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Computers and Structures 86 (2008) 330–339

www.elsevier.com/locate/compstruc

Structural components in shape memory alloy

for localized energy dissipation
S. Casciati, L. Faravelli *

Department of Structural Mechanics, University of Pavia, Via Ferrata 1, 27100 Pavia, Italy

Available online 21 March 2007

Abstract

Cu-based shape memory alloys (SMA) offer their feature of superelastic hysteresis at sustainable costs, and for a window of temper-
atures applicable to most of civil engineering applications. Structural components can easily be obtained in the form of wires or plates.
Their insertion in standard structures produces devices for local energy dissipation under dynamic loading. Several solutions are exper-
imentally investigated throughout the paper.
 2007 Elsevier Ltd. All rights reserved.

Keywords: Dissipative devices; Hysteresis; Shaking table test; Shape memory alloys; Superelasticity; Training

1. Introduction A numerical study of the latter implementation is

reported in Ref. [5]. Nevertheless, before such a SMA
Refs. [1–3] provide a summary and review of the use of device can be actually installed, the adequacy of the austen-
shape memory alloy (SMA) properties in engineering appli- ite temperature window, the material training effects and its
cations. They cover the research activity developed in overall brittleness need to be deeply investigated. In fact, it
China, Europe, Japan and USA. The applications are was recently documented in [6–8] that the austenite temper-
based either on the shape memory effect, which is shown ature window of Ni–Ti alloys could prevent the designer
by these alloys in their martensitic phase [4], or on the from applications subject to broad day-night and/or win-
superelastic hysteretic loops shown in their austenitic ter–summer temperature excursions. The devices should
phase. The latter property, in particular, allows one to be operative from 20 C up to 80 C, and a single Ni–
implement SMA devices able: Ti alloy is unable to span over all the range preserving
the wished superelastic character.
• to dissipate energy during the dynamic vibration An alternative Cu-based alloy is therefore taken under
induced by environment or man-made excitations; this consideration. It will be shown below that its temperature
is due to the wide hysteretic loop shown by the material window is consistent with most of the civil engineering
constitutive law; applications. Some results achieved within its experimental
• to undergo relative displacement between their ends characterization were preliminarily reported in [9–11]. This
without significant variations of the associated force; paper restarts the process from scratch, i.e., all the experi-
this is achieved by giving the alloy a pre-tension which ments are carried out on new specimens and under testing
centers its response on the flat plateau of its hysteresis specifications which allow the authors to emphasize the
loop. features of interest.
After a specific thermo-mechanical characterization, the
*
Corresponding author.
constitutive law of the analyzed Cu-based SMA samples is
E-mail address: lucia@dipmec.unipv.it (L. Faravelli). statically determined by testing on the available universal
URL: http://dipmec.unipv.it (L. Faravelli). material testing machine. For this purpose, a suitable

0045-7949/$ - see front matter  2007 Elsevier Ltd. All rights reserved.
doi:10.1016/j.compstruc.2007.01.037
 S. Casciati, L. Faravelli / Computers and Structures 86 (2008) 330–339 331

number of SMA samples are produced from bars of the ini- Table 1
tial length of 1 m in the form of bars. Specimens of the Results of the DSC test on different samples of material
same material in the form of wires and plates are then used Temperature Virgin material Treated material Treated and trained
to undergo dynamic tests. Mf (C) 55 34 47
The wires are mounted as braces of a three-storey steel Ms (C) 46 27 23
frame model. The structure is placed on a shaking table As (C) 25 23 30
Af (C) 18 13 9
and its dynamic response is recorded in order to quantify
the ability of the SMA devices to dissipate energy. Analo-
gously, the SMA plates are introduced as the upper edges repeated for samples of virgin material, treated material,
of the columns of a single-storey steel frame model. For and treated and trained wires; the results are summarized
each test, accelerometers mounted on each story record in Table 1. Therefore the producer specifications reported
dynamic responses for different excitation time histories. at the beginning of this section refer to the treated and
These data are then analyzed to capture the nonlinear con- trained material.
tribution of the SMA plates. There is an additional temperature of interest for the
application pursued in this paper. Indeed, as the ambient
2. Thermo-mechanical characterization of a copper-based temperature increases, the superelastic hysteretic loop
SMA shrinks, and it completely disappears after a certain limit
temperature is reached. The maximum temperature for
The tested alloy has label AH140 (the supplier being the which the material response still shows a hysteretic loop
French company Trefilmetaux). Its chemical composition is estimated to be higher than 150 C, for the material
in weight percentage is given as follows: under investigation. This leads one to conclude that the
Al ¼ 11:8%; Be ¼ 0:5%; Cu ¼ 87:7%: offered window of temperatures (from 20 C to 150 C)
The following values of the transformation temperatures covers all the expected implementations in civil engineering
were provided by the producer: problems.

