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International Journal of Mechanical Sciences 43 (2001) 26572677

Mechanical behaviour of shape memory alloys forseismic applications

2. Austenite NiTi wires subjected to tension

Mauro Dolce , Donatello Cardone

Department of Structures, Geotechnics and Applied Geology, University of Basilicata,C. da Macchia Romana, 85100 Potenza, Italy

Received 8 May 2000; received in revised form 19 January 2001

Abstract

The results of cyclic tensile tests on superelastic NiTi shape memory alloy (SMA) wires are presentedand discussed. The tests were carried out within a large experimental test programme for the MANSIDEProject, with the scope of verifying the suitability of SMA superelastic wires as kernel components forseismic protection devices.

The mechanical behaviour is described by means of four fundamental quantities, namely: secant sti-ness, energy loss per cycle, equivalent damping and residual strain. The sensitivity to temperature andstrain rate, as well as the inuence of strain amplitude and the eects due to repeated cyclic deformation,are analysed in detail.

The experimental results show that the characteristics of the superelastic wires are well suited forseismic applications, as both the recentring and the energy dissipating features of the devices can beeasily obtained. Moreover, the inuence of the investigated parameters, within their usual range ofvariation in seismic protection devices, is compatible with the use of superelastic wires for practicalapplications. ? 2001 Published by Elsevier Science Ltd.

Keywords: Shape memory alloys; Experimental tests; Superelasticity; Fatigue resistance; Seismic protection devices

1. Introduction

Special devices for passive control of vibrations can signicantly improve the performancesof structural systems subjected to earthquakes [1]. Several types of seismic devices are, nowa-days, available. Current technologies, however, present some limitations related to ageing and

Corresponding author. Tel.: +39-0971-205-107; fax: +39-0971-205-070.E-mail addresses: [email protected] (M. Dolce), [email protected] (D. Cardone).

0020-7403/01/$ - see front matter ? 2001 Published by Elsevier Science Ltd.PII: S 0 0 2 0 -7 4 0 3 (0 1 )0 0 0 5 0 - 9

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2658 M. Dolce, D. Cardone / International Journal of Mechanical Sciences 43 (2001) 26572677

Nomenclature

Fs; Ff critical stresses at which martensitic transformation starts and nishes, respec-tively

Is; If critical stresses at which inverse martensitic transformation starts and nishes,respectively

normal stress normal strain displacementf frequency of loading

F forceT temperature

Ks secant stinessWD energy loss per cycleWd energy loss per unit weighteq equivalent viscous damping

durability, reliability in the long run, substitution after strong earthquakes, dependence of me-chanical performances on temperature and geometry restoration at the end of a strong earthquake.Shape memory alloys (SMAs) [25] have the potential to eliminate most of the limitations in-volved in current technologies, owing to their extraordinary fatigue resistance, superelasticity orshape memory eect, stability of their characteristics and high corrosion resistance.

With the purpose of exploring the potentials of SMAs in seismic protection uses, designingand manufacturing SMA-based devices, as well as testing devices and structural systems, aspecic research project (MANSIDEMemory Alloys for New Seismic Isolation and EnergyDissipation Devices) was funded by the European Commission, within the BRITE-EURAMProgramme, in 1996.

In Table 1 the prerequisite that a SMA should satisfy in order to be eectively used in seismicprotection devices are summarised. The suggestions given in Table 1 are from a bibliograph-ical investigation, made within MANSIDE, on the properties of various SMA types, namely:

NiTi-based, CuAlNi-based, CuZnAl-based, FeMn[Si]-based and MnCu-based. In the light of theprerequisites reported in Table 1, NiTi SMAs appear to be the best candidates for the use in

seismic applications. Actually, Table 1 can be seen as a memorandum for the material producerto select the most appropriate alloy composition and thermomechanical treatment. Then, thenal user will design the mechanical behaviour of the device (force levels, displacement am-

plitudes, shape of the hysteresis loops) by simply choosing the stress mode and=or arrangementof the SMA components inside the device, as well as their geometry and number.

