Fatigue characterization of a Cu-based shape memory alloy

Transcription

1 Proc. Estonan Acad. Sc. Phys. Math., 27, 56, 2, Fatgue characterzaton of a Cu-based shape memory alloy Fabo Cascat, Sara Cascat, and Luca Faravell Department of Structural Mechancs, Unversty of Pava, Va Ferrata 1, 271 Pava, Italy; fabo@dpmec.unpv.t Receved 15 January 27 Abstract. Applcatons of a Cu-based shape memory alloy n monuments retrofttng were conceved, desgned, and tested. The polycrystallne nature of the materal requres a prelmnary dscusson n order to allow the extenson of propertes whch are well known for monocrystallne specmens. Furthermore, one of the man drawbacks of the nvestgated alloy s ts brttleness. Therefore, fatgue tests were carred out and the results of those conducted under cycles of torson loadng unloadng are reported. In partcular, the dentfcaton of the response range, whch s most sutable for structural engneerng applcatons, s pursued. Key words: compresson tests, fatgue tests, shape memory alloy, tenson tests, torson tests, thermal treatment. 1. INTRODUCTION Shape memory alloys (SMAs) have been the object of theoretcal, expermental, and numercal nvestgatons by experts n mathematcs [ 1 3 ], physcs [ 4 7 ], metallurgy [ 8 ], as well as n engneerng scences [ 9,1 ]. As underlned n [ 11 ], however, movng from mcroscale to macroscale often requres begnnng the studes from scratch, snce the results acheved earler may be useless. The next secton summarzes the mcrostructural theory, but also emphaszes the dffculty n generalzng the results of macroscale tests. Ths s manly due to the nfluence of the thermomechancal hstory of the specmen. Under these premses, the results of macroscale tenson/compresson tests and torson tests on the selected Cu-based alloy are llustrated. Fnally, the fatgue characterzaton of the alloy s dscussed wthn the assgned testng condtons. 27

2 2. GOVERNING RELATIONS Mcrostructural theory [ 12 ] s based on the crystallographc and physcal knowledge of the materal structure and mechancs of deformaton. Indeed, t takes account of geometrcal and physcal peculartes of the deformaton mechansms. Let us consder a representatve volume of the alloy, V, and denote wth V the volumes of ts mcroregons. The macroscopc deformaton tensor ε s obtaned by averagng the mcrodeformaton tensors ε over all mcroregons: V ε = ε = Φε, V (1) where Φ s the th volume fracton. A polycrystal conssts of grans characterzed by dfferent crystallographc orentatons. The orentaton of the grans nfluences most of the propertes. Therefore, t s convenent to consder the grans as the volumes of the mcroregons specfed above. Snce the gran deformaton ε refers to the crystallographc bass, whle the macroscopc deformaton refers to the laboratory bass, n order to derve the ε, some rotaton matrces must be ntroduced n Eq. (1), as s common n contnuum mechancs. Each mcroregon (.e. gran) deformaton s regarded as the sum of dfferent mechansms: elastcty, thermal expanson, phase transformaton, mcroplastcty, [1] [2] [3] [4] and plastcty. Let ε ', ε ', ε ', ε ', and ε [5] ' denote these contrbutons, respectvely. The thrd and fourth of those requre further explanaton. If, n the generc th gran, one observes up to N varants of martenste, the volume fracton of the n th varant s wrtten as Φ n N. Each martenste varant s characterzed by the lattce deformaton, D n, by whch t was obtaned from the parent phase. It follows that the correspondng phase transformaton contrbuton s gven by ε N [3] ΦnDn N n= 1 1 ' =. (2) The plastc accommodaton s an rreversble deformaton occurrng n the places of local stress concentratons. Mcroplastc deformaton, geometrc ncompatbltes, and addtonal stresses caused by the martenste accommodaton reman n the materal even after the reverse transformaton. Ths causes the ncompleteness of the stran recovery. Here the followng expresson s postulated for the mcroplastcty addendum: p n ε 1 ' =, (3) N [4] p Φn Dn N n= 1 where Φ s the measure of the mcrostran produced at the accommodaton of the crystal, whch belongs to the n th varant of martenste n the gran. 28

