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Structural health monitoring of an asymmetrical SMA reinforced composite using embedded

FBG sensors

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2013 Smart Mater. Struct. 22 125015

(http://iopscience.iop.org/0964-1726/22/12/125015)

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IOP PUBLISHING SMART MATERIALS AND STRUCTURES

Smart Mater. Struct. 22 (2013) 125015 (11pp) doi:10.1088/0964-1726/22/12/125015

Structural health monitoring of anasymmetrical SMA reinforced compositeusing embedded FBG sensors

Mei-po Ho1, Kin-tak Lau1, Ho-yin Au2, Yu Dong3 and Hwa-yaw Tam2

1 Department of Mechanical Engineering, The Hong Kong Polytechnic University, Kowloon,Hong Kong SAR, People’s Republic of China2 Department of Electrical Engineering, The Hong Kong Polytechnic University, Kowloon,Hong Kong SAR, People’s Republic of China3 Department of Mechanical Engineering, School of Civil and Mechanical Engineering, Faculty ofScience and Engineering, Curtin University, Australia

E-mail: mmktlau@polyu.edu.hk

Received 23 July 2013, in final form 16 October 2013Published 5 November 2013Online at stacks.iop.org/SMS/22/125015

AbstractEmbedded actuator and sensor technology provides accurate structural health monitoring andproper structural response of a structure in any harsh servicing situation. This paper describesthe fabrication of a smart composite by embedding shape memory alloy (SMA) wires andfibre Bragg grating (FBG) sensors into a glass fabric reinforced polymeric composite.Mechanical performances of the composite under martensitic and austenitic stages of theSMA wires were studied, and its natural frequencies were also measured accordingly. Theresult shows that the shift of the natural frequency arises from temperature change, thuschanging the mechanical properties of the SMA wires. The changes of strain, stress, curvature,and damping ratio were predicted from an asymmetrical lamination model. It was found thatthis model demonstrates certain attractive effects, including mechanical properties, the changeof shape, and the natural frequency upon activation of the SMA wires.

(Some figures may appear in colour only in the online journal)

1. Introduction

The potential of glass fibre reinforced plastics (GFRPs) inthe global market is enormous, and this global market willgrow to a total of US $29.4 billion in 2013 [1]. GFRPshave already been employed widely in aerospace, automotiveengineering, railway, and wind energy industries for manyyears. However, their main disadvantage is their complexfailure mechanisms. Smart materials have attracted growinginterest as they responds to environmental stimuli in particularconditions, and this has lead to many potential applications.Embedded sensor and actuator technology is a promisingsolution to provide active control on composite structures.Therefore, the market tends to focus on the development ofsmart composites whose properties are altered appropriatelyin response to environmental fluctuations, rather than onconventional GFRPs. These smart composites are defined as

an integrated structure consisting of actuating and sensingdevices to form a smart system similar to a human body [2–4].

Fibre reinforced composites with embedded shapememory materials have been extensively focused on becauseof their superior potential for the applications of vibrationaland structural controls [5]. The advantages of shape memoryalloy (SMA) in the field of actuating systems include(1) high reversible strain, (2) high damping capacity,(3) large reversible change of mechanical and physicalcharacteristics, and (4) high recovery stresses [6]. SMAcomposites demonstrate their extraordinary performance inadjusting their shape, vibration, acoustic transmission, andimpact resistance through a centralized control system; forinstance, vibration control can be achieved by controllingthe stiffness of SMA wires with heat, and thus the wholecomposite structure [7].

A fibre Bragg grating (FBG) sensor is an optical fibresensing technology that has drawn enormous attention for

10964-1726/13/125015+11$33.00 c© 2013 IOP Publishing Ltd Printed in the UK & the USA

Smart Mater. Struct. 22 (2013) 125015 M-P Ho et al

over 20 years [8–11]. The advantages of FBG sensors includethe following: (1) they are light in weight, (2) they aresmall in size, without degradation of structural integrity,(3) they are insensitive to electromagnetic interference, (4)they have a high degree of multiplexability, and (5) theyhave the ability to be used in environmentally unfavourableconditions [12]. Embedding an FBG sensor into a compositehelps to monitor the curing temperature of its structure duringthe manufacturing process; the sensor can subsequently beused for lifetime performance monitoring [13].

