Mechanicalbehaviourofshapememoryalloysfor … · 2008. 12. 16. · M. Dolce, D. Cardone/International Journal of Mechanical Sciences43(2001)2657–2677 2661 detwinnedmartensite.InFig.1,

International Journal of Mechanical Sciences 43 (2001) 2657–2677

Mechanical behaviour of shape memory alloys forseismic applications

2. Austenite NiTi wires subjected to tension

Mauro Dolce ∗, Donatello CardoneDepartment 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 sti7-

ness, energy loss per cycle, equivalent damping and residual strain. The sensitivity to temperature andstrain rate, as well as the in9uence of strain amplitude and the e7ects due to repeated cyclic deformation,are analysed in detail.The experimental results show that the characteristics of the superelastic wires are well suited for

seismic applications, as both the recentring and the energy dissipating features of the devices can beeasily obtained. Moreover, the in9uence 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 signi<cantly 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 0020-7403(01)00050-9

2658 M. Dolce, D. Cardone / International Journal of Mechanical Sciences 43 (2001) 2657–2677

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 loadingF forceT temperatureKs secant sti7nessWD 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 (SMA’s) [2–5] have the potential to eliminate most of the limitations in-volved in current technologies, owing to their extraordinary fatigue resistance, superelasticity orshape memory e7ect, stability of their characteristics and high corrosion resistance.With the purpose of exploring the potentials of SMA’s in seismic protection uses, designing

and manufacturing SMA-based devices, as well as testing devices and structural systems, aspeci<c research project (MANSIDE—Memory 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 e7ectively used in seismic

protection 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, Ni–Ti SMA’s appear to be the best candidates for the use inseismic applications. Actually, Table 1 can be seen as a memorandum for the material producerto select the most appropriate alloy composition and thermomechanical treatment. Then, the<nal 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 Ni–Ti 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 SMA’s in seismic devices. Sev-eral Nickel–Titanium specimens, having di7erent shapes (wires and bars), geometric (diameterand length) and physical characteristics (alloy composition, thermomechanical treatment,

M. Dolce, D. Cardone / International Journal of Mechanical Sciences 43 (2001) 2657–2677 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 5–35◦C for buildings and −5–45◦C for bridges

Low sensitivity to strain rate or to frequency in sinusoidal vibrations, in the range 0.4–1 Hz,for seismic isolation techniques [1], and 1–10 Hz, for energy dissipation techniques [1].

Stability of cyclic behaviour:0:96�1;1=�1; i6 1:1, 0:96�2;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 di7erent stress states (tension, compression, torsion, bendingand shear). For each group of tests, di7erent strain levels, strain rates and temperatures wereconsidered.In a companion paper [6], the peculiar properties of SMA’s are reviewed, the complete plan of

the experimental investigation is described and the results of the torsion tests on SMA-martensite


Fig. 1. Schematic stress–strain 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 SMA’s, precedes the presentation of theexperimental results.

2. Superelasticity of SMA’s

Superelasticity [7–12] is one of the most attractive properties of SMA’s. 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 stress–strain cyclic curve of a superelastic SMA. It is characterised

by <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


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 SMA’s suits the optimal requirements of a seismic

control device. Indeed, they could provide the device with (i) energy dissipation capability, toreduce acceleration and displacements caused by earthquakes, (ii) self-centring capability, tobring 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 sti7ness, to limit displacementsunder service actions or moderate earthquakes. Moreover, a seismic SMA based device sti7ensin case of unpredicted strong actions (branch 4), thus assuring a good control of displacementseven under unforeseen strong earthquakes.Although the use of superelastic SMA’s appears to be very appealing under di7erent points

of view, some aspects have to be carefully examined:

1. The properties and the mechanical behaviour of SMA’s strongly depend on alloy compositionand thermomechanical treatment (see for example [13–16]).

2. Superelasticity is highly sensitive to temperature:

• All SMA’s are superelastic only at some temperatures, i.e. between Af and Md [9–11]:to be useful in civil engineering applications, the superelastic range must be as wide aspossible 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 truebecause of the latent heat of transformation which causes the self-heating of the material. Asthe strain rate increases, the self-heating becomes signi<cant, causing a rise of some degreesof the internal temperature. This yields modi<cations 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 SMA’s changes with repeated cyclic deformations [19–21].