M s ¼ 18  C; M f ¼ 47  C;
As ¼ 20  C; Af ¼ 2  C; 2.2. The material constitutive law

where ‘‘M’’ and ‘‘A’’ denote martensite and austenite, The stress–strain relationship which characterizes the
respectively, and ‘‘s’’ and ‘‘f’’ stay for ‘‘start’’ and ‘‘finish’’, investigated material in a quasi-static environment is deter-
respectively. This means that the lower value of the temper- mined by testing several specimens under repeated cycles of
ature window mentioned in the introduction is 18 C. loading–unloading. This phenomenological approach,
The upper value corresponds to the disappearance of the although formerly not very elegant, allows to identify the
hysteresis under loading–unloading. The producer does typical behavior of the material, and to quantify the entity
not provide any specification on this value of temperature, of its governing variables.
but it was estimated larger than 150 C. For this purpose, the MTS 858 Microbionix II universal
testing machine, available at the Vibration Laboratory of
2.1. Thermal treatment and transformation temperatures the Department of Structural Mechanics of the University
of Pavia, is used. The machine is equipped with a thermal
One basic aspect, in order to manage a SMA material is chamber and an axial extensometer. The latter one is
to specify the thermal treatment that each specimen needs mounted as soon as the test temperature is achieved in
to preliminarily undergo. For the Cu Al Be alloy under the thermal chamber, so that temperature compensation
investigation, bar specimens of 5.3 mm diameter are heated is ensured. The extensometer is adopted because the linear
for 4 min at 850 C. The cooling to ambient temperature variable differential transducer (LVDT) of the machine is
(22 C) and the immersion in boiling water for 120 min fol- unable to provide completely reliable results [9], due to
low this process. Since the heating time depends on the the excessive flexibility of the machine frame. The tested
cross-section size, the wire samples of diameter 1 mm are specimens are bars of actual diameter 5.3 mm.
kept at 850 C for 1 min and the plate specimens, of thick- Due to the dependence of the material behavior on tem-
ness 2 mm and width 20 mm, are kept at 850 C for 5 min. perature, the tests are performed at 30, 50, and 70 C and
After the thermal treatment, the material response does their results are reported in Fig. 1a–c, respectively, for a
not initially reproduce itself in subsequent cycles of load- strain rate of 0.1 millistrain/s. By comparing the curves in
ing–unloading. The response only stabilizes after several Fig. 1, it can be observed that the thickness of the hyster-
cycles are performed. This phenomenon is reported in the etic loop decreases for increasing temperatures.
literature as ‘‘training’’, while ‘‘ageing’’ denotes a thermal During each test, a first sequence of 10 loading–unload-
recovery [12]. ing cycles is performed in traction, in order to achieve the
The transformation temperatures can be estimated by a training of the material. The unloading phase of each cycle
differential scanning calorimeter (DSC) test [2]. This was starts when a 2% strain is reached. Once the material
332 S. Casciati, L. Faravelli / Computers and Structures 86 (2008) 330–339

30˚ C - strain rate low

300
a
200

stress [Mpa] 100

0
-0.010 -0.005 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035

-100

-200

-300
strain
50˚C - strain rate low
400
b
300

200
stress [Mpa]

