Electromechanical admittance based integrated health monitoring of adhesive bonded beams using surface bonded piezoelectric transducers

International Journal of Adhesion and Adhesives 94 (2019) 84–98

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International Journal of Adhesion and Adhesives journal homepage: www.elsevier.com/locate/ijadhadh

Electromechanical admittance based integrated health monitoring of adhesive bonded beams using surface bonded piezoelectric transducers

T

Mahindra Rautela∗, C.R. Bijudas Department of Aerospace Engineering, Indian Institute of Space Science and Technology, Thiruvananthapuram, 695547, Kerala, India

A R T I C LE I N FO

A B S T R A C T

Keywords: Electromechanical admittance Adhesive joints Integrated health monitoring Piezoelectric transducers Coupled-domain harmonic analysis Artificial neural networks

Adhesive bonded structures are gaining attention in engineering and research communities due to their advantages over conventional joining methods. Non-destructive testing and health monitoring of adhesive bonded structures are challenges requiring focused research. Piezoelectric transducers are used for the actuation and sensing purposes in structural health monitoring procedures. These transducers which are adhesive bonded, get disbonds from the host structure during their service period. Presence of a transducer disbond between the transducer and host structure can be inferred as structural disbond and may produce false alarms. It is necessary that both the types of disbonds are distinguished from each other so that an integrated health monitoring procedure can be developed. This paper presents the use of electromechanical admittance technique for the integrated health monitoring of adhesive bonded beams using surface bonded piezoelectric patches. Electromechanical admittance model for one degree of freedom system is revisited and used as a governing model for the adhesive bonded beams. The analytical results are validated with simulations and experimental results. Conventional non-destructive techniques like X-ray and ultrasonics testing are also employed to justify the use of the electromechanical admittance scheme for disbond detection in the adhesive bonded structures. The electromechanical admittance values (both real and imaginary parts) for three levels of transducer and structural disbonds along with the combination cases are collected from the precision impedance analyzer in a frequency range of 1–30 kHz. Numerical study of coupled-domain harmonic analysis is utilized to study the disbond cases. It is shown that the directional shifting of the electromechanical admittance spectrum distinguishes both the types of disbonds. In addition, artificial neural networks are also employed on electromechanical admittance data from simulations and experiments to predict disbond type and the severity levels.

1. Introduction The electromechanical (E/M) admittance-based structural health monitoring (SHM) method utilizes PWAS (piezoelectric active wafer sensor) transducer to harmonically excite higher modes of vibration of a structure. Higher modes of vibration are much localized and it is easier to detect smaller sized damages. The transducers act as actuators and sensors simultaneously in this procedure. When the PWAS is provided with harmonically alternating voltage, it vibrates (converse piezoelectric effect) and so is the structure (represented in Fig. 1). The vibrational response, which is a characteristic of a particular structure alters the current flowing through PWAS (direct piezoelectric effect). The amount of alteration in the current depends on the mechanical coupling between the PWAS and the structure at different frequencies. This modulation, in turn, changes the E/M admittance of the PWAS. When the external excitation matches with the structural

∗

natural frequencies, the structural displacements shoot up and so is the current flowing through the PWAS. The peaks in the E/M admittance is similar to the peaks in structural response/frequency response function. In short, the E/M admittance of the PWAS mimics the structural dynamic response of the structure. Any damage or delamination introduces a change in the local stiffness due to which natural frequencies of the structure gets modified (natural frequency depends on stiffness). This causes a variation in the E/M admittance w.r.t the undamaged structure. Liang et al. [1]. proposed an analytical expression for the E/M admittance for one degree-of-freedom spring-mass-damper system driven by a PWAS actuator for the determination of the actuator power consumption and the system energy transfer. Chaudhry et al. [2] used the E/M admittance model for the local area health monitoring of brackets connecting a tail section of Piper Model 601P airplane to the fuselage. Frequency range of 100–150 kHz is selected on the basis of factors like

Corresponding author. (Mahindra RAUTELA). E-mail addresses: [email protected] (M. Rautela), [email protected] (C.R. Bijudas).

https://doi.org/10.1016/j.ijadhadh.2019.05.002 Accepted 5 May 2019 Available online 24 May 2019 0143-7496/ © 2019 Elsevier Ltd. All rights reserved.

International Journal of Adhesion and Adhesives 94 (2019) 84–98

M. Rautela and C.R. Bijudas

Fig. 1. Schematic of electromechanical (E/M) admittance based structural health monitoring system. PWAS is excited by providing harmonic voltage using measurement system. The structure to be monitored vibrates and current modulation in PWAS is presented in the form of E/M admittance by the measurement system.

studied the detection of weak adhesive bonds in carbon reinforced polymers using thickness mode of PWAS. The bond is artificially weakened using release agent contamination (RE) using Silicon, moisture absorption (MO) and bad curing temperature (CS). Apart from this aging effect is also included by taking the reading of RE and MO after 18 months. Zhuang, Fotis, Dugnani and Chang [18–21] have studied the bond-line integrity using the embedded PWAS. It is observed that bond-line degradation starts from the ends and reaches towards the center. Theoretical model is constructed and is validated using FEM and experiments. Roth and Giurgiutiu [22] studied adhesive bonds through the E/M impedance based structural health monitoring. Predictive modeling is introduced to find the optimum frequency for the disbond detection. The effect of disbond on the E/M impedance is studied experimentally through an impedance analyzer. Introduction of new peaks in the damaged sample is validated with the FEA and Laser Doppler velocimetry results. Artificial Neural Networks (ANN) has emerged as a powerful tool to predict and classify the faults of machines, equipments and structures. An ANN is a collection of neurons in the form of layers, used to process the incoming data and provide output based on a non-linear function of sum of its inputs. Each connection in the network is randomly assigned with an initial weight and a bias for the neuron. The activation number of the neuron is decided by the weights, biases and the activation of the previous layer. The loss/error between the predicted and the actual output (called cost function) is reduced using gradient descent. The algorithm for computing this gradient efficiently is called back propagation. The weights, biases and the activation are updated while propagating backwards. This process of selecting the best possible weights and bias is called learning. There can be multiple layers of neurons to approximate the required relation between output and input. Basic architecture of artificial neural network is shown in Fig. 2, having X as inputs, Y as outputs and 1 hidden layer of neurons. The output of 1st hidden layer can be expressed mathematically as,

