Propagation of guided Lamb waves in bonded specimens using piezoelectric wafer active sensors

Adrian Cuc*, Victor Giurgiutiu**, University of South Carolina, Department of Mechanical

Engineering, Columbia, SC 29208

ABSTRACT

The nondestructive evaluation (NDE) of adhesively bonded structures is a complex process. Earlier work has confirmed that ultrasonic waves are influenced by the properties of the material in which they travel. Acousto-ultrasonic methods have been widely used by previous researchers to generate ultrasonic waves in plates and bonded structures for flaw detection, visualization, and measurements of the local properties of the jointed materials. This paper will present the methods and principles used for generation and propagation of ultrasonic guided waves (Lamb waves) using piezoelectric wafer active sensors (PWAS). Keywords: Ultrasonic, Lamb waves, Damage detection, NDE, Wave propagation, PWAS

1. INTRODUCTION

Ultrasonic nondestructive evaluation is of highly importance for several industries. Even though ultrasonic inspection has been used for several decades, the demands of the actual economy have pushed the development of NDE methods further and further. New ultrasonic methods are being developed, and there is a transition from the conventional ultrasonic methods using coupled transducers, to more advanced technologies using embedded ultrasonic sensors. These sensors will generate guided ultrasonic waves, which will travel within the tested subject, and will provide information about the existence and location of possible flaws. The beneficiary of such modern detection technologies will be industries varying from aerospace to automotive applications. Today’s aircraft fleet is an aged fleet that needs more and more tedious inspection for cracks, corrosions and delaminations. These examinations are done mainly manually using visual inspection, which is expensive, time consuming and makes the aircrafts inoperable for a long time. The use of NDE methods will enable semi and full automation of the entire inspection process, reduce the time of inspection and move the maintenance approach from a scheduled maintenance to on-demand maintenance. Early detection of such flaws will prevent catastrophic failures and what is most important will save human lives. Automotive industry is also going to benefit from such modern technologies. Weight is an important issue and a factor that affects the performances of a car as well as the price. That is why aluminum, non-ferrous alloys and composite materials are used to create new assemblies with reduced weight and increased strength against corrosion and collisions. Such materials cannot be welded or joined using bolted connections. The only alternative is to use structural adhesives and permanently join them together. The highly automated process of car manufacturing requires an automated process of inspecting such joints. The NDE methods have the capabilities of real time automated inspection.

In order to use ultrasonic methods for NDE of metallic structures the physical phenomenon of wave generation and wave propagation must be understand. Early work was conducted using bulk waves for thickness measurements. Conventional ultrasonic transducers were used to introduce pressure waves in the multilayer joint typically using a coupling gel between the transducer and the structure. In the past years, researchers focused their attention on using guided waves, namely Lamb waves, for flaw detection. Lamb waves can be excited using conventional ultrasonic transducers and a wedge between the transducer and the specimen. This paper will present the techniques used to generate guided waves (Lamb waves) in specimen consisting of thin metallic layers joined together through an adhesive layer. The work will introduce small, inexpensive, nonintrusive, unobtrusive devices that can be surface mounted and able to excite and detect Lamb waves.

____________________________________________________________ *aicuc000@engr.sc.edu; phone (803) 777-0619, fax: (803) 777-0106 **victorg@sc.edu; phone: (803) 777-8018, fax: (803) 777-0106