Tension loading–unloading tests on Ni-Ti SMA wires have been carried out by many researchers[17–32]. 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 actualpotential of SMA’s 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 seismic

devices, the cyclic behaviour of SMA’s under high strain rates and various strain amplitudes,as well as the e7ects 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


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. Allthe 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: −10–40◦C temperature, 0.2–4 Hz frequency of loading, 10–20consecutive loading cycles.

3. Tensile tests

3.1. Testing programme

The experimental tests described in this paper were carried out on austenite wire sampleswith 1–2 mm diameter and 200 mm length. Several kinds of wires were considered, di7ering inalloy composition (Ni–Ti-[Nb] about 50 at% Ni) and=or thermomechanical treatment (% coldworking and annealing temperature [13,15,16]). Unfortunately, no more speci<c material-relatedinformation were available from the manufacturer.First of all, cyclic tests on pre-tensioned wires, at room temperature (≈ 20◦C), frequency

of loading ranging from 0.01 to 4 Hz (strain rate 0.0008–0:32 s−1) and strain amplitude upto 10%, were carried out. Subsequently, loading–unloading tests under temperature control,between 40◦C and −10◦C (step 10◦C), at about 7% strain amplitude and 0.02–0:2 Hz frequencyof loading, were carried out. During the tests, the surface temperature of wire was measuredby thermocouples.

3.2. Tests at room temperature

Fig. 2, shows the results of a series of loading–unloading 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 “training”cycles 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 constantduring each test, varies from 0.02 to 4 Hz.In Fig. 2, the trends of secant sti7ness, energy loss per unit weight and equivalent damping

are reported as a function of frequency of loading, for di7erent strain amplitudes. Some typicalstress–strain diagrams at di7erent frequencies are also given. As can be seen, the mechanicalbehaviour of SMA-austenite wires in tension clearly depends on frequency and changes sig-ni<cantly when passing from pseudo-static (0:02 Hz) to dynamic conditions (0.2–4 Hz). Whenincreasing the strain rate, indeed, the hysteresis loops narrow and translate upwards, while thebranches of the curve relevant to the phase transformations harden, thus yielding an increase inthe stress levels. Therefore, secant sti7ness increases (by about 15% in the range 0.02–0:2 Hz),while energy loss and equivalent damping decrease by about 18% and 25%, respectively, in


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


the range 0.02–0:2 Hz. In particular, equivalent damping drops from about 8–9% to about 6%,when frequency rises from 0.02 to 0:2 Hz.The above-said e7ects must be ascribed to the di7erent heat exchange modalities with ambient

at di7erent 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 stress–strain relationship, during four di7erent 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 itpropagates 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 di7er-ent position (between the middle and the end of the wire in the test of Fig. 3). Extensometerand thermocouple view the phase transformation in di7erent 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 di7erent branches are clearly visible. The<rst 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 horizontalbranch 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 transformationbefore the thermocouple. As a consequence, the seventh branch stays higher up than the fourth.


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 di7erent loading–unloading cycles.

While the instantaneous temperature of the wire oscillates around the ambient temperature(30◦C), with excursions of the order of 12–16◦C, the average temperature remains practicallyunchanged during all the loading history, equal to the ambient temperature. In this case, there-fore, the only e7ect 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.


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 di7erent loading–unloadingcycles.

The stabilisation of the average temperature results in a di7erence 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.


Fig. 5. Trend of the average material temperature at di7erent 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 di7erent loading

frequencies, again for the test shown in Fig. 2. To obtain comparable curves, time is normalisedwith respect to the loading period. Di7erent trends are observed for di7erent 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 thehighest 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 at 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 constantbehaviour beyond 0:2 Hz frequency.To examine the e7ects of strain amplitude on the parameters under study, Fig. 6 shows the

hysteresis loops corresponding to <ve loading–unloading cycles at di7erent strain amplitudes,namely 1.5–2.5–3.5–4.5–5.5–7.5%. The test was carried out at 30◦C temperature and 0:01 Hzfrequency on a 1:84 mm diameter wire sample. The stress–strain 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 while

increasing 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.