amount of PZT-structure interactions, structural dynamics information and sensitivity towards near field and far field damages. In another work, Chaudhry et al. [3] has focused on debond detection between 12ply composite patch and an aluminum plate using impedance analyzer in a series of frequency intervals. In one section of this work, structural crack growth in dog bone specimen has been detected using thr impedance analyzer in two frequency intervals (10–12 kHz, 18–20 kHz). It is seen that the E/M impedance based method is sensitive to detect minor debonds and crack growth. Giurgiutiu and Rogers [4] have also worked to develop an analytical expression of the E/M admittance using frequency response function (FRF) of axial and flexural vibrations for thin beams. Single input single output FRF of a structure is equivalent to its dynamic mechanical compliance, which is the ratio of the structural response and the forcing function in the frequency domain. Mechanical impedance at a point is the ratio of the applied force and the velocity at that point and mechanical admittance (also called mobility) is the reciprocal of the mechanical impedance. FRF, dynamic mechanical compliance, admittance and impedance of a structure are mathematically complex quantities and their spectra possess similar characteristics. This model is validated with the experimental results on four different kinds of beams, i.e., single thickness narrow beam, double thickness narrow beam, single thickness wide beam and double thickness wide beam [5]. Some other efforts are also put to refine the E/M impedance model [6,7]. The E/M admittance based method is used for the damage detection in circular plates, space structures, aging aircraft panels, FRP reinforced concrete, concrete and excavation structures [8–15]. Sensor integrity plays a vital role in the structural health monitoring approach. Giurgiutiu and Zagrai [16] mentioned the self diagnosis of the PWAS/PZT for the first time. During their service period, there might be disbonding of PWAS from the host structure due to several factors like the loss of adhesion, cracking of hardened adhesive, external loadings, environmental factors like dust, dirt, repeated cycle of heating, cooling, etc. Lead Zirconate Titanate(PZT) is a ceramic which is brittle in nature, any impact on the structure might develop cracks in the PWAS also. There may be false alarms if the sensor diagnostics is neglected. It is shown that the imaginary part of the E/M admittance might be a good indication of the sensor integrity. A free resonance peak is seen at 267 kHz for free-free PWAS which is a measure of a full PWAS disbond. Adhesive bonded structures are gaining attention of engineers/scientists over conventional joining methods. With the introduction of super glues, adhesive bonds possess high strength. Bolted and riveted joints are prone to stress concentration due to the presence of bolt hole or rivet hole. This hole becomes the location of crack origination as well. Adhesive joints have less weight as compared to bolted or riveted joints and are suited for aerospace and automotive applications. Adhesive bonded components develop shearing action from the ends due to which the disbond starts and in the course of time, it reaches towards the center. This makes their health monitoring procedure a difficult task and requires more attention. Malinowski et al. [17] have

Y1 = f1 (W0 + W1T X1)

(1)

where, Y1 is the output matrix, W0 is bias, W1 is the weight matrix, and X1 is the input matrix. The loss or error can be computed mathematically as, n

E=

∑ ( [Ti] − [Y1i]) 1

(2)

where, [Y1] is the output from 1st layer and [T] is the desired output. Lopes et al. [23]. have introduced the artificial neural networks with the E/M impedance technique to study the effect of damages on the E/M impedance. A total of 8 elements (features) are used to train the ANN. These features include both the real and imaginary values for (1) the area between the damaged and undamaged E/M impedance curves, (2) RMS of each curves, (3) RMS difference and (4) the correlation coefficient (CC). The experiments are performed on 1/4 scale steel bridges joints having loosened bolts at different locations near the 85

International Journal of Adhesion and Adhesives 94 (2019) 84–98

M. Rautela and C.R. Bijudas

damages artificial neural network with back propagation is used. Novel use of certain E/M characteristics with ANN is the highlight of the present work. 2. Theoretical background PWAS works on piezoelectric effect. PWAS constitutive equations using 1-D assumptions are given by equation (3) (Actuation equation) and equation (4) (Sensing equation) [9].

S1 = s11E T1 + d31 E3

(3)

D3 = εT33E3 + d31 T1

(4)

where S1 is the mechanical strain, T1 is the mechanical stress, E3 is the electric field, D3 is the electrical displacement, s11E is the mechanical compliance of the material measured at zero electric field (E = 0), εT33 is the dielectric permittivity measured at zero mechanical stress (T = 0), and d31 represents the piezoelectric strain coupling effect. PWAS behavior is modified when it is affixed to a structure. The structure acts as a flexible boundary condition to the PWAS. For a 1D system, kstr is seen as two springs of stiffness 2kstr in parallel at both ends of PWAS. Consider the PWAS having dimensions la, ba , ta (la > ba > > ta ). A harmonic electric field is produced due to application of a harmonic potential difference (Fig. 3) and is assumed to be uniform over the surfaces of the PWAS. The E/M impedance/admittance of PWAS is altered due to the frequency dependent dynamic structural stiffness acting as a boundary condition at both ends. Now, for this case the boundary conditions are not stress free as in the unconstrained PWAS. The motion of PWAS is constraint by the opposing spring force acting on both ends. The boundary conditions at both ends become:

Fig. 2. Basic architecture of artificial neural networks.