100

0
-0.010 -0.005 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035
-100

-200

-300

-400
strain

70˚ C - strain rate low

c 500

400

300
stress [Mpa]

200

100

0
-0.010 -0.005 0.000 0.005 0.010 0.015 0.020 0.025 0.030 0.035
-100

-200

-300

-400
strain
Fig. 1. Cyclic testing of a bar of diameter 5.3 mm: with 10 cycles of training at 2% of strain with very low deformation rate; (a) 30 C; (b) 50 C and (c)
70 C.

response becomes stable, a second sequence of three load- sion, with the minimum strain set at 0.5%. This third
ing–unloading cycles is carried out in traction, and the sequence allows one to evaluate the re-absorption of the
strain value at which the unloading occurs is now 3%. martensite produced by the mechanical strain during the
These larger cycles have the purpose of checking the effect previous cycles in tension. At the end of each cycle in ten-
of the stabilization at a lower limit strain: actually the sion, the residual of martensite causes the diagrams in
response seems stabilized. They show enlarged hysteresis Fig. 1 to skew to the right, and this obstacles the re-center-
loops, i.e., a greater production of martensite during each ing of the SMA device.
single loading. The number of cycles after which the material response
Lastly, the asymmetry of the material behavior in ten- becomes stable, depends on the strain rate at which the
sion and in compression is investigated by applying three cycles are performed. In particular, this number increases
further cycles of loading–unloading, this time in compres- with the strain rate. Therefore, the tests in Fig. 1 are
 S. Casciati, L. Faravelli / Computers and Structures 86 (2008) 330–339 333

repeated at a faster strain rate, equal to ten times the pre- and b, respectively, by plotting the computed stress versus
vious one (i.e., 1 millistrain/s). The number of loading– the time. A similar behavior is obtained by comparing the
unloading cycles, within the first sequence, is increased to signals recorded at 30 C.
50 in order to reach the training in traction, whereas the In Fig. 3a, the training shows a slow increasing, up to
successive two sequences in tension and in compression the convergence of the peak stress value, which is always
are the same as before. positive, i.e., a traction. By contrast in Fig. 3b the test
Fig. 2 shows the diagrams obtained from the tests at speed prevents the alloy from recovering all the martensite,
30 C, 50 C, and 70 C with this fast strain rate of 1 milli- whose residual strain corresponds to a final compression
strain/s. At high temperature, the stress response is lower stress at the end of each unloading. Here the training is
than the one recorded in Fig. 1. Moreover, to facilitate achieved by a slow decrease (increase in absolute value),
the comparison between Figs. 2 and 1, a sequential repre- up to the convergence, of this final compression stress.
sentation of their cycles at 50 C is provided in Fig. 3a As a result the stress peak in tension cycles is lower and

Fig. 2. Cyclic testing of a bar of diameter 5.3 mm: with 50 cycles of training at 2% of strain with deformation rate 10 times the one of Fig. 1; (a) 30 C; (b)
50 C and (c) 70 C.
334 S. Casciati, L. Faravelli / Computers and Structures 86 (2008) 330–339

a 400
50˚ C - strain rate low

300

stress [Mpa]
200

100

6445 sec
0

-100

-200

-300

-400
time
50˚ C - strain rate high
b 400

300

200
stress [Mpa]

100

0
2210 sec

-100

-200

-300
time
Fig. 3. Cyclic testing of a bar of diameter 5.3 mm at 50 C: (a) low strain rate; (b) strain rate 10 times than in (a).

the stress peak modulus in compression is higher. For III. the residual of martensite which shifts the diagram in
this reason the re-centering by the compression cycles the sense of the deformation,
vanishes. IV. the asymmetric response in tension and compression,
In the test at 70 C of Fig. 2c, one initially records the V. the decrease of the hysteresis as the temperature
same trend as in Fig. 3b, but later on an austenite recovery increases.
occurs, and this re-centers the subsequent cycles.
In conclusion, the main features of the material behavior The asymmetric behavior of the alloy prevents the direct
represented by Figs. 1 and 2 are typical of SMA and they use of bars in dissipation devices. The asymmetry problem
can be summarized as follows: can be overcome either by having the alloy working only in
tension (wires) or by having the alloy section crossed by a
I. the superelastic behavior, neutral plane, which results in a symmetric behavior in
II. the decay from the virgin curve due to training, positive and negative bending (plates).