2. PIEZOELECTRIC WAFER ACTIVE SENSORS

Piezoelectric wafer active sensors (PWAS) are inexpensive transducers (Figure 1) operating on the piezoelectric principle. The direct piezoelectric effect is manifested when the applied stress on the sensor is converted into electric charge. The inverse effect, conversely, will produce strain when a voltage is applied on the sensor. In this way the PWAS can be used as both, transmitter and receiver. Piezoelectric actuators were used initially by Crawley et al1,2 and Fuller et al.3 Tzou and Tseng4 and Lester and Lefevbre5 modeled the piezoelectric sensor/actuator design for dynamic measurement and control. The use of piezoelectric sensors for structural health monitoring and the Lamb waves for damage detection was pioneered by Chang Fu-Kuo and his collaborators6,7,8,9 who have studied the generation and the reception of elastic waves in composite materials. In their studies, passive reception of elastic waves was used for impact detection, and the pitch-catch method using low-frequency Lamb waves was used for damage detection. Other researchers10-16 have studied the propagation of Lamb waves and the use of different wave propagation methods (pitch-catch, pulse-echo) as well as standing wave methods (electromechanical impedance) for damage detection. Recently, Giurgiutiu and his collaborators17,18,19,20 have studied in detail and characterized the piezoelectric wafer active sensors used for damage detection with guided Lamb waves. When excited by an alternating electric voltage, the PWAS acts as an electromechanical resonator. The modeling of a free piezoelectric sensor is useful for understanding the electromechanical coupling between the mechanical vibration

response and the complex electrical response of the sensor. As a resonator the PWAS has the property of performing mechanical resonances under direct electrical excitation. The resonant frequencies depend only on the wave speed (a material constant) and the geometric dimensions. The electric field is produced by applying a harmonic voltage

ˆ( ) i tV t Ve ω= between the top and bottom surfaces. The resulting electric field, 3 /E V h= , is assumed uniform over the piezoelectric wafer. For a harmonic voltage excitation the electric field and the response are in the form 3

ˆ ˆ,i t i tE Ee u ueω ω= = , where 1̂( )u x is the x-dependant complex amplitude and incorporates any phase difference between the excitation and response.

The general piezoelectric constitutive equations in the tensor notation are:

ijkl

jk

Eij kl kij k

Tj kij ki k

S s T d E

D d T Eε

= +

= + (1)

where ijkls is the mechanical compliance of the material measured at zero electric field (E = 0), Tjkε is the dielectric

permittivity measured at zero mechanical stress (T = 0), and kijd represents the piezoelectric coupling effect. Under the one-dimensional assumptions, the general constitutive equations for strain and electric displacement reduce to the simpler expressions: 1 11 1 31 3

ES s T d E= + (2)

333 31 1 3TD d T Eε= + (3)

where S1 is the strain, T1 is the stress, D3 is the electrical displacement, 11Es is the mechanical compliance at zero electric

field, 33Tε is the dielectric constant at zero stress, and d31 is the induced strain coefficient.

3. GENERATION OF ULTRASONIC GUIDED WAVES WITH PWAS

For embedded nondestructive evaluation (NDE) applications, PWAS can be used as embedded transducers. PWAS can act as both Lamb wave transmitter and Lamb wave receiver. The sensors couple their in-plane motion with the particle motion of Lamb waves on the material surface. The in-plane PWAS motion is excited by the applied oscillatory voltage through the 31d piezoelectric coupling. Optimum excitation and detection happen when the PWAS length is an

2 in (50 mm)

PWAS array

Figure 1 Array of PWAS mounted on an aluminum

plate

odd multiple of the half wavelength of particle Lamb wave modes. The PWAS action as ultrasonic transducers is fundamentally different from that of conventional ultrasonic transducers. Conventional ultrasonic transducers act though surface tapping, applying vibrational pressure to the surface of the object. PWAS, on the other hand, act through surface pinching and are strain coupled with the object surface.

3.1. Coupling between PWAS and host structure The transmission and reception of Lamb waves between the PWAS and the structure is achieved through the adhesive layer. The adhesive layer acts as a shear layer, in which the mechanical effects are transmitted through shear effects. Figure 2 shows a thin wall structure of thickness t and elastic modulus E, with a PWAS of thickness ta and

elastic modulus Ea attached to its upper surface through a bonding layer of thickness tb and shear modulus Gb. The PWAS length is la while the half-length is a =la / 2. In addition, the definition d = t / 2 is used. Upon application of an electric voltage, the PWAS experiences an induced strain:

31ISAVdt

ε = (4)