An extensive experimental investigation on NiTi SMA elements was carried out for MAN-SIDE at the University of Basilicata (Italy) and the University of Leuven (Belgium), in orderto nd the best way to exploit the particular properties of SMAs in seismic devices. Sev-eral NickelTitanium specimens, having dierent shapes (wires and bars), geometric (diameterand length) and physical characteristics (alloy composition, thermomechanical treatment,

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M. Dolce, D. Cardone / International Journal of Mechanical Sciences 43 (2001) 26572677 2659

Table 1Prerequisites of SMA to be used in passive control devices

Martensite Austenite

High energy dissipation Superelasticity

High fatigue resistance

Low sensitivity to temperature in the range 535

C for buildings and 545

C for bridges

Low sensitivity to strain rate or to frequency in sinusoidal vibrations, in the range 0.41 Hz,for seismic isolation techniques [1], and 110 Hz, for energy dissipation techniques [1].

Stability of cyclic behaviour:0:961; 1=1; i6 1:1, 0:962; 1=2; i6 1:1

where i is the number of the cycle produced by an earthquake

No degradation for environmental actions or as low as possible(applications on buildings are much less sensitive than applications on bridges)

2 6%, 2 12% or as large as possible

4=2 2, 4=2 2 or as large as possible

E26 0:10 E1 or as low as possible

E36 0:5 E1 or as low as possible

E1 30; 000 MPa (as large as possible) E1 70; 000 MPa (as large as possible)

1 300 MPa or as large as possible 1 500 MPa or as large as possible

3=16 1:5 or as low as possible

material phase), were tested under dierent stress states (tension, compression, torsion, bendingand shear). For each group of tests, dierent strain levels, strain rates and temperatures wereconsidered.

In a companion paper [6], the peculiar properties of SMAs are reviewed, the complete plan ofthe experimental investigation is described and the results of the torsion tests on SMA-martensite

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Fig. 1. Schematic stressstrain curve of superelastic shape memory alloy, showing the phenomena associated withthe deformation process.

and SMA-austenite bars are given and discussed. In this paper, the main experimental re-sults of tensile tests on SMA-austenite wires are presented and discussed. A short introductionon superelasticity, the peculiar property of austenitic SMAs, precedes the presentation of theexperimental results.

2. Superelasticity of SMAs

Superelasticity [712] is one of the most attractive properties of SMAs. It implies the at-tainment of very large strains (at least one order of magnitude greater than common metals)without any residual deformation upon unloading, while dissipating a considerable amount ofenergy.

Fig. 1 shows a schematic stressstrain cyclic curve of a superelastic SMA. It is characterisedby ve branches. Branches 1 and 4 correspond to the elastic deformation of the two stable phasesof SMA, respectively, austenite and martensite. Branches 2 and 3 correspond, respectively, tothe forward (from austenite to detwinned martensite) and inverse (from detwinned martensiteto austenite) phase transformation. Branch 5 corresponds to the onset of plastic deformation of

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detwinned martensite. In Fig. 1, Fs and Ff represent the critical stresses at which the forwardtransformation, respectively, starts and nishes, while Is and If are those at which the inversetransformation, respectively, starts and nishes.

The mechanical behaviour of superelastic SMAs suits the optimal requirements of a seismiccontrol device. Indeed, they could provide the device with (i) energy dissipation capability, toreduce acceleration and displacements caused by earthquakes, (ii) self-centring capability, to

bring back the structure to its initial position when earthquake is over, (iii) good control of theforce transmitted by the device to the structure, (iv) high initial stiness, to limit displacementsunder service actions or moderate earthquakes. Moreover, a seismic SMA based device stiensin case of unpredicted strong actions (branch 4), thus assuring a good control of displacementseven under unforeseen strong earthquakes.

