The Effect of Mean Stress on Damage Predictions for Spectral Loading of Fiberglass Composite Coupons 1


 Raymond Farmer
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1 EWEA, Specal Topc Conference 24: The Scence of Makng Torque from the Wnd, Delft, Aprl 92, 24, pp The Effect of Mean Stress on Damage Predctons for Spectral Loadng of Fberglass Composte Coupons Herbert J. Sutherland John F. Mandell Sanda Natonal Laboratores Montana State Unversty Albuquerque, NM Bozeman, MT Abstract: In many analyses of wnd turbne blades, the effects of mean stress on the determnaton of damage n composte blades are ether gnored completely or they are characterzed nadequately. Mandell, et al [] have recently presented an updated Goodman dagram for a fberglass materal that s typcal of the materals used n wnd turbne blades. Ther formulaton uses the MSU/DOE Fatgue Data Base [2] to develop a Goodman dagram wth detaled nformaton at thrteen Rvalues. Usng these data, lnear, blnear and full Goodman dagrams are constructed usng mean and 95/95 fts to the data. The varous Goodman dagrams are used to predct the falure stress for coupons tested usng the WISPERX spectrum [3]. Three models are used n the analyses. The frst s the lnear Mner s rule commonly used by the wnd ndustry to predct falure (servce lfetmes). The second s a nonlnear varaton of Mner s rule whch computes a nonlnear Mner s Sum based upon an exponental degradaton parameter. The thrd s a generalzed nonlnear resdual strength model that also reles on an exponental degradaton parameter. The results llustrate that Mner s rule does not predct falure very well. When the mean Goodman dagram s used, the nonlnear models predct falures near the mean of the expermental data, and when the 95/95 Goodman dagram s used, they predct the lower bound of the measured data very well. Keywords: wnd, blades, fatgue, spectral, fberglass. Introducton In many analyses of wnd turbne blades, the effects of mean stress on the determnaton of damage n composte blades are ether gnored completely or they are characterzed nadequately. Mandell, et al [] have recently presented an updated characterzaton of the fatgue propertes for fberglass materals that are * Sanda s a multprogram laboratory operated by Sanda Corporaton, a Lockheed Martn company, for the U.S. Department of Energy under contract DEAC494AL85 typcally used n wnd turbne blades. Ther formulaton uses the MSU/DOE Fatgue Data Base [2] and a threeparameter model to descrbe the mean SN behavor of the fberglass at thrteen dfferent R values. The Rvalue for a fatgue cycle s defned as: mn R = σ σ max, () where σ mn s the mnmum stress and σ max s the maxmum stress n a fatgue stress cycle (tenson s consdered postve and compresson s negatve). The results are typcally presented as a Goodman dagram n whch the cyclestofalure are plotted as a functon of mean stress and ampltude along lnes of constant Rvalues. Ths dagram s the most detaled to date, and t ncludes several loadng condtons that have been poorly represented n earler studes. Ths formulaton allows the effects of mean stress on damage calculatons to be evaluated. Usng feld data from the Long term Inflow and Structural Test (LIST) program, Sutherland and Mandell [4] have shown that the updated Goodman dagram predcts longer servce lfetmes and lower equvalent fatgue loads than prevous analyses. Ths predcton s a drect result of the lower damage predcted for the hghmeanstress fatgue cycles as a result of usng the updated Goodman dagram. To valdate ths result n a controlled set of experments, the spectral loadng data of Wahl et al [5] s evaluated usng the updated Goodman dagram. These data are from coupons that were tested to falure usng the WISPERX spectrum [3]. Sx formulatons for the SN behavor of fberglass are used: the frst three use mean fts of the SN data to construct a lnear, blnear and full (3 Rvalues) Goodman dagram and the second three usng 95/95 fts to construct smlar dagrams (the 95/95 ft mples that, wth a 95 percent level of confdence, the materal wll meet or exceed ths desgn value 95