The induced strain is transmitted to the structure through the bonding layer interfacial shear stress (τ). For harmonic varying excitation, the shear stress has the expression ( , ) ( ) i t

ax t x e ωτ τ= . The PWAS expansion is transmitted to the structure through the bonding layer which acts predominantly in shear. The shear stress intensity

and distribution depend on the relative deformation of the PWAS and the structure. Crawley et al.2 developed a 1-D strain analysis using the Euler-Bernoulli hypothesis across the plate thickness, i.e., uniform displacement for axial motion, and linear displacement for flexural motion. The resulting interfacial shear stress in terms of hyperbolic functions can be written as:

sinh( )cosh

aa ISA

t xx E aa a

ψτ εα ψ

Γ = ⋅ Γ + Γ (5)

where a a

EtE t

ψ = , and the shear lag parameter 2 1b

a a b

GE t t

α ψψ+

Γ = ⋅ ⋅ .

The parameter α depends on the stress and strain distribution across the structural thickness. For low-frequency coupled axial-bending motion this parameter takes the value α = 4. This value is changing as the frequency changes. The shear transfer along the PWAS is controlled by the product between the shear lag parameter, Γ, and the sensor half-length a. For low values of the Γ a product, the shear transfer is distributed along the PWAS length, and the shear stresses have a relatively low intensity. For high values, the shear transfer is localized towards the end of the sensor and the shear stress has high intensity.

3.2. Axial waves excited by PWAS Assume a one-dimensional medium in which an external force induces an actuation strain, 0 ( , )x tε . Such an actuation strain may be induced by surface mounted PWAS applied symmetrically to the top and bottom surfaces. Considering an infinitesimal element of length dx, applying Newton’s law and considering a harmonic excitation the strain becomes: 2

0 eε ξ ε ε′′ ′′− = (6) where 2 2 2

0 cξ ω= is the wave number of axial waves in the one-dimensional medium. Applying a space-domain Fourier transform on Eq. (6) yields to:

2

2 20

eξε ε

ξ ξ=

−% % (7)

Equation (7) represents the solution in the Fourier domain. Taking the inverse space-domain Fourier transform yields the solution in the space domain:

2

2 20

1( ) ( )2

i xex e dξξε ε ξ ξ

π ξ ξ

+∞

−∞

=−∫ % (8)

Figure 2 Interaction between the PWAS and the

structure showing the bonding layer interfacial stress τ(x)

For an ideally bonded PWAS, the induced strain is uniform over the PWAS length. The space-domain strain distribution is the rectangular pulse function:

,

( )0,a

ex a

xotherwise

εε

<=

(9)

Recalling Eq. (7) and taking inverse Fourier transform, the space-domain solution is:

2 20

2 sin( )2

i xa ax e dξε ξ ξε ξπ ξ ξ

+∞

−∞

=−∫ (10)

The integral in Eq. (10) can be solved analytically using the residue theorem and a semicircular contour (C) in the complex ξ domain. The strain response due to a harmonically oscillating PWAS perfectly bonded to the structure has the form: 0( )

0( ) (sin ) i x tax i a e ξ ωε ε ξ −= (11)

From Eq. (13) the it can be seen that the response amplitude follows a sinusoidal variation with respect to the parameter 0aξ . Response peaks are observed at odd integer multiplies of 2π .

3.3. Flexural waves excited by PWAS Consider the general equation of flexural vibrations under external moment excitation, Me(x,t): ( , )eEIv Av M x tρ′′′′ ′′+ =&& (12) Assuming harmonic variation in the time domain and considering the excitation curvature eκ , the general equation of flexural vibrations becomes: 4

F ev vξ κ′′′′ ′′− = (13) where

ee

MEI

κ = , 2

4 22F

AEI aρ ωξ ω= = ,

22

3EI d Ea

Aρ ρ= =

Applying a space-domain Fourier transform on Eq. (13) yields to: 4 4 2( )F evξ ξ ξ κ− = − %% (14) The solution of Eq. (14) is:

2

4 4 eF

ξε κξ ξ−

=−

% % (15)

Taking the inverse space-domain Fourier transform yields the solution in the space domain:

2

4 40

1( )2

i xev x e dξξ κ ξ

π ξ ξ

+∞

−∞

−=

−∫ % (16)