Although the use of superelastic SMAs appears to be very appealing under dierent pointsof view, some aspects have to be carefully examined:

1. The properties and the mechanical behaviour of SMAs strongly depend on alloy compositionand thermomechanical treatment (see for example [1316]).

2. Superelasticity is highly sensitive to temperature:

All SMAs are superelastic only at some temperatures, i.e. between Af and Md [911]:to be useful in civil engineering applications, the superelastic range must be as wide as

possible and must be centred around the average service temperature. The transformation critical stresses increase linearly while increasing the temperature,

with growth rate ranging from 3 up to 20 MPA=

C [12].

3. Although it is said that superelasticity is an isothermal phenomenon, this is practically not true

because of the latent heat of transformation which causes the self-heating of the material. Asthe strain rate increases, the self-heating becomes signicant, causing a rise of some degreesof the internal temperature. This yields modications in the shape of the hysteresis loops,such as an apparent hardening of the plateau relevant to the phase transformations [17,18].

4. The mechanical behaviour of SMAs changes with repeated cyclic deformations [1921].

Tension loadingunloading tests on Ni-Ti SMA wires have been carried out by many researchers[1732]. Most of them, however, were simply characterisation tests of material, aimed at in-vestigating the phase transformation phenomena for limited strain rate, strain amplitudes andtemperature ranges. The relevant results cannot provide exhaustive information about the actual

potential of SMAs for seismic applications. This is because, in seismic applications, the strainhistory is cyclic and the strain amplitude is not constant but it ranges, during the same cyclichistory, from very small values (corresponding to the elastic deformation of austenite) to verylarge values (corresponding to the elastic deformation of martensite). Moreover, the strain ratesof interest are much higher than those considered in previous studies.

In order to evaluate the possibility of using an SMA as a dissipating material in seismicdevices, the cyclic behaviour of SMAs under high strain rates and various strain amplitudes,as well as the eects due to repeated cyclic deformation, must be examined.

To this end, an accurate test programme was carried out at the University of Basilicata (Italy)and at the University of Leuven (Belgium), within the activities of the MANSIDE project. Here

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the most important results of the experimental investigation are reported and discussed, whilemore detailed information can be found in Refs. [33,34]. The tests were planned to reproducethe typical work conditions the SMA wires would be subjected to inside seismic devices. All

the tests were then carried out by applying sinusoidal cyclic deformation to wire samples. Strainrate, strain amplitude, number of cycles and room temperature were selected as test parameters.Their values were carefully selected, taking into account their respective ranges of interest forseismic applications, namely: 1040

C temperature, 0.24 Hz frequency of loading, 1020consecutive loading cycles.

3. Tensile tests

3.1. Testing programme

The experimental tests described in this paper were carried out on austenite wire sampleswith 12 mm diameter and 200 mm length. Several kinds of wires were considered, diering inalloy composition (NiTi-[Nb] about 50 at% Ni) and=or thermomechanical treatment (% coldworking and annealing temperature [13,15,16]). Unfortunately, no more specic material-relatedinformation were available from the manufacturer.

First of all, cyclic tests on pre-tensioned wires, at room temperature ( 20

C), frequencyof loading ranging from 0.01 to 4 Hz (strain rate 0.00080:32 s1) and strain amplitude upto 10%, were carried out. Subsequently, loadingunloading tests under temperature control,

between 40

C and 10

C (step 10

C), at about 7% strain amplitude and 0.020:2 Hz frequencyof loading, were carried out. During the tests, the surface temperature of wire was measured

by thermocouples.

