PROBLEM OF LOW CYCLE FATIGUE OF TURBOMACHINES

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PROBLEM OF LOW CYCLE FAIGUE OF URBOMACHINES Joury em*, Khakm Azmetov* and Alexander Fakeev* *Department of Mathematcal Smulaton, Central Inttute of Avaton Motor Keyword: thermomechancal fatgue, cyclc

1 PROBLEM OF LOW CYCLE FAIGUE OF URBOMACHINES Joury em*, Khakm Azmetov* and Alexander Fakeev* *Department of Mathematcal Smulaton, Central Inttute of Avaton Motor Keyword: thermomechancal fatgue, cyclc tre-tran loop Abtract Model of cyclc tre-tran curve and correponded damage model for mulaton of nonothermal cyclc loadng and etmaton of turbomachnery component lfe tme are developed. Change of Bauchnger' effect, Young' modulu and parameter of hardenng a functon of accumulatve platc tran are decrbed by the cyclc model of materal. Model of damage baed on reachng value of accumulatve platc tran to ultmate tate at cyclc loadng. Smulaton of nonothermal platcty of turbomachnery component baed on Fnte Element Method [FEM] code whch ue the theory of tran platcty for calculaton that wa generalzed to cyclc nonothermal loadng. Reult of calculaton of turbne engne component uch a dc, hghloaded concentrator of blade lock and turbne blade under cyclc loadng are preented. 1 Introducton urbomachnery component work under nonothermal and tranent loadng whch generate alternatng platc tran under tran cyclng n tre concentrator. herefore problem of mathematcal mulaton of tretran tate actual to decrbe nfluence of platcty and creep under nonothermal cyclc loadng. Partcularly th problem actual on the degn tage of Ga urbne Engne [GE] part wth the tre concentrator (dc wth hole, turbne blade and etc.) for etmatng of low cycle fatgue [LCF]. hee tre concentrator are local and change tree and tran from the nomnal value n the ome local regon of component. herefore n the mot cae tree and tran n thee regon practcally have not nfluence on the common tre-tran tate of the component. Common tre-tran tate can be decrbed by calculatng of knetc of tree and tran n the tructure. It poble on the bae of the technology of multdcplnary mulaton that allow creatng vrtual model of component or engne [1-3]. h vrtual model evaluate the knetc of thermal tate, preure, nomnal dplacement, tran and tree n the component of tructure by the multaneouly calculatng ga flow n the cavte of the engne, tranent thermal conductvty and deformable old mechanc. Reult of that analy determne temperature and boundary condton (dplacement and tree) for the mprovement of the elected regon around the concentrator. ranton to reearch of regon of concentrator requre more accuracy analy of elatoplatc tate. In that cae t neceary to take nto account feature of nonothermal cyclc loadng. Cyclc tre-tran curve preent a concepton about thee feature. h paper dedcate to decrbe of model mulatng of knetc of tre-tran tate and lfe predcton of low cycle fatgue of concentrator regon. Model of platcty ung n the paper are baed on approxmaton cyclc tre-tran curve by three parameter decrbng of Bauchnger effect, cale of tranformaton of nonlnear part of tre-tran curve and Young' modulu and dependng on total accumulatve platc tran [4]. Nonothermal loadng condered by the concepton of thermomechancal urface [5] generalzng on nonothermal cyclc loadng. 1