The integral in Eq. (16) can be solved analytically using the residue theorem and a semicircular contour (C) in the complex ξ domain. Adding the harmonic variation in the time domain yields the complete solution:

( )( ) ( )( , )4 4

F Fi x t x i te F e F

F F

iv x t i e e eξ ω ξ ωκ ξ κ ξξ ξ

− − −= +% %

(17)

The first term in Eq. (17) represents a propagating wave, while the second term represents a vibration that is decaying fast with x. This term represents a local vibration that does not propagate and is called an evanescent wave. Retaining only the propagating wave part in Eq. (17) will give:

( )( )( , )4

Fi x te F

F

v x t i e ξ ωκ ξξ

−=%

(18)

The strain solution can be derived as:

( )( )4

Fi x tex Fy i e ξ ωεε ξ −=

% (19)

For an ideally bonded PWAS, the excitation moment is represented by a rectangular pulse function. The following expression for the strain at the material surface undergoing flexural wave excitation can be derived after mathematical calculations:

( )( ) 3 (sin ) Fi x ta Fx i a e ξ ωε ε ξ −= (20)

Response peaks are observed at odd integer multiples of 2π . Maximum excitation of flexural waves will occur when the PWAS length is an odd-integer multiple of the flexural half wavelength (2 1) 2a Fl m λ= + .

3.4. Lamb waves excited by PWAS For the analysis consider the surface-mounted PWAS shown in Figure 3. The sensor is excited electrically with a time-harmonic voltage i tVe ω− . As a result of the applied voltage the sensor will expand and contract, and a time harmonic interfacial shear stress, ( ) i tx e ω

ατ− develops between the PWAS and the structure. The stress on the upper

surface is given by: [ ]0( ) ( ) ( ) ( )yx ay h

x x H x a H x aτ τ τ== = + − − (21)

where H(x) it the Heaviside step function. Applying the space domain Fourier on the excitation we obtain:

[ ]0 ( ) ( ) ( ) i xa x H x a H x a e dxξτ τ

+∞−

−∞

= + − −∫% (22)

Recalling the wave equations in terms of the potential functions and the Lame constants:

22

1

pcφ φ∇ = && , 2

2

1

scψ ψ∇ = && (23)

where 2 ( 2 ) /pc λ µ ρ= + is the speed of the pressure wave; 2 /sc µ ρ= is the speed of the shear vertical wave; , ,λ µ ρ are the two Lame constants and the density, respectively. The displacement in the x and y directions in terms of the two potentials are:

xux yφ ψ∂ ∂

= +∂ ∂

, yuy xφ ψ∂ ∂

= −∂ ∂

(24)

Applying the space domain Fourier transform to the wave equations, displacements, stresses and strains we obtain:

2 2

2 22 20, 0p S

d dc cdy dyφ ψφ ψ+ = + =% %% % (25)

,x yd du i u idy dyψ φξφ ξψ= + = −

%%% %% % (26)

2

222yx

didy yφ ψτ µ ξ ξ ψ

∂= + + ∂

% %%% ,

22 2

2 2yyd di

dydyφ ψτ λ ξ φ µ ξ φ ξ

= − + + − −

% %% %% (27)

The general solution for Eq. (25) has the form:

1 2

1 2

sin( ) cos( )sin( ) cos( )

A py A pyB qy B qy

φψ= += +

%

% (28)

where 2 2 2 2pp cω ξ= − , 2 2 2 2

sq cω ξ= − , and ξ are the directional wave numbers. The constants, A2, B1 and A1, B2 correspond to the two possible motions: symmetric and anti-symmetric (Figure 3a).

(a) (b) Figure 3 (a) Symmetric and anti-symmetric particle motion; (b) symmetric and anti-symmetric loading

Symmetric solution

The boundary conditions for the symmetric case are: ,x x y yd d d d

u u u u− + − += = −% % % % (29)

, 02a

yx yx yy yyd d d d

ττ τ τ τ

− + − += − = = =

%% % % % (30)

The strain at the upper surface for the symmetrical motion can be calculated as:

2

S Sx d

S

Ni

Dτεµ

= −%

% (31)

where ( )2 2 cos cosSN q q pd qdξ ξ= + , ( )22 2 2cos sin 4 sin cosSD q pd qd pd qdξ ξ= − + .