3.2. Tests at room temperature

Fig. 2, shows the results of a series of loadingunloading tension tests on 1:84 mm diameteraustenitic wire. The wire is slightly pre-tensioned ( 0:5%). All the tests were carried out atroom temperature ( 20

C), on the same wire sample, and were preceded by some trainingcycles aimed at stabilising the material behaviour (see afterwards). Each test is characterised byfour sequences of cycles, each sequence being made of two cycles, at maximum strain equalto about 5%, 6%, 7.5% and 9%, respectively. The frequency of loading, which is kept constant

during each test, varies from 0.02 to 4 Hz.In Fig. 2, the trends of secant stiness, energy loss per unit weight and equivalent dampingare reported as a function of frequency of loading, for dierent strain amplitudes. Some typicalstressstrain diagrams at dierent frequencies are also given. As can be seen, the mechanical

behaviour of SMA-austenite wires in tension clearly depends on frequency and changes sig-nicantly when passing from pseudo-static (0:02 Hz) to dynamic conditions (0.24 Hz). Whenincreasing the strain rate, indeed, the hysteresis loops narrow and translate upwards, while the

branches of the curve relevant to the phase transformations harden, thus yielding an increase inthe stress levels. Therefore, secant stiness increases (by about 15% in the range 0.020:2 Hz),while energy loss and equivalent damping decrease by about 18% and 25%, respectively, in

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Fig. 2. Cyclic tensile tests on pre-tensioned superelastic wires: mechanical behaviour as a function of strain amplitudeand frequency of loading.

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the range 0.020:2 Hz. In particular, equivalent damping drops from about 89% to about 6%,when frequency rises from 0.02 to 0:2 Hz.

The above-said eects must be ascribed to the dierent heat exchange modalities with ambient

at dierent strain rates. As strain rate increases, indeed, the heat-exchange condition increasinglydigresses from the isothermal one. The latent heat of transformation causes the specimen toself-heat and then increase its average temperature during test. At the same time, during eachloading cycle, the specimen temperature oscillates around an average value, according to thesinusoidal variation of strain: the instantaneous temperature rises upon unloading, the forwardtransformation being exothermic, and decreases upon unloading, the inverse transformation beingendothermic. Both the hardening of the transformation branches and the narrowing of the cycle,resulting in a reduction of energy loss, are caused by the instantaneous temperature variation.The possible increase of the average temperature produces an upward translation of the cycle.

In Fig. 3, some plots showing the trend of the material temperature during ten consecutive

cycles at 0:01 Hz frequency and 6.5% strain amplitude are reported. The test was carried out ona virgin 1 mm diameter wire sample. Fig. 3(a) shows the temperature-time history as well asthe average value for each cycle, and Fig. 3(b) shows the material temperature versus the strainamplitude and the corresponding stressstrain relationship, during four dierent loading cycles.As can be seen, the material temperature increases during loading while it decreases during un-loading, following a quasi-sinusoidal trend, like the imposed strain. Actually, neglecting the rstcycle, which has to be examined separately, and focusing the attention on the strain range inwhich the phase transformations take place, the temperature-strain relationship is practically lin-ear. As it was clearly proved in Ref. [17], the deformation is inhomogeneous and local in natureduring the phase transformations. Initially, stress-induced martensite nucleates in a few locations(most likely at the specimen ends, because of the stress concentrations due to grips), then it

propagates elsewhere from the nucleation sites. As a consequence, the local strain measured byan extensometer placed in a certain position (in the middle of the wire in the test of Fig. 3)is out of phase with respect to the temperature recorded by a thermocouple placed in a dier-ent position (between the middle and the end of the wire in the test of Fig. 3). Extensometerand thermocouple view the phase transformation in dierent times. This observation explainsthe apparent irregularity characterising the linear relationship between strain and temperatureduring the phase transformation, but it can also explain the anomalous strain-temperature curvecharacterising the rst cycle. During loading, ve dierent branches are clearly visible. Therst branch is horizontal (no increase in temperature while increasing strain), corresponding tothe elastic deformation of austenite. The second branch of the strain-temperature curve seem-

ingly appears before the phase transformation starts. According to Shaw and Kyriakides [17],it is because the phase transformation propagates from the ends to the middle of the wire,that the thermocouple records the transformation before the extensometer. A new horizontal

branch follows the second. Probably, this is simply an experimental error. Less believable isthe fact that the increase in the transformation stresses due to self-heating causes the nucleationof martensite in a cooler region away from the propagating front. During the fourth branch,temperature increases again. Finally, it tends to stabilise, as transformation becomes complete(fth branch). During unloading, the inverse transformation propagates from the middle to theends of the specimen. In this case, therefore, the extensometer records the phase transformation

before the thermocouple. As a consequence, the seventh branch stays higher up than the fourth.