2 JOURY EMIS, KHAKIM AZMEOV AND ALEXANDER FAKEEV 2 heory 2.1 Model of nonothermal cyclc tretran curve hree parametrc model [6, 7] ung for mulaton of elatoplatc tre-tran repone under othermal cyclc loadng generalzed to cae of nonothermal condton. h make poble to decrbe dependence of Bauchnger effect, nonlnear part of tretran curve and Young' modulu veru total accumulatve platc tran under nonothermal cyclc loadng. Such approach at fxed temperature wa confrmed for decrpton cyclc tre-tran curve everal tructural materal [6, 7]. he thermomechancal urface under cyclc or complex loadng condered. Part of th thermomechancal urface locatng between othermal cyclc tre-tran curve at temperature 1, 2 and at current value of p accumulatve platc tran d decrbed by relaton: modulu; f(ε,) a tre-tran curve at the frt halfcycle; f a cyclc tre-tran curve at temperature [6, 7]. It hould be noted that parameter a(χ, ), b(χ, ) and d(χ, ) depend on accumulatve platc tran χ and characterze cyclc tretran curve at temperature. a) * * F p (, ), F (1 ) f1 f2, (1) d, * E, * E d, f d, b, * * f, b, * 1, 2 a,, ; ; * a, / d, * * * * (2) where * and * are tre and tran n local coordnate ytem repectvely (Fg. 1a); a(χ,) a ze of elatc zone of loadng urface; b(χ,) a tranformaton coeffcent of nonlnear part of ntal tre-tran curve; d(χ,) a coeffcent of varaton of Young' modulu; ε and σ are the ntal yeld tre and tran; ε p a platc tran; E a ntal Young' b) Fg. 1. Model of thermomechancal urface: a) - tretran curve for othermal cyclc loadng; b) - part of thermomechancal urface at varou halfcycle For mulaton of nonothermal cyclc loadng t neceary to calculate othermal tre-tran curve f k+1 for temperature on the each k + 1 halfcycle (Fg. 1a). Alo t neceary to take account of platc tran χ k accumulated n prevou halfcycle. hen thermomechancal urface F k+1 calculated for the k + 1 halfcycle (Fg. 1b). Nonothermal cyclc tre-tran curve on the k + 1 halfcycle located on th urface n tre-trantemperature coordnate. Determnng parameter of th urface occurred wth takng nto account of drecton of loadng. 2

3 PROBLEM OF LOW CYCLE FAIGUE OF URBOMACHINES Materal parameter a(χ,), b(χ,) and d(χ,) ung for varaton of cyclc curve under othermal loadng are depended a functon on accumulatve platc tran. For varou temperature thee parameter are determned from expermental othermal tre-tran curve under hard or oft loadng. After determnng χ(n,), a(n,), b(n,) and d(n,) for each temperature t may be poble to determne requred relaton a(χ,), b(χ,) and d(χ,) for requred temperature and accumulated platc tran range. 2.2 Model verfcaton Baed on the equaton (1) and (2) a program of expermental data proceng and mulaton of pecmen tet under nonothermal cyclc loadng wa developed. Verfcaton of th program under othermal and nonothermal loadng wa performed n paper [8]. Expermental reult of nckel baed uperalloy under othermal and nonothermal cyclc loadng were preented n [9]. Frequency of othermal and nonothermal loadng wa Hz (400 econd per cycle). Influence of creep tran wa neglected. emperature of all experment wa n range from 571 C to 823 C. ype of loadng cycle wa hard. Stre-tran curve and materal parameter were defned from othermal tet. Materal parameter a and b of the alloy at temperature 571 C, 700 C, 823 C hown on Fg. 2. Smulaton of n-phae and out-phae tet are carred out. he 67th and 68th halfcycle for all type of loadng condered a table hytere loop. In both cae of the mulaton loop for 1-3, 10-11, and halfcycle are hown on Fg. 3. Fg. 2. Materal parameter at dfferent temperature: a) parameter a; b) parameter b (1-571 C, C, C) Fg. 3. Hytere loop under nonothermal loadng: a) n-phae tet; b) out-phae tet (1 - experment, 2 - mulaton) 3

4 JOURY EMIS, KHAKIM AZMEOV AND ALEXANDER FAKEEV Comparon of expermental data of table hytere loop and reult of mulaton of nphae tet hown on Fg. 3a. Stran ampltude wa equal 0.6%. emperature wa equal 823 C at maxmum of tenon and temperature wa equal 571 C at maxmum of compreon. Smulaton and expermental reult of table hytere loop of out-phae tet are hown on Fg. 3b. Parameter of out-phae tet were equvalent to one of n-phae tet. 2.3 Damage model In paper [4, 6, 7] baed on expermental reult t wa determned that at room temperature the number of halfcycle to falure n f for everal tructural materal under varou loadng program (oft loadng, hard loadng, random loadng) depend on ultmate value of accumulated platc tran χ max by next relaton: n f = (χ max / δ) γ (3) where δ and γ materal contant. LCF othermal expermental data at temperature 700 C and 823 C [9] allow by leat-quare method to calculate materal parameter δ and γ of the damage model. Accumulatve platc tran a functon of the number of cycle to falure wa calculated by the model (1-2). For comparon on Fg. 4a expermental reult of LCF are hown by pont and reult of the damage model (3) hown by lmt curve that calculated by parameter and. Smlarly baed on LCF expermental data of IN738LC alloy [10] n temperature range 400 С С applcablty of the damage model wa verfed. Baed on othermal data at 400 С and 900 С the parameter of the LCF model were calculated by leat-quare method. Expermental reult of LCF are hown on Fg. 4b by pont. Lmt curve on Fg. 4b calculated by parameter δ and γ that were defned from expermental data. 3 Fnte element analy Conder cyclc deformaton when load vector {F} appled to component by the followng program F F... 0 max mn max F (4) If tran and tre vector n body pont {ε} k and {σ} k correpond to end of the k th halfcycle of loadng and one {ε} k+1 and {σ} k+1 correpond to end of the (k + 1) th halfcycle then for each halfcycle a varatonal relatonhp carred out q d F q u d FS u q S R ud R S u q q S ds ds (5) Fg. 4. Relaton between cumulated platc tran to falure max and number of halfcycle to falure: a) nckel-bae uperalloy, b) IN738LC alloy 4