3 Although the above relatonshps are dffcult to apply at a macroscale level, they show how the materal response s affected by the plastc accommodaton resultng from both the thermal processes and the stress cycles. Thermal treatments and stress tranng are therefore ntroduced to optmze the materal predctablty. 3. TENSION/COMPRESSION TESTS The Cu-based alloy whch was selected among those avalable on the market has 11.8 wt% Al and.5 wt% Be. It s cast n ngots of 6 kg, from whch specmens n the form of wres, bars or plates can be obtaned [ ]. The followng phase transformaton temperatures were obtaned by the dfferental scannng calormeter test: martenste starts at 46 C and fnshes at 55 C; austente starts at 25 C and fnshes at 18 C. Fgure 1a provdes the stress stran dagram expermentally obtaned from a wre wth a dameter of 1 mm. The tenson test was conducted n dsplacement control, wthout mountng any extensometer, snce t requres a larger specmen secton. The strans were therefore obtaned by dvdng the span measurements of the lnear varable dfferental transducer (LVDT), mounted on the testng stress[mpa] Stress, MPa (a) E-2-1.E+ 2.E-2 4.E-2 6.E-2 8.E-2 1.E-1 1.2E-1 1.4E-1-2 Stran stran Stress, MPa Stress [MPa] E+ 2.E-2 4.E-2 6.E-2 8.E-2 1.E-1 1.2E-1-1 Stran Stran Fg. 1. (a) Loadng unloadng cycles on a wre of round secton wth a dameter of 1 mm: test n dsplacement control; stran computed by the LVDT. Test to rupture of a wre of round secton wth a dameter of 3.5 mm: test n dsplacement control; stran measured by the extensometer. 29

4 machne, by the ntal length. The comparson wth the result (Fg. 1b) of a test to rupture carred out on a wre wth a dameter of 3.5 mm of the same alloy (even f comng from a dfferent stock) and mountng the extensometer, shows that the man characters of the alloy are accurately captured n Fg. 1a. The followng remarks arse from Fg. 1: (a) The vrgn curve s abandoned after the frst unloadng. The hgher s the stran reached durng the loadng, the wder s the gap, whch stablzes after some cycles of the same ampltude. The frst unloadng produces small resdual strans, whch are due to some martenste volume whch does not recover nto austente; the resdual stran becomes sgnfcant when a stran of 5 6% s reached durng the loadng cycle. (c) Unloadng s badly conducted n dsplacement control; ndeed, at very low values of stran, the resdual dsplacements are assocated wth negatve loads, whch theoretcally should not be allowed n the wre. (d) Unloadng can be correctly performed n force control, but the machne allows t only for specmens of sgnfcant secton. Otherwse, the tunng of the testng machne would become a dffcult task, often wthout soluton. It s worth notcng that thermal treatment could be ntroduced to mprove the alloy response n the range of stran up to 4%. In the followng the hollow specmens shown n Fg. 2a wll be consdered. They were obtaned from bars wth the external dameter of 15 mm, by removng the nternal materal to form a ppe wth the nternal dameter of 12 mm. The results of compresson and tenson tests at ambent temperature are gven n Fg. 3. (a) Fg. 2. (a) A SMA specmen for the fatgue test and the testng envronments: grps and thermal chamber. 21