A multi-layer asymmetric composite structure startsto be bent when subjected to a temperature change. Anasymmetric structure is formed by orientating fabric layers indifferent directions or constructing the structure using distinctmaterials with different mechanical properties and coefficientsof thermal expansion (CTEs). The asymmetrical laminationof a composite can result in the combined effect of bendingmoment and laminate extension. Another phenomenon isthe formation of curvature resulting from an action tobending of an asymmetrical laminate under temperaturechange [14]. An undesirable formation of the curvature isunfavourable to a composite structure if it is applied toreal-life engineering applications. Korakianitis et al [15] havefound that the change of curvature of a composite bladeaffects the aerodynamic profile of the blade seriously, whichin turn induces some problems of vibration and stalling ofthe airflow. Besides, they have also found that an appropriateblade curvature design results in maximizing the aerodynamicperformance with a prevention of flow separation [15].

However, existing studies of SMA reinforced compositeshave revealed the lack of basic understanding of the effecton their temperature change, especially the issues concerningthe generation of distinct thermal expansions because oftheir hybrid material properties. Therefore, the mechanicaland acoustic properties of these composites have to be wellunderstood before implementing them in real-life engineeringapplications. In this paper, the mechanical and dynamicproperties of an asymmetric SMA reinforced compositesubjected to a temperature change have been investigatedthrough experimental and theoretical approaches.

2. Experimental study

2.1. Materials

Ni–Ti alloy SMA wires with a diameter of 0.2 mm were usedin the current study. Polymeric matrix GY251 epoxy resinmixed with GY956 hardener was supplied by Shing Hingchemical Co., Ltd. The ratio of the epoxy resin to the hardenerwas 5:1. The plain weave glass fabrics (style AF218) that wereused to make a composite were supplied by Colan, Australia.

The FBG sensors used in this study were written inpolyimide-coated, standard monomode optical fibres. Thegratings were fabricated and centred in λB = 1540, 1536, or1530 nm, with a gauge length of 8 mm.

2.2. Sample manufacturing

The optical fibres and SMA wires were cleaned by ethanolapplied to a lint-free wipe to remove contaminants including

Figure 1. Model of the composite for (a) the strain and temperaturecalibrations and (b) the experimental and theoretical analyses.(G represents a layer of glass fabric.)

dust particles, human hand oils, and so on, in order to enhancethe adhesion of the optical fibre and SMA wires to thesurrounding epoxy matrix.

Composite samples were made by a hand lay-up process,which was followed by vacuum bagging and mounting insidea frame. The frame was used for prestraining and aligning theSMA wires and optical fibres in the right direction. In total,eight plies of glass fabrics were used. The length, width, andthickness of the composite beam for the calibration and tensiletests were 200 mm × 30 mm × 1.94 mm, respectively. Twotypes of lamination symmetric and asymmetric compositewere prepared. Symmetrical composite beams were fabricatedfor temperature and strain calibration tests. The SMA wiresand the optical fibre were embedded in the same plane andat the mid-thickness of the composite beam, as shown infigure 1(a). The asymmetric composite beam was fabricatedas indicated in figure 1(b).

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Smart Mater. Struct. 22 (2013) 125015 M-P Ho et al

Figure 2. 1λB/λB versus (a) the applied load and (b) the strain variation in the strain calibration test at room temperature.

For the composite beam fabricated asymmetrically, sixlayers of glass fabric were underneath the SMA wires, and theoptical fibre and two layers were placed above. The distancebetween the SMA wires and the optical fibre with a prewrittenFBG grating (FBG sensor) was 5 mm. In total, five SMA wireswere embedded in parallel into the composite.