5 PROBLEM OF LOW CYCLE FAIGUE OF URBOMACHINES where q = k, k + 1 the halfcycle number; {F Ω }, {R Ω }, {F S }, {R S } vector of volume load and malgnment and urface load and malgnment repectvely. o uppoe that {R Ω }, {R S } are equal zero on the (k + 1) th halfcycle and ubtract from relaton (4) at q = k + 1 mlar one at q = k t obtaned that a problem of tre-tran condton mulaton by change of loadng halfcycle came to oluton a next problem k 1 d F k 1 u d FS u k 1 S R ud R S uds k k S ds (6) If pecfy a relaton form Δσ(Δε) the equaton (6) by well-known method wll be came to fnte element problem K U F k 1 k 1 k 1 F 0 (7) where [K] k+1 tffne matrx of the (k + 1) th halfcycle defnng by tep-by-tep approach; {ΔU k+1 } and {ΔF k+1 } vector of ncrement of dplacement and loadng at halfcycle, correpondngly; β correctng multply; {F 0 } correctng vector. In that cae for dplacement vector at the (k + 1) th halfcycle t rghtly U U U, (8) k 1 k k 1 whle tran and tre n а calculated pont are related by mlar relaton k 1 k k 1;. k 1 k k 1 (9) he equaton (6) (8) how elf corrected algorthm for the problem oluton. It can be condered to varou model of platcty dependng on feature of cyclc loadng. For the mot component of turbomachne procee of force and temperature varaton are ynchronou. In th cae t can be aumed that varaton of tree and tran are proportonal. hee condton are decrbed by tran platcty theory whch wa generalzed on cyclc loadng [11]. Platc tran appear n the local regon by the nfluence of elatc dplacement of the all tructure on the boundary whch valdate th aumpton. h type of loadng mlar to "hard" one. In th cae t can be poble to conder large value of ncrement of load, temperature, tree, tran and dplacement and each tep condered a one half-cycle. 4 Calculaton reult 4.1 Overpeed tet he mulaton of the overpeed tet of the dc condered (Fg. 5). Stran platcty theory whch wa generalzed on cyclc loadng appled n the mulaton becaue experment were carred out at contant temperature. Fg. 5. Overpeed tet dc cheme Generalzed planar treed tate wa mulated n the dc. All computaton were carred out by FEM analy. For the mprovng of accuracy of analy and numercal tablty knematc boundary condton wa defned n ntegral form. In the mulaton of the overpeed tet a rotaton frequency ncreaed up to fracture ntaton whch wa determned by non-top node dplacement ncreang after fracture ome fnte element. On each halfcycle damage falure level D = χ(n) / χ max (n) determnng n the proce of analy. If damage falure level n an element verge toward unty the element excluded from analy by technology of "ded" element [11]. On Fg. 6 relaton of radal dplacement of pont of dc hub and rm veru dc rotaton frequency are hown. Dplacement harply ncreae at the crtcal revoluton and fracture ntaton of the dc begnnng. On the Fg. 7 poble pattern of dc fracture wth varou number of hole are hown. he dc wth x hole faled at crack propagaton to the merdonal drecton 5

JOURY EMIS, KHAKIM AZMEOV AND ALEXANDER FAKEEV (Fg. 7a). he dc wth ten hole begn to fal to the cylndrcal drecton then crack propagaton contnue to the radal drecton (Fg. 7b).

herefore th model can be appled to the analy of dc LCF. 4.2 urbne dc lock he turbne dc lock and equvalent notched pecmen are condered (Fg. 8).