5 (a) 5-4.5E-2-4.E-2-3.5E-2-3.E-2-2.5E-2-2.E-2-1.5E-2-1.E-2-5.E-3.E+ 5.E-3-5 stress [MPa] Stress, MPa stran Stran Stress, MPa stress [MPa] E-2.E+ 1.E-2 2.E-2 3.E-2 4.E-2 5.E-2 6.E-2 7.E-2-5 Stran stran Fg. 3. Stress stran dagram for the specmen n Fg. 2a: (a) compresson test, tenson test. It s worth notng that both the test specfcatons and the specmen nature are dfferent from those of Fg. 1: (1) the test s conducted n deformaton control durng the loadng, and n load control durng the unloadng; (2) before the test, the specmen undergoes thermal treatment: 4 mn at 85 C, then out at ambent temperature (water quenched), and fnally 2 h at 1 C. The scannng electron mcroscopy shows re-crystallzaton and gran growth after thermal treatment. Furthermore, thermal treatment slghtly ncreases the phase transformaton temperatures. From the dagrams of Fg. 3 we can see that () the plateau level has sgnfcantly decreased by thermal treatment; () n tenson there s a good recover of stran, even after a loadng up to 6% of deformaton; () n compresson, un-recovered strans are recorded for any level of peak deformaton. Fatgue tests under tenson loadng unloadng cycles were dscussed n [ 16,17 ]. Ths paper consders only the tests conducted under torson cycles. The framework n whch these tests were carred out s clarfed n the next secton. 211

6 4. TORSION TESTS The unversal testng machne n Fg. 2b s b-axal,.e., t mounts two hydraulc actuators: axal and torsonal. Tests utlzng the latter actuator requre specmens of crcular secton wth the external dameter of 15 mm. The ultmate moment of the actuator s 1 N m. In order to reach the materal plateau, specmens of hollow crcular secton and nternal dameter of 12.5 mm were used. The tests were conducted wthout mountng the torsonal extensometer, snce ts placement requres specmens of a gven varable shape (external dameter 15 mm at the top and bottom, but 12.5 mm n the mddle). Ths would have requred a too extensve modfcaton transformaton of the avalable alloy peces. The specmens underwent several torson tests drven n angle control. The results of two tests are plotted n Fg. 4: up to rupture (whch occurred when the rotaton reached 5 ; Fg. 4a) and 1 loadng unloadng cycles n the range 5 1 (Fg. 4b). Torson moment, N mm torson moment [N mm] (a) angle Angle, [deg] deg Torson moment, N mm Angle, deg Fg. 4. Torson moment angle dagram: (a) up to rupture, 1 cycles n the range

7 The man dfferences from the axal tests dscussed n the prevous secton are the larger nternal dameter and the prelmnary thermal treatment of the specmen. Here the alloy s left at 1 C for only 1 mn nstead of 2 h. Ths does not satsfactorly prevent the mcroplastcty effect dscussed n secton 2. The consequence s evdent n Fg. 4b, where each loadng unloadng cycle occurs wth a loop characterzed by a lower value of the resdual stress. Snce the subject nvestgated n ths paper s the alloy durablty, ths partal thermal treatment was ntroduced as a penalty n terms of cycles stablzaton, but also as a form of preventon from excessve brttleness. 5. FATIGUE TESTS Specmens of geometry desgned for torson tests, after the specfed thermal treatment, underwent several torson loadng unloadng cycles, each of them enterng the stress plateau where austente transforms nto martenste. Fatgue tests are usually conducted n load control. However, ths was not allowed for the alloy under nvestgaton. Indeed, (a) loadng unloadng cycles produce the heatng of the specmen; due to the thermoelastc propertes of the alloy, ths heatng requres hgher values of the load to be appled n order to reach the plateau; mcroplastcty develops along both the prncpal drectons of compresson and tenson stran drecton, thus alterng the deformaton effect of any gven load value. As a consequence, t was decded to run the tests n angle control, by assgnng the peak values at the torson angle. Then tme hstores of the maxmum torson moment were recorded (Fg. 5). Two dfferent cases of cyclng between two postve values of the peak angles and of cyclng around the zero angle are represented n the same fgure. They lead to the rupture mechansms shown n Fg. 6a and 6b, respectvely. Both tests were conducted at a frequency of 1 cycle per second. The angle range s 7.5 for Fg. 5a,b. The observed response, however, s qute dfferent. The maxmum moment ncreases a lttle n Fg. 5a (manly due to the heatng); after the frst materal deteroraton after 3 cycles, the specmen survves up to 1 cycles. Fgure 5b emphaszes a much larger ncrease n the maxmum moment, caused here by the resdual strans left durng each prevous cycle n the opposte drecton: a resdual stran n compresson results n a hgher plateau level met n tenson, when the rotaton sgn changes. Moreover, n Fg. 5b the materal deteroraton s mmedately followed by the falure of the specmen, whch survves less than 2 cycles. These dfferent responses were approached n [ 16 ] by characterzng each fatgue test by three values of the number of cycles: at the frst deteroraton, at the pont where the curves present a 45 tangent as n Fg. 5, and at the startng pont of the fnal decay. Of course, such an approach makes the two cases n Fg. 5 fully dfferent, snce the three trplets are (3, 1, 11 ) and (17, 17, 185), respectvely. 213