4 PZTs. The data processed on ANN is able to detect and localize the damages in 1/4 scale bridge joints. Jiyoung Min et al. [24]. have studied the optimal frequency for damages as well as the damage types and severity using the neural networks due to loosened bolts and notches in lab scale pipe model. The frequency range (10–100 kHz) is divided into nine sub ranges and for each sub-range, five impedance measurements are performed using the impedance analyzer. Temperature compensated correlation coefficient as damage indices are calculated for each range. It is shown that different sub-frequency ranges have different sensitivity towards the damages and changes in the boundary conditions. A neural network is constructed using 9 input nodes, having CC values for nine frequency ranges, 2 hidden layers of 16 and 9 neurons respectively, 4 output nodes consisting the damage type and severity. The neural network is trained for 8 damage cases. The algorithm is run for 30,000 epochs, when error is reduced to 0.001%. Two damages cases are used for validation, which are not used for training. An error of 12.3% and 11.3% is seen, which is considered within limits by the author. Other authors have also made an effort to solve vibration based SHM problem using neural networks [25–28]. The accuracy offered by neural networks in health monitoring ranging from a small data to a very large data is proved to be reliable and promisable. Bonding layer introduces its own stiffness and damping in the system. Any damage to the bonding layer influences the properties of the system. Transducer abnormalities like disbond and crack may interfere with the developed system of detecting the structural disbonds. They can produce false alarms which may force a maintenance stoppage to search for structural disbond/damage, which are not present. If both the types of damages influence the E/M admittance curves in different ways, then a criterion to separate them has to be established. The main objective of the paper is to distinguish the structural damage in the form of a disbond (structural disbond) from the PWAS disbond (transducer disbond) in adhesively bonded beams. The present work aims to achieve this classification using detailed experiments and numerical studies. In order to classify the type and severity levels of

l l T1 ⎛+ a ⎞ ba ta = −2kstr u1 ⎛+ a ⎞ ⎝ 2⎠ ⎝ 2⎠

(5)

l l T1 ⎛− a ⎞ ba ta = 2kstr u1 ⎛− a ⎞ ⎝ 2⎠ ⎝ 2⎠

(6)

Using equation (5), equation (6) and substituting in PWAS constitutive equations (equation (3) and equation (4)) and using straindisplacement relation, we get,

sE l l l S1 ⎛+ a ⎞ = u′1 ⎛+ a ⎞ = −2kstr 11 u1 ⎛+ a ⎞ + d31 E3 ba ta ⎝ 2 ⎠ ⎝ 2⎠ ⎝ 2⎠

(7)

sE l l l S1 ⎛− a ⎞ = u′1 ⎛− a ⎞ = 2kstr 11 u1 ⎛− a ⎞ + d31 E3 ba ta ⎝ 2 ⎠ ⎝ 2⎠ ⎝ 2⎠

(8)

Equilibrium equation in 1-direction along with strain-displacement relation yields axial wave equation

∂2u1 ∂ 2u = c 2 21 2 ∂t ∂x1 where,

c2

=

1 E ρs11

(9) and c is the speed of axial wave.

The general solution of the axial wave equation

Fig. 3. Schematic of PWAS constrained by the presence of structure under electrical harmonic excitation. kstr presents itself in the form of two springs at both ends to constrain the PWAS. 86

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M. Rautela and C.R. Bijudas

u1 (x1, t ) = uˆ (x1) e ιωt

(10)

Table 1 Properties of PZT. [Courtesy: Sparkler ceramics manual].

ω

where, uˆ (x1) = C1 sin γx1 + C2 cos γx1 and γ = c called the wave number. Substituting the boundary conditions (equation (5) and equation (6)) in equation (10) and solving for C1, C2 yields.

1 1 C1 = uISA 2 ϕ cos ϕ + r sin ϕ

(11)

C2 = 0

(12)

Property Elastic Constants

The displacement and strain field (from strain-displacement relation) becomes

uˆ1 (x1) =

sin γx1 1 uISA 2 ϕ cos ϕ + r sin ϕ

Sˆ1 (x1) = SISA

ϕ cos γx1 ϕ cos ϕ + r sin ϕ

where, ϕ =

γl , 2

r=

kstr , kPWAS

kPWAS =

uISA = d31 Eˆ3 la, SISA = d31 Eˆ3

where, k31 =

E εT s11 33

+l /2

ba

∫ −l/2 ∫ 0

where, Anw =

0.36 0.73 3100

7500kg / m3

2 l

, γnu =

(23) nu π , l

ωnu =

E γnu ρ

D3 dx1 dx2

ba la ⎞ ⎟ ta

(17)

(18)

of PZT, and V is the excitation

⎠

The electric current is

Iˆ = ιωQˆ

, ωnw = γn2w

EI ρA

, σnw =

cosh γj l − cos γj l

The dynamic structural stiffness, kstr (ω) could be obtained from frequency dependent single input single output FRF (equation (21)), such that kstr (ω) is the inverse of FRF. The stiffness ratio, r is obtained as k (ω) r = kstr . The PWAS is located at 40 mm from left end. The properties PWAS of steel (E = 220 GPa, μ = 0.3,ζ = 0.01), PWAS is mentioned in Table 1. In order to select the operating frequency range, ϕ cot ϕ and stiffness ratio, r are plotted against the frequency range (Refer Fig. 4 and Fig. 5). It is observed that at lower frequencies ϕ cot ϕ is of order less than 1 whereas stiffness ratio, r reaches above 20. At higher frequencies (nearly 125 kHz–175 kHz), ϕ cot ϕ is varying abruptly from in both negative and positive directions. This nature can introduce complexity in disbond classification at higher frequency range, therefore, lower frequency range is more preferred for disbond classification. Therefore, the frequency range, 1–30 kHz is adopted to use the analytical model for the current work. The E/M admittance is formulated for a certain number of modes