250

200
stress [MPa]

150

100

50

0
0 0.005 0.01 0.015 0.02 0.025 0.03 0.035
-50
strain

Fig. 4. Cyclic testing of a specimen from a plate of thickness 2 mm at ambient temperature.

 S. Casciati, L. Faravelli / Computers and Structures 86 (2008) 330–339 335

To ensure that the different technologies used to pro- are alternatively mounted as braces between the base and
duce plates or bars from the alloy ingot do not influence the first storey, in order to compare the dynamic responses
their mechanical behavior, a test similar to the one of of the structure in its two configurations.
Fig. 1a, but without any compression and the strain rate The excitation is the realization of a segment of white
increased three times, is carried out on a plate of thickness noise in the frequency range below 25 Hz. The dynamic
2 mm. After the training, three cycles at 2.5% of maximum responses of the third floor, in the two cases of steel and
strain are followed by three cycles at 3% of maximum SMA wires, are reported in Fig. 6a and b, respectively.
strain. The results of this test are given in Fig. 4. The comparison of the two responses in Fig. 6a and b
shows that the replacement of steel with SMA wires does
3. Preliminary dynamic tests not significantly reduces the acceleration peak values. On
the other hand, the adoption of SMA wires results in a sig-
A preliminary investigation was performed to investi- nificant lower root-mean-square value of the response and
gate the effects, on the dynamic response of a structure, its higher damping is made evident by the immediate decay,
of added wires produced from ingots of the same Cu-based as soon as the excitation ends after 8000 sampled points
alloy characterized in the previous section. (see Fig. 6).
A three storey steel frame model is placed on a 1 m by A further investigation was then conducted to quantify
1 m shaking table as shown in Fig. 5. The second storey the ability of SMA plates to dissipate energy.
is rigidly braced by steel elements, while the third one is
un-braced. Steel wires or SMA wires (of 1 mm diameter)
4. Elements with SMA plates components

4.1. Test setup

To investigate the effects of copper-based SMA devices

on the response of a structure under dynamic loading,
the SMA specimens in form of plates are used as compo-
nents of a simple structural scheme. In particular, they
are installed at the upper edges of the columns of a sin-
gle-storey, single bay steel frame. Each column is con-
structed by assembling with bolts the steel elements and
SMA plates in Fig. 7a. The resulting column in Fig. 7b
and c presents a ‘‘sandwich’’ cross-section in which a rub-
ber layer is embedded to allow a quick decay of the
response.
The steel storey is then fixed to the columns with a fur-
ther series of bolts, and the resulting one-degree-of-free-
dom model in SMA-steel composite is placed on the
Fig. 5. The SMA wires installed at the bottom of the three storey frame. shaking table (Fig. 8). Two mono-axial, Kinemetrics

a 0.4
b 0.4

0.3 0.3

0.2
acceleration [V]

acceleration [V]

0.2
0.1
0.1
0
0
-0.1
-0.1
-0.2

-0.2 -0.3

-0.3 -0.4
0 0.5 1 1.5 2 0 0.5 1 1.5 2
4 4
number of recorded points x 10 number of recorded points x 10

Fig. 6. Response to a white-noise band realization: (a) SMA wires and (b) steel wire. The solid line is the excitation of the shaking table, the dotted line is
the acceleration at the top of the three storey frame.
336 S. Casciati, L. Faravelli / Computers and Structures 86 (2008) 330–339

Fig. 7. Column in steel-SMA composite: (a) elements to be assembled, (b) front view, and (c) lateral view.