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Fig. 3. (a) Material temperature-time history during ten consecutive cycles at 0:01 Hz frequency and 6% strainamplitude; and (b) material temperature versus strain during dierent loadingunloading cycles.

While the instantaneous temperature of the wire oscillates around the ambient temperature(30

C), with excursions of the order of 1216

C, the average temperature remains practicallyunchanged during all the loading history, equal to the ambient temperature. In this case, there-fore, the only eect due to self-heating (cooling) that results from the forward (inverse) phasetransformation is the instantaneous increase (decrease) of the stress required for the transforma-tion itself. The apparent change in the shape of the hysteresis loops while increasing the numberof cycles is not, therefore, caused by temperature variations but rather by the stabilisation of thematerial behaviour due to repeated cycling. The corresponding reduction in energy dissipationresults in a progressive reduction of the temperature excursion from about 16

C to about 12

C.

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Fig. 4. (a) Material temperature-time history during eight consecutive cycles at 0:02 Hz frequency and strain am-plitude increasing from 55% to 9%; and (b) material temperature versus strain during dierent loadingunloadingcycles.

The stabilisation of the average temperature results in a dierence of the temperatures at thebeginning and end of the experiment equal to half the excursion at the last cycle.Fig. 4 shows the trend of the material temperature for the test already considered in Fig. 2,

both as a function of time and strain, during eight consecutive cycles at 0:02 Hz, and strainamplitude increasing from about 5% to about 9%. The test was carried out using a previouslycycled 1:84 mm diameter wire sample. In this case, the strain was calculated as the total elonga-tion divided by the sample length. This led to decidedly more regular strain-temperature curves.However, because of the greater diameter, it is likely that the externally measured temperatureis not exactly the same as the internal temperature. Also, in this case, the average material tem-

perature remains practically constant, as it stabilises very rapidly at the ambient temperature.

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Fig. 5. Trend of the average material temperature at dierent frequencies of loading.

Quasi-sinusoidal variations around this value occur. The temperature excursion increases from10

C to about 14

C, according to the increase of the strain excursion.Fig. 5 shows the trends of the average temperature as a function of time for dierent loading

frequencies, again for the test shown in Fig. 2. To obtain comparable curves, time is normalisedwith respect to the loading period. Dierent trends are observed for dierent frequencies. Whilefor the low frequency, namely 0:02 Hz, the average temperature, after the initial increase at rst,decreases and progressively stabilises at a value very close to the ambient temperature, for the

highest frequency, namely 0:2 Hz, the trend is always increasing, according to the increasingstrain amplitude. In this last case, the temperature increase at each strain amplitude change isvery apparent. As expected, the average temperature increases while increasing the frequency,

but stabilises beyond a certain frequency value. Actually, the average temperature variation,after eight cycles with increasing amplitude, is about 1

C at 0:02 Hz, 2

C at 0:05 Hz, 4

C at0:1 Hz, and only 6

C a t 0:2 Hz instead of 8

C, as would be the case in a linear sequence.This consideration is in accordance with the results of Fig. 2, which clearly show a constant

behaviour beyond 0:2 Hz frequency.To examine the eects of strain amplitude on the parameters under study, Fig. 6 shows the

hysteresis loops corresponding to ve loadingunloading cycles at dierent strain amplitudes,

namely 1.52.53.54.55.57.5%. The test was carried out at 30

C temperature and 0:01 Hzfrequency on a 1:84 mm diameter wire sample. The stressstrain cycles reported in Fig. 6 werepreceded by twenty cycles at 6%, aimed at stabilising the material behaviour. In Fig. 6, thetrend of the energy loss per unit weight and the equivalent damping as a function of the strainamplitude are also reported.