(16)

sin ϕ ⎡ 2 ⎧ ⎞⎫⎤ 1 − ⎜⎛ ⎟ Qˆ = CVˆ ⎢1 − k31 ⎥ ⎨ ϕ cos ϕ + r sin ϕ ⎠ ⎬ ⎝ ⎩ ⎭⎦ ⎣

1

∫ 0l Wn2w (x ) dx

(24)

sinh γj l + sin γj l

3. Analytical results

The displacement terms can be replaced from displacement field (equation),

voltage, Vˆ =

− 265 × 10−12 C/N

Wnw (x ) = Anw [coshγnw x + cosγnw x − σnw (sinhγnw x + sinγnw x )]

u (+la/2) − u1 (−la/2) ⎞ ⎫ ⎤ ⎡ 2 ⎧ Qˆ = εT33Eˆ3 ba la ⎢1 − k31 1 − ⎜⎛ 1 ⎟ ⎥ ⎨ d31 Eˆ3 ⎠⎬ ⎝ ⎩ ⎭⎦ ⎣

Eˆ3 . ta

550 × 10−12 C/N

(15)

called E/M coupling coefficient which is a measure

where, C is the Capacitance (C = εT33

d33 Piezo. coupling coefficient k31 k33

where, Anu =

of the conversion of electrical energy into mechanical energy and vice verse. The electric charge can be obtained by integrating electrical displacement (equation (15)) over the area of electrodes

Qˆ =

15 × 10−12m2/ N

Unu (x ) = Anu cosγnu x

Using both constitutive equations and strain-displacement relation, the electric displacement can be re-written as:

2 d31

21 × 10−12m2/ N

E s33 Piezo. charge coefficient d31

of a beam with a free-free boundary condition is given by equation (23) and equation (24).

(14)

u′1 ⎞ ⎤ 2 ⎛ D3 = εT33Eˆ3 ⎡ ⎢1 − k31 ⎜1 − d31 Eˆ3 ⎟ ⎥ ⎠⎦ ⎝ ⎣

E s11

Dielectric Constant, KT Density, ρ

(13)

ba ta El , s11 a

Value

(19)

and E/M admittance, Y =

Iˆ Vˆ

1 ⎡ 2 ⎧ ⎞⎫⎤ Y = ιωC ⎢1 − k31 1 − ⎜⎛ ⎟ ⎥ ⎨ ϕ cot ϕ + r ⎠ ⎬ ⎝ ⎩ ⎭⎦ ⎣

(20)

On the other hand, the overall frequency response function (FRF) is the summation of axial FRF and flexural FRF assuming beam to follow Euler-Bernoulli assumption.

H (ω) = Hu (ω) + Hw (ω)

(21)

H (ω) =

−Unu (x a) + Unu (x a + la) 1 ⎡ h 2 +⎛ ⎞ ⎢∑ 2 2 ρA nu ωnu + 2ιζωnu ω − ω ⎝2⎠ ⎣

∑ nw

−W ′nw (x a) + W ′nw (x a + la) ⎤ ⎥ ωn2w + 2ιζωnw ω − ω2 ⎦

(22) Fig. 4. Variation of ϕcotϕ and r in low frequency range (1 kHz- 30 kHz).

The mode shapes for axial (Unu (x ) ) and bending vibration (Wnw (x ) ) 87

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M. Rautela and C.R. Bijudas

Table 2 Properties of adhesive (Araldite). [Courtesy: Hunstman Araldite 2011-A/B manual]. Property

Value

Young's modulus Poison's Ratio Density

2 GPa 0.361 1200 kg / m3

Lap shear strength at different cure temperature (max. τ lap at t = 50–100 mm and 1:1 ratio of resin and hardener) 25degC for 8 h 25degC for 24 h 70degC for 1 h. 100degC for 10 min.

4.9 MPa 14.7 MPa 21.5 MPa 25.5 MPa

between 1 and 30 kHz, i.e, 1 axial (26.23 kHz) and 6 transverse bending modes (1.6 kHz, 4.44 kHz, 8.703 kHz, 14.3 kHz, 21.4 kHz, 30 kHz). The real and imaginary part of E/M admittance spectrum are shown in Fig. 6 and Fig. 7.

Fig. 5. Variation of ϕcotϕ in high frequency range (2 kHz-250kHz).

4. Experimental study 4.1. Specimen preparation Steel beams having dimensions 100 mm × 8 mm × 1.5 mm, Young's modulus of 200 GPa and Poisson's ratio 0.3 are used for the experiments and the simulations. Two steel beams are bonded using a commercially available epoxy based adhesive called Araldite. Most adhesives are viscoelastic in nature but when cured and hardened, they behave as a linear elastic isotropic material [17–22]. However, more accurate results can be obtained by using viscoelastic models. SP-5H ferroelectric PZTs are used and are bonded on double thickness steel beam using Araldite (Properties of PZT and Araldite is shown in tbl1Tables 1 and 2tbl2). A total of 10 specimen are prepared for 10 study cases (Table 3). PZT of dimensions 7 mm × 7 mm × 0.5 mm is bonded at 40 mm from left end. The snapshot of all specimen is shown in Fig. 9. 32 steel beams are cut from a steel plate of 1.5 mm thick and finished to remove any protrusions. The beams are placed in isopropyl alcohol/acetone for 1 h to remove any oil and dirt from the surfaces. The surfaces are wiped out with cotton. Sand paper is used to introduce roughness at 40 mm so that the PWAS could be easily bonded. The preparation of specimen took several attempts. Three different methods are tried in order to introduce beam and transducer disbond. Shaving blades of thickness 50 μm and different widths (according to the amount of disbond) are introduced between the beam and both the beams are held using a bench vise at first. After 3 h, blades are pulled out from the beams using pliers and then held between clips, then

Fig. 6. Real Part of analytical EMA model for constrained PWAS.

Table 3 10 Modeled cases of PZT disbond. beam disbond and their combinations.

Fig. 7. Imag. Part of analytical EMA model for constrained PWAS.

88

Case

Features

1 2

Pristine beam l 4

Quarter PZT disbond ( a )

3

Half PZT disbond

4

Three quarter PZT disbond (

5

la 2

6 7 8

la Beam disbond 2la Beam disbond

9

Quarter PZT disbond

12

Half PZT disbond ( a ) + la Beam disbond

l ( a) 2

3la ) 4

Beam disbond

l 4 l ( a) 4

Quarter PZT disbond ( a ) +

l 2

la 2

Beam disbond

+ la Beam disbond

International Journal of Adhesion and Adhesives 94 (2019) 84–98

M. Rautela and C.R. Bijudas

Fig. 8. Schematic representation of pristine case and two types of disbonds: PWAS disbond and Beam disbond.