Anti-symmetric solution

To solve for the strain at the upper surface for the anti-symmetrical motion we follow the same procedure as for the symmetrical motion. The boundary conditions are: ,x x y yd d d d

u u u u− + − += − =% % % % (32)

0,2a

yx yx yy yyd d d d

ττ τ τ τ

− + − += = = − =

%% % % % (33)

The strain at the upper surface for the anti-symmetrical motion is:

2

A Ax d

A

NiD

τεµ

= −%

% (34)

where ( )2 2 sin sinAN q q pd qdξ ξ= + , ( )22 2 2sin cos 4 cos sinAD q pd qd pd qdξ ξ= − + .

Total solution

The complete response to the PWAS excitation is obtained by combining the symmetric and anti-symmetric responses:

2

S Ax d

S A

N Ni

D Dτεµ

= − +

%% (35)

Applying the inverse Fourier transform and adding the harmonic time behavior we move from the wave number domain back into the space domain:

( )12 2

i x tS Ax d

S A

N Ni e dD D

ξ ωτ τε ξ

π µ

+∞−

−∞

−= +

∫

% %% (36)

The integral in Eq. (36) is singular at the roots of DS and DA which are the symmetric and anti-symmetric eigenvalues of the Rayleigh-Lamb equations, i.e.,

0 1 2, , ,....S S Sξ ξ ξ (symmetric motion) and

0 1 2, , ,....A A Aξ ξ ξ (anti-symmetric motion). At low frequencies,

i.e. 0ω → , only two eigenvalue exist, 0Sξ and 0

Aξ . At higher frequencies several other eigenvalues exist. To solve Eq. (36) the residue theorem is used and a contour consisting of a semicircle in the upper half of the complex ξ plane and the real axis (Figure 4). The total solution for the strain at the upper surface is:

( ) ( )( ) ( ) ( ) ( )1( , )2 ( ) ( )

S A

S A

S S A Ai x t i x tS A

x S AS A

N Nx t e eD D

ξ ω ξ ω

ξ ξ

τ ξ ξ τ ξ ξε

µ ξ ξ− −

= + ′ ′ ∑ ∑

% % (37)

Figure 4 Contour for evaluating the inverse Fourier

transform integral.

Integration with respect to x yields the displacement:

( ) ( )( ) ( ) ( ) ( )1 1 1( , )2 ( ) ( )

S A

S A

S S A Ai x t i x tS A

x S S A AS A

N Nu x t e eD D

ξ ω ξ ω

ξ ξ

τ ξ ξ τ ξ ξµ ξ ξ ξ ξ

− − = + ′ ′

∑ ∑% %

(38)

4. EXPERIMENTAL RESULTS

Experimental work has been conducted to validate the assumption that small PWAS can excite Lamb waves in bonded specimens which will propagate and will be received by other PWAS acting as receivers. Experimental work was also performed to establish PWAS-based methods for detecting disbonds. Both traveling wave methods (pitch-catch and pulse-echo) and standing wave methods (electromechanical impedance) have been explored.

4.1. PWAS Lamb-wave tuning in bonded specimens An aluminum lap-joint specimen was fabricated using two aluminum 2024T3 stripes as shown in Figure 5.