accelerometer, FBA-11, are used during the dynamic tests. damping features of both systems are also increased by
Sensor 1 is installed on the shaking table in order to the insertion of the rubber layer.
measure the excitation (input), while sensor 2, on the
frame-storey, provides the structural response (output). A 4.2. Dynamic characterization
corresponding two-channel acquisition system samples
the signals at a rate of 250 points per second, and an First, the excitation is given as the realization of a seg-
anti-aliasing filter is applied at 20 Hz. ment of white noise of maximum amplitude 20 mm and
In order to appreciate the contribution of the SMA duration 600 s, in a frequency range lower than 25 Hz.
plates to the dynamic behavior, two frames are actually Due to the low intensity of the white noise by which the
tested: the second differs from the first one in having the shaking table is excited, the corresponding recorded signals
SMA plates replaced by steel plates. The different mechanic are very sensitive to the accelerometer disturbance (noise).
properties of the two materials translate into different res- Hence, the results are given in terms of a power spectral
onance frequencies and different damping properties, as density (PSD) function (instead of a transfer function) to
confirmed by the experimental results in Table 2. The improve their clearness. However, for a white noise excita-
tion, the shape of the PSD coincides with the one of the
transfer function and only the ordinate values are different.
The precise determination of the last ones is not significant
for the purposes of the topic discussed in this paper, and
therefore the PSD representation does not affect the gener-
ality of the results.
Fig. 9 refers to the frame entirely made by steel. By con-
sidering successive signal windows, Fig. 9b gives evidence
of the fact that the resonance frequency does not change
as the test proceeds.
A different behavior is recorded when the same excita-
tion is applied to the frame with SMA plates. These tests
are repeated twice, and, before each of them, the thermal
treatment of Section 2.1 on the SMA components is also
repeated. The SMA material of the first test is thermally
Fig. 8. Single-storey frame mounted on the shaking table, and instru-
treated and undergoes a training loading–unloading
mented with mono-axial accelerometers (with the active axis along the sequence before the white-noise is applied. The second test
direction of the shaking table piston). exploits a treated alloy, but the Cu-based alloy receive its
training during the first temporal window of the white-
noise excitation.
Table 2 The results of the two tests are reported in Figs. 10 and
Main dynamic properties of the assembled frame 11, respectively. From their observation, it is evident that
Resonance frequency [Hz] Damping [%] the resonance occurs in the first window at a frequency
2.949 Steel plates 1.13 value lower than the one obtained from the average on
Steel plates and rubber 1.35 eight signal windows. This is due to the increase of the
secant stiffness as the test proceeds (see Fig. 1) and it
2.225 SMA plates and rubber 1.79
emphasizes an independence from the previous history
 S. Casciati, L. Faravelli / Computers and Structures 86 (2008) 330–339 337

-3
x 10
a b 4.5
0.03
Power Spectral Density Function

Power Spectral Density Function

4

0.025 3.5

3
0.02
2.5
0.015 2

1.5
0.01
1
0.005
0.5

0 0
2.4 2.6 2.8 3 3.2 3.4 3.6 2.6 2.7 2.8 2.9 3 3.1 3.2 3.3 3.4
Frequency [Hz] Frequency [Hz]

Fig. 9. PSD functions derived from the signal measured when testing the frame with steel plates: (a) single Fourier transform of 217 points; (b) four
functions obtained by averaging 32 Fourier transform of 212 points over eight windows. The diamonds represent the first window.

a x 10
-3

b 14 x 10
-4

18
Power Spectral Density Function

Power Spectral Density Function

16 12

14 10
12
8
10

8 6

6 4

4
2
2
0
0
2 2.05 2.1 2.15 2.2 2.25 2.3 2.35 2.4 1.5 2 2.5 3
Frequency [Hz] Frequency [Hz]

Fig. 10. Frame with SMA plates: PSD function evolution when the initial window follows a program of tests: (a) single Fourier transform of 217 points;
(b) four functions obtained by averaging 32 Fourier transform of 212 points over eight windows. The diamonds represent the first window.

