A sensor charge output deviation method for delamination detection using isolated piezoelectric actuator and sensor patches

Composites: Part B 37 (2006) 583–592 www.elsevier.com/locate/compositesb

A sensor charge output deviation method for delamination detection using isolated piezoelectric actuator and sensor patches Ping Tan, Liyong Tong

*

School of Aerospace, Mechanical and Mechatronic Engineering, The University of Sydney, Sydney, NSW 2006, Australia Received 23 July 2005; received in revised form 10 March 2006; accepted 16 March 2006 Available online 16 May 2006

Abstract Delamination is one of the most prevalent failure mechanisms for laminated composites. To secure the safety of composite structures, it is required and necessary to develop cost-effective and efficient delamination detection techniques and methods. In this paper, a dynamic analytical model, namely sensor charge output deviation method is proposed to identify a delamination embedded in a cantilever laminated composite beam bonded with isolated piezoelectric actuator and sensor patches. Two pairs of collocated piezoelectric patches are bonded on top and bottom surfaces of the beam and used as actuators for exciting the composite beam. Another piezoelectric patch with gridding electrode pattern on its top surface is bonded on the top surface of the host beam and is employed as a sensor to record the required voltage and thus the sensor charge output along the beam. The effects of some major geometric parameters and the type of applied electric voltage on the sensor charge output distribution and delamination detection sensitivity are discussed in this paper. A comparison between the analytical models using isolated piezoelectric actuator and sensor patches and that using integrated piezoelectric sensor/actuator layer, which was developed previously, is conducted. For the baseline case considered here, there is an excellent agreement of the first three order frequencies between the present finite element analysis and analytical models.  2006 Elsevier Ltd. All rights reserved. Keywords: A. Materials; B. Delamination; C. Analytical model

1. Introduction Delamination is known to possibly occur during the laminated composite fabrication process or in the service life such as through impact by a foreign object. The presence of a delamination not only significantly changes the static and dynamic characteristics of a composite structure, it also has a potential to cause catastrophic failure. Therefore, the enormous potential of laminated composite in structural engineering has been obstructed because of lacking of a reliable and on-line delamination detection method. Over the past few years, various non-destructive delamination monitoring methods have been introduced. For

*

Corresponding author. Tel.: +61 2 93516949; fax: +61 2 93514841. E-mail address: [email protected] (L. Tong).

1359-8368/$ - see front matter  2006 Elsevier Ltd. All rights reserved. doi:10.1016/j.compositesb.2006.03.007

example, vibration techniques and methods [1–3] were developed for investigation of the effect of delamination on the vibration response of laminated composites. These methods can usually be used to identify the presence of delaminations, but not the size and location of delaminations. Several studies using the embedded fiber Bragg grating (FBG) sensor for the delamination detection in a laminated composite were conducted [4–6]. It was reported [7] that the embedded optical fibers significantly reduce the fatigue life of composite structures. An electric resistance change method was proposed by Todoroki et al. [8–11] for identification of internal delaminations according to the electric resistance changes between equally-spaced electrodes, which are mounted on a laminated composite specimen surface. However, this method is limited to graphite fibre reinforced plastics composites. Recently, the present authors developed several dynamics analytical models for identification of a delamination embedded in a laminated

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P. Tan, L. Tong / Composites: Part B 37 (2006) 583–592

PZT sensor Composite beam

PZT actuator Delamination PZT actuator Fig. 1. A cantilever laminated composite beam bonded with isolated PZT actuators and sensor.