2 percent of the tme). These formulatons of the Goodman dagram are used wth Mner s Rule and two nonlnear resdual strength models to predct the measured lfetme of the coupons. 2 Fatgue Data The DOE/MSU fatgue database 2 contans over 88 test results for over 3 materal systems [2]. The database contans nformaton on composte materals constructed from fberglass and carbon fbers n a varety of matrx materals that are typcally used n wnd turbne applcatons. References 2, 6 and 7 provde a detaled analyss of data trends and blade substructure applcatons. Recent efforts to mprove the accuracy of spectrum loadng lfetme predctons for fberglass compostes have led to the development of a more complete Goodman dagram than prevously avalable. 2. Constant Ampltude Data The materal under consderaton here s a typcal fberglass lamnate that s called DD6 n the DOE/MSU Database. Ths lamnate has a [9//±45/] S confguraton wth a fber volume fracton of.36. The 9 and ples are D55 sttched undrectonal fabrc, the ±45 ples are DB2 sttched fabrc, and the resn s an orthopolyester. Mandell et al [2, 5] descrbed the test methodologes used to obtan the data cted here. Ths materal has a statc tensle strength of 625 MPa and a compressve strength of 4 MPa. The 95/95 strength values are 5 MPa and 357 MPa, respectvely. These strength values were determned at a stran rate smlar to that of the fatgue tests. For llustratve purposes, the constant ampltude data at R =,. and are shown n Fg.. A complete set of the data for all thrteen Rvalues s avalable n Refs. and Curve Fts 2... Mean Ft As presented by Mandell et al [], the constant ampltude data at 3 Rvalues were ft wth a threeparameter equaton of the followng form: 2 The database s avalable on the SNL webste: Maxmum Cyclc Stress, MPa Maxmum Cyclc Stress, MPa Maxmum Cyclc Stress, MPa , Log(N) Fgure a: R=. Mean Curve Ft 95/95 Curve Ft Data , Log(N) Fgure b: R=. Mean Curve Ft 95/95 Curve Ft Data , Log(N) Fgure c: R= Mean Curve Ft 95/95 Curve Ft Data Fgure : SN Curves at Three RValues for Database Materal DD6 b σ σo σ = aσ ( N c ) σ O, (2) where σ s the maxmum appled stress, σ O s the ultmate tensle or compressve strength (obtaned at a stran rate smlar to the Hz fatgue tests), N s the mean number of constantampltude cycle to falure, and a, b, and c are the fttng parameters. The results of these fts are summarzed n the Table and llustrated n Fg.. p. 2
3 The parameters n these curve fts were selected to provde the best ft to the expermental data and to provde a 9 cycle extrapolaton stress whch was wthn ten () percent of the extrapolaton from a smple twoparameter power law ft to the fatgue data havng lfetmes greater than cycles [] /95 Ft Usng the technques cted n Ref. 8 and 9 and the Standard Practce cted n Ref., the 95/95 curve fts were also determned for these data. The 95/95 ft mples that, wth a 95 percent level of confdence, the materal wll meet or exceed ths desgn value 95 percent of the tme. For these calculatons, we use a onesded tolerance lmt, whch has been computed and tabulated for several dstrbutons by a number of authors. Typcally, these tabulatons take the followng form: * X X , X =  c αγ x, (3) where X and X X. are the sample average and the standard devaton, respectvely. The parameter c α,γ s tabulated as a functon of the confdence level ( α), probablty γ and the number of data ponts n. For fatgue fts, the ndependent varable s the stress σ and the dependent varable s the logarthm of the number of cycles to falure N. Thus, the sample average s the log (N) determned from Eq. 2 and the standard devaton X X s gven by: X x n 2 2 ( X  X) = = ( n) { log N ( σ)  log N ( σ) } = = ( n) n 2 2. (4) Thus, the number of cycles to falure for the 95/95 ft s gven by: log [ N 95/95] = log [ N ]  log [ N o ], (5) where log [N o ] s tabulated for each of the thrteen R values n the Table. As shown n Fg., ths technque works well for the fatgue data. However, ths technque does not yeld the 95/95 statc strength that s determned from statc strength data, see the dotted lnes n the fgure. To rectfy ths stuaton, the 95/95 fatgue curve was fared nto the measured 95/95 statc strength, as Table: Parameters for the Thrteen RValues for Materal DD6 and for Small Strands RValue Model (Equaton 2) 95/95 (Equaton 5) a b c log (N o ) * *Assumes a frequency of Hz. shown by the sold lnes n the fgure [] s For the analyss of SN data, the preferred characterzaton s the Goodman dagram. In ths formulaton, the cyclestofalure are plotted as functons of mean stress and ampltude along lnes of constant Rvalues. Between Rvalue lnes, the constant cyclestofalure plots are typcally, but not always, taken to be straght lnes. Varous Goodman dagrams for the DD6 fberglass composte are shown n Fgs. 2 and 3. These fgures are presented n ncreasng level of knowledge about the SN behavor of the fberglass composte materal. Fgures 2a and 3a llustrate the lnear Goodman dagram. In these two fgures, the dagrams are constructed usng the statc strength values for the tensle and compressve ntercepts of the constant lfe curves wth the horzontal axs of the dagram and the SN data for the R = (see Fg. a) for the ntercepts of the vertcal axs. The blnear Goodman dagrams, shown n Fgs. 2b and 3b, are constructed by addng the R =. SN data (see Fg. b) to the dagram. The full Goodman dagrams, shown n Fgs. 2c and 3c, are constructed by addng the data for the remanng eleven Rvalues Mean s The Goodman dagrams shown n Fg. 2 were constructed usng Eq. 2 and the nformaton n the Table. Fgures 2a and 2b, use the mean statc strengths for the ntercepts of the constantlfe curves p. 3
4 4 3 2 Cycles Cycles Fg. 2a: Lnear Fg. 3a: Lnear Cycles R = Cycles R = Fg. 2b: BLnear Fg. 3b: BLnear 5 R = .5 R = 2 R =. 4 Cycles R = 3 2 R =.5 2 R = 2 4 R =.7 R =.43 6 R =.8 R =.9 R = R = 2 R = R = 2 R =.43 R =. R = .5 R =. Cycles 2 R =.5 4 R =.7 6 R =.8 R = Fg. 2c: Full Fg. 2. Mean s for Database Materal DD6, Ft wth Eq. 2 Fg. 3c: Full Fg /95 s for Database Materal DD6, Ft wth Eqs. 2 and 3 p. 4
5 4 3 2 Mean Ft 95/95 Ft Cycles R = R = 2 R = Lnear BLnear Full 5 Cycles Fg. 5: Comparson of the Three Goodman Dagrams at 5 Cycles Fg. 4a: Lnear 6 Cycles Mean Ft 95/95 Ft R =. Fg. 4b: BLnear R = 2 R = R = Cycles R = 2 4 R =.7 R =.43 6 R =.8 R =.9 R = Fg. 4c: Full Mean Ft 95/95 Ft R =. R =.5 Fg. 4: Comparson of Mean and 95/95Goodman Dagrams wth the mean stress (horzontal) axs. Fg. 2c departs from tradtonal formulatons n that the ntercept for tensle mean axs (R = ) s not the mean statc strength. Rather, the ntercept s a range of values based upon tmetofalure under constant load. These data were converted to cycles by assumng a frequency of cycles/second, typcal of the cyclc tests. Njssen et al [2] have hypotheszed a smlar formulaton prevously /95 The Goodman dagrams cted n Fg. 3 were constructed usng Eqs. 2 and 6, the nformaton n the Table, and the farng of the SN curves nto the 95/95 statc strengths. Agan, the tensle ntercept n Fg. 3c s a range of values based upon tme under load Comparson The Goodman dagrams presented n Fgs. 2 and 3 are compared wth one another n Fgs. 4 and 5. As shown n Fg. 4, the general shapes of the varous Goodman dagrams are unchanged by converson from the mean values to the 95/95 values. The sgnfcant dfferences n the Goodman formulatons are hghlghted n Fg. 5. The area near the R = axs s very mportant. Ths s the regon where the fberglass composte s n transton between compressve and tensle falure modes and many of the stress cycles on a wnd turbne blade have an Rvalue near. The effect of the mode change on fatgue propertes s llustrated by the drect comparson of the constant lfe curves for the three Goodman dagrams. In Fg. 5, the constant lfe curves for the three formulatons of the Goodman dagram at 5 cycles are compared to one another. Four dstnct regons of comparson are noted: () the regon of relatvely hgh compressve mean stress (< R <,.e., essentally the regon to the left of R = ); (2) the p. 5
6 regon of relatvely low compressve stress ( < R < ;.e., essentally the regon between R = and R = ); (3) the regon of relatvely low tensle stress ( < R < ;.e., essentally the regon between R = and R =.); and (4) the regon of relatvely hgh tensle stress ( < R < ;.e., essentally the regon to the rght of R =.). In the frst and thrd regons, the three formulatons le close to one another. Thus, each of the three formulatons wll predct approxmately the same damage rate for the stress cycles n ths range. For the fourth regon (hgh tensle stress) the database formulaton s below the lnear and blnear formulatons. Thus, the database formulaton s more severe (.e., t produces a shorter predcted servce lfetme) than the other two. And, fnally, for the second regon (low compressve stress), the database formulaton s above the lnear and blnear formulatons. Thus, t s less severe. Regons 2 and 3 are where the composte s n transton between compressve and tensle falure modes. 2.2 WISPERX Spectral Data Wahl et al [5] have conducted spectral loadng tests of coupons usng the WISPERX spectrum [3]. The WISPERX spectrum s the WISPER spectrum wth the small ampltude fatgue cycles removed. The WISPERX spectrum, see Fg. 6, conssts of over 25, peaksandvalleys (load reversal ponts) or slghtly over 4 cycles. The orgnal formulaton of the spectrum s n terms of load levels that vary from to 64 wth zero at load level 25. When normalzed to the maxmum load n the spectrum, the load levels take the values shown n the fgure. The mnmum load level s.6923 and, of course, the maxmum load level s.. Fgure 6 llustrates that the WISPERX spectrum s prmarly a tensle spectrum wth a relatvely small number of compressve cycles. 3 Damage Models Typcally, the wnd ndustry uses Mner s rule to estmate damage under spectral loads. Many other models for damage estmaton have been proposed. Two, whch are nvestgated here, are the nonlnear Mner s Sum proposed by Hwang et al [3] and the nonlnear resdual strength model proposed by Yang et al [4]. Here, we wll refer to the latter model as the generalzed nonlnear model. Wahl et al [5] provdes a complete descrpton of these models. 3. Mner s Rule Mner s rule defnes the damage D, predcted for a tme nterval T, as Normalzed Load Reversal Ponts Fg. 6: Normalzed WISPERX Spectrum n ( σ ) ( σ ) D =, (6) N where n s the numberofcycles, N s the numberofcycles to falure and σ descrbes the stress level of the fatgue cycle. For our case, where we wll be usng the Goodman dagrams to determne N, σ s dvded nto two components: the mean stress σ m and the ampltude σ A of the stress cycle. Falure occurs when D equals one. The predcted servce lfetme L, s the tme T requred for the damage D (T) to accumulate to a value of one. 3.2 Resdual Strength Models 3.2. Nonlnear Mner s Sum Model Mner s rule may also be used to descrbe the resdual strength of compostes, see the dscusson by Wahl et al [5]. In ts general form, the nonlnear Mner s sum model has the followng form: σ n R j =  σ o j = N, (7) j where [σ R /σ o ] s the rato of the resdual strength to the statc strength σ o after step and the exponent s the nonlnear degradaton parameter. As dscussed n 3., N j s evaluated at the mpled stress state (σ m, σ A ) of n j. Falure occurs when the current value of the resdual strength (σ R ) s exceeded by the ( +) cycle, see the dscusson n Generalzed Nonlnear Model A generalzed nonlnear resdual strength model, also see the dscusson by Wahl et al [5], takes the form: p. 6