2.3. FBG detection system

An array of at least two FBG sensors was used in eachcomposite sample. One of the FBGs was embedded inside thecomposite beam as a strain sensor while another was attachedto the composite beam’s surface as a mechanical-strain-freesensor to compensate for the thermal strain effect. A pigtailof the array was spliced into a patchcord and connectedto an interrogator. A PC with the LabView program wasconnected to the interrogator for data acquisition. Interrogatormodels sm125 and sm130, from Micron Optic Inc., wereused in the experiment for static and dynamic measurements,respectively. The sampling frequency and measurementresolution of the static machine were 1 Hz and 1 pm, and thecorresponding values for the dynamic machine were 2000 Hzand 5 pm.

2.4. Symmetrical composites

2.4.1. Temperature and strain calibration of the FBGsensors. An FBG sensor can be made using differentfabrication techniques, and consequently different sensingproperties are obtained. Therefore, the strain and temperaturesensitivity coefficients of the FBG sensor should bedetermined experimentally by conducting the calibration testprior to any property test of the composite beams. In thisstudy, the calibration of strain and wavelength shift of thesensor was determined by performing a simple uniaxial tensiletest of the sample, as shown in figure 1, at room temperature.The change of strain was measured with a surface-mountedstrain gauge. The wavelength shift induced by the applied

strain ε at constant temperature is given by the followingequation [16]:

1λB = λB(1− Pe)ε = Kεε, (1)

where Pe is the photoelastic coefficient of the fibre and Kεis the strain sensitivity. The linear correlations between thechange of 1λB/λB with the change of applied load and thechange of 1λB/λB with the change of strain are shown infigures 2(a) and (b). Kε is obtained as the slope of the graphof 1λB/λB versus the strain variation (µε), which is equalto 7.5× 10−7 ((pm/pm)/µε). The result indicates that every1.16 pm shift of the Bragg wavelength of the FBG sensorcorresponds to 1 µε in the case of 1541 nm wavelength.

To calibrate the thermal-induced strain of the FBG sensor,the composite beam was heated up by the embedded SMAwires via electrical resistance heat, that is, by applying thecurrent to the wires and using their electrical resistanceproperties in order to generate heat themselves. Since theSMA wires were embedded into the composite beam which isrelatively thin, the surface temperature of the composite beamat the location where the wires were embedded should be veryclose to the temperature of the SMA wires. The simultaneouswavelengths of the strain-free FBG were recorded from roomtemperature to 35 ◦C. According to the temperature changemeasured by thermocouples, the corresponding wavelengthshift is given by [16]

1λB/λB = ST1T, (2)

where the temperature sensitivity coefficient ST = α + ξ , inwhich α is the thermal expansion coefficient and ξ is thethermo-optic coefficient. The linear correlation between thechange of 1λB/λB and the temperature is shown in figure 3.ST was obtained as the slope of the graph of 1λB/λB versusthe change of temperature. From figure 3, it can be see thatST is 6.2 × 10−6 ((pm/pm)/◦C−1). This result demonstratesthat every 9.55 pm shift of the Bragg wavelength of theFBG sensor corresponds to 1 ◦C in the case of 1541 nmwavelength.

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Smart Mater. Struct. 22 (2013) 125015 M-P Ho et al

Figure 3. Temperature calibration for the FBG sensor.

2.5. Unsymmetrical composites

2.5.1. Mechanical properties. A tensile test was conductedto obtain the Young’s modulus of the composite beam, asshown in figure 1(b). The composite beams were mountedonto the MTS testing machine (Alliance RT/50) withtailor-made supporting fixtures for the test. The crossheadspeed of the test was 1.5 mm min−1. The phase transformationtemperatures of the SMA wires were measured by using adifferential scanning calorimeter (DSC), and the results arelisted in table 1. A DC supplier was used to supply electricalcurrent into the wires to generate electrical resistance heatto a specified temperature. The properties of the compositebeams at the SMA’s transformation temperatures, namely themartensite finish temperature (Mf) and the austenite finishtemperature (Af), are shown in table 1.