composite beam [12–14]. The presence, size and axial location of a delamination were identified on the basis of monitoring the sensor charge output (SCO) distribution along the beam length for the first three order frequencies, when the host beam was excited externally or by an actuator. In these models, integrated piezoelectric (PZT) actuator and/ or sensor were bonded on the whole host beam surface, and employed to excite the beam, and then detect the delamination in the beam. It was noted from the research previously conducted by authors [12–14] that the piezoelectric sensor can only effectively identify the size and location of a delamination which is beneath the sensor. Therefore, in order to cost-effectively detect delaminations embedded within a large laminated composite structure, it is suggested to bond piezoelectric sensors on the surface of the composite segment where delaminations are expected to most likely develop. In this paper, an effective sensor charge output deviation (SCOD) method using isolated PZT actuator and sensor patches is presented to identify a delamination in a laminated composite beam. These PZT patches are bonded on laminated composite beam segment surfaces (see Fig. 1). A discussion of the effects of the adhesive thickness, sensor length, actuator location and length, as well as the type of applied electric voltage on the SCO distribution and delamination detection sensitivity (DDS) is conducted, followed by a comparison of the first three order frequencies between the present finite element analysis (FEA) model and SCOD method. A comparison of the SCO and DDS for the beams bonded with an integrated PZT layer and isolated PZT patches is also carried out in this investigation. 2. Sensor charge output deviation method for delamination detection Fig. 2 shows a schematic of a cantilever laminated composite beam bonded with several isolated PZT actuator and sensor patches. A delamination embedded in the host beam is assumed to occur throughout the width of the host beam. The delamination front lines are considered to be straight and perpendicular to the length direction of the beam. The sensor covers the top surface of the beam segment beneath which a delamination is considered to most likely develop.

II

Xa

VI

IV III

I

V

VIII VII

IX

ls

la

ld +V3

lsl

PZT actuator

tg

Delamination

Adhesive layer

PZT sensor

Lb

Fig. 2. A schematic of a cantilever laminated composite beam with a delamination and bonded with isolated PZT actuator and sensor patches.

For the sake of investigating the influence of the size and location of the isolated actuator and sensor patches on the SCO measured from gridding electrodes, which are evenly distributed along the sensor length, we divide the beam system into nine major span-wise regions, namely I–IX shown in Fig. 2. The PZT patches bonded on the top and bottom surfaces of the beam segments located in regions II and VIII are chosen as actuators, and a PZT patch bonded on the top surface of the beam segments located in regions IV–VI is considered as a sensor. For PZT actuators, both top and bottom surfaces are fully metalized, while for the PZT sensor, the bottom surface is fully metalized and the top surface will be metalized with a pattern of electrode strips separated by uniform gaps, namely gridding electrode (see the PZT sensor in Fig. 1). The electric voltage or electric field is applied along the actuator thickness direction. On the basis of Fig. 2, the host beam system can be considered to be made up of one component for the beam segments in regions I, III, VII, IX, two components for those segments in regions IV, VI, and three components for the segments in regions II, V, VIII. Each segment can be modelled as a Bernoulli–Euler beam (see the free-body diagram in Fig. 3 for the segments in the region II). It is worth pointing out that the contact and friction between the upper and lower delaminated beam segments in the region V are not considered in this investigation, and thus it is assumed that there is no stress transferring between these two segments. By using the cor-

P. Tan, L. Tong / Composites: Part B 37 (2006) 583–592

T2ua

M2 b T2b

M2la

T2ua + dT2ua

σ 2ua τ 2ua

Q 2b

τ 2ua

σ 2la

Q2la

According to the classical beam theory and the constant peel and shear strain assumptions, the required values of T, M, s and r can be obtained. Such as, for the upper PZT actuator in the region II, the corresponding longitudinal force, bending moment, shear and peel stress existed between the top actuator and host beam are given by

M2ua + dM2ua

M2ua Q2ua

τ 2la

Q2ua + dQ2ua

σ 2ua

τ 2la

σ 2la

T2la

M2b + dM2b T2b + dT2b Q2b + dQ2b

T 2ua ¼ bY a ta

T2la + dT2la Q2la + dQ2la

Fig. 3. A free-body diagram for the segments in the region II.

r2ua ¼ responding free-body diagram for each segment and the classical beam theory under the assumptions of constant peel and shear strains through the adhesive layer thickness in adhesively bonded joint [15], the dynamic equations of motion for the host beam, PZT sensor and actuator segments in the region k (k = I–IX) can be obtained. Such as for the segments in the region II, their corresponding equations are given by For the upper PZT actuator segment:

ð1Þ

For the host beam segment: qb Ab € u2b ¼

ð2Þ

For the lower PZT actuator segment @T 2la @Q2la € 2la ¼  s2la b; qa Aa w  r2la b; @x @x @M 2la s2la bta  Q2la þ ¼0 @x 2

