18 TH INTERNATIONAL CONFERENCE ON COMPOSITE MATERIALS NONLINEAR CONSTANT LIFE MODEL FOR FATIGUE LIFE PREDICTION OF COMPOSITE MATERIALS T. Prk 1, M. Ki 1, B. Jng 1, J. Lee 2, J. Prk 3 * 1 Grdute School, Kore Aerospce University, Koyng, Republic of Kore, 2 Srt UAV Developent, Kore Aerospce Reserch Institute, Dejeon, Republic of Kore, 3 School of Aerospce nd Mechnicl Engineering, Kore Aerospce University, Koyng, Republic of Kore * Corresponding uthor (jungsun@ku.c.kr) Keywords: Coposites, Life prediction, S-N curves, Constnt life digr 1 Introduction Coposite terils re widely used to ircrft nd spcecrft due to its light-weight, yet excellent echnicl properties copred to etl by using its directionl chrcteristics. Mny studies hve been done for ftigue filure of coposite teril becuse ftigue is one of the in cuses of filure. For estiting the ftigue life, the criticl points re the S-N type selection, sttisticl interprettion of ftigue dt, selection of the pproprite constnt life digr forultion, ftigue filure criterion, nd the dge sution rule [1,2]. Aong these criticl points, we focused on the effect of CLD forultion on life prediction. The clssic liner Goodn digr[3] is the ost widely used CLD, becuse of its siplicity. But it is not suitble for coposite terils becuse of its dge echniss under tension nd copression is different. Therefore stright lines connecting the UTS nd UCS with points of the R 1 line for different nubers of cycles re not cpble to describe the ftigue behvior of coposite terils. Severl different odels hve been presented in the literture to properly describe chrcteristics of coposite terils. Strting fro the bsic ide of Goodn digr nd the nonliner Gerber eqution, different odifictions were proposed. Bsed on the liner interpoltion between different S-N curves in odified Goodn digr concept[4-6], nlyticl expressions of ny desired S-N curve so clled piecewise liner CLD is developed by Philippidis et l [2]. Coprison of CLDs by predicting bility of new S-N curve shows tht piecewise liner CLD is the ost ccurte of the copred forultions when ore thn three S-N curves vilble. More ccurte estition of ftigue life is possible with incresing nuber of S-N curves. But it cnnot properly describe for ftigue behvior with vrying R-rtio when fewer S-N curves vilble due to its liner chrcteristics. Kwi[7,8] proposed nonliner CLD tht cn be derived by using only one criticl S-N curve. The criticl R-rtio is equl to the rtio of the UCS over UTS of the exined teril. The in drwbck of this odel is the need for experientl dt for this specific S-N curve. Therefore, it cnnot be pplied to existing ftigue dtbses. However, the iniu ount of dt required is n dvntge of the ethodology. In this study, nonliner constnt life digr forultion is proposed nd the influence of the constnt life digr forultion on the prediction of the ftigue life ws exined. The proposed odel needs three or ore S-N curves nd requires nonliner regression process. With sll nuber of vilble S-N curves, proposed CLD odel cn describe ftigue behvior ore properly with vrying R-rtio copred to piecewise liner odel which is currently the ost ccurte CLD. The ost coonly used CLD forultions re evluted ccording to its ccurcy of estition for unknown S-N curves. Bsed on the results, recoendtions concerning the pplicbility, dvntges nd disdvntges of ech of the exined CLD forultions re discussed. 2 Theories of CLD odel Constnt life digr ws creted to consider the effect of the en stress nd teril nisotropy on the ftigue life of the coposite teril. CLD cts s ster digr nd represents constnt ftigue life behvior for entire rnge of loding type (cop-