8 Moment, N [Nmm] (a) Tme, [s] s Moment, N [Nmm] Tme, Tme s [s] Fg. 5. Evoluton of the maxmum torson moment n tme: (a) cycles n the range (2.5, 1 ); cycles n the range ( 3.5, 3.5 ). Tests conducted at ambent temperature. (a) Fg. 6. Mechansm of rupture after fatgue torson cycles (a) n a postve angle range, around the zero angle. 214

9 In order to smplfy the presentaton of the results, each test s here characterzed by the number of cycles after whch the maxmum torson moment goes back to the ntal value. The results of dfferent tests are summarzed n Fg. 7: they were conducted at ambent temperature as well as at 7 C usng the thermal chamber n Fg. 2b. The followng observatons can be made from Fgure 7: (a) the relatonshp between the torson angle and number of cycles to falure can be convenently nterpolated as lnear n the case of cycles around zero; a sort of saturaton s met for large rotatons n the case of cycles between postve peaks; by ncreasng the temperature up to 7 C a sgnfcant reducton n the number of cycles to falure s detected; the coeffcent of lnear regresson decreases by one order of magntude; (c) n all cases, the alloy s able to survve thousands of cycles, whch s reasonably expected n energy dsspaton devces durng strong wnds or earthquakes y =.1x R 2 =.8995 Angle range, deg y =.11x R 2 =.914 Postve range Ambent Alternate ambent Alternate 7 C Alternate ambent Lnear reg. Alternate 7 Lnear reg Tme, s = Cycles number Fg. 7. Angle range of the fatgue test vs. number of survved cycles. Postve ranges start from 2.5. Alternate tests span from one half of the angle range to + one half of the angle range. 215