Figure 4 shows the stress–strain curve obtained fromthe tensile test and conducted at (a) room temperature and(b) 50 ◦C. Notwithstanding that the Young’s modulus of thecomposite beam at T < Mf is higher than that measured atT > Af, the strength of the composite beam at T < Mf is lower

Table 1. Material and mechanical properties of the SMA andcomposite materials.

Description

SMA

Coefficient of thermal expansion (CTE)Martensite (◦C−1) 6.6×10−6

Austenite (◦C−1) 11× 10−6

Transformation temperatures (◦C)Martensite finish (◦C) 20Martensite start (◦C) 35Austenite finish (◦C) 60Austenite start (◦C) 45

Glass fibre epoxy composite

Young’s modulus (GPa) 25CTE of glass fibre (m3 ◦C−1) 4× 10−6

CTE of epoxy (m3 ◦C−1) 55× 10−6

SMA compositeYoung’s modulus at RT (MPa) 2900Young’s modulus when T > Af (MPa) 2470Density (kg m−3) 2500

than that at temperature above Af. This result confirms thatthe composite beam is more ductile when the SMA wire is inits martensitic state as compared to that in the full austeniticphase.

At the beginning of the tensile test, it is interesting to seethat the force required to generate strain is lower, as expected.This phenomenon is due to the realignment of a curvedcomposite beam that was formed by the differential thermalexpansions of plies inside the composite beam upon heating.Therefore, the force was initially used for straighteningthe composite beam instead of stretching the SMA wires.Therefore, the Young’s modulus of the composite beammeasured during the tensile testing at a temperature above Afwas lower than that at a temperature below Mf. Most previousstudies ignored this thermal distortion effect, which, however,is a crucial factor for any precise smart control system. Afterthe curved composite beam was aligned, the stress startedincreasing as the SMA wires effectively took part of the load

Figure 4. Result of the tensile test at (a) room temperature and (b) T > Af (50 ◦C).

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Smart Mater. Struct. 22 (2013) 125015 M-P Ho et al

Figure 5. Strain response when the temperature increases under thestrain gauge investigation (number of layers = 9).

via a stress transfer mechanism between the wires and thesurrounding matrix [17].

Figure 5 shows the strain responses at the top surfaceof the composite beam when the temperature increases fromroom temperature to 35 ◦C. Since both ends were fixed bythe predesigned testing fixture, no longitudinal expansionwas allowed during the heating process. Instead, theunsymmetrical nature of the composite beam induced bendingof the composite beam’s surface due to unsymmetricalthermal expansions of the top surface and the bottom surface.Therefore, the longitudinal strain of the top surface was lowerthan the longitudinal strain of the bottom surface when thecomposite beam was heated up by the SMA wires.

As seen from figure 6, a good bonding at the interfacesbetween the optical fibre and the matrix and between the SMAwire and the matrix was obtained, so that the stress could betransferred from the matrix to the SMA wire. It is proved thatthe shift change of wavelength of the FBG is due to the changeof temperature.

2.5.2. Change of strains. An SMA reinforced compositebeam for longitudinal and transverse strain analyses is shownin figure 7. Figures 8(a)–(c) depict the reflected spectra ofan FBG sensor extracted at room temperature, 1T = 20 ◦C,and 1T = 40 ◦C. Figures 8(d)–(f) show the reflected spectraof FBG 1, FBG 2, and FBG 3 obtained according to thechange of temperature. The change of the strain shifts theBragg wavelength by dilating or compressing the grating andchanging the effective index of light in the optical fibre. Infigure 8(e), it can be see that the reflected light intensityis increasing as the temperature rises. As the compositebeam was deformed owing to distinct thermal expansion ofthe asymmetric lamination, this induced a pressure shift inthe composite. The composite was bent due to the thermalexpansion, and thus the intensity of the reflected light waschanged.