ression-copression, tension-copression, nd tension-tension loding). CLD kes it possible to estite S-N curve for specific loding ptterns for which no experientl dt exist. The in preters of CLD re the en stress,, the lternting stress,, nd the R-rtio, which defined s the iniu stress over the xiu stress. 2.1 Liner CLD The liner CLD odel is bsed on single S-N curve tht should be experientlly derived under fully reversed loding( R 1 ). Constnt life lines re creted by connecting constnt life dt points nd sttic strength. Unknown S-N curves re siply clculted by liner interpoltion. This CLD odel constitutes odifiction of the Goodn line[3]. The generl forule of the odel re: (1 ( / UTS)), For (1) (1 ( / UCS)), For (2) where, is the cyclic stress plitude for given constnt vlue of life N under ftigue loding. 2.2 Piecewise liner CLD [2] The piecewise liner CLD is derived by liner interpoltion between known S-N curves in the ( ) plne. A liited nuber of experientlly deterined S-N curves long with the ultite tensile nd copressive stresses of the terils re required for this CLD odel. Typiclly, S-N curves representing the entire rnge of possible loding re used for piecewise liner CLDs, norlly t R.1 for tension-tension loding, R 1for tension-copression loding, nd R 1 for copression-copression loding ptterns. Constnt life lines re constructed by connecting the se ftigue life cycle dt points on ech of the S-N curves. By liner interpoltion between known vlues of ftigue nd strength dt, unknown S-N curves re estited. Following nlyticl expressions for the description of ech region of the piecewise liner CLD were developed in [2]. 1. If R is in the T-T sector of the CLD, nd between UTS nd the first known R-rtio in the tension region, R 1TT, UTS ' (3) UTS r' r,1tt 1TT where, ' nd ',1 TT re the stress plitudes corresponding to R ' nd R 1TT, respectively nd ri (1 Ri) / (1 Ri), nd r' (1 R')/(1 R'). 2. If R is locted between ny of two known R- rtios, R i nd R i+1, i, ( r' ri 1) ' (4) i, ( r r') ( r' r ) i i, 1 3. If R is in the C-C region of the CLD, nd between UCS nd first known R-rtio in the copression region, R 1CC, UCS ' (5) UCS r' r,1cc 1 CC where, ' nd ',1 CC re the stress plitudes corresponding to R ' nd R 1CC, respectively. 2.3 Kwi s CLD [7,8] Kwi nd his coworkers developed n syetric constnt life digr, designted the nisoorphic constnt ftigue life (CFL) digr in [7]. Min feture of this forultion is tht it cn be constructed by using only one experientlly derived S-N curve, which is clled criticl S-N curve. The R-rtio of this S-N curve is defined s the rtio of the UCS over UTS of the teril. The forultion is bsed on three in ssuptions: 1. The stress plitude for given constnt vlue of ftigue life is gretest t the criticl stress rtio. 2. The shpe of the CFL curves chnges progressively fro stright line to prbol with incresing ftigue life. 3. The digr is bounded by the sttic filure envelope tht consists of two stright lines connecting the pek point on the criticl stright line with the UTS nd UCS, respectively. The CFL forultion depends on the position of the en stress, σ, in the doin [σ C, σ T ] s follows. (2 ) ( ), UTS UTS (6) (2 ) ( ), UCS UCS where, nd represent the lternting nd en stress coponents of the ftigue stress for given constnt vlue of life N under ftigue loding t the criticl stress rtio, UCS / UTS. The i1
NONLINEAR CONSTANT LIFE MODEL FOR FATIGUE LIFE PREDICTION OF COMPOSITE LAMINATES vrible denotes the ftigue strength rtio nd it is defined s x (7) B where, B (>) is the reference strength to define the pek of the sttic filure envelope in the ( ) plne. 2.4 Teyoung s CLD odel In this study, nonliner constnt life odel ws developed to describe ftigue behvior of coposite terils. Plotting constnt life dt in ( ) plne using S-N curves for different R-rtio shows constnt life dt vries with ftigue life cycles s well s lod type(i.e. copression or tensile lod). Constnt life line chnges its shpe depending on ftigue life cycles, N. It usully shows prbolic for(concve or convex) or liner for. In proposed CLD, nonlinerity is reflected yet it hs siple eqution nd clcultions. This forultion depends on the position of the en stress nd ftigue strength under fully reversed loding t given vlue of ftigue life. Following siple expressions re representing the proposed constnt life digr odel: T 1, For UTS (8) C 1, For UCS (9) where, is the cyclic stress plitude for given constnt vlue of life, N, under fully reversed loding. The tensile nd copressive fitting preter, α T nd α C, is clculted by nonliner regression. This vrible reflects the trend of the constnt life dt position. 