75 mm

80 mm

Bond line

Simulated disbonds

1220 mm

AluminumBond line

PWAS array

1 ……………. 11 A

B

C Aluminum

(a) (b)

Figure 5 (a) Lap-joint specimen consisting of two aluminum stripes bonded together; (b) Location of the PWAS on the lap-joint specimen

HP 33120Signal generator

Tektronix TDS210 Digital Oscilloscope

Computer

GPIB

HP 33120 Signal generator

Tektronix TDS210 Digital Oscilloscope

Lap-joint specimnen

PWAS

Disbond Disbond

Disbonds

(a) (b)

Figure 6 The instrumentation set-up used in the pitch-catch experiment: (a) location of PWAS on the lap-joint specimen; (b) schematic of the instrumentation set-up

The two aluminum stripes are 80mm x 1220mm, and 75mm x 1220mm with a thickness of 1mm. They were bonded together using an epoxy paste adhesive, Loctite Hysol® EA 9309.3NA. The overlap of the two aluminum stripes is 20mm. The disbonds were artificially created using Mylar® polyester film that was introduced between the two aluminum stripes and produced a discontinuity of the adhesive layer. Next, the specimen was instrumented with an array of PWAS sensors as presented in Figure 5(b). The sensor array has 11 columns and three rows (A, B, and C). One row of sensors (A) is located on the top aluminum plate, the second row on the bond line (B), and the third row is located on the second aluminum plate (C). The spacing between each column of sensors is 100 mm and the distance between PWAS on row A and PWAS on row B is 30mm. The distance between PWAS on row B and PWAS on row C

is 28mm. The instrumentation set-up is shown in Figure 6. An HP 33210 signal generator was used to produce a 3-count sinusoidal tone burst with a frequency of 390 kHz. The wave traveled through the specimen and was capture using a Tektronix TDS210 digital oscilloscope. To study the propagation of Lamb waves, the dispersion phenomenon needs to be addressed. Wave dispersion may occur when the wave speed varies with frequency. Lamb waves are dispersive in nature meaning, the wave speed depends on the product of frequency and thickness of the plate in which the Lamb waves are traveling. The physical phenomenon can be explained considering a wave packet, or a tone burst, as shown in Figure 7a. The tone burst consists of a carrier frequency (tone) and has a short duration in time (burst). In the frequency domain, there is a dominant frequency fc, and other side frequencies.

t

Am

plitu

de (m

V)

a) b)

f A

mpl

itude

(mV

)

fc

side frequenciesFFT

IFFT

Figure 7 (a) 5-count sine tone burst; (b) frequency spectrum of the tone burst signal

For non-dispersive wave propagation, the shape of the wave is preserved and the wave speed is constant. All frequency components in the wave packet travel with the same speed and the packet keeps its shape. For dispersive wave propagation, each frequency component travels with a different speed (wave speed is a function of frequency c = c(f)) hence the wave packet spreads out, it disperse. The degree of dispersion depends on the spectrum bandwidth.

4.2. Wave propagation methods Lamb waves traveling in bonded specimens encounter complex phenomena at the bond interface. Part of the energy of the incident wave will be transmitted through the bond layer from one metallic plate to the other. At the same time mode conversion and diffraction of the Lamb wave take place. The propagation of the Lamb wave will become highly complicated several modes propagating at the same time. The viscoelastic behavior of the adhesive layer will cause damping, attenuation of the Lamb wave energy, and frequency shifts. Many researchers have addressed the propagation of Lamb waves in adhesively joints in the last decade. This study will address the possibility to introduce Lamb waves in such bonded specimens using small, unobtrusive PWAS.

s0_100kHz

0

0.05

0.1

0.15

0.2

0.25

0 20 40 60 80 100 120 140Time (micro-sec)

Am

plitu

de

a4-a5 a4-a6 a4-a7s0_100kHz

0

0.05

0.1

0.15

0.2

0.25

0 20 40 60 80 100 120 140

Time (micro-sec)

Ampl

itude

b4-b5 b4-b6 b4-b7Waves traveling on the aluminum sheet

Waves traveling along the bond line

(a) (b)

Figure 8 (a) S0 mode Lamb waves traveling in the aluminum material on the top plate; (b) S0 mode Lamb waves traveling along the bond line