7 * σ R σ  σ n o + ( n) =, (8) σo σo N ( σm, σa) where n s the current number of stress cycles and (n  )* s the number of prevous equvalent cycles determned for the current stress level. The prevous equvalent cycles s the number of cycles whch would gve the resdual stress rato [σ R /σ o ] f cycled only at (σ m, σ A ). If Eq. 8 s rewrtten as: σ R σ  σ o * = n + ( n), (9) σo σo N ( σ, R) * = A n + ( n) then, * A ( n ) = A  ( n), or () monotoncally decreasng functon. 4 Damage Predctons The models cted n Secton 3 are used here to predct the falures of the coupons tested under the WISPERX load spectrum dscussed n Secton 2. The expermental cyclestofalure, as a functon of the maxmum stress n the spectrum, for materal DD6 are shown as the dscrete data ponts n Fg. 7 [5]. 4. Mner s Rule The predctons for Mner s rule usng the three meanvalue Goodman dagrams (see Fg. 2) are shown n Fg. 7a. The lnear Goodman dagram predcts the longest lfetmes (cyclestofalure) and the full Goodman dagram predcts the shortest lfetmes. Notce that the mean fts do not pass through the mean of the data: rather, all three formulatons predct servce lfetmes that are sgnfcantly hgher than the measured lfetme. A = *  ( n ) ( n )   A. () For ths analyss, we have computed the resdual strength sequentally usng Eqs. 8 through for each halfcycle of the sequence Resdual Strength Rato As defned by Eqs. 7 and 9, the resdual strength of the composte after steps for both resdual strength models s σ R ( σ R) = ( σ o) +. (2) σ o Falure occurs when the maxmum stress of the next cycle [σ + ] MAX exceeds the current tensle resdual strength or the mnmum stress of the next cycle [σ + ] MIN exceeds the current compressve resdual strength: [ σ ] ( σ ), + MAX R + Tensle or (3) [ σ ]  ( σ ). + MIN R + Compressve Whle Eq. 2 s rather obvous, ths equaton mples that the resdual tensle and compressve strength are beng reduced proportonally,.e., the rato of the resdual stress to the statc strength s a Lnear BLnear Full Number of WISPERX Passes: 2 Fg. 7a: Falures Predcted Usng the Mean Full Goodman Dagram Number of WISPERX Passes: 2 Lnear BLnear Full Fg. 7b: Falures Predcted Usng the 95/95 Full Goodman Dagram Fg. 7: Comparson of to Predcted Falure usng Lnear Mner s Rule p. 7
8 Mner's Sum.95 Number of WISPERX Passes: Number of WISPERX Passes: 2 General. General.265 Fg. 8a: Falures Predcted Usng the Mean Full Fg. 9a: Falures Predcted Usng the Mean Full Mner's Sum.95 Number of WISPERX Passes: General. General.265 Number of WISPERX Passes: 2 Fg. 8b: Falures Predcted Usng the 95/95 Full Fg. 8: Comparson of to Predcted Falure usng the Mner s Sum Resdual Strength Models Fg. 9b: Falures Predcted Usng the 95/95 Full Fg. 9: Comparson of to Predcted Falure usng the Generalzed Resdual Strength Models The predctons for Mner s rule usng the three 95/95 Goodman dagrams (see Fg. 3) are shown n Fg. 7b. Agan, the lnear Goodman dagram predcts the longest lfetmes (cyclestofalure) and the full Goodman dagram predcts the shortest lfetmes. Ths comparson llustrates that the lnear 95/95 Goodman dagram predcts servce lfetmes that are hgher than the measured lfetme, and, the full 95/95 Goodman dagram predcts lfetmes near the mean of the expermental data. Thus, Mner s rule does not predct the measured lfetmes very well. Even the 95/95 Goodman dagrams are nonconservatve n that they predct longer servce lfetmes than those measured n the tests usng the WISPERX load spectrum. At best, the full 95/95 Goodman dagram predcts the mean of