a
-3
x 10 -4

b x 10

12 10
Power Spectral Density Function

Power Spectral Density Function

10
8

8
6

6
4
4
2
2
0
0
2 2.05 2.1 2.15 2.2 2.25 2.3 2.35 2.4 1.8 2 2.2 2.4 2.6 2.8 3
Frequency [Hz] Frequency [Hz]

Fig. 11. Frame with SMA plates: PSD function evolution when the initial window incorporates the training: (a) single Fourier transform of 217 points; (b)
four functions obtained by averaging 32 Fourier transform of 212 points over eight windows. The diamonds represent the first window.
338 S. Casciati, L. Faravelli / Computers and Structures 86 (2008) 330–339

(i.e., a behavior without ‘memory’) after several loading– Increasing Frequencies @ Amplitude 2.5 mm
unloading cycles. Decreasing Frequencies @ Amplitude 2.5 mm
12
10

Amplification
4.3. Nonlinear effects
8
The identified natural frequency of the model can be 6
used to better investigate the nonlinear effects and the dis- 4
sipation introduced by the SMA devices. For this purpose, 2
two specific experiments were carried out by assigning sinu- 0
soidal inputs to the shaking table. In the first test, the fre- 1 1.25 1.5 1.75 2 2.25 2.5 2.75 3
Frequency [Hz]
quency of the excitation is fixed at a value of 2.1 Hz, near
to the resonant one, and it is kept constant throughout the Fig. 13. Diagram of the amplification factor versus the excitation
test. The maximum span (i.e., the sinusoidal amplitude) is frequency for a span of 5 mm.
slowly increased from 1 to 3.5 mm, with a rate of about
0.25 mm every 20 s. A fully linear system would not show therefore outlined at the intensity level at which the test
any change of the resonance frequency, but, for constant was carried out.
damping, it would present a linear relationship between
the peak amplitude of the response and the excitation span. 5. Conclusions
By contrast, the plot of Fig. 12 reveals that such a
behavior only occurs for small span values. Then, as the This paper focuses on proving, in a laboratory environ-
span increases, the response slowly increases. Such a phe- ment, the feasibility of dissipating energy by utilizing wires
nomenon is also contributed by an increase of damping or plates made of a Cu-based shape memory alloy. The
as the test proceeds. The external fibers are gradually trans- adoption of plates in a device preserves the otherwise miss-
formed from austenite into martensite as the span ing symmetry of the response (due to the asymmetric mate-
increases. This causes that the hysteresis area increases rial behavior), and it facilitates the self-re-centering of the
after every loading–unloading cycle. device after the end of the external excitation.
The second test uses, as excitation, a sinusoidal of con-
stant maximum amplitude 2.5 mm. Its frequency varies Acknowledgements
within an interval centered around the resonance. The fre-
quency is varied of 0.05 Hz at every step of duration 20 s. This research was developed within the FP6 European
First, an increase from 1 Hz to 4 Hz is pursued. The Union project WIND-CHIME (WIde-range Non-intrusive
decrease in the reverse sense is then recorded by performing Devices toward Conservation of Historical Monuments in
a separate experiment. The results are plotted together in the Mediterranean Area), coordinated by the University of
Fig. 13. In the proximity of the resonance, the two Pavia. Some experimental results were achieved in fulfill-
obtained responses are no longer coincident, and an insta- ment of the duties of the Italian National Research Council
ble branch is outlined toward the left of the peak. In other (CNR) research program for which Prof. A. Di Tommaso,
words, when the frequency is decreased the peak is reached of the University of Venice (Italy), is serving as national
at a frequency value lower than the one corresponding to coordinator.
the peak of the ascending branch. A light softening-type The authors are thankful to Marco Domaneschi and
response [13], rather than one of the hardening type, is Mauro Mottini for their help in conducting the experi-
ments. They also acknowledge that the DSC results were
34 obtained at SINTEF (Trondheim, Norway) by Dr. C.
32 van Eijk.
The authors also thank the manuscript referees for their
30 constructive remarks.
A/ω2 [mm]

28
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