The propagation of the Lamb waves in the specimen using the pitch-catch method is shown in Figure 8. For this method we used a pair of two sensors, one being the transmitter and the other one the receiver. The excitation signal was a 3-count sine burst at 390 kHz. This frequency range produced an S0 mode Lamb wave. The wave signal was then received at three consecutive sensors 100 mm apart. The first set of data was acquired for sensors located on the aluminum layer only and the second set of data was acquired from sensors located on the bonded layer. The results shown clearly demonstrate the capability of our PWAS to send and receive Lamb waves in the aluminum material itself and along the bond line. It can be observed that for the waves traveling in the aluminum layer there is attenuation of the signal as the distance increases but the dispersion is very little. However, the Lamb waves traveling along the bond line show a strong dispersion even for the S0 mode, as shown in Figure 8b. This is to be expected because of the damping effect of the adhesive layer. Figure 9 presents the attenuation of the Lamb waves traveling in the aluminum layer only and along the bond line. The energy of the signal traveling along the bond line is less than the energy of the signal traveling outside the bond line, thus

the signal is weaker, the adhesive layer absorbing part of the energy of the transmitted wave.

a0_30kHz

-0.005

-0.003

-0.001

0.001

0.003

0.005

0.007

20 40 60 80 100 120 140 160 180 200

Time (micro-sec)

Ampl

itude

b4 b5 b6a0_30kHz

0.0007

0.0009

0.0011

0.0013

0.0015

0.0017

40 60 80 100 120 140 160 180 200

Time (micro-sec)

Ampl

itude

b4 b5 b6PWAS b4 close to disbond

PWAS b5 and b6

Figure 10 Pulse-echo method. A0 mode Lamb wave collected at three sensors: PWAS b4 closest to disbond.

Another wave propagation method is the pulse-echo. Particular for the pulse-echo method is that the same sensor is used as both transmitter and receiver. The fabricated lap-joint specimen incorporates two artificial disbonds. We used the pulse-echo method to excite A0 mode lamb waves using a 3-count sine burst at 120 kHz frequency. The purpose of this experiment was to prove the possibility to also excite and generate anti-symmetric low frequency Lamb mode waves able to propagate in bonded specimens. Figure 11 shows the three signals received by the three consecutive sensors. Signals received by PWAS b5 and b6 have a very consistent pattern and do not present any additional reflections in the time domain. On the other hand, the signal received at PWAS b4 which is close to the disbond shows a different pattern and reflection from the disbond is present in the time domain spectrum.

4.3. Standing wave method The impedance method is a damage detection technique complementary to the wave propagation techniques. The mechanical impedance method consists of exciting vibrations of bonded plates using a specialized transducer that simultaneously measures the applied normal force and the induced velocity. The electro-mechanical (E/M) impedance method is an emerging technology that offers distinctive advantage over the mechanical impedance method. While the mechanical impedance method uses normal force excitation, the E/M impedance method uses in-plane strain. The

y = 0.3413e-0.0066x

R2 = 0.9841

y = 0.1643e-0.0056x

R2 = 0.98060

0.02

0.04

0.06

0.08

0.1

0.12

0.14

0.16

0.18

0.2

0 100 200 300 400Distance (mm)

Am

plitu

de (m

V)

AluminumBondExpon. (AluminumExpon. (Bond)

S0 Lamb mode

Outside bond line

Bond line

Figure 9 Attenuation of the S0 Lamb wave mode

traveling outside the bond line and along the bond line

mechanical impedance transducer measures mechanical quantities (force and velocity/acceleration) to indirectly calculate the mechanical impedance, while the E/M impedance active sensor measures the E/M impedance directly as an electrical quantity.

HP4194A Impedance Analyzer

Bondespecim

#1 #2 #3

Aluminum strips Simulated delamination

Epoxy adhesive

PWAS

GPIB

Computer HP4194A Impedance Analyzer

Figure 11 Instrumentation set-up for the E/M impedance method.