The most important nding is that the energy loss increases more than linearly whileincreasing the strain amplitude (see also Fig. 2). This occurs because the stress levels attainedduring the inverse martensitic transformation (i.e. upon unloading) decreases as strain amplitudeincreases. In other words, the hysteresis loops expand downwards when increasing the strainamplitude.

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Fig. 6. Cyclic loadingunloading tensile tests on austenite superelastic wire: inuence of strain amplitude.

Another remarkable nding is that the equivalent damping increases practically linearly atlow-medium strain amplitudes (15%), while it slightly decreases (see Fig. 1) at large strain

amplitudes (510%), in spite of the increase of energy dissipation. This last eect has to beascribed to the strong hardening that takes place, during loading, as soon as the forward marten-sitic transformation ends. As known, this phenomenon, which always occurs in both austeniticand martensitic SMAs, is related to the elastic deformation of the detwinned martensite found atthe end of the phase transformation (SMA-austenite) or detwinning process (SMA-martensite).This aspect can be looked at as a favourable eect in seismic applications. Actually, it impliesthat a structural system endowed with seismic SMA-based devices stiens, rather than soften-ing, if the expected design seismic action is exceeded, thus guaranteeing an excellent controlof displacements.

Fig. 7 compares the results of two cyclic tensile tests on a 1 mm diameter austenite (supere-

lastic) wire. At the beginning of the tests, the material was virgin. The wire was pre-strainedat about half the maximum cyclic strain. Both tests were carried out at 20

C temperature and0:01 Hz frequency of loading, but each at dierent strain amplitudes, respectively, 5% and 7.5%.In the enclosed tables, the values of secant stiness, energy loss per unit weight and equivalentdamping relevant to dierent loading cycles are reported. The eects due to repeated cyclicdeformation are apparent. In particular, the hysteresis loops translate downwards and narrow.As a consequence, the energy loss and the stress levels decrease, as well as the equivalentdamping. Passing from 5% to 7.5% strain amplitude, the energy loss increases more than lin-early, while the equivalent damping decreases, due to the large elastic stress attained by thedetwinned martensite.

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Fig. 7. Two consecutive cyclic loadingunloading tensile tests on virgin specimen, showing the inuence of numberof cycles and strain amplitude.

Looking at the seismic applications, some considerations can be made with reference to thedescribed results. It can be said that the cyclic behaviour of austenite wires is substantiallyinsensitive to strain rate, in the range of interest for frequency (0.24 Hz) and number of cycles(1020). In that frequency range, the values of the equivalent damping of a wire subjected toloadingunloading cycles are of the order of 57%. It is, then, quite low when compared tothe commonly required values of equivalent damping.

The superelastic properties of SMA wires, as they result from the above-mentioned shownexperiments, can be exploited to obtain a variety of hysteretic behaviours in seismic devices[35]. An example is to use pre-tensioned superelastic wires in order to cycle around the midpointof their hysteresis curve. Fig. 8(a) shows the cyclic behaviour of a wire sample pre-strained at3.5% and then cycled between 1% and 6%. If the pre-tensioned wires work in opposition to oneanother, as shown in Fig. 8(b), the upward motion of the central point is assisted by spring A,while it is resisted by spring B. The downward motion is symmetric, with the role of the twosprings reversed. The result of such a particular conguration is a wide hysteresis loop and anapparent threshold value of force. Indeed, this is obtained because the total force is the dierence

between the tension forces of the two springs, one being increased while the other decreases.

A totally dierent behaviour is obtained if the pre-tensioned wire is subjected only to tensionincrease, whichever the sign of the device displacement is, owing to a special mechanism. Inthis case, the cycle of Fig. 8(c) is obtained, thus realising a strongly recentring device, whichallows the structural system to recover its initial conguration, even in the presence of large

parasite forces.