4.2. Non-destructive testing 4.2.1. X-ray radiography X-Ray Radiography is performed on the specimen using 450 kV Xray tube made by VARIAN medical systems. Both views, side and the top view of 15 samples are irradiated with X-Ray at 80–120 kV. It is seen that X-rays are able to penetrate the steel without any additional attenuation/energy loss from the structural disbond. This is due to the lower thickness of disbonds. A small central patch of different contrast is seen in sample no. 9 in Fig. 10. This is due to the presence of a broken shaving blade at that position for the specimen no. 9. The PWAS is only

Fig. 9. All sixteen experimental beam specimen: Two beams are joined by an adhesive layer including PWAS attachment on the surface by the adhesive. Disbonds are introduced in both the layers to form different cases.

beams are allowed to keep curing for minimum of 1 day. After curing, the surface are wiped out using acetone. PWAS is bonded at 40 mm in the same way but using Teflon sheets of different widths. The schematic of three cases is shown in Fig. 8 whereas all specimen are presented in Fig. 9. PWAS is placed only on 10 specimen. The thickness of adhesive layer plays an important role. The thickness of the adhesive should be small in order to reduce the shear lag effect but on the other hand, maximum shear lap strength is achieved when adhesive (Araldite) thickness approaches 50 μm –100 μm range [Huntsman Araldite 2011-A/B Manual]. It is essential to measure the adhesive thickness in order to validate analytical and experimental results. A microscope with automatic base to move the lens to new positions is utilized to visualize and measure the adhesive thickness through a computer display. The adhesive thickness of all samples is collected at different locations. The mean thickness of the adhesive between the beams is measured around 35 μm and between beam and PWAS, it is around 15 μm .

Fig. 10. X-ray Radiography (from top) using X-ray tube made by VARIAN medical systems at 120 kV. 89

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bonded on sample 1 at that time and it's impression is visible in the Xray radiograph along with it's wires. 4.2.2. Ultrasonic testing Ultrasonic pressure waves are sent from the top surface of the beam. If there is a damage, an extra reflection (called new echo) is seen on the screen. Three kinds of ultrasonic testing is performed i.e., linear array, phased array, air-coupled automated C-scan. Omniscan MX2 manufactured by OLYMPUS is used for the phased array study. In phased array, the bottom surface of the ultrasonic transducer has multiple piezo elements (10–128 elements). These are excited in a pattern so that the ultrasonic waves can be propagated at angles also without moving the probe. But the size of probe available is 10 mm which is more that 8 mm (width of beam) and creating difficulty in disbond detection. SONDA Airscan from QMI is used for ultrasonic C-Scan. Aircoupled Ultrasonic C-Scan testing is automated using some hydraulic actuators. The ultrasonic transmitter and the receiver are adjusted parallel to each other and specimen is placed in between. Both transmitter and receiver are hydraulically moved vertically and horizontally. This method is unable to detect any damage due to air coupling as well as big sizes of the transmitter and the receiver. Immersion coupling with high frequency and phased array transducer might detect such small disbonds [29]. The transducer size of manual linear array ultrasonic testing is 6 mm. Omniscan MX2 from OLYMPUS is used at High-Pass 10 MHz frequency. The transducer of UT is moved on the surface of the beam. It is observed that at every location there are a lot of intermediate peaks. These reflections are due to bottom surface of the beam-1, top surface of bonding layer, bottom surface of the bonding layer, top surface of the beam-2 and bottom surface of the beam-2. It is summarized that UT is not able to detect adhesive disbonds in beam/plates having very low adhesive thickness with the available setup of straight linear ultrasonic probes.

Fig. 12. Pictorial representation of experimental set-up.

4.3. Precision impedance analyzer Fig. 13. Real EMA for Case-1 (experimental-pristine).

Impedance analyzer provides a constant voltage signal (in our case, +1 Vrms) at a selected frequency. Real and imaginary parts of the steady state current are recorded at that frequency. The frequency is incremented and the process is repeated up to the end frequency. The real and imaginary part of the current is converted into electrical admittance or impedance and presented in the E/M admittance vs frequency or E/M impedance vs frequency plots. The impedance analyzer has very low impedance (25 Ω) which is obvious for an impedance measuring device [30]. In our study, HP-4294A precision impedance analyzer is used having frequency range of 5 Hz–40 MHz (See schematic of experimental setup in Fig. 11 and snapshot in Fig. 12). E/M admittance plots in the form of real part (conductance) and imaginary part (susceptance) is collected for a total of 12 cases from impedance analyzer. E/M admittance spectrum is shown in Fig. 13 to Fig. 20. It is observed from Figs. 15 and 16 that as the level of

Fig. 14. Img. Ema for Case-1 (experimental-pristine).

transducer disbond is increased, baseline slope of E/M admittance curves (both real and imaginary) are shifted upward but peaks remained at their respective locations. This behavior is more dominant in the imaginary part (see values on Y axis for both graphs) (see Fig. 14). On the other hand, with an increase in the level of structural disbond, some of the peaks are shifted from their position but with a less

Fig. 11. Schematic of experimental setup (impedance analyzer). 90

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Fig. 18. Img. EMA for Case-5,6,7 (experimental-Beam disbond). Fig. 15. Real EMA for Case-2,3,4 (experimental-PWAS disbond).

Fig. 19. Real EMA for Case-8,9,12 (experimental-combinations). Fig. 16. Img. EMA for Case-2,3,4 (experimental-PWAS disbond).

Fig. 20. Img. Ema for Case-8,9,12 (experimental-combinations). Fig. 17. Real EMA for Case-5,6,7 (experimental-Beam disbond).

