D is the total damage, D

Transcription

1 Lie Science Jounal 03;0(3s hp:// Themo-Mechanical Faigue (TMF Lie Pedicion in Gas Tubine Blades Aash Rahmani, Ghiam Eslami, Ramin Soleimani epamen o Mechanical Engineeing, Aha Banch, Islamin Azad Univesiy, Aha, Ian epamens o Engineeing, Ajabshi Banch, Islamin Azad Univesiy, Ajabshi, Ian * o Coesponig Auho: aa_ahmani@yahoo.com Absac: A Tubine blade, which is a main high empeaue componen o a gas-ubine o powe geneaion does no oleae he exisence o cacks as i oaes a a high speed. Consequenly, he developmen o an analyical mehod o evaluae he emaining lie o cack iniiaion is equied. The accuacy o emaining lie evaluaion by an analyical mehod lagely depends on inelasic consiuive equaions expessing on a ceep-aigue lie evaluaion mehod using such equaions o esimae he emaining lie o cack iniiaion. Theeoe, in his pape, we sudied ceep-aigue damage mechanism o gas ubine blades which is capable o descibe inelasic behavio o he maeial and he damage mechanism. Fo his pupose we use Themo-Mechanical Faigue (TMF lie pedicion models ake ino accoun he ineacion beween aigue and ceep a vaying empeaues. [Rahmani A, Eslami G, Soleimani R. Themo-Mechanical Faigue (TMF Lie Pedicion in Gas Tubine Blades. Lie Sci J 03;0(3s:546-55] (ISS: hp:// 86 Key Wods: Faigue-Ceep, Lie Time, TMF, Tubine Blades.. Inoducion Tubine ho-secion componens, such as blades, ae designed o opeae in high- empeaue envionmens, wih high hemal gadiens and mechanical loads. Repeaed engine sa- up and shudown opeaions subjec componens o cyclic sains which ae geneaed boh hemally and mechanically. These hemo-mechanical aigue (TMF cycles cause mico sucual maeial damage o he componens, and lead ulimaely o aigue cack iniiaion and ailue. Advanced high empeaue aigue lie pedicion mehodologies ae needed o decide when o eplace componens, in ode o incease eliabiliy and sevice lie, and educe mainenance coss. Pedicing he lives o blades subjec o hemomechanical aigue coninues o be a gea challenge. In he las ou decades much wok has been peomed in modeling aigue cack iniiaion o a ange o maeials. Many eseaches have examined ceep-aigue cack iniiaion and popagaion modes in geneal [, ]. Some o hem emphasizes on sudying he eec o speciic paamees such as hold ime, Geomey, maeial paamees and meallugical poblems [3-5]. Also, a lage numbe o models o isohemal cack iniiaion and lie pedicion appoaches and vaiaions exis, [6, 7]. In his pape, we deine he inelasic deomaion behavio and ceep-aigue damage mechanism o Ti-6Al-4V, a maeial o gas ubine blades. Fo his pupose we use Themo-Mechanical Faigue (TMF lie pedicion models ake ino accoun he ineacion. Because o he aigue-ceep pocess, i is necessay o uilize a viscoelasic maeial model in he inie elemen analysis. 3. amage Analysis umeous appoaches have been developed o pedic he oal lie in maeial which opeaed in high empeaue, he simples and mos common appoach o pedic aigue lie involves he linea damage summaion model. The Linea amage Summaion (S model is he simples expession o ceep-aigue lie pedicion. I ignoes he micosucual deails o he damage pocess. I was inoduced is by Taia [8] as ollows: oal aigue ceep ( is he oal damage, oal aigue and ceep ae he aigue damage and ceep damage especively. The damage summaion ule assumes ha ailue occus when he sum o he aigue damage and he ceep damage is equal o a ciical value. I, he ailue is occued. oal. Faigue amage Thee ae commonly hee ecognized oms o aigue, High Cycle Faigue (HCF, Low Cycle Faigue (LCF and Themo-Mechanical Faigue (TMF. HCF is usually associaed wih low sess levels and low ampliude high equency elasic sains. LCF is isohemal aigue whee he sain ange duing aigue cycling exceeds elasic sain ange and causes inelasic deomaions so ha he maeial exhibis a sho numbe o cycles o ailue. In he ohe wods, Low- Cycle Faigue (LCF will ake place when he empeaue is below he ceep hp:// 546 liesciencej@gmail.com