3.3. Tests under temperature control

Fig. 9(a) shows some typical stressstrain diagrams at dierent temperatures, ranging from40

C to 10

C, of step 10

C. They were recorded during loadingunloading tests at 0:02 Hz

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Fig. 8. Hysteretic behaviour available by using pre-strained superelastic SMA wires in dierent mechanisms.

and about 7% strain amplitude. All the six tests were carried out on the same sample andwere preceded by ten training cycles at 7%, aimed at stabilising the material

behaviour.

For each temperature, the critical stresses relevant to the forward and the inverse phasetransformation have been evaluated. It is assumed that they coincided with the ordinates of theintersection points between tangent lines. Based on these values, the starting and completingtransformation lines have been drawn in Fig. 9(b). As can be seen, their trend is clearly linear,with slopes ranging from 6 to 7 MPa=

C. The transformation temperatures in the stress-freestate can be estimated at the intersection points between the aforesaid lines and the horizontalaxis. In this case, Af is about 5

C. The superelastic range (T Af), then, clearly suits thetypical temperature range of interest. The residual strain observed in the cycle at 10

C is dueto the presence of martensite at the end of unloading. It is, obviously, recovered as soon as thetemperature rises above 5

C.

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Fig. 9. Austenite wire in tension: (a) stressstrain curves at dierent temperatures; and (b) starting and completingtransformation stresses as a function of temperature.

Fig. 10. Austenite wire in tension: energy loss per unit weight (left) and equivalent damping (right) as a functionof temperature.

By examination of the experimental results, it turns out that the real eect of an increasein temperature is an upward translation of the hysteresis loops. Both the loop shape and itsinternal area do not change signicantly while varying temperature. As shown in Fig. 10(a),in fact, the energy loss per unit weight remains practically constant while changing temper-ature. On the contrary, the secant stiness increases linearly while increasing temperature, sothat the equivalent damping decreases linearly while increasing temperature. As can be seen inFig. 10(b), it drops from about 13% to about 8%, when temperature rises from 10

Cto 40

C.By assuming T = 20

C as reference temperature, the percentage dierences in the mechan-ical behaviour due to temperature result of the order of 20% in terms of forces and of the

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order of 15% in terms of equivalent damping, being 10

C, 40

C, the temperature range underconsideration. The sensitivity to temperature, though not negligible, appears to be compatiblewith the practical utilisation, considering that even stronger dependence on temperature

can be found in other, currently used, seismic devices, such as those based onpolymers.

In order to evaluate the inuence of the number of cycles on the mechanical behaviourof SMA-austenite wires in tension, four virgin specimens were subjected to repeated cyclicdeformation at dierent temperatures, namely: 1020 30 and 40

C. On each specimen, twoseries of cycles were carried out, the rst consisting of ten cycles at 6% strain amplitude and0:02 Hz frequency, the second consisting of twenty cycles at 6% strain amplitude and 0 :1 Hzfrequency.

Fig. 11 shows the hysteresis loops relevant to rst, second, fth, tenth, twelfth and thirtiethloading cycle. At any temperature, the progressive changes in the loop shape are apparent,

especially if one compares the rst and the tenth cycle. The most important eects causedby repeated cyclic deformations can be identied in a decrease of the critical stress inducingmartensite, in a decrease of the stress hysteresis (i.e. of the area inside the single loop) and inthe accumulation of a residual strain. The dierence between the tenth cycle and the twelfthcycle has to be ascribed to the change of frequency, while the shape of the twelfth and thirtiethcycles are quite similar.

Fig. 12 shows the trend of the energy loss per unit weight, the equivalent damping and theresidual strain as a function of the number of cycles, for four dierent temperatures. The eectof the frequency change (from 0.02 to 0:1 Hz) is apparent in the discontinuity between the tenthand the twelfth cycle, which separates the two series of cycles. Focusing the attention on thetwo branches separately, the following observations hold. The higher the temperature the more

pronounced is the variation in the mechanical behaviour due to repeated cycling. At 20C (thetypical service temperature), a decrease of about 45% in the energy loss and of about 30% inthe equivalent damping, as well as a residual strain of the order of 0.5%, are observed after therst ten cycles. On the contrary, during the following twenty cycles the energy loss decreasesless than 15% and the equivalent damping less than 10%, while the residual strain gains littlemore than 0.1%.

