches) s represettive, oe c immeditely ote from the tble tht eve for the more grdul bled-out cse, the life is substtilly reduced (to pproximtely 80, 65, d 50 percet, respectively) of the origil life estimte. The life rtios preseted i the tble show the close correltio betwee life d the stress cocetrtio fctor. These results oly reiforce commo sese sice they show tht the more grdul the bled-out, the closer to iitil life oe chieves

10 Depth (d) ich Effects Of Bled-Out Shpe O Crck Growth Life Rtio Legth (L) ich k t Life Rtio Coditio Grdul Bled Out Less Grdul Bled Out 9.6.0

11 EXAMPLE 9.6. Effect of Repir Iitil Crck Size To justify removig shllow crcks with bled-out repir procedures, Exmple 9.6. is exteded by cosiderig the effect of repir iitil crck size. As bsis for compriso, the life rtio equtio, LR Life (Repir) Life (Blueprit) will gi be employed, d the blueprit (s-mufcturig) LIFE is clculted usig LIFE π ) kt M C(. σ o d + f M ( d + d ) with o ich. Thus, the blueprit LIFE is 90 cycles, s clculted i Exmple The purpose of this exmple is to show tht if oly prt of the crck remis fter bled-out there c be substtil life improvemet over tht clculted for the blueprit LIFE. The effect of repir iitil crck size o crck growth life ws clculted usig LIFE C(. σ M o ( f d ) ( M d ) π ) kt wheres the iitil crck size o ws vried log with legth (L) d depth (d) of the bled-out. The results re summrized i the followig tble s fuctio of the vrious geometric prmeters cosidered. As expected, the tble shows tht iitil repir crck size substtilly ffects the dmge tolert life of the bled-out. I fct, compred to the other prmeters cosidered, it domites. Bsed o this tble, the importce of the vribles o life is; o - most sigifict, k t - sigifict, d d - lest sigifict. Thus, durig bled-out repir, the objective is to remove s much of the dmge s possible (d hopefully ll) with miimum mout of shpe chge. 9.6.

12 Effect of Repir Iitil Crck Size o Crck Growth Life Rtio Repir Iitil Crck Size ( 0 ) ich Depth (d) ich Legth (L) ich k t Life Rtio