The effect of a piezoelectric wafer active sensor affixed to the structure is to apply a local strain parallel to the surface that creates stationary elastic waves in the structure. Through the mechanical coupling between the PWAS and the host structure, on one hand, and through the electro-mechanical transduction inside the PWAS, on the other hand, the drive-point structural impedance is directly reflected into the effective electrical impedance as seen at the active sensor terminals. For this experiment we used the same specimen presented in Figure 5. An HP4194A impedance analyzer was used to measure the E/M impedance signature of the PWAS attached to the structure. Based on initial exploratory tests, the frequency range 650 kHz to 2 MHz was selected. Measurements of the real part of the electromechanical impedance for several sensors were taken. Repeated sampling of the data indicated a stable and reproducible pattern of the impedance spectrum. The results for two measurements are presented in Figure 12.

0

10

20

30

40

50

60

70

80

650 850 1050 1250 1450 1650 1850

Frequency (kHz)

Rea

l Z

a5_650-2000 b5_650-2000

0

10

20

30

40

50

60

650 850 1050 1250 1450 1650 1850

Frequency (kHz)

Rea

l Z

a6_650-2000 b6_650-2000Resonant spectrum for sensor A6 located on the Al plate

Resonant spectrum for sensor B6 located on the bond line

Resonant spectrum for sensor A7 located on the Al plate

Resonant spectrum for sensor B6 located on the bond line

Figure 12 Real part of the electromechanical impedance spectrum

As seen in Figure 12, the resonant spectrum of the sensors placed on the aluminum plate is consistent from one sensor to another and is different from the resonant spectrum of the sensors placed on the bond line. These observations clearly reveal the fact that, as anticipated, the adhesive layer has a big impact on the propagation of the Lamb waves from one aluminum layer to the other. The adhesive layer acts like a damper dissipating part of the wave energy.

0

100

200

300

400

500

600

10 20 30 40 50 60 70 80 90 100Frequency [kHz]

Re

Z, [O

hms]

Response from bonded areas PWAS #1&3

New peaks due to disbonding PWAS #2

Figure 13 E/M impedance spectrum for a lap-joint specimen.

A second lap-joint specimen has been fabricated. Two aluminum strips, 178 x 37 x 1.55 mm, where bonded using an epoxy paste Hysol® EA 9309.3NA. The disbonding of the two aluminum strips was simulated as a discontinuity of the epoxy paste in the middle of the specimen, having the length of 25 mm. Using an HP4194A impedance analyzer the E/M impedance was measured in three locations in the range of 10 ÷ 100 kHz. The real part of the E/M impedance spectrum recorded at the three sensors PWAS #1, PWAS #2, and PWAS #3 is presented in Figure 13. It can be observed that the frequency response is very similar for PWAS # 1&3 which are located on a bonded area, but is different for PWAS #2 located on the disbond. We can clearly see new sharp peaks in the frequency spectrum due to disbond.

5. CONCLUSION

This paper has presented the mechanism through which piezoelectric wafer active sensors (PWAS) can excite and detect guided waves (Lamb waves). It was found that PWAS couple intimately with the surface-motion patterns of the guided Lamb wave traveling in thin-wall structures. The analysis started with a brief description of the PWAS and their ability to work as resonators. Next the coupling between the PWAS and the host structure through the adhesive layer was studied. The analysis was performed in the wavenumber space. The inverse Fourier transform was used to return to the physical space. A general solution was obtained for a generic expression of the interfacial shear stress distribution. It was also shown that based on the response of the strain wave the PWAS transducers are better suited for the excitation and detection of Lamb waves at high frequencies that the conventional ultrasonic transducers. The work presented has shown that PWAS in spite of their small dimensions are suitable for embedded ultrasonic nondestructive evaluation and are capable to excite the structure and generate guided Lamb waves that will travel across the adhesive layer. This emerging technology requires a sustained effort and continue development to achieve its full potential and to be able to be deployed on a full-scale structural health monitoring system.

ACKNOWLEDGMENTS

This material is based upon work supported by the National Science Foundation under Grant # CMS-0408578 and CMS-0528873, Dr. Shih Chi Liu Program Director and by the Air Force Office of Scientific Research under Grant # FA9550-04-0085, Capt. Clark Allred, PhD Program Manager. Any opinions, findings, and conclusions or recommendations expressed in this material are those of the authors and do not necessarily reflect the views of the National Science Foundation or the Air Force Office of Scientific Research.

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