It can be concluded that the mechanical behaviour of the uncycled specimen is decidedlydierent from the behaviour of the cycled specimen. The reason is probably the occurrenceof slips during the stress-induced martensitic transformation [17]. In fact, slips result in resid-ual strains upon unloading as well as in the presence of internal stresses, which facilitate the

formation of stress-induced martensite. As a consequence the critical stress for inducing marten-site decreases and the hysteresis loops become narrower.The diagrams of Fig. 12 indicate that the mechanical behaviour of the material stabilises

more and more while increasing the number of cycles, becoming quite insensitive to cyclingafter a certain number of cycles, as already noted in Refs. [19,20]. In view of practical ap-

plications, an important observation is that one should anticipate the training cycling [36]before the installation of the device, to obtain a stable superelastic behaviour during an earth-quake. Alternatively, one could rely upon an initially more favourable behaviour of the material(larger energy dissipation and equivalent damping), considering however some decay during theexcitation and a quite dierent behaviour in case of a subsequent seismic event.

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Fig. 11. Eects of repeated cyclic deformation on stressstrain curves at various temperatures and two dierentstrain rates.

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Fig. 12. (a) Eects of repeated cyclic deformation on energy loss; (b) equivalent damping; and (c) residual strainat various temperatures.

4. Conclusion

As part of a more extensive experimental investigation on the mechanical behaviour of shapememory alloys to be used in seismic applications, several NickelTitanium austenitic wires weretested under tensile stress. Their superelastic behaviour has been deeply investigated, focusing

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on the dependence of the mechanical properties on temperature, loading frequency and numberof cycles. The relevant eects require a careful design of the specic material to be used andof the particular mechanism exploiting SMA components in a seismic device.

The dependence on temperature of the tested materials appears compatible with the normalrange of ambient temperature variations, if this is assumed to be of the order of 50

C. Thechange of mechanical properties appears compatible with current applications and smaller thanthe changes occurring in other materials often used in seismic devices.

Loading frequency aects the behaviour of SMAs, especially when passing from very lowfrequency (0:01 Hz or even less) to the frequency range of interest for seismic applications(0.24 Hz). A considerable decrease of energy loss and equivalent damping occurs because ofthe increase of temperature, due to the latent heat of transformation, which cannot be dissipatedin case of high strain rates. However, the behaviour is stable within the useful range for seismicapplications, thus encouraging the use of austenitic wires.

The number of undergone cycles considerably aects the superelastic behaviour of austeniticSMAs, worsening the energy dissipating capability and increasing the cyclic strain hardening.However, it stabilises after few cycles, whose number is of the same order as the number ofcycles that would be experienced during a strong earthquake. To get a stable behaviour, then,a device should be subjected to a pre-established initial training. The initial training could bea part of the testing programme for the qualication and the acceptance of the device. Analternative strategy could rely on the better energy dissipation properties of the virgin material,and then on avoiding or limiting any preliminary training of the device, before its use in astructural system.

A general consideration regards the low equivalent damping of the typical loadingunloadingcycle of an austenite wire. This results in a better performance of SMA when used in a recen-

tring mechanism [35]. If superelastic wires must play an eective energy-dissipating role, somepre-straining has to be applied, which must be of the order of half the maximum strain of thetransformation range. In this case, the cycling within the transformation range shall be madearound the pre-strain value. The use of pre-strained wires, arranged to realise two counteractingsuperelastic springs, result in an even more eective energy dissipation mechanism. Re-centringand energy dissipating mechanisms can be combined together to optimise the performances ofSMA-based devices, according to the specic need of the single application [35].

References

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