3 Experientl dt The predicting ccurcy of ll the exined CLD forultions ws ssessed on two constnt plitude dt sets retrieved fro the dtbses. Ftigue dt fro tests under vrious stress rtio including tension tension, tension copression, nd copression copression loding cn be found in these dtbses. 3.1 Mteril #1 GFRP ultidirectionl speciens cut t 45 off-xis fro linte with stcking sequence of [/(±45) 2 /] T, [6]. The constnt plitude ftigue test results re considered s the first exple for coprison of the CLD forultions. The selected test set is consisted of 57 vlid ftigue dt points which re distributed in four S-N curves, t stress rtios of.5,.1, -1 nd 1. The xiu cyclic stress level rnged between 45 nd 13 MP, nd loding cycles t filure between 142 nd 3.46 illion. Tests were conducted t frequency of 1 Hz. Detils of the teril nd testing procedures cn be found in [5]. The UTS for this teril ws deterined s 139 MP, nd the UCS ws 16 MP. 8 7 6 5 4 3 2 1 C T 1 3 1 4 1 5 1 6 1 7 Fig.1. Dependence of the fitting preter, α, on life for teril #1. 1.6 1.4 1.2 1.8.6.4 C T.2 1 3 1 4 1 5 1 6 1 7 Fig.2. Dependence of the fitting preter, α, on life for teril #2. 3
C [MP] A [MP] D [MP] B [MP] 3.2 Mteril #2 The second teril is GFRP ultidirectionl speciens with stcking sequence of [9//±45 /] S, bsed on experientl ftigue dt fro the DOE/MSU dtbse[9]. In the DOE/MSU dtbse the teril hs the code ne DD16. The teril ws tested under constnt plitude for 12 R- rtios(.9,.8,.7,.5,.1, -.5, -1, -2, 1, 2, 1.43, nd 1.1). For coprison of CLD forultions, experientl dt were collected under six R-rtios (.8,.5,.1, -.5, -1, 1). The xiu stress level ws between 85 nd 5 MP, nd loding cycles t filure rnged fro 27 cycles to 3.4 illion. Detils of the teril nd test conditions cn be found in [9]. The UTS for this teril ws deterined s 632 MP, nd the UCS ws 42 MP. 4 Results Three of four(teril #1), nd four of six(teril #2) existing S-N curves nd the sttic strength vlues were used s input dt. The sttic strength rtio for the Kwi CLD re -.76, nd -.63, but no S-N curve under this R-rtio is vilble. So S-N curve t R 1 ws used for the construction of the liner nd the Kwi CLD. Fig.1. nd Fig.2. show chnge in fitting preter for ech teril. With incresing ftigue life cycles, copressive fitting preter, α C, shows significnt chnges, while tensile preter, α T, slightly chnging. 4.1 Mteril #1 CLDs bsed on the different forultions presented in Fig.3. Liner nd Kwi CLDs re inccurte for the exined teril, while the prediction of the piecewise liner digr for the S-N dt t R.5 is ccurte(r 2 =.85). For Kwi s odel, bsence of criticl S-N dt ight be the reson for the inccurte result. S-N dt prediction for the teril #1 by Proposed CLD odel ws shown the ost ccurte result(r 2 =.9). Fig.4. shows predicted S-N curves of different CLD forultions. 1 8 R=1 Used exp. dt Dt f or v lidtion Constnt lif e lines 1 8 R=1 Used exp. dt Dt f or v lidtion Constnt lif e lines 6 R=.1 6 R=.1 4 R=.5 4 R=.5 2 2-15 -1-5 5 1 15 [MP] -15-1 -5 5 1 15 [MP] 1 8 R=1 Used exp. dt Dt f or v lidtion Constnt lif e lines 1 8 R=1 Used exp. dt Dt f or v lidtion Constnt lif e lines 6 R=.1 6 R=.1 4 R=.5 4 R=.5 2 2-15 -1-5 5 1 15 [MP] -15-1 -5 5 1 15 [MP] Fig.3. Constnt life digrs for teril #1 (A-liner, B-piecewise liner, C-Kwi, D-Teyoung).