2.5.3. Change of natural frequency. The natural frequenciesof the composite beams were measured with a Bruel & Kjær(B&K) accelerometer for calibration. The configuration of

Figure 6. Scanning electron micrographs of (a) an SMA wire,(b) an optical fibre, and (c) a sample comprising an SMA wire, anoptical fibre, and glass fibre reinforced epoxy.

the B&K set-up included an accelerometer, charge amplifier,pulse front-end pulse dongle, and a computer for time signaland spectrum analysis. The frequency range of the set-up was0–250 Hz.

A series of cantilever composite beams was impacted ata distance of approximately 15 mm from the clamped end.The frequency response functions of the clamped–free samplerecorded by an accelerometer and FBG sensor are plotted infigure 9. Obviously, the natural frequencies obtained by the

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Smart Mater. Struct. 22 (2013) 125015 M-P Ho et al

Figure 7. An experimental model of the composite for thelongitudinal and transverse strain analyses. (G represents a layer ofglass fabric.)

two different techniques are the same. The response peak issharp, and it represents the natural frequency of 29.1 Hz forthe composite at room temperature.

Figure 9. Natural frequencies obtained from the FBG sensor and aB&K system.

Figure 10 shows the comparison of natural frequencies ofthe samples obtained from the FBG sensor at T < Mf and T >Af. The natural frequency of the cantilever composite beam is

Figure 8. Reflected spectra of a grating extracted at (a) room temperature, (b) 1T = 20 ◦C, and (c) 1T = 40 ◦C. Reflected spectra of(d) FBG 1, (e) FBG 2, and (f) FBG 3 obtained according to the change of temperature.

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Smart Mater. Struct. 22 (2013) 125015 M-P Ho et al

Figure 10. Natural frequencies obtained from the FBG sensor atdifferent temperatures.

shifted from 29.1 Hz to 26.5 Hz when T > Af. During theexperiment, it was found that the embedded SMA wires couldregulate the natural frequency of the cantilever compositebeams. The natural frequency of the cantilever compositebeams depends on their dimension and constitution, thenumber of embedded SMA wires, and their transformationtemperatures. However, the decrease of the natural frequencyof the cantilever composite beams at T > Af was mainly dueto the generation of an internal compressive stress by themismatch of thermal expansions between the layers of glassfibre/epoxy, SMA wires, and optical fibre [18, 19]. Sincethe SMA wires and the optical fibre were not embedded inthe neutral axis of the samples, the mismatch of the thermalexpansion would therefore cause the bending of the sampleaccordingly upon heating.

Figure 11 illustrates the vibration response of thecantilever composite beam subject to a localized impactloading. The damping properties of the cantilever compositebeam at T < Mf and T > Af were analysed by an FFTanalyser. In figure 11, it can be seen that, when thetemperature increases, a reduction in the vibration amplitudeoccurs. Besides, the excitation is attenuated when thetemperature increases. During the experiment, it was foundthat the damping properties and natural frequency of thecantilever composite beams could be modulated by increasingtheir temperature. This phenomenon was due to the changeof the modulus, induced internal stress, and geometry of thecantilever composite beam.

3. Theoretical analysis

3.1. The relationship of temperature and curvature of theunsymmetrical composite

Figure 12 shows the theoretical model of an unsymmetricalcomposite plate. For thin plates subjected to small deforma-tions, the fundamental assumptions of Kirchhoff’s hypothesisfor plates are summarized as follows [20–23].

Figure 11. Settling time of the composite at (a) T < Mf and(b) T > Af.

Figure 12. Laminate stacking sequence nomenclature.(G represents a layer of glass fabric.)

(1) Deflections of the mid-surface are relatively smallcompared to the thickness of the composite plate, and theslope of the deflected plate is small.

(2) The mid-plane is unstrained (ε = 0) when the plate issubjected to pure bending.

(3) Plane sections that are initially normal to the mid-planeremain normal to the mid-plane after bending.

(4) Normal out-of-plane strains are assumed to be zero whenplate deflections are due to bending.

(5) The condition σz = 0 is assumed to be valid.