ð4Þ

Y ad ð1  mad Þ ðw2b  w2ua Þ ð1  2mad Þð1 þ mad Þtad

ð7Þ

where e31a is the piezoelectric constant for a PZT actuator with linear and orthotropic properties, and E31 is the electric field applied through the actuator thickness. Y, G and m are Young’s modulus, shear modulus and Poisson’s ratio whereas the subscript ad stands for the adhesive layer. By taking Fourier transformation with respect to time for the equations of motion, we have the following differential equations 

qa Aa €u2ua ¼

oT 2b þ ðs2la  s2ua Þb; ox oQ2b € 2b ¼ þ ðr2la  r2ua Þb; qb Ab w ox oM 2b ðs2la þ s2ua Þbtb  Q2b þ ¼0 ox 2

@u2ua  e31a bta E31 ; @x

bY a t3a @ 2 w2ua M 2ua ¼  ð5Þ 12 @x2      1 @w2ua @w2b 1 @w2ua @w2b s2ua ¼ G þ þ tb ta þ 2 2tad @x @x @x @x  u2b  u2ua ð6Þ þ tad

M 2la + dM2la

oT 2ua oQ € 2ua ¼ 2ua þ r2ua b; þ s2ua b; qa Aa w ox ox oM 2ua s2ua bta  Q2ua þ ¼0 ox 2

585

qa Aa €u2la ¼

ð3Þ

where q, A, u, w, b, t, Q, T, M, s and r stand for the density, cross-sectional area, longitudinal displacement, transverse displacement due to bending, width of the beam system, thickness, shear force, longitudinal force, bending moment, shear and peel stress existed between the actuator and host beam, respectively. The subscripts a and b represent actuator and beam whereas the subscripts 2ua, 2b, 2la refer to upper actuator, beam and lower actuator in the region II.

 dU k ¼ Ak U k dx

ð8Þ

where the over-bar represents the Fourier transformation  with respect to time, U k is the state vector and Ak is a matrix for the region k. For example, for the host beam  segment in the region I, its corresponding state vector U 1 and matrix A1 are given by h i U 1 ¼ u1b w1b @w@x1b T 1b Q1b M 1b ð9Þ 3 2 0 0 0 0 bY1b tb 0 7 6 6 0 0 1 0 0 0 7 7 6 7 6 7 6 12 7 6 0 0 0 0 0  bY b t3b 7 6 7 ð10Þ A1 ¼ 6 7 6 7 6 q A x2 0 0 0 0 0 7 6 b b 7 6 7 6 2 7 6 0 q A x 0 0 0 0 b b 5 4 0

0

0

0

1

0

where x is a natural frequency. By solving Eq. (8), we have 

U k ðxk Þ ¼ C k eAk xk

ð11Þ

in which j=1–9 for regions I–IX, respectively; xk=0–lk (lk  is the length of region j),C k ¼ U k ðxk Þjxk ¼0 .

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P. Tan, L. Tong / Composites: Part B 37 (2006) 583–592

For the cantilever beam system considered here, a total of 36 applicable boundary conditions can be obtained, which are listed below: For the fixed end of the host beam; @w1b ¼0 u1b ¼ 0; w1b ¼ 0; @x

on a sensor element with the length of Dx and located at x = xs, is given by Z xs þDx2 e31s jes ðn; xÞjdn; qðxs ; xÞ ¼ b xs Dx 2

For the left and right hand side of upper and lower actuators

Dx Dx  xs  lsl þ ls  ð25Þ 2 2 where e31s is the piezoelectric constant for a PZT sensor with linear and orthotropic properties, and lsl is the distance of the left hand side edge of the sensor from the fixed end (see Fig. 2). Using Eq. (25), the SCO distribution along the sensor surface can be obtained. It is worth pointing out that the accuracy for using SCOD method to identify the size of a delamination will depend on the number and size of the electrode strips evenly distributed in the x direction.