Fig. 6. Cyclic loading–unloading tensile tests on austenite superelastic wire: in9uence of strain amplitude.

Another remarkable <nding is that the equivalent damping increases practically linearly atlow-medium strain amplitudes (1–5%), while it slightly decreases (see Fig. 1) at large strainamplitudes (5–10%), in spite of the increase of energy dissipation. This last e7ect 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 SMA’s, 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 e7ect in seismic applications. Actually, it impliesthat a structural system endowed with seismic SMA-based devices sti7ens, 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 di7erent strain amplitudes, respectively, 5% and 7.5%.In the enclosed tables, the values of secant sti7ness, energy loss per unit weight and equivalentdamping relevant to di7erent loading cycles are reported. The e7ects 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.


Fig. 7. Two consecutive cyclic loading–unloading tensile tests on virgin specimen, showing the in9uence 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 (0.2–4 Hz) and number of cycles(10–20). In that frequency range, the values of the equivalent damping of a wire subjected toloading–unloading cycles are of the order of 5–7%. 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 shown

experiments, 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 con<guration is a wide hysteresis loop and anapparent threshold value of force. Indeed, this is obtained because the total force is the di7erencebetween the tension forces of the two springs, one being increased while the other decreases.A totally di7erent 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 con<guration, even in the presence of largeparasite forces.

3.3. Tests under temperature control

Fig. 9(a) shows some typical stress–strain diagrams at di7erent temperatures, ranging from40◦C to −10◦C, of step 10◦C. They were recorded during loading–unloading tests at 0:02 Hz


Fig. 8. Hysteretic behaviour available by using pre-strained superelastic SMA wires in di7erent 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 materialbehaviour.For each temperature, the critical stresses relevant to the forward and the inverse phase

transformation 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.


Fig. 9. Austenite wire in tension: (a) stress–strain curves at di7erent 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 e7ect of an increasein temperature is an upward translation of the hysteresis loops. Both the loop shape and itsinternal area do not change signi<cantly 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 sti7ness 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 di7erences in the mechan-

ical behaviour due to temperature result of the order of 20% in terms of forces and of the


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 temperaturecan be found in other, currently used, seismic devices, such as those based onpolymers.In order to evaluate the in9uence of the number of cycles on the mechanical behaviour

of SMA-austenite wires in tension, four virgin specimens were subjected to repeated cyclicdeformation at di7erent temperatures, namely: 10–20–30 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 thirtieth

loading 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 e7ects causedby repeated cyclic deformations can be identi<ed 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 di7erence 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 the

residual strain as a function of the number of cycles, for four di7erent temperatures. The e7ectof 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 morepronounced is the variation in the mechanical behaviour due to repeated cycling. At 20◦C (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 the<rst 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 decidedly

di7erent 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 theformation 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 di7erent behaviour in case of a subsequent seismic event.


Fig. 11. E7ects of repeated cyclic deformation on stress–strain curves at various temperatures and two di7erentstrain rates.


Fig. 12. (a) E7ects 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 Nickel–Titanium austenitic wires weretested under tensile stress. Their superelastic behaviour has been deeply investigated, focusing


on the dependence of the mechanical properties on temperature, loading frequency and numberof cycles. The relevant e7ects require a careful design of the speci<c 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 normal

range 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 a7ects the behaviour of SMA’s, especially when passing from very low

frequency (0:01 Hz or even less) to the frequency range of interest for seismic applications(0.2–4 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 a7ects the superelastic behaviour of austenitic

SMA’s, 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 quali<cation 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 loading–unloading

cycle 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 e7ective 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 e7ective energy dissipation mechanism. Re-centringand energy dissipating mechanisms can be combined together to optimise the performances ofSMA-based devices, according to the speci<c need of the single application [35].

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Documents

Mechanicalbehaviourofshapememoryalloysfor … · 2008. 12. 16. · M. Dolce, D. Cardone/International Journal of Mechanical Sciences43(2001)2657–2677 2661 detwinnedmartensite.InFig.1,