For a thin laminated plate, in which the total laminatethickness is usually small compared to other plate dimensions,the plane stress relationship between Cartesian stresses andstrains is

σx

σy

τxy

= [Q]εx

εy

γxy

, (3)

where ε, σ , τ , and γ are the strain, stress, shear stress, andshear strain, respectively. [Q] is the in-plane elements of the

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Smart Mater. Struct. 22 (2013) 125015 M-P Ho et al

stiffness matrix under plane stress condition. Each laminatethrough the thickness may have a different fibre orientationand consequently a different [Q], [Q]GF and [Q]SMA. Underconditions of plane stress, the Cartesian components of thestress in the kth layer are

σx

σy

τxy

k

= [Q]

ε0

x

ε0y

γ 0xy

+ z

κx

κy

κxy

. (4)

The above relationship is assumed to be valid for anylayer of the laminate. However, the strain variation througha laminate is a function of both mid-surface strain andcurvature, and it is continuous through the plate thickness,whereas the stress is not required to be continuous through theplate. The loads and the moments incorporated with thermalloads and thermal moments are expressed as{

N

M

}=

[A B

C D

] {ε0

κ

}−

{NT

MT

}, (5)

where N is the external load, M is the external moment, NT isthe thermal load, and MT is the thermal moment.

[A] =N∑

k=1

[Q]k(zk − zk−1) (6)

[B] = 12

N∑k=1

[Q]k(z2k − z2

k−1) (7)

[D] = 13

N∑k=1

[Q]k(z3k − z3

k−1) (8)

{ε0

MT

}=

[A∗ B∗

C∗ D∗

] {NT

κ

}(9)

[A∗] = [A]−1 (10)

[B∗] = [A]−1[B] (11)

[C∗] = [B][A]−1 (12)

[D∗] = [D] − [B][A]−1[B] (13){

ε0

κ

}=

[A′ B′

C′ D′

] {NT

MT

}(14)

[A′] = [A∗] − [B∗][D∗]−1[C∗] (15)

[B′] = [B∗][D∗]−1 (16)

[C′] = −[D∗]−1[C∗] (17)

[D′] = [D∗]−1. (18)

When a two-phase model consisting of the austenite andmartensite phases connected in series is applied, the elasticmodulus of the SMA wire can be expressed as [24],

EL =EAEM

EM + ξ(EA − EM), (19)

where ξ , EA, and EM are the volume fraction of martensite,and the elastic moduli of the parent phase and the martensite

Figure 13. Responses of (a) a longitudinal strain, (b) a transversestrain, and (c) a stress in different layers with the change oftemperature.

phase, respectively. If the volume fraction of martensiteis assumed to be linearly proportional to the temperature,the longitudinal thermal expansion coefficient [20] can beobtained as

α1 =υfEf1αf1

E1

υmEmδm

E1. (20)

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Smart Mater. Struct. 22 (2013) 125015 M-P Ho et al

Figure 14. Generation of curvature in (a) a longitudinal directionand (b) a transverse direction as a result of the temperature change.

The transverse thermal expansion coefficient is given by [20],

α2 = υfαf2 + υmαm + υfvf12(αf1 − α1)

+ υmνm(αm − α1). (21)

According to the data listed in table 1, the theoreticalresponses of strain and stress at different layers with thechange of temperature are shown in figure 13. The neutralaxis is shifted and no longer exists in the middle throughthe thickness of the model. The difference in strain betweenthe bottom layer and the upper layer increases when thetemperature increases. The composite plate was bent becauseof the distinct thermal expansion to cause strain decreasing inthe upper layers but increasing in the lower layers. Figure 14shows the curvature in the longitudinal and transversedirections as a result of the temperature change.

In figure 15, it is found that the strains in both casesdecrease, but the stresses increase with increasing volumefraction of embedded SMA wires. The magnitude of stressesprovides a general trend from positive to negative valueswhen moving from the bottom layer to the upper layer. Thisis apparently attributed to the internal compressive stressesgenerated in the upper layer and the tensile stress in thebottom layer of the composite plate. Figure 16 shows that the

Figure 15. Responses of (a) a strain and (b) a stress in differentlayers with different SMA volume fraction at 1T > Af.

curvature decreases with increasing volume fraction of SMAwires in the SMA reinforced composite, so the modulus of thecomposite increases.