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coupled node is grounded. PWAS is excited with a sweep harmonic signal from 2 to 30 kHz. Damping is not modeled in the current study. After the analysis, electric charge is collected from the top electrode and E/M admittance is calculated for all the 16 cases. It is seen from Fig. 23 and Fig. 24 that peaks are on their respective positions but the baseline slope is shifted upward. The slope shifts are more visualized in imaginary part as compared to the real part. On the other hand, slope change is not observed but peaks are shifted from their original positions in Fig. 25 and Fig. 26. In order to observe both peaks positions and the slope more closely, column bar chart is used for peak position (See Fig. 27) and plot for slope changes (See Fig. 28). It is evident from Fig. 27 that the peak shifts are insignificant for the case of transducer disbonds (case 2 to case 4) but for the structural disbonds (case 5 to case 7) significant peak shifts are seen. The combination case of transducer disbond with structural disbond has a peak shift similar to the case of structural disbond (Case 2 has same peak frequency as that of Case-8, 11, 14). New peaks are produced for Case 3 and Case 4, referred to as peak int 1 = 14.980 kHz and peak int 2 = 6.880 kHz in Fig. 29. These intermediate peaks are also seen when combination cases of case-3 and case-4 are considered (i.e, in Case 11,12,13 and Case 14,15,16). The intermediate peaks also shifted in the combination cases depending on the amount of the structural disbond. The slope change is dominant for the cases of transducer disbond but for pure structural disbond cases, it is similar to the pristine case. The slope change is insignificant when pure transducer disbond is compared to their combination cases in Fig. 28. Such intermediate peaks are not seen in the experimental study.

extent without any significant change in the baseline slope (Figs. 17 and 18). It is seen from the combination case (Figs. 19 and 20) that the slope of the imaginary part remains unchanged for red and green plots (both La/4 PWAS disbond) but significant slope change is seen in blue curve (Case 9: La/4 - PWAS disbond & La - Beam disbond) as compared to the other two. 5. Numerical study In this study, ANSYS APDL-18.1 platform is used for the finite element analysis. Electrical and structural domains are utilized simultaneously, therefore, called coupled-domain analysis. 8-noded SOLID 185 3D-element is used to model the adhesive and the beam having 3° of freedom (Translation in 3 directions: UX, UY, UZ) at each node whereas 8-noded SOLID5 element is used to model the PWAS. The element has 6-DOF at each node (UX, UY, UZ, TEMP, VOLT, MAG). The steel beam as well the adhesive is modeled as isotropic materials whereas PWAS is defined as a transversely isotropic material. The thickness of the adhesive are taken as 15 μm and 35 μm for PWAS-beam and beam-beam interface respectively. The dimensions, properties of steel, adhesive and PWAS are taken as mentioned in experimental study. 5.1. FEM- PWAS with beam Sixteen cases are modeled considering different levels of PZT disbond and beam disbonds (a structural damage) including one undamaged case. If the length of the PWAS is La , then PWAS disbonds of La /4, La /2,3La /4 and beam disbonds of La /2, La , 2La along with the combinations of both the disbonds are modeled. These sixteen cases are mentioned in Table 4. The pictorial representation of the three cases is shown in Fig. 8. Modal analysis is the preliminary step for any dynamics analysis. In this work, Block Lanczos scheme is utilized to numerically solve for modal frequencies and mode shapes. Modal frequencies and mode shapes for the pristine case from 2 to 30 kHz are shown in Fig. 21. First transverse bending mode at 1.6 kHz died out in EM admittance response in analytical (Fig. 6) and experimental results (Fig. 13). Therefore, it is taken out of the current frequency range in the numerical study. Coupled field harmonic analysis (structural and electric) is performed in ANSYS APDL-18.1. VOLT degree of freedom of PWAS is coupled at a single node for top and bottom surfaces (See Fig. 22). The top coupled node of the PWAS is provided with +1 Vrms and bottom

5.2. FEM-PWAS without beam In order to observe the intermediate peaks, E/M admittance of a free PZT and PZT with boundary conditions La/4 fixed, La/2 fixed, 3 La/4 fixed and fully fixed on one surface are modeled (See Fig. 29). It is seen in Fig. 30 that as the disbond is increased from La/4 to 3La/4, the free vibration response becomes more prevalent (8-peaks in 3La/4 disbond, 5-peaks in both La/2 and La/4 disbonds). This is due to the vibration cantilever action of PWAS disbond. This action is more rigorous at higher disbonds. This study unearthed a new way of detecting the amount of PWAS disbond. The introduction of these peaks in the E/M admittance spectrum is also visualized in Fig. 27. A lot of the peaks are seen before the resonance peak of the free-PWAS (175 kHz) but peaks at 100 kHz and 45 kHz corresponding to the La/2 debond and 3La/4 disbond respectively in Fig. 31 are of major concern. When the PWAS is fully fixed, no peaks are observed at the lower frequency range since it is constrained to produce any planar motion but at 1.278 MHz thickness mode begins to appear. A fixed boundary condition on the bottom surface of the PWAS instead of placing the PWAS on to a structure is a different way of looking EM admittance spectrum but both are similar in some sense. A structure is a flexible entity having some kstr (ω) associated with it whereas a fixed boundary condition produces kstr (ω) = ∞. But Fig. 30 is useful in a sense that it has given an indirect insight about the new peaks which would also be present when the PWAS is attached to the structure. The only difference is that intermediate/new peaks are shifted to higher frequencies in the presence of the fixed boundary condition. Taking this into account, peak at 100 kHz in La/2 PWAS disbond corresponds to an intermediate peak of 14.98 kHz (blue bar) and small peak at 45 kHz corresponds to an intermediate peak at 6.88 kHz (maroon bar) in Fig. 27.