T ijka ¼ be31a E31 ta ; Qijka ¼ 0; M ijka ¼ 0:

3. Computational results and discussions

ð12Þ

For the free end of the host beam; T 9b ¼ 0; Q9b ¼ 0; M 9b ¼ 0 For the left and right hand side of the sensor; T 5ks ¼ 0; Q5ks ¼ 0; M 5ks ¼ 0

ð13Þ

ð14Þ

ð15Þ

where i = 2 for the region II and 8 for the region VIII; j = u for the upper actuator and l for the lower actuator; k = l for the left hand side of sensor or actuator, and r for the right hand side of sensor or actuator. A total of 66 continuity conditions exist at the interface between regions I and II–VIII and IX in order to ensure the displacements and forces to be identical at the interfaces. Such as for the host beam, the continuity conditions which exist at the interface between regions IV and V are given by: u4b þ

tb  tu @w4b ¼ u5ub 2 @x

ð16Þ

u4b 

tb  tl @w4b ¼ u5lb 2 @x

ð17Þ

w4b ¼ w5ub

ð18Þ

w4b ¼ w5lb

ð19Þ

@w4b @w5ub ¼ @x @x

ð20Þ

@w4b @w5lb ¼ @x @x

ð21Þ

T 4b ¼ T 5ub þ T 5lb

ð22Þ

Q4b ¼ Q5ub þ Q5lb

ð23Þ

M 4b ¼ M 5ub þ M 5lb  T 5ub

tb  tu tb  tl þ T 5lb 2 2

ð24Þ

A numerical solution of the governing Eq. (11) together with their boundary and continuity conditions will give the required natural frequencies and absolute value of the strain distribution along the sensor segment surface (i.e. |es(x, x)|). Hence, for a selected natural frequency (i.e. x), the SCO measured from an electrode strip, which is coated

where lsl þ

To investigate the effectivity of the present SCOD method on delamination detection and to study the effects of the major parameters on the SCO distribution along the sensor surface, a baseline case considered in this section is a cantilever laminated composite beam system with beam length Lb = 0.6 m, beam width b = 0.025 m and host beam thickness tb = 1.9 mm. A delamination with delamination length ld = 0.04 m and delamination gap tg = 0.00038 mm is located at the host beam mid-plane and mid-length Xd = 0.3 m, where Xd is the distance of the delamination centre from the fixed end. The distance of the actuators located in regions II and VIII from the fixed end, (i.e. Xa) is chosen to be 0.135 and 0.465 m, respectively. The PZT sensor or actuator thickness (i.e. ts, ta) is selected to be 0.4 mm and that of adhesive layer tad is chosen to be 0.15 mm. The length of an actuator la is chosen to be 0.03 m while that of the PZT sensor ls is selected to be 0.06 m. The number of gridding electrode is chosen to be 31. The beam and the PZT sensor or actuators are made of T300/F593 plain weave composite and TRS610 PZT material, respectively. The required complex Young’s modulus for the host beam, PZT sensor or actuator and adhesive layers are equal to 57.8(1 + 0.011i), 60.24(1 + 0.011i) and 2.15(1 + 0.011i)GPa, respectively. The piezoelectric constant for the actuator or sensor (i.e. e31a, e31s) is chosen to be 9.9 C/m2. The density for the host beam, PZT sensor or actuator and adhesive layers are selected to be 1521.4, 7800 and 1600 kg/m3, respectively [14,16,17]. The stiffness of the gridding electrode is neglected owing to their small size relative to those for the laminated beam, PZT sensor and actuators. An initial impulse V3(t) = V3d(t), where V3 = 10 V, d(t) = 1 when t = 0 and d(t) = 0 when t 6¼ 0, is applied to the PZT actuator in the thickness direction. 3.1. Delamination identification using the SCOD method For the baseline case mentioned above, the SCO distributions for a beam with delamination are obtained using

P. Tan, L. Tong / Composites: Part B 37 (2006) 583–592

Delamination

2.5E-09 perf del

2.0E-09

SCO (C)

1.5E-09

1.0E-09

5.0E-10

0.0E+00 0.27

0.28

0.29

0.3

0.31

0.32

0.33

0.34

X (m) (a) For the case of vibration mode I

clearly indicate the tips of a delamination. The difference of SCO for the beams with and without delamination is about 11% at the left delamination tip and 18% at the right tip for the case of vibration mode I, 5% at the left tip and 3% at the right tip for the vibration mode II, and 184% at the left tip and 77% at the right tip for the vibration mode III. Therefore, it is clear that the presence, size and axial location of a delamination embedded in a cantilerver laminated composite beam can be effectively identified using the present SCOD method. Fig. 4 also indicates that predicted SCO distributions for vibration modes I and III are more sensitive to the presence of a delamination compared to vibration mode II. This is consistent with the finding mentioned in Ref. [14] for the case of a laminated composite beam bonded with an integrated PZT sensor/ actuator layer. Hence, in the Section 3.2, we only consider the cases for vibration mode I and III. 3.2. Effects of major geometric parameters on the SCO distribution and delamination detection sensitivity