3.2. Damping ratio and damping coefficients of thecomposites

The damping ratio of the composite under the change oftemperature can be evaluated by measuring the vibrationamplitude in free vibration motion using the followingdamping equation [19]:

ζ =δ√

(2π)2 − δ2, (22)

where δ = ln u1u2

; δ is the natural logarithm of the ratio ofany two successive displacement amplitudes (u1 and u2) inthe same direction. Figure 17 shows the damping ratio ofthe composite plate with the change of temperature. Theinternal damping of the material was changed accordingto the different temperatures. The maximum damping ratiois achieved when 1T = 60 ◦C. The damping ratio tends

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Smart Mater. Struct. 22 (2013) 125015 M-P Ho et al

(a) (b)

Figure 16. Generation of curvature in (a) the longitudinal direction and (b) the transverse direction at 1T > Af as a result of the differentSMA volume fraction.

Figure 17. Damping ratio of the composite with the change oftemperature.

to increase when the temperature and the curvature ofthe composite plate increase, as a result of the thermalexpansion of the asymmetric laminate. Additionally, theenergy dissipation arises from the internal friction at theinterface of the stress-induced martensite. After 1T > 60 ◦C,the damping ratio decreases, which is ascribed to the polymersoftening as the glass transition temperature starts at around65 ◦C.

The mathematical expression of the natural frequency ofthe composite is [22, 25]

f =ω1

2π=

12π

√λ2EI

σAR4 , (23)

where E is the Young’s modulus, I is the moment of inertia,A is the cross-sectional area, R is the radius of the curvedcomposite beam, σ is the density of the composite, and λ isequal to 1.875 for the first mode of vibration. Figure 18 showsthat the natural frequency increases with the temperaturechange from 0 to 15 ◦C owing to the thermal expansion of

Figure 18. Natural frequency of the composite with the change oftemperature.

the composite. When the temperature changes above 15 ◦C,the decrease of the natural frequency can be mainly due to thereduction of the Young’s modulus.

4. Conclusion

The mechanical and dynamic properties of a smartasymmetric composite made from glass fibre reinforcedepoxy with embedded SMA wires and FBG sensor werestudied in this paper. The experimental and theoreticalanalyses have shown that the composite underwent anabnormal shift of its neutral axis due to the formationof curvature upon heating up the SMA wires, and thusthe composite. The natural frequency decreased as thetemperature of the composite increased above the austenitefinish temperature of the SMA wires. However, due to thechange of the Young’s modulus of the SMA wires, thedamping ratio increases with the increase of temperature untilreaching the glass transition temperature of the epoxy. Theformation of curvature was due to the differential thermalcoefficients of expansion of the different materials in thecomposite, which thus induced an internal stress to deformthe composite. In this study, we proved that SMA wires and

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Smart Mater. Struct. 22 (2013) 125015 M-P Ho et al

FBG sensors can be effectively used as intrinsic actuators andsensors for a smart composite system. However, the formationof internal stresses, which may alter the geometry of acomposite structure, is an issue that has not be thoughtfullydiscussed elsewhere in the past. The use of embedded sensorscan provide reliable information to the system in any case inwhich the deformation may reach a critical state.

Acknowledgment

This project was support by a University Research Grant(G-YK84) from The Hong Kong Polytechnic University.

