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Applied Composite Materials

Low-velocity impact-induced delamination detection by use of the S0 guided wavemode in cross-ply composite plates: a numerical study

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Manuscript Number:

Full Title: Low-velocity impact-induced delamination detection by use of the S0 guided wave

mode in cross-ply composite plates: a numerical studyArticle Type: Original Research

Keywords: Fiber-reinforced plastic composites . Guided waves . Asymmetric delamination . Finiteelement method . Material damping

Corresponding Author: khazar hayatHanyang University

Ansan-si, Gyeonggi-do KOREA, REPUBLIC OF

Corresponding Author SecondaryInformation:

Corresponding Author s Institution: Hanyang University

Corresponding Author s SecondaryInstitution:

First Author: khazar hayat

First Author Secondary Information:

Order of Authors: khazar hayat

Sung Kyu Ha, PhD

Order of Authors Secondary Information:

Abstract: Finite element method based numerical simulations are performed to identify low-velocity impact-induced asymmetrically-located delamination in the [0/903]S and[0/90]2S composite plates, respectively, using a fundamental symmetric guided wavemode (S0). The wave attenuation effect due to the viscoelasticity of the compositematerial is modeled by calculating the Lamb wave attenuation constants and using theRayleigh proportional damp-ing model. The estimated sizes and locations of thedelamination in both plates were in good agreement with the experimentalmeasurements. Moreover, the analysis of wave structure of the impacted plates showsthat when the S0 mode propagates through the damaged region, the delaminationmouth opens up due to the presence of standing waves, which are generated as aconsequence of multiple reflections of trapped waves with the delaminationboundaries.

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Low-velocity impact-induced delamination detection by

use of the S 0 guided wave mode in cross-ply composite

plates: a numerical studyK. Hayat . S. K. Ha

Department of Mechanical Engineering, Hanyang University #1271, Sa1-dong, Ansan, Kyunggi-do, 425-791South Korea

e-mail: hayatkhaza@hanyang.ac.kr, sungha@hanyang.ac.kr

Tel.: +82-31-400-4066, Fax.: +82-407-1034

Abstract Finite element method based numerical simulations are performed to identify low-

velocity impact-induced asymmetrically-located delamination in the [0/90 3]S and [0/90] 2S

composite plates, respectively, using a fundamental symmetric guided wave mode (S 0). The

wave attenuation effect due to the viscoelasticity of the composite material is modeled by

calculating the Lamb wave attenuation constants and using the Rayleigh proportional damp-

ing model. The estimated sizes and locations of the delamination in both plates were in good

agreement with the experimental measurements. Moreover, the analysis of wave structure of

the impacted plates shows that when the S 0 mode propagates through the damaged region, the

delamination mouth opens up due to the presence of standing waves, which are generated as a

consequence of multiple reflections of trapped waves with the delamination boundaries.

Keywords Fiber-reinforced plastic composite, guided waves, delamination, finite element

method.

Introduction

Due to their high specific strength, low density, and corrosion resistant properties, fiber-

reinforced plastic (FRP) composite materials are considered to be promising structural mate-

rials. However, it is also well known that these composite materials are prone to damage

caused by accidental impact during manufacturing, assembly, handling, and transportation

because of their low transverse strength. Depending on the impact velocity, the damage can

be in the form of compressive strength reduction, matrix cracking, fiber breakage or delami-

nuscriptck here to download Manuscript: L ow-velocity impact-induced delamination cetection by use of the S0 guided wave mode in cross-k here to view linked References

mailto:hayatkhaza@hanyang.ac.krmailto:hayatkhaza@hanyang.ac.krhttp://www.editorialmanager.com/acma/viewRCResults.aspx?pdf=1&docID=2647&rev=0&fileID=26492&msid={364518E2-D09C-422F-B6B6-9F7FF51D953D}http://www.editorialmanager.com/acma/download.aspx?id=26492&guid=29aff0aa-bc05-46ca-be4c-a82d98286f7e&scheme=1http://www.editorialmanager.com/acma/viewRCResults.aspx?pdf=1&docID=2647&rev=0&fileID=26492&msid={364518E2-D09C-422F-B6B6-9F7FF51D953D}http://www.editorialmanager.com/acma/viewRCResults.aspx?pdf=1&docID=2647&rev=0&fileID=26492&msid={364518E2-D09C-422F-B6B6-9F7FF51D953D}http://www.editorialmanager.com/acma/download.aspx?id=26492&guid=29aff0aa-bc05-46ca-be4c-a82d98286f7e&scheme=1mailto:hayatkhaza@hanyang.ac.kr

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nation. High velocity impact damage is visible and can be identified by visual inspection.

However, low velocity impact damage, which often manifests as delamination, has a high

rate of occurrence and appears in a subsurface. Contrary to symmetric delamination occurring

near the mid-plane of a composite plate, asymmetric delamination, which is near the plate

surface, is particularly dangerous because it can easily cause buckling under compressive

loads. Moreover, asymmetrical delamination is hard to identify using conventional ultrasonic

normal-incidence pulse-echo techniques because of its location near the structure surface.