8.0E-10 7.0E-10 6.0E-10

SCO (C)

587

To discuss the influence of the actuator location on the SCO distribution and delamination detection sensitivity

5.0E-10 4.0E-10 3.0E-10

2.5E-09 V32low

2.0E-10 Perf 1.0E-10 0.0E+00 0.27

V32up 2.0E-09

Del

V38low V38up

0.28

0.29

0.3

0.31

0.32

0.33

0.34

SCO (C)

X (m) (b) For the case of vibration mode II

1.5E-09

1.0E-09

2.5E-09 Perf Del

SCO (C)

2.0E-09

5.0E-10

1.5E-09

0.0E+00 0.27

0.28

0.29

0.3

0.31

0.32

0.33

0.34

X (m) 1.0E-09

(a) For the case of vibration mode I 3.0E-09

5.0E-10

V32low V32up

2.5E-09

V38low

0.28

0.29

0.3

0.31

0.32

0.33

0.34

X (m)

(c) For the case of vibration mode III

Fig. 4. Variation trends of SCO distribution for the beams with and without delamination.

SCO (C)

0.0E+00 0.27

V38up

2.0E-09

1.5E-09 1.0E-09 5.0E-10

the present SCOD method, and plotted in Fig. 4(a)–(c) for cases of vibration mode I, II and III. For the convenience of comparison, the corresponding SCO distributions for the beam without delamination are also shown in Fig. 4. From Fig. 4, it is noted that the abrupt axial discontinuities in the SCO distribution measured from the PZT sensor

0.0E+00 0.27

0.28

0.29

0.3

0.31

0.32

0.33

0.34

X (m)

(c) For the case of vibration mode III

Fig. 5. Variation trends of SCO distributions for the cases of V32up, V32low, V38up, V38low.

588

P. Tan, L. Tong / Composites: Part B 37 (2006) 583–592

Table 1 The values of DDS and ABD for the cases of V32 and V38 DDS/ABD (%/·1010)

Left tip

Right tip

V32

V38

V32

V38

Vibration mode I Vibration mode III

7.18/1.53

7.2/0.14

12.88/2.01

12.87/0.19

112.43/7.25

112.42/8.33

43.56/7.1

43.6/8.15

(DDS) which was defined in Ref. [18], an electric voltage with a value of 10 V is applied to the actuator bonded on the top or bottom surface of the host beam in region II or VIII, respectively, and their corresponding SCO distributions are plotted in Fig. 5(a) for the case of vibration mode I and (b) for vibration mode III. In Fig. 5, the V32up, V32low, V38up and V38low stand for the electric voltages, which are, respectively, applied to the actuator located on the upper beam surface in the region II, lower beam surface in the region II, upper surface and lower surface in the region VIII. It is noted from Fig. 5 that the SCO distribution for the case of V32up (or V38up) is consistent with that for the case of V32low (or V38low). Hence, it may conclude that for the cases considered here, the SCO distri-

bution measured from the sensor does not depend on the selection of the beam surface on which an actuator is bonded. However, the actuator location in the x direction affects the SCO distribution significantly. Fig. 5 shows that for the case of vibration mode I, the SCO value for an actuator location in region II is much higher than that in the region VIII, while for the case of vibration mode III, the SCO value for an actuator location in the region VIII is greater than that in the region II. This finding is consistent with that reported in Ref. [14]. By using Eq. (27) in Ref. [18], the required DDS values can be obtained for both left and right delamination tip and are listed in Table 1. Also, the absolute values of the SCO discrepancy at the left (or right) delamination tip (i.e. ABD) are tabulated in Table 1. From Table 1, it is noted that the actuator location along the x direction slightly affect the value of DDS and ABD except for the ABD value in the case of vibration mode I. The ABD value for the case of V38 is much smaller than that of V32. The values for the rest of major parameters to be investigated here are chosen to be 0.03 and 0.06 m for la, 0.06 and 0.1 m for ls, and 0.15 and 0.3 mm for tad. Their corresponding SCO distributions are plotted in Figs. 6–8, 2.5E-09