10 6. CONCLUSIONS Pursung the feasblty of dsspatng energy by explotng the hysteress cycles of SMA elements requres an nvestgaton of materal durablty. Ths study provdes some expermental results obtaned by performng torson tests at ambent temperature and at 7 C. Smlar tests whch were conducted under cycles of axal loadng are reported n [ 17 ]. The results of the torson tests are qute postve n vew of the adopton of the studed Cu-based SMA n dsspatve devces. A mnmum of a few hundreds of survved cycles have to be expected for applcatons n sesmc engneerng and a few thousands for applcaton n wnd engneerng. Both requrements are largely satsfed wthn reasonable angle ranges. A negatve nfluence of very hgh temperatures must also be underlned. Ths requres further tests to be performed to defne the allowed temperature range. A further aspect presently under nvestgaton concerns the nfluence of the duraton of prelmnary thermal treatment. ACKNOWLEDGEMENT The results summarzed n ths paper were acheved wthn the research project WIND-CHIME (Wde-range Non-ntrusve Devces toward Conservaton of Hstorcal Monuments n the Medterranean Area) of the 6th Framework Plan of the European Unon, for whch the frst author s servng as coordnator. REFERENCES 1. Achenbach, M., Atanackovc, T. and Muller, I. A model for memory alloys n plane stran. Int. J. Solds Struct., 1986, 22, Fremond, M. Mécanque des mleux contnues. C. R. Acad. Sc., Sére II, 1987, 34, Patoor, E. and Berveller, M. Les Allages à Memore de Forme. Hermès, Pars, Torra, V. (ed.). Proceedngs COMETT Course: the Scence and Technology of Shape Memory Alloys. Unversty of Balears Islands, Palma de Mallorca, Span, Volkov, A., Evard, M., Kurzeneva, L., Lkhachev, V. and Sacharov, V. Mathematcal modellng of martenstc nelastcty and shape memory effects. Tech. Phys., 1996, 41, Leclercq, S. and Lexcellent, C. A general macroscopc descrpton of the thermo-mechancal behavor of shape memory alloys. J. Mech. Phys. Solds, 1996, 44, Berezovsk, A., Engelbrecht, J. and Maugn, G. A thermoelastc wave propagaton n nhomogeneous meda. Arch. Appl. Mech., 2, 7, Funakubo, H. Shape Memory Alloys. Gordon and Breach Scence Publshers, Saadat, S., Salchs, J., Noor, M., Hou, Z., Davood, H., Bar-on, I., Suzuk, Y. and Masuda, A. An overvew of vbraton and sesmc applcatons of NT shape memory alloy. Smart Mater. Struct., 22, 11, Cascat, F., Magonette, G. and Marazz, F. Technology of Semactve Devces and Applcatons n Vbraton Mtgaton. John Wley & Sons, Chchester, UK,

11 11. Aurccho, F., Faravell, L., Magonette, G. and Torra, V. (eds). Shape Memory Alloys. Advances n Modellng and Applcatons. CIMNE, Barcelona, Span, Volkov, A. and Cascat, F. Smulaton of dslocaton and transformaton plastcty n shape memory alloy polycrystals. In Shape Memory Alloys. Advances n Modellng and Applcatons (Aurccho, F., Faravell, L., Magonette, G. and Torra, V., eds). CIMNE, Barcelona, Span, 21, Cascat, S. and Faravell, L. Thermo-mechanc characterzaton of a Cu-based shape memory alloy. In Proceedngs SE4, Osaka, Japan (Tachbana, E., Spencer, B. F., and Muka, Y., eds). Bandoh Prntng, Osaka, 24, Cascat, F. and Faravell, L. Expermental charactersaton of a Cu-based shape memory alloy toward ts explotaton n passve control devces. J. Phys. IV, 24, 115, Cascat, S. and Faravell, L. Structural components n shape memory alloy for localzed energy dsspaton. Comput. Struct., 27 (accepted). 16. Galluzzo, A. Durabltà d element struttural n lega a memora d forma. Master s Degree Thess, Dept. of Structural Mechancs, Unversty of Pava, Cascat, S. and Faravell, L. Fatgue tests of a Cu-based shape memory alloy. In Proceedngs of 4th World Conference on Structural Control & Montorng, San Dego, 26 (to appear). Vasel (Cu) põhneva kujumäluga sulam väsmuskarakterstkud Fabo Cascat, Sara Cascat ja Luca Faravell Monumentde restaureermsel on kasutatud ja katsetatud vasel (Cu) põhnevad kujumäluga sulamed. Uurngu kaugemaks eesmärgks ong nende sulamte omaduste määramne. Monokrstalllse proovkeha hästtuntud omaduste laendamne kogu materjalle nõuab täpsemad uurngud materjal polükrstalllsest olemusest. Näteks on uurtud sulamte peamseks puuduseks nende haprus. Artkls on krjeldatud väsmuskatsed ja nende tulemus tsükllsel väändekoormusel. Ert on püütud määratleda sulamte sobvamad rakendusvsd konstruktsoondes. 217