NONLINEAR CONSTANT LIFE MODEL FOR FATIGUE LIFE PREDICTION OF COMPOSITE LAMINATES 4.2 Mteril #2 Constnt life digrs ccording to the described odels re presented in Fig.5. The liner CLD is ccurte only for the prediction of the curve t the stress rtio, R.5 (R 2 =.86) but filed to ccurtely predict the curve t R.8. Kwi s odel filed to ccurtely predict the curve for both S-N dt t R.5 nd R.8. Inpproprite ssuption of criticl S-N dt ight be the reson for the inccurte result. The piecewise liner CLD predicted Tble.1. Predicting bility of the CLD forultions in ters of the coefficient of deterintion (R 2 ). Mt. #1 Mt. #2 R=.5 R=-.5 R=.8 Liner.5.86.51 Pw. liner.85.91.83 Kwi.5.78.49 Proposed.9.83.74 A [MP] 35 3 25 2 15 1 5 R=1 R=-.5 R=.1 Used exp. dt Dt for vlidtion Constnt lif e lines R=.5 R=.8-6 -4-2 2 4 6 8 [MP] best result in both cses. The predictions of proposed CLD odel is slightly lower ccurcy thn tht of piecewise CLD. Fig.5. nd 6. show predicted S-N curve of CLD forultions. For R.5, it is observed tht proposed odel predicted conservtive S-N curve. x [MP] 14 12 1 8 6 Exp. dt Liner Pw. Liner Kwi Tey oung 1 3 1 4 1 5 1 6 1 7 Fig.4. Predicted S-N curves for teril #1 (R=.5). B [MP] 35 3 25 2 15 1 5 R=1 R=-.5 R=.1 Used exp. dt Dt f or v lidtion Constnt lif e lines R=.5 R=.8-6 -4-2 2 4 6 8 [MP] C 35 3 25 R=-.5 Used exp. dt Dt for vlidtion Constnt lif e lines D 35 3 25 R=-.5 Used exp. dt Dt for vlidtion Constnt lif e lines [MP] 2 15 1 5 R=1 R=.1 R=.5 R=.8 [MP] 2 15 1 5 R=1 R=.1 R=.5 R=.8-6 -4-2 2 4 6 8 [MP] -6-4 -2 2 4 6 8 [MP] Fig.5. Constnt life digrs for teril #2 (A-liner, B-piecewise liner, C-Kwi, D- Teyoung). 5
5 Conclusions Nonliner constnt life odel ws developed nd proposed to describe ftigue behvior of coposite terils. And coprison of the coonly used nd proposed odels for derivtion of constnt life digrs for coposite terils ws crried out in this pper. Four ethods were described nd their prediction ccurcy ws evluted over constnt plitude ftigue dt of GFRP terils. As shown in result, inpproprite choice of constnt life digr cn produce very optiistic or very conservtive S-N curves, which could overestite or underestite life. Thus, the selection of n ccurte CLD forultion is essentil for the ccurcy of ftigue life prediction. The siplicity is offered by Liner nd Kwi s odel. These odels need iniu dt sets, but for Kwi s odel, dditionl experient of criticl S-N is inevitble becuse ost of the dtbses do not hve criticl experient dt. In this pper, the bsence of criticl S-N dt ight be the reson for the inccurte result. The piecewise liner odel predicted reltively ccurte S-N dt. But piecewise liner odel cnnot describe nonlinerity of ftigue behvior. The proposed nonliner CLD odel is reltively siple with siple equtions nd nonliner regression. The proposed odel predicted reltively ccurte S-N curves nd well described nonlinerity of ftigue life distribution. For ore relistic description of the ftigue behvior of coposite teril dditionl reserch will be perfored to iprove the ccurcy of this odel. References [1] I. P. Bond Ftigue life prediction for GRP subjected to vrible plitude ftigue. Coposites: Prt A, Vol. 3, pp 961-97, 1999. [2] T. P. Philippidis nd A. P. Vssilopoulos Life prediction ethodology for GFRP lintes under spectru loding. Coposites: Prt A, Vol. 35, pp 657-666, 24. [3] J. Goodn Mechnics pplied to engineering. Longn, Green & copny, London, 1899. [4] J. F. Mndell, D. D. Sborsky, L. Wng nd N. K. Whl New ftigue dt for wind turbine blde terils. Journl of Solr Energy Engineering, Vol. 125, pp 56-514, 23. [5] H. J. Sutherlnd nd J. F. Mndell Optiized constnt life digr for the nlysis of fiberglss coposites used in wind turbine bldes. Journl of Solr Energy Engineering, Vol. 127, pp 563-569, 25. [6] T. P. Philippidis nd A. P. Vssilopoulos Coplex stress stte effect on ftigue life of GRP lintes. Prt I, experientl. Interntionl Journl of Ftigue, Vol. 24, pp 813-823, 22. [7] M. Kwi nd M. Koizui Nonliner constnt ftigue life digrs for crbon/epoxy lintes t roo teperture. Coposites: Prt A, Vol. 38, pp 2342-2353, 27. [8] M. Kwi A ethod for identifying syetric dissiilr constnt ftigue life digrs for CFRP lintes. Key engineering terils, Vol. 334-335, pp 61-64, 27. [9] J. F. Mndell nd D. D. Sborsky DOE/MSU coposite teril ftigue dtbse. Sndi Ntionl Lbortories, SAND97-32, 21. x [MP] 35 3 25 2 Exp. dt Liner Pw. Liner Kwi Tey oung x [MP] 7 6 5 4 Exp. dt Liner Pw. Liner Kwi Tey oung 15 3 1 1 3 1 4 1 5 1 6 1 7 Fig.6. Predicted S-N curves for teril #2 (R=-.5). 2 1 3 1 4 1 5 1 6 1 7 Fig.7. Predicted S-N curves for teril #2 (R=.8).