2 Lie Science Jounal 03;0(3s hp:// egime o when a componen is aeced by isohemal cycling. Isohemal LCF es has been used o deemine he peomance o maeials applied in componens as ubine blades and disks. Resuls o a LCF es may be used in he omulaion o empiical elaionships beween cyclic vaiables o sess, oal sain, plasic sain and aigue lie. They ae nomally pesened as cuves o cyclic sess o sain vesus lie o cyclic sess vesus plasic sain and examinaion o such cuves and compaison wih monoonic sess, sess- sain cuves gives useul inomaion egading cyclic sabiliy o a maeial. LCF Lie lies usually in he ange beween 0 o 5 0 cycles. The esponse o a maeial subjeced o cyclic loading is pesened in he om o hyseics loops. The oal widh o he loop is he oal sain ange while he oal heigh o he loop is he oal sess ange. The Toal sain is he sum o he elasic sain and he plasic sain. Thee ae wo essenial ypes o TMF cycles: In- Phase cycle and Ou-o Phase cycle which ae descibed as below: In- Phase Cycle This is when he sain and he empeaue ae cycled in phase, see Figue ypical example is a cold spo in a ho envionmen, which a high empeaue will be loaded in ension and a low empeaue loaded in compession. Ou- O Phase Cycle This is when he sain and he empeaue ae cycled in coune phase, see Figue Typical example is a ho spo in a cold envionmen, which a low empeaue will be loaded in ension and a high empeaue loaded in compession. Figue : The Ou-Phase Themo-mechanical Faigue cycle Figue : The In-Phase Themo-mechanical Faigue cycle Themo mechanical Faigue (TMF is a unique ype o aigue in which maeial is simulaneously, subjeced o lucuaing loads and empeaues, and he heoy o TMF Addesses he ceep-aigue ineacions ha occu. When ho-secion componens ae subjec o high empeaue hemal cycles concuenly wih mechanical sain cycles, TMF Condiions esuling in mico-sucual damage occu. The lieime o he componens unde such TMF Loading is quie dieen om isohemal lie pedicion obained a he maximum empeaue o opeaion, because in TMF he ceep damage o he maeial should ake ino accoun and i is geaes. As shown in Figue 3, unde In-phase cyclic loading condiions, he maximum ensile sain occus a he same ime as he peak empeaue, and he maximum compessive sain occus a he minimum empeaue. In conas, unde ou- ophase cycles, he maximum ensile sain occus a he minimum empeaue, and maximum compessive sain a he peak empeaue. Figue 3: In-Phase and Ou- o- phase TMF loading paens Fo aigue damage calculaion we use he mehod o univesal slopes. This mehod has he advanage o using maeial daa obainable om simple ensile ess. Based on The Basquin and Coin- Manson elaionship, he oal sain ange can be expessed as: hp:// 547 liesciencej@gmail.com

3 Lie Science Jounal 03;0(3s hp:// ( E Whee e p b b c B ( C( ( 3.5 u ( ( E Whee is ulimae acue sess and, 3 ( ( ( ( 3 x y y z z x xy yz zx c (3 ( is he cyclic sengh coeicien, b is he cyclic sengh exponen and vaying om o - 0.4, E is Young s modulus, is he numbe cycles o ailue a a given sain-ange, is aigue duciliy coeicien and c is aigue duciliy exponen and anges om -05 o The Sains in Eq. (3 ae expessed as sain ampliudes ha ae a hal o he sain anges. The Relaion beween sain and numbes o evesals o ailue can be pesened in a log-log plo as shown in Figue 4. Eq. (3 is wien as: u Figue 4: Sain-Lie elaions (4 / (5 Using Eqs. (4 And (5, we can esimae he value o and hen, he aigue damage,, is calculaed as: (5 Whee is numbe o compleed cycles in paicula sess, heeoe: n i aigue (6 Aexp( RT Ln Ln A RT i Ln A Ln LnA Ln( Ln A Ln Ln i Whee i implies he dieen case o loadings. 4. Ceep amage When ubine blades opeae a empeaue which is geae han 40% T mel ceep occus and should be consideed as damage. Ceep ess ake a long ime o peom making he geneaion o design daa expensive and he lead ime beween developing a new alloy and is exploiaion excessive. The ac ha hee is an Ahenius elaion beween ceep ae and empeaue has led o a numbe o ime-empeaue paamees o be developed which enable exapolaion and pedicion o ceep aes o ceep upue imes o longe imes han have been measued. They also enable aing compaisons o be made beween dieen maeials. I is impoan ha no sucual changes occu in he egion o exapolaion, bu since hese would occu a shoe imes o highe empeaues i is sae o pedic below he empeaue o which daa is known han above. One paamee used is he Lason-Mille Paamee, which is deived by aking naual logs o Ahenius equaion: (6 RT (8 T( C Ln P (9 R Whee C Ln A Ln, is he Lason-mille Consan and P is he Lason-Mille Paamee o a RT (7 Whee A, ae empiically deemined ceep R consans coesponding o he ime, T, a which he accual o a pe-deined amoun o ceep sain is eached. I we assume ha he ceep sain o upue,, is a consan ove he empeaue ange o inees, and he majo pa o he ceep sain is seady sae ceep, hen he aveage ceep ae ove he lie o upue,, o he specimen is: hp:// 548 liesciencej@gmail.com