References

[1] 2013 World Glass Fibre Reinforced Plastic (GFRP)Composites Market (2013–2023) Propects for Fibreglass &GRP Visiongain

[2] Sippola M, Lindroos T and Brander T 2007 Adaptivecomposite structures in shape control applications J. Struct.Mech. 40 65–79

[3] Yoon H J, Constantini D M, Linberger H G, Salathe R P,Kin C G and Michaud V 2006 In situ strain and temperaturemonitoring of adaptive composite materials J. Intell. Mater.Syst. Struct. 17 1059

[4] Schrooten J, Michaud V, Parthenios J, Psarras G C, Galiotis C,Gotthardt R, Manson J A and Humbeeck J V 2002 Progresson composites with embedded shape memory alloy wiresMater. Trans. 43 961–73

[5] Hill K O and Meltz G 1997 Fiber Bragg grating technologyfundamentals and overview J. Lightwave Technol.15 1263–76

[6] Qi B, Bannister M, Liu X, Michie A, Rajasekera L andAshton B 2004 Response of an embedded fibre Bragggrating to thermal and mechanical loading in a compositelaminate Mater. Forum 27 93–100

[7] Morey W W, Meltz G and Glenn W H 1989 Fibre optic Bragggrating sensors Proc. SPIE 1169 98–107

[8] Crosby P A, Doyle C, Tuck C, Singh M and Fernando G F1999 Multi-functional fibre optic sensors for cure andtemperature monitoring Proc. SPIE 3670 144

[9] Lin W, Zhang C, Li L and Liang S 2012 Review ondevelopment and applications of fiber-optic sensorsPhotonics and Optoelectronics (SOPO) (New York: IEEE)pp 1–4

[10] Ling H Y, Lau K T and Cheng L 2004 Determination ofdynamic strain profile and delamination detection of

composite structure using embedded multiplexed fibre-opticsensors Compos. Struct. 66 317–26

[11] Kobayashi A, Ogihara S, Yoshinari H and Takeda N 1999Damage development in composite laminates withembedded SMA wires Proc. 6th Japan Int. SAMPE Symp.pp 65–8

[12] Jones R M 1973 Buckling and vibration of unsymmetricallylaminated cross-ply rectangular plates AIAA J. 11 1626–32

[13] Yuvaraj M and Senthilkumar M 2012 Comparative study onvibration characteristics of a flexible GFRP compositebeam using SMA and PZT actuators Manuf. Indust. Eng.11 28–33

[14] Lau K T, Zhou L M and Tao X M 2002 Control of naturalfrequencies of a clamped–clamped composite beam withembedded shape memory alloy wires Compos. Struct.58 39–47

[15] Korakianitis T 1987 A design method for the prediction ofunsteady forces on subsonic, axial gas-turbine blades ThesisMassachusetts Institute of Technology, Cambridge, MA

[16] Wei Z G, Tang C Y and Lee W B 1997 Design and fabricationof intelligent composites and based on shape memoryalloys J. Mater. Process. Technol. 69 68–74

[17] Ma N and Song G 2002 Control of a shape memory alloyactuator using pulse width (PW) modulation. Smartstructures and materials 2002; modeling, signal processingand control Proc. SPIE 4693 348–59

[18] Lau K T 2002 Vibration characteristics of SMA compositebeams with different boundary conditions Mater. Des.23 741–9

[19] Chiang C C 2011 Curing monitoring of composite materialusing embedded fiber Bragg grating sensors Advances inComposite Materials—Analysis of Natural and Man-MadeMaterials pp 346–60

[20] Kollar L P 2003 Mechanics of Composite Structures(Cambridge: The University of Cambridge Press)

[21] Staab G H 1999 Laminar Composite (Oxford:Butterworth–Heinemann)

[22] Robaiy M J, Shjary M A and Janaby M Y 2010 Free vibrationof curved beam with varying curvature and taper ratio IraqiJ. Mech. Mater. Eng. 10 44–57

[23] Sabir A B and Ashwell D G 1971 A comparison of curvedbeam finite elements when used in vibration problemJ. Sound Vib. 18 133–9

[24] Sakuma T, Mihara Y, Ochi Y and Yamauchi 2006Constitutive equation with consideration of slip-deformedmartensite in the deforming of Ti–Ni shape memory alloyMater. Trans. 47 704–10

[25] Riyah N K, Arz Y R and Ahmed N E 2009 Effect of layersarrangement on the response of sandwich compositecantilever plate Anbar J. Eng. Sci. 2 82–95

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