6 JOURY EMIS, KHAKIM AZMEOV AND ALEXANDER FAKEEV (Fg. 7a). he dc wth ten hole begn to fal to the cylndrcal drecton then crack propagaton contnue to the radal drecton (Fg. 7b). he dc wth twelve hole faled at crack propagaton to the cylndrcal drecton (Fg. 7c). rotaton frequency n the cycle defned the value of number of cycle to falure. herefore th model can be appled to the analy of dc LCF. 4.2 urbne dc lock he turbne dc lock and equvalent notched pecmen are condered (Fg. 8). All reearch wa baed on expermental reult of low cycle fatgue of notched pecmen under othermal loadng at the varou temperature that were carred out by.k. Bragna n CIAM [12]. Fg. 6. Dplacement of pont of dk hub and rm at the radal drecton veru rotaton frequency Fg. 8. Concentrator: a) turbne dc lock; b) equvalent pecmen Specmen materal nckel alloy AI698. emperature of experment were 20 C, 400 C и 650 C. ype of loadng wa zero-tocompreon tre cycle. Axymmetrc tre tate wa mulated n notched pecmen. Materal parameter of cyclc model at the temperature 20 C and parameter of LCF model were performed n paper [11]. Materal parameter of cyclc model at the temperature 600 C wa calculated by the proceng expermental data from paper [13]. Stre-tan tate hown on Fg. 9. c) Fg. 7. Overpeed tet fracture pattern: a) 6 hole dc; b) 10 hole dc; c) 12 hole dc Reult of mulaton of platcty regon how that type of dc fracture correpond to model of lmtng tate whch can be developed baed on method of charactertc for rgdplatc body. Smulaton of cyclc loadng lead to the mlar pattern of falure. However maxmal Fg. 9. Notched pecmen at crack ntaton under the tre ampltude 300 MPa and temperature 20 C: a) effcent tree, b) effcent tran 6

PROBLEM OF LOW CYCLE FAIGUE OF URBOMACHINES Baed on reult of the cyclc loadng LCF curve of the notched pecmen under varou tre ampltude wa calculated at the temperature 20 C (Fg. 10a) and 650 C (Fg.

7 PROBLEM OF LOW CYCLE FAIGUE OF URBOMACHINES Baed on reult of the cyclc loadng LCF curve of the notched pecmen under varou tre ampltude wa calculated at the temperature 20 C (Fg. 10a) and 650 C (Fg. 10b). Smulaton reult are hown by lne and crcle. Expermental reult are hown by quare. ampltude Δε = 1.5% hown on Fg. 11b. Modfyng parameter of temperature and loadng t poble to etmate admble tran near the hole and to calculate LCF curve (Fg. 11c). a) a) b) b) Fg. 10. AI698 alloy LCF curve for notched pecmen at dfferent temperature: a) 20 C, b) 650 C 4.3 LCF mulaton of turbne blade Numercal analy of turbne blade carred out. he turbne blade (Fg. 11a) work under nonothermal cyclc loadng (temperature range 20 С С n pont A). Materal of turbne blade a nckel baed uperalloy. here are hole for emon a coolng ga on the external urface n pont A n the blade. Structural FEM analy how that maxmum value of tre and platc tran are located n the pont A near the hole. Behavor of cyclc tre and cyclc tran near hole wth tran c) Fg. 11. urbne blade FEM analy: a) tre-tran tate; b) cyclc tre-tran curve n the crtcal pont (I halfcycle, II halfcycle, III halfcycle); c) turbne blade LCF curve Proce of crack growth and etmate of crack extenon velocty are mulated by ncludng "ded" element model [11]. On the Fg. 12 the pattern 1 accord to the crack ntaton n the hole for emon a coolng ga. he pattern 2 how the mddle of crack growth proce and excepted "ded" element from 7

JOURY EMIS, KHAKIM AZMEOV AND ALEXANDER FAKEEV analy whch damage falure level wa equal unty. he pattern 3 accord to moment when crack nvolve all volume between hole. Fg. 12.