6.0E-09

ls01 ls006 2.0E-09

la006

5.0E-09

la003

SCO (C)

SCO (C)

4.0E-09

3.0E-09

1.5E-09

1.0E-09

2.0E-09 5.0E-10 1.0E-09

0.0E+00 0.27

0.28

0.29

0.3

0.31

0.32

0.33

0.0E+00 0.25

0.34

0.27

0.29

X (m)

X (m)

0.31

0.33

0.35

(a) For the case of vibration mode I

(a) For the case of vibration mode I 3.0E-09 7.0E-09

ls01 2.5E-09

la006

6.0E-09

ls006

la003 2.0E-09

SCO (C)

SCO (C)

5.0E-09 4.0E-09 3.0E-09

1.0E-09

2.0E-09 1.0E-09 0.0E+00 0.27

1.5E-09

5.0E-10

0.28

0.29

0.3

0.31

0.32

0.33

0.34

X (m)

(c) For the case of vibration mode III

Fig. 6. Variation trends of SCO distribution for the cases of la=0.03 and 0.06 m.

0.0E+00 0.25

0.27

0.29

X (m)

0.31

0.33

0.35

(c) For the case of vibration mode III

Fig. 7. Variation trends of SCO distribution for the cases of ls=0.06 and 0.1 m.

P. Tan, L. Tong / Composites: Part B 37 (2006) 583–592

tion embedded in a cantilever laminated composite beam than that for la = 0.03 m. According to the diagrams shown in Fig. 7, we note that the effect of the sensor length ls on the SCO distribution is minor, and thus it is recommend that for cost effectivity, the size of ls should be chosen as small as possible. Fig. 8 reveals that an increase in tad will cause a slight increase in the value of SCO for both case of vibration mode I and III.

2.5E-09 tad03

SCO (C)

2.0E-09

589

tad015

1.5E-09

1.0E-09

5.0E-10 6E-11 0.0E+00 0.27

perf 0.28

0.29

0.3

0.31

0.32

0.33

0.34

del

5E-11

X (m)

(a) For the case of vibration mode I SCO (C)

4E-11

2.50E-09 tad03

SCO (C)

2.00E-09

tad015

3E-11

2E-11

1.50E-09

1E-11

0 0.27

1.00E-09

0.29

0.31

0.33

X (m) 5.00E-10

(a) For the case of vibration mode I

0.00E+00 0.27

0.28

0.29

0.3

0.31

0.32

0.33

7E-12

0.34

X (m)

6E-12

(c) For the case of vibration mode III

5E-12

Table 2 The values of DDS and ABD for cases of la=0.06 and 0.03 m DDS/ABD (%/·1010) Vibration mode I Vibration mode III

Left tip la=0.03 m 7.18/1.53

4E-12

perf del

3E-12 2E-12 1E-12 0 0.27

0.29

0.31

0.33

X (m)

(b) For the case of vibration mode II 8E-12 perf 7E-12

del

6E-12 5E-12

SCO (C)

respectively, in which only one major parameter changes and the rest remain the same as those for the baseline case. From Fig. 6, we found that the SCO value increases with an increase in la for both cases of vibration mode I and III. This is expected owing to that an increase in actuator length will result in a larger shear force at the interface between the actuator and host beam, and thus cause a large deformation of the beam. For the DDS and ABD, their corresponding values for the cases of la = 0.03 and 0.06 m are listed in Table 2. From Table 2, it is revealed that the values of DDS and ABD for the case of la = 0.06 m are equal to or greater than those for la = 0.03 m except for the DDS in the case of right delamination tip and vibration mode III. It means that the sensor for the case of la = 0.06 m are more sensitive to a delamina-

SCO (C)

Fig. 8. Variation trends of SCO distribution for the cases of tad=0.15 and 0.3 mm.