4 Lie Science Jounal 03;0(3s hp:// paicula sess, ( 0. Ploing expeimenal daa o Ln vesus gives a saigh T The values o C ange om 35 o 60, bu is ypically 46. Figue 5 shows ha C is independen o sess bu P is uncion o sess and empeaue. line wih slope P and inecep a 0 T (7 o C. (a (b ceep n i i Ri Figue 5: (a Sess upue daa as upue ime. (b L-M Paamee Accoding o he Lason-Mille equaion, we calculae he upue ime and consequenly, ceep damage as: (0 Whee, ae he ime spen and upue ime a a i Ri paicula sess/ empeaue. 5. Finie Elemen Model The Finie Elemen (FE model consiss o wo ineelaed models. The hemal model calculaes he empeaue disibuion in he componen, based on he hea inpu om he ho gas. The mechanical model calculaes he sesses and sains in he blades, caused by he vaying empeaue disibuion and he exenally applied loads. The hemal model calculaes he empeaue disibuion in he componen. Fo each inie elemen on he suace o he componen, he hea anse coeicien ollows om he CF model. Wih he hemal conduciviy α o he maeial, he empeaue disibuion in he blade can be calculaed. The maeial which is used o FE model is Ti-6Al-4V wih below chemical, physical and mechanical popeies: Table: Chemical popeies o Ti-6Al-4V (Gade 5 C H Fe O Al V Ti Balance ( g / cc ( w/ mk Table: Physical popeies o Ti-6Al-4V (Gade 5 Reducion o Aea (% Elongaion (% in Table3: Mechanical popeies o Ti-6Al-4V (Gade 5 Young's modulus [Gap] Yield sengh [Mpa] Ulimae sengh [Mpa] Poisson Raio HRC hp:// 549 liesciencej@gmail.com

5 Lie Science Jounal 03;0(3s hp:// 6. Resuls A mesh was poduced using 5040-nodded isopaameic bick elemens, each wih 7 inegaion poins, while convecion bounday condiions wee obained om CF analyses. A ansien hemal analysis was hen peomed, and used in he sess analysis. The inal disibuion o he blade meal empeaues is shown in Figue 6. These esuls wee used in a saic sess analysis o deemine he hemal sesses and, in paicula, he maximum sess value a each poin in he blade. Figue 6: Tempeaue disibuion by hemal analysis Ceep-Faigue amage 0 amage (* Time (h (*000 Faigue amage Ceep amage Toal amage Figue 7: amage Plos Once he sesses wee ound, a ceep sep was peomed, which each o he oal damage paamee oal. A his poin a cack was assumed o have omed a he elevan elemen. Figue 7 shows maximum values o aigue, ceep and oal damage wih condiions ha ae used i solved his poblem. I Is clea ha aigue damage is moe han ceep damage and blades ae involved a ailue when hey opeae moe han 3900 hou whee oal damage exceeded a value o uniy,. Also, The Ceep damage ae was oal iniially highe han he aigue ae, bu as sess elaxaion occued, his dopped o consideably. hp:// 550 liesciencej@gmail.com

6 Lie Science Jounal 03;0(3s hp:// 7. Conclusion In his pape, we use an inegaed analysis o lie pedicion o gas ubine blades by TMF model and ceep-aigue ineacion. Fo his, he accuacy o he empeaues calculaed wih he hemal FE Model is mainly deemined by he accuacy o he hea anse coeicien value which is calculaed by CF. Then, he esuls povide a codeing in MATLAB involved he ollowing calculaions: - Full ceep analysis consiss o ceep sain calculaions (Eq. 6, pediced ceep upue (Eq. 8, ceep damage (Eq Cycles numbe o ailue,, (Eq. 3, aigue and oal damages (Eqs. 6,. Reeences. Ryuichi. O, Takayuki. K, Misuyoshi. T, Hideki. M, " Iniiaion And Gowh O Small Cacks In Ceep Faigue O Oxide ispesion- Senghened Supealloys A Elevaed Tempeaue," Japan Sociey O Mechanical Enginees, Tansacions A, Vol. 59, o. 560, pp , Apil Maile. K, Klenk. A, Ganache J, Schellenbeg. G, Tame M, "Ceep and Ceep Faigue Cack Behavio o IC- and 9C- Seels," Key Engineeing Maeials (03-986, Vols. 7-74, pp , Gemma A. E, "Hold- Time Eec o a Single Oveload on Cack Readaion A Elevaed Tempeaue," Engineeing Facue Mechanics, Vol., o. 4, pp , uggan T. V and Sabin. P," The Eec o Geomey on Cack Fomaion, Advances In Reseach on he Sengh and Facue o Maeials," Poceedings o he Fouh Inenaional Coneence on Facue, Vol. 3A (A , ew Yok, Pegamon Pess, pp. 85-9, Beman I, Gangadhaan A. C, Jaisingh G. H, Gupa G., " Eecs O Maeial Paamee Vaiabiliy On Buckling And Ceep Faigue Ineacion A Elevaed Tempeaue" Tansacions, Seie JJounal O Pessue Vessel Technology, Vol. 98, pp , Febuay Salam I, Tauqi A, Khan A., "Ceep- Faigue Failue o an Aeo Engine Tubine Blades," Engineeing Failue Analysis, Vol. 9, pp , 00. M. H. Sabou, R. B. Bha, "Lieime Pedicion in Ceep-Faigue Envionmen". 7. Taia, S., Relaionship Beween Themal Faigue And Low- Cycle Faigue A Elevaed Tempeaue, ASTM STP 50, pp. 80-0, 973. /8/03 hp:// 55 liesciencej@gmail.com