measured data. 4.2 Resdual Strength Models The two nonlnear resdual strength models dscussed above were used to predct the lfetmes of the coupons subjected to spectral loadng usng the WISPERX spectrum. The predctons of these models are summarzed n Fgs. 8 and Nonlnear Mner s Sum Model Note the slopes of the predcted lfetme curves shown n Fg. 7 are consstent wth the data, but they are shfted to the rght of the data. The nonlnear Mner s sum model descrbed n Eq. 7 shfts the predcton to the left. Usng a tralanderror method, a value of =.95 was chosen as the best ft to the experentally measured lfetme data usng the 95/95 Goodman dagram. The predctons for ths resdual strength model are shown n Fg. 8. As shown n ths fgure, the lfetme curves predcted by Mner s rule wth the full Goodman dagrams have been shfted to the left by approxmately a halfdecade of cycles. These predctons are n very good agreement wth the measured lfetmes. Namely, the predcted lfetmes are near the mean of the data, see Fg. 8a, when the mean full Goodman dagram s used p. 8
9 Number of WISPERX Passes: 2 Mner's Sum.95 General.265 Fg. a: Falures Predcted Usng the Mean Full Mner's Sum.95 General.265 Number of WISPERX Passes: 2 Normalzed Resdual Strength General.265 General. General.8.2 Number of WISPERX Passes: Cycles to Falure Fg. a: Falures Predcted Usng the Mean Full Normalzed Resdual Strength General.265 General. General.8.2 Number of WISPERX Passes: Cycles to Falure Fg. b: Falures Predcted Usng the 95/95 Full Fg. : Predcted Falure usng the Lnear and the Nonlnear Models Fg. b: Falures Predcted Usng the 95/95 Full Fg. : Resdual Strength usng the Generalzed Nonlnear Model and are at or totheleftof the measured lfetmes when the 95/95 full Goodman dagram s used, see Fg. 8b Generalzed Nonlnear Model The predctons for the generalzed nonlnear resdual strength model usng the mean and the 95/95 full Goodman dagrams (see Fg. 3c and 4c) are shown n Fg. 9. As shown n ths fgure, for =, the predcton les essentally on top of the fullgoodman Mner s rule predcton. Usng the value chosen by Wahl et al [5] of =.265, the predctons are n general agreement wth the data. Namely, the predcted lfetmes are near the mean of the data when the mean full Goodman dagram s used, see Fg. 9a, and are at or totheleftof when the 95/95 full Goodman dagram s used, see Fg. 9b. Thus, the generalzed nonlnear model wth an exponent of.265 s also a good predctor of the measured lfetme when used wth the full Goodman dagram. Note the steps n the predcted lfetme, at approxmately 425 MPa and 5x 3 cycles n Fg. 9a (the begnnng of the plot), and at approxmately 4 MPa and 4 cycles n Fg. 9b. These steps are a drect result of the WISPERX spectrum. As shown n Fg. 6, ths load spectrum contans one very large tenson cycle after approxmately 5 cycles. Ths cycle s the cause of falure at both levels of the cted steps: the predcted falure n Fg. 9a occurs at the frst occurrence of ths relatvely large cycle, and t occurs at the second occurrence n Fg. 9b. For ths falure, the resdual strength s progressvely decreasng, untl t encounters ths relatvely large cycle that exceeds the current resdual strength of the composte. If ths plot had been constructed wth fner resoluton, other, smlar steps would be present Resdual Strength Comparsons Fgures and llustrate the predcted resdual falure strength of the composte usng the lnear Mner s rule and the two nonlnear resdual strength models. p. 9