Table 4 16 Modeled cases of PZT disbond. beam disbond and their combinations. Case

Features

1 2

Pristine beam

3

Half PZT disbond ( a )

4

Three quarter PZT disbond (

l 4

Quarter PZT disbond ( a ) l 2

5

la 2

6 7 8 9 10 11 12 13 14 15 16

la Beam disbond 2la Beam disbond Case-2 + Case-5 Case-2 + Case-6 Case-2 + Case-7 Case-3 + Case-5 Case-3 + Case-6 Case-3 + Case-7 Case-4 + Case-5 Case-4 + Case-6 Case-4 + Case-7

3la ) 4

Beam disbond

5.3. FEM-PWAS cracking Effect of PWAS cracking on the E/M spectrum is also simulated in ANSYS APDL-18.1. The PWAS is cracked from center till half of its thickness (See Fig. 32). The E/M admittance curves for PWAS cracking is presented in Fig. 33 and Fig. 34. The slope of both real and imaginary 92

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Fig. 21. Frequencies and Modes shapes from 2 kHz to 30 kHz for pristine beam.

Fig. 22. FE model (a) meshed model (b) VOLT dof of top and bottom nodes are coupled.

Fig. 23. Real EMA for Case-1,2,3,4 (FEM-PWAS disbond).

Fig. 24. Imag. EMA for Case-1,2,3,4 (FEM-PWAS disbond).

curves reduce w.r.t pristine curve but resonance peak remains at their respective positions. The effect of slope change is more dominant in imaginary part. The sharpness of the resonance peaks is reduced with the cracking.

propagation [31] is used to classify two most common types of disbonds in adhesive bonded structures i.e, transducer disbond and structural disbond. The algorithm is written in PYTHON script. The E/M admittance spectrum data from simulations (15 disbonding cases, 1 pristine case, 1400 features for each) and experiments (9 damage cases, 1 pristine, 801 features for each) is processed in two different ANNs. Two real numbers allotted to each case are the amount of both disbonds respectively. For example, Case 1 - Pristine: Transducer disbond (TD) = 0, Structural disbond (SD) = 0, Case 2: La/4 Transducer

6. Artificial neural networks approach for disbond type and severity Artificial

neural

network

(ANNs)

with

probabilistic

back 93

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Fig. 28. Baseline slope of Img EMA spectrum for all simulation cases.

remaining 1-data set for the simulations (Case 7). ANN on simulation results are shown in Table 5. On the other hand, 9 × 801 input nodes (9 cases); a hidden layer of 16 neurons with 100 epochs is used to train ANN on experimental results. Validation is done for 1 data set (Case 2). ANN on experimental results are shown in Table 6. It is seen from Tables 5 and 6 that R2 coefficient, which is a statistical measure of the data fit in regression problem, is near to 91.5% whereas, mean square error is nearly 5.4% for simulations.

Fig. 25. Real EMA for Case-1,5,6,7 (FEM-BEAM disbond).

7. Discussions All three results (analytical, simulations and experiments) are compared in order to prove the validity of the results. No damage based analytical model is presented, therefore, all the three results are first compared for pristine case in Fig. 35 and Fig. 36. The peaks in the E/M admittance spectrum corresponds to the modal frequencies. The corresponding mode shapes are presented in Fig. 21. There are a total of 6 dominant peaks in Fig. 35. Peaks nearly at 4.5 kHz, 8.5 kHz, 14 kHz, 21 kHz, 26 kHz, 28.5 kHz (at 30 kHz in analytical results) corresponds to 2nd, 3rd, 4th, 5th, 1st axial mode, 6th transverse bending modes respectively. No peaks are seen for lateral bending and torsional modes. The E/M coupling is absent due to the lack of piezoelectric coefficient in those directions. Resonance peaks in the simulations and the experimental results are matched closely in Figs. 35 and 36. Structural damping of steel is modeled in the analytical formulation. The damping due to the presence of the adhesive is not considered in the analysis due to its limited influence in the peak locations. The resonance peaks in experimental spectrum is smaller as compared to the analytical and the experimental results. The damping effect might also be responsible for the little peak shifts in both the simulation and the experimental results. The small mismatch between simulations and experimental results might be due

Fig. 26. Imag EMA for Case-1,5,6,7 (FEM-BEAM disbond).

disbond, TD = 0.25, SD = 0, Case 5: La/2 Structural disbond, TD = 0, SD = 0.5 etc. An input matrix of 15 × 1400 nodes (15 cases), a hidden layer of 64 neurons with 40 epochs is used to train the neural network on the results obtained from the FEM simulations. Validation is done on the

Fig. 27. Resonance frequency vs simulation cases for different peaks (shown by color bars). (For interpretation of the references to color in this figure legend, the reader is referred to the Web version of this article.) 94

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Fig. 29. FEM-PWAS model without beam with different boundary conditions on bottom surface (free PWAS, 3 La/4 fixed, La/2 fixed, La/4 fixed, fully fixed PWAS).

Fig. 31. EMA spectrum of FEM-PWAS model without beam-Zoomed In view (1–150 kHz).

Fig. 30. EMA spectrum of FEM-PWAS model without beam for different B.C (1–500 kHz).

to the self-impedance of impedance analyzer. Other factors like thickness of adhesive layer, temperature dependence of PWAS, self-impedance of impedance analyzer etc. might have also caused such variations. But these variations are under limit. The last resonance peak in analytical spectrum is neither matching with the numerical results nor with the experimental results (30 kHz in analytical and 28.5 kHz in experiments and simulations). The shifts are due to the 1-DOF assumption in E/M admittance model. Both the bonding layers are not incorporated into the analytical model. The model is simplified with a beam and a PWAS on it. Adhesive has a low thickness due to which the shear lag effect is not considered in the model. The change in the Young's modulus of the beam is insignificant with the introduction of lower modulus thin layer of adhesive. These three reasons might be responsible for the peaks mismatch. The simplified analytical model is working well at lower modes but there is a mismatch at higher modes.

Fig. 32. Centrally cracked PWAS FE model.