4E-12 3E-12 2E-12 1E-12

Right tip la=0.06 m 7.18/3.46

la=0.03 m 12.88/2.01

la=0.06 m 12.89/4.55

0 0.27

0.29

0.31

0.33

X (m)

(c) For the case of vibration mode III

112.43/7.25

193.59/17.98

43.56/7.1

37.03/17.36

Fig. 9. Variation trends of SCO distribution for the beams with and without delamination in the case of sinusoidal voltage.

590

P. Tan, L. Tong / Composites: Part B 37 (2006) 583–592

3.3. Influence of applied electric voltage on the SCO and DDS In order to investigate the type of electric voltage applied through the thickness of an actuator, two different types of voltage, namely initial impulse voltage V3d(t) and sinusoi-

Table 3 The values of DDS and ABD for cases of V3sin x0t and V3d(t) DDS/ABD (%/·1010)

Left tip

Right tip

V3sin x0t

V3d(t)

V3sin x0t

V3d(t)

Vibration mode I Vibration mode III

7.18/0.04

7.18/1.53

14.78/0.05

12.88/2.01

112.43/0.02

112.43/7.25

43.56/0.02

43.56/7.1

1.2

0.4

dal voltage V3sin x0t, are used, where x0 is the frequency for the input sinusoidal voltage. By using the present SCOD method, the corresponding SCO distributions for the beams with and without delamination are plotted in Fig. 4 for the case of initial impulse voltage (IIV) and Fig. 9 for the case of sinusoidal voltage (SV). A comparison between Fig. 4 and Fig. 9 reveals that the delamination size and location detected using IIV are in consistence with that using SV for the case of t = 1 s and x0 is chosen to be close to the inherent frequency of the beam system. This can be further proven by a comparison of their normalized sensor charge output (NSCO) distribution, which was defined in Ref. [13]. The NSCO distributions for both cases are shown in Fig. 10. From Fig. 10, we note that the NSCO distributions obtained using IIV overlap on those gained using SV. However, it is interesting by comparing Fig. 4 with Fig. 9 that the value of SCO for the case of IIV is about two-order larger than that of SV. The DDS and ABD values for both cases are listed in Table 3. From Table 3, we found that the DDS values for the case of SV are the same as that of IIV except for the case of vibration mode I at the right delamination tip, but the ABD values for SV case are much smaller than those for the IIV case.

0.2

4. Verification of the present SCOD method

IIV 1

SV

NSCO

0.8

0.6

0.4

0.2

0 0.27

0.28

0.29

0.3

0.31

0.32

0.33

X (m)

(a) For the case of vibration mode I 1.2 IIV 1

SV

NSCO

0.8

0.6

0 0.27

0.28

0.29

0.3

0.31

0.32

0.33

X (m)

(b) For the case of vibration mode II 1.2 IIV 1

SV

NSCO

0.8

0.6

0.4

0.2

0 0.27

0.28

0.29

0.3

0.31

0.32

0.33

X (m)

(c) For the case of vibration mode III

Fig. 10. Variation trends of NSCO distribution for the cases of instant impulse voltage (IIV) and sinusoidal voltage (SV).

In order to verify the present SCOD method, a 2D plane strain FEA model was established using the FEA software Strand7 [19] and the required data for the baseline case. A comparison of the first three order frequencies between the present FEA model and SCOD method reveals that there is a very good agreement between them. The percentage difference between these two methods is 0.29% for the case of vibration mode I, 0.1% for vibration mode II and 0.13% for vibration model III, respectively. For the case of ls = 0.06 m, a comparison of the SCO distributions between cantilever beams bonded with isolated piezoelectric actuator and sensor patches (see Fig. 1) and that with an integrated piezoelectric sensor/ actuator layer (see Fig. 1 in Ref. [14]) is conducted here. The corresponding SCO distributions along the sensor surface are shown in Fig. 11 for both vibration mode I and III, in which Int and Iso stand for integrated and isolated actuator and sensor, respectively. It is worth mentioning that the SCO plotted in Fig. 11 were obtained using the material properties and geometric parameters employed in the Ref. [14]. It is found from Fig. 11 that the presence, size and location of a delamination detected using the SCOD

P. Tan, L. Tong / Composites: Part B 37 (2006) 583–592

ABD values are closely related to the type of PZT sensor and actuator considered.