10 The major dfference between the three models s llustrated n Fg.. As shown n ths fgure, the loss of resdual strength as fatgue cycles accumulate s very dfferent for the three models. For Mner s rule, the composte retans ts strength for most of ts lfetme, and, as falure approaches, ts resdual strength drops precptously. For the nonlnear Mner s sum, wth =.95, the resdual strength curve mantans the same form, but s shfted to the left,.e., t predcts a shorter lfetme. For the generalzed nonlnear resdual strength model wth =.265, the resdual strength starts decreasng almost mmedately and contnues to decrease untl falure occurs. 5 Concludng Remarks The updated Goodman dagrams presented here have been developed usng the MSU/DOE Fatgue Data Base [2]. The sx dagrams constructed here are based upon SN data obtaned at thrteen dfferent Rvalues. Separate Goodman dagrams were constructed usng both the mean and the 95/95 representatons of the data. The effects of these mproved representatons of the behavor of fberglass compostes were llustrated usng coupons tested to falure usng the WISPERX load spectrum. Ths load spectrum s prmarly a tensle load spectrum. These comparsons llustrate that when a Mner s rule damage crteron s used the mean fts of the data do not predct falure very well, whle the 95/95 fts predct falures near the mean of measured data. Both a nonlnear Mner s sum model and a generalzed nonlnear resdual strength model, when used wth the 95/95 full Goodman dagram, predct the lower bound of the measured data very well, and when used wth the mean full Goodman dagram, predct the mean lfetme very well. 6 References [] Mandell, J.F., D.D. Samborsky, N.K. Wahl, and H.J. Sutherland, Testng and Analyss of Low Cost Composte Materals Under Spectrum Loadng and Hgh Cycle Fatgue Condtons, Conference Paper, ICCM4, Paper # 8, SME/ASC, 23. [2] Mandell, J.F., and D.D. Samborsky, DOE/MSU Composte Materal Fatgue Database: Test Methods, Materals, and Analyss, Report SAND9732, Sanda Natonal Laboratores, Albuquerque, NM, 997. [3] Ten Have, A.A., WISPER and WISPERX: Fnal Defnton of Two Standardzed Fatgue Loadng Sequences for Wnd Turbne Blades, NLRTP 9476U, Natonal Aerospace Laboratory NLR, Amsterdam, the Netherlands, 992, [4] Sutherland, H.J., and J.F. Mandell, "Effect of Mean Stress on the Damabe of Wnd Turbne Blades," 24 ASME Wnd Energy Symposum, AIAA/ASME, 24. [5] Wahl, N.K., J.F. Mandell, D.D. Samborsky, Spectrum Fatgue Lfetme and Resdual Strength for Fberglass Lamnates, Report SAND22546, Sanda Natonal Laboratores, Albuquerque, NM, 22. [6] Mandell, J.F., D.D. Samborsky, and D.S. Carns, Fatgue of Composte Materals and Substructures for Wnd Turbne Blade, Contractor Report SAND2277, Sanda Natonal Laboratores, Albuquerque, NM, 22. [7] Mandell, J.F., D.D. Samborsky, D.W. Combs, M.E. Scott and D.S. Carns, Fatgue of Composte Materal Beam Elements Representatve of Wnd Turbne Blade Substructure, Report NREL/SR , Natonal Renewable Energy Laboratory, Golden, Co, 998. [8] Echtermeyer, T., E. Hayman, and K.O. Ronold, Estmaton of Fatgue Curves for Desgn of Composte Lamnates, CompostesPart A (Appled Scence and Manufacturng), Vol. 27A, No. 6, 996, p [9] Sutherland, H.J., and P.S. Veers, The Development of Confdence Lmts For Fatgue Strength Data, 2 ASME Wnd Energy Symposum, AIAA/ASME, 2, pp [] ASTM, E7399, Standard Practce for Statstcal Analyss of Lnear or Lnearzed StressLfe (SN) and StranLfe (en) Fatgue Data, ASTM, Conshohocken, PA. [] Kensche, C.W., "Effects of Envronment," Desgn of Composte Structures Aganst Fatgue, R. M. Mayer, ed., Mechancal Engneerng Pub. Lmted, Bury St Edmunds, Suffolk, UK, 996, pp [2] Njssen, R.P.L, D.R.V. van Delft and A.M. van Wngerde, Alternatve Fatgue Lfetme Predcton Formulatons for varable Ampltude Loadng, 22 ASME Wnd Energy Symposum, AIAA/ASME, pp. 8. [3] Hwang, W., and K.S. Han, Cumulatve Damage Models and MultStress Fatgue Lfe Predcton, J. of Composte Materals, Vol. 2, March, 986, pp [4] Yang, J.N., D.L. Jones, S.H. Yang, and A. Meskn, A Stffness Degradaton Model for Graphte/Epoxy Lamnates, J. of Composte Materals, Vol. 24, July, 99, pp p.
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