95

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Table 6 Results of ANN on experiments, T-Training, V-Validation. Cases

Actual TD

Actual SD

Predicted TD

Predicted SD

T-7 T-5 T-6 T-1 T-9 T-3 T-8 T-12 T-4 V-2

0 0 0 0 0.25 0.5 0.25 0.5 0.75 0.25

2 0.5 1 0 1 0 0.5 1 0 0 0.8453

0.0022 0.0012 0.0035 −0.0044 0.3581 0.3611 0.3431 0.3894 0.7551 0.3145 Mean sqr error

1.9864 0.5699 0.9356 −0.0041 0.6067 0.6040 0.6208 0.5966 0.0266 0.6319 0.0421

R2 coeff.

Fig. 33. Effect of PWAS cracking on Real EM admittance w.r.t pristine (FEM).

Fig. 35. Comparison of analytical, simulations and experimental results of E/M admittance real part for pristine case.

Fig. 34. Effect of PWAS cracking on Img EM admittance w.r.t pristine (FEM). Table 5 Results of ANN on simulations, T-Training, V-Validation. Cases

Actual TD

Actual SD

Predicted TD

Predicted SD

T-16 T-9 T-1 T-15 T-14 T-3 T-12 T-4 T-6 T-10 T-13 T-5 T-2 T-8 T-11 V-7

0.75 0.25 0 0.75 0.75 0.5 0.5 0.75 0 0.25 0.5 0 0.25 0.25 0.5 0

2 1 0 0.5 1 0 1 0 1 2 2 0.5 0 0.5 0.5 2 0.9147

0.7572 0.2637 0.0157 0.7458 0.7495 0.4836 0.5021 0.7448 0.0483 0.2728 0.5138 0.0281 0.2290 0.2446 0.4905 0.0578 Mean sqr error

1.3833 0.9425 −0.0101 1.0423 0.9229 0.0223 1.0025 0.3480 0.9686 2.0299 2.0019 0.4420 0.1005 0.4688 0.5136 0.8431 0.0548

R2 coeff

Fig. 36. Comparison of analytical, simulations and experimental results of E/M admittance imaginary part for pristine case.

for beam disbond the peaks shift leftwards. This shift is more visualized in the imaginary part as compared to the real part. When there is a structural damage (in the form of disbond here), the localized stiffness of the structure reduces. The natural frequency depends on the stiffness, therefore, it is reduced which caused the peaks shift to lower frequencies (leftward shift). Stiffness ratio term, ‘r’ in E/M admittance formulation (equation (20)) is responsible for this shift. Equation-20 is

In order to obtain good results at higher frequency range, it is necessary to incorporate the effect of bonding layer in the analytical model. It is explained earlier in experimental and numerical study that for transducer disbond, the E/M admittance curves shift upward whereas 96

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Fig. 40. Comparison of analytical, simulations and experimental results of E/M admittance imag. part for CASE-2.

Fig. 37. Effect of k31 on the real part of EMA.

plotted for 4 different values of k31 in Fig. 37 and Fig. 38. The upward shifts in the baseline slope with insignificant peak shifts as’k31’ is varied from 100% (no PWAS disbond) to 25% (3La/4 PWAS disbond) which corresponds to degradation in the E/M coupling between the host structure and the PWAS. This change is more evident in the imaginary case as compare to the real case. It can be related that’k31’ is responsible for upward shifts of baseline slope due to the PWAS disbond. The analytical model is updated with’k31’ variations and used for comparison purpose. Analytical, simulations and experimental results for La/4 transducer disbond is compared in Fig. 39 and Fig. 40. All the peaks are present in all the three results except for the last peak (6th transverse bending mode) which is absent or died out in the experimental results and more distant in analytical results. The 6th transverse bending mode is appeared for pristine case in Figs. 35 and 36. The axial mode at 21 kHz is appeared dominantly in experimental results. When there is a crack in PWAS, the amount of charge accumulation and collection is reduced, in turn, the electrical capacitance is degraded. It is seen from Fig. 34 that the curve is shifted in downward direction in the presence of a crack in the PWAS. The downward shift is caused due to the loss of capacitance (‘C’ term) in the E/M admittance formulation. It is seen from the ANN based damage detection scheme that the damage detection, severity and classification are predicted on a higher extent even with a lack of sufficient amount of data. On the other hand, R2 coefficient is 84.5% and mean square error is 4.2% for the experiment. Case 7 is used for validation of ANN on simulation data as shown in Table 5. The desired value set is [TD, SD] = [0, 2] whereas, [0.05, 0.843] is predicted by ANN. Case 2 is used for validation of ANN on experimental data as shown in Table 6. The desired value set is [0.25 0] and the predicted value set is [0.3144, 0.6310]. Both validation cases are able to detect the disbond with limited accuracy for severity prediction. The accuracy in the experimental results may be influenced by the lack of data. Only three levels of damage severity for each disbond is processed in ANN. The data can be used to predict disbond classification. For [0.05, 0.843] value, it should lie in Case-6 or Case-7 whereas, [0.3144, 0.6310] should lie in Case-7 or Case-8.

Fig. 38. Effect of k31 on the imag. part of EMA.

8. Conclusions Fig. 39. Comparison of analytical, simulations and experimental results of E/M admittance real part for CASE-2.

It is found that the 1-DOF analytical model works well for the low frequency modes but finds it difficult to predict higher modes accurately. Conventional non-destructive techniques are not robust enough to detect disbonds in adhesive bonded structures. It is concluded from the analytical, experimental and numerical results that both the types of 97

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disbonds can be distinguished from each other. PWAS disbond causes an increase in the baseline slope of the imaginary part of E/M admittance spectrum. On the other hand, the resonance peaks of the spectrum shift leftward in the presence of a beam disbond. It is seen that both the disbonds are uncoupled in the low frequency range, so, it is easier to classify the disbonds even in combination case situations. Peak splitting, new peaks and sharp peaks are some additional features for disbond detection. Artificial neural networks have demonstrated that disbond classification can be effectively achieved. A large amount of data in real time can improve the efficiency of damage detection using artificial neural networks further. Extending the technique to plates with minimum amount of sensors incorporating the uncertainties in damage sizes, locations and properties is an area for future research work.

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