8 JOURY EMIS, KHAKIM AZMEOV AND ALEXANDER FAKEEV analy whch damage falure level wa equal unty. he pattern 3 accord to moment when crack nvolve all volume between hole. Fg. 12. Crack growth pattern n the crtcal pont 6 Concluon Preented reult ndcate a probablty of applcaton of the nonothermal cyclc tretran curve model generalzng the theory of tran deformaton platcty on cyclc nonothermal loadng and the damage model for calculaton tre-tran tate and lfe tme predcton for hgh treed tructure of turbomachne under proportonal loadng. For the complex loadng an nfluence of force and temperature on the tre-tran tate can be etmate f the tme tep q are mall and relaton between tree and tran determned by theory of platc flow that can be generalze on nonothermal cyclc loadng [14]. Reference [1] em Y.M., Selvanov A.V. hermomechancal model of engne. Engneerng Encyclopeda. Vol. IV - 21, Book 3: Avaton motor. Edtor: Skbn V.A., em Y.M., Sounov V.A. Mocow: Mahnotroene, 2010, pp (In Ruan). [2] em Y.M., Selvanov A.V., Yurchenko G.G. Smulaton of thermotreed tate of HPC rotor wth accordng econdary flow. Herald of SGAU. No. 6 (30), pp , (In Ruan). [3] em Y.M. Selvanov A.V., Yurchenko G.G. HPC Degn Baed on Multdcplnary Numercal Smulaton. Proceedng of 10th European Conference on urbomachnery: Flud Dynamc and hermodynamc EC-2013, Lappeenranta, Fnland, pp , [4] em Y.M. Platcty and creep of the GE part under cyclc loadng. Strength and Dynamc Problem n GE. Mocow, No. 4, pp 32-50, (In Ruan). [5] Brger I.A., Shorr B.F., Demanuhko I.V. and other. hermal trength of machne component. Mocow, Mahnotroene, 1975, 455 p. (In Ruan). [6] Putchkov I.V. em Y.M. Analytcal decrpton of the cyclc elatoplatc deformaton of tructural materal. J. Strength of Materal, Vol. 20, Iue 9, pp , (In Ruan) [7] Putchkov I.V. em Y.M. Dowon A.L. Damr D. Development of a fnte element baed tran accumulaton model for the predcton of fatgue lve n hghly treed component, Int. J. Fatgue, Vol. 17, No. 6, pp , [8] em Y.M., Azmetov Kh.Kh., Fakeev A.I. LCF mulaton under nonothermal loadng. Mechancal fatgue of metal. Proceedng of 16th nternatonal colloquum, Brno, Czech Republc, pp , [9] Lang Jn, Pelloux R.M., Xe Xhan. hermomechancal fatgue behavor of a nckel bae uperalloy, Chn. J. Met. Sc. echnol., Vol. 5, pp 1-7, [10] Xja Wu. Lfe predcton of Ga urbne Materal. Ga turbne, pp , [11] em Y.M., Azmetov Kh.Kh., Zuzna V.M. Lowcycle fatgue mulaton and lfe-tme predcton of hgh treed tructure. Sold State Phenomena. ran ech Publcaton, Swtzerland, Vol , pp , [12] Brger I.A., Dulnev R.A., Balahov B.F. and other. Structural trength of materal and component of GE. Mocow, Mahnotroene, 1981, 232 p. (In Ruan). [13] Makhutov N.A., Rachuk V.S., Gadenn M.M. Strength and reource of Lqud-fuel engne. Mocow, Nauka, 2011, 525 p. (In Ruan). [14] em J.M. Appled problem of thermoplatcty analy. Engneerng Encyclopeda. Edt. Comm.: K.V. Frolov (Chef) and other. Dynamc and trength of machne. Mechanm and Machne heory. Vol. 1-3 n 2 book. Book 1. Ed. n Chef K.S. Kolenkov, Mocow: Mahnotroene, 1994, pp (In Ruan). Contact Author Emal Addre tejoum@cam.ru Copyrght Statement he author confrm that they, and/or ther company or organzaton, hold copyrght on all of the orgnal materal ncluded n th paper. he author alo confrm that they have obtaned permon, from the copyrght holder of any thrd party materal ncluded n th paper, to publh t a part of ther paper. he author confrm that they gve permon, or have obtaned permon from the copyrght holder of th paper, for the publcaton and dtrbuton of th paper a part of the ICAS 2014 proceedng or a ndvdual off-prnt from the proceedng. 8

Chapter 6 The Effect of the GPS Systematic Errors on Deformation Parameters

Chapter 6 The Effect of the GPS Sytematc Error on Deformaton Parameter 6.. General Beutler et al., (988) dd the frt comprehenve tudy on the GPS ytematc error. Baed on a geometrc approach and aumng a unform