4.0E-09 Int

3.5E-09

591

Iso 3.0E-09

5. Conclusions

SCO (C)

2.5E-09 2.0E-09 1.5E-09 1.0E-09 5.0E-10 0.0E+00

0

0.05

0.1

0.15

0.2

0.25

0.3

0.25

0.3

X (m)

(a) For the case of vibration mode I 3.5E-09 Int

3.0E-09

Iso

SCO (C)

2.5E-09 2.0E-09 1.5E-09 1.0E-09 5.0E-10 0.0E+00

0

0.05

0.1

0.15

0.2

X (m)

(c) For the case of vibration mode III

Fig. 11. Variation trends of SCO distribution for the cases using isolated (Iso) and integrated (Int) PZT actuator and sensor.

method with isolated actuator and sensor patches are consistent with those using an integrated sensor/actuator layer, even though the SCO values for the case using integrated sensor/actuator layer are greater than that using isolated actuator and sensor patches. This may be caused by the higher vibration frequency inhabited in a beam system with an integrated sensor/actuator layer compared to that with isolated actuator and sensor patches. Also, for the case using an integrated sensor/actuator layer, the stress created by an actuator segment transfers to the sensor segment, and thus result in a larger strain within the sensor segment. The DDS and ABD values for both cases using integrated and isolated PZT sensor and actuator are tabulated in Table 4. From Table 4, it is noted that the DDS and

Table 4 The values of DDS and ABD for cases of isolated and integrated PZT sensor and actuator DDS/ABD (%/·1010)

Left tip Isolated

Integrated

Isolated

Integrated

Vibration mode I Vibration mode III

5.38/0.18

6.06/1.82

15.06/0.24

12.4/1.89

47.28/3.02

35.42/5.95

24.95/3.05

29.76/5.83

Right tip

A sensor charge output deviation (SCOD) method using isolated actuator and sensor patches is proposed, and then employed to identify a delamination embedded in a cantilever laminated composite beam. By using the present SCOD method for the baseline case considered in this paper, we note that the actuator length and location in the x direction affect the value of SCO, DDS and ABD significantly. The effects of ls and tad on the SCO, DDS and ABD values are minor. Hence, it is suggested that for cost effectivity, the size of ls should be chosen as small as possible. For the type of the applied electric voltage considered here, its influence on the SCO and ABD is significant but that on the DDS is minor. The present investigation also reveals that the presence, size and location of a delamination detected using the SCOD method with isolated actuator and sensor patches are consistent well with those using an integrated sensor/actuator layer, even though the SCO values for the case using integrated sensor/actuator layer are greater than that using isolated actuator and sensor patches. An excellent agreement of the first three order frequencies between the present finite element analysis and analytical models prove that the present SCOD method can be effectively used to identify a delamination within a laminated composite beam. Acknowledgements The authors are grateful to the support of Australian Research Council via a Discovery-Project Grant Scheme (grant no. DP0209504) and University of Sydney via University Postdoctoral Research Fellowship. References [1] Saravanos DA, Hopkins DA. Effects of delaminations on the damped dynamic characteristics of composite laminates: analysis and experiments. J Sound Vib 1996;192(5):977–93. [2] Campanelli RW, Engblom J. The effect of daminations in graphite/ PEEK composite plates on modal dynamic characteristics. Compos Struct 1995;31:195–202. [3] Tenek LH, Henneke EG, Gunzburger MD. Vibration of delaminated composite plates and some applications to non-destructive testing. Compos Struct 1993;23:253–62. [4] Takeda S, Okabe Y, Yamamoto T, Takeda N. Detection of edge delamination in CFRP laminates under cyclic loading using smalldiameter FBG sensors. Compos Sci Technol 2003;63:1885–94. [5] Takeda S, Okabe Y, Takeda N. Delamination detection in CFRP laminates with embedded small-diameter fiber Bragg grating sensors. Compos Part A Appl Sci Manuf 2002;33:971–80. [6] Ling HY, Lau KT, Cheng L. Determination of dynamic strain profile and delamination detection of composite structures using embedded multiplexed fibre-optic sensors. Compos Struct 2004;66: 317–26. [7] Lee DC, Lee JJ, Yun SJ. The mechanical characteristics of smart composite structures with embedded optical fiber sensors. Compos Struct 1995;32:39–50.

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