Several non-destructive inspection (NDI) techniques such as X-ray or ultrasonic C-scan

are available to identify low-velocity impact-induced delamination in a plate-like composite

structure; however, the inspection process is tedious, costly, and time consuming in large

structures such as composite wind turbine blades. NDI methods based on guided waves have

the potential for long-range inspection of the composite structures. Guided waves are known

to travel long distances, covering large cross-sectional areas of a structure, and to provide in-

formation regarding its integrity. The wave features change as the propagating waves interact

with the defects and geometrical attributes of the structure.

Researchers have used fundamental symmetric (S 0) and anti-symmetric (A 0) guided

wave modes, and the changes in the wave features (e.g., time of flight (TOF) and wave am-

plitude attenuation to determine the size and location of the damages in the composite plates

[1-11] . Guo and Cawley successfully used the reflection of the S 0 mode to locate the delami-

nation in the cross-ply composite laminates and observed that the amplitude of the S 0 mode

reflection from a delamination is strongly dependent on the delamination location across the

thickness of the laminate [1] . For delamination located symmetrically across the thickness, no

reflection was observed because of the zero shear stress at that delamination interface. Tan et

al. [2] showed S 0 mode amplitude reduction during scanning over delamination for the unidi-

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rectional carbon composite plate. The amplitude attenuation occurs mainly due to the local

stiffness reduction at the damaged region. A quick inspection technique for carbon composite

plates using S 0 mode was presented by Toyama et al. [3] . The proposed damage detection

technique is based on the changes in the wave velocity and the amplitude over the delamina-

tion region. A similar study was also reported for glass composite plates [4] . The time-of-

flight (TOF) and the reflection coefficients of the A 0 and S 0 modes in the pulse-echo configu-

ration were used by Hu et al. [5,6] for delamination detection of the composite laminates. It

was found that the A 0 mode is more effective than the S 0 mode for short length delamination

located near the mid-plane of the laminates. Ramdas et al. studied the interaction of the A 0

mode with symmetric and asymmetric delamination in the composite plates and proposed a

methodology to detect the size of delamination without requiring a base-line signal from

healthy laminates [10,9,11] .

Apart from these experiments, the researchers have also used numerical simulations to

study the propagation of the guided waves and their interaction with the defects in the com-

posite structures. Hayashi et al. [12] studied multiple reflection at the delamination edges

for the cross-ply laminates using a strip element method (SEM). The investigation of the in-

fluence of the delamination size and location on the wave propagation in a cantilever multi-

layer beam using the spectral finite element method (SFEM) was reported in [13] . Studies

of the interaction of the A0 mode with delamination and associated mode conversion using

the finite element method (FEM) have been presented in [10,9,11] .

One of the main difficulties involved in simulations of guided wave propagation in fiber

reinforced composites is the modeling of the wave attenuation caused by the material s vis-

coelastic nature. Many authors [5,4,8,10,9,11,6 ,13-15 ,12 ,16,17 ,1] have performed numerical

work either to compare numerical predictions with experimental findings, and/or to investi-

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gate the guided wave propagation in plate type structures, but without modeling the material

damping effect, which is a major source of attenuation of the propagating waves in the com-

posite media. For metallic structures, the material damping effect is small and can be neglect-

ed; however, it becomes significant for the FRP composite materials [18] and should be in-

cluded in simulations. For effective implementation of the NDI technique, numerical simula-

tions with material damping incorporated can better assist understanding of the propagation

of guided waves. Therefore, in the present work, the FEM simulations with material damping

incorporated are carried out to detect and size the low-velocity impact-induced asymmetrical

delamination in the [0/90] 3S and [0/90 2]S composite plates, respectively, using the propagat-

ing S 0 mode. Moreover, the complex interaction of the S 0 mode with the delamination is also

investigated.

This paper begins with a brief discussion of the numerical simulation of the wave propaga-

tion problem, followed by study of the S 0 mode propagation in an isotropic aluminum plate to

verify the FEM approach. Numerical simulations of guided wave propagation in the intact

and impacted cross-ply composite plates are then carried out. This section also includes in-

formation regarding the calculation of Lamb wave attenuation constants (LACs), which are

used together with the Rayleigh proportional damping model to implement the material

damping effect. In the results and discussion sect ion, a comparison of the results from simula-

tions (with and without material damping incorporated) and from experiments is presented,

followed by estimation of the delamination size and its front-end location. At the end of this

section, the delamination response to the passing S 0 mode and the delamination mouth-

opening phenomenon due to the presence of standing waves is described. Finally, the conclu-

sions and future work are presented.

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Numerical Simulation of Guided Wave Propagation

Guided waves require structural boundaries for their propagation. There are two distinct

families of guided wave modes in plate-like structures: symmetric (S n) and anti-symmetric

(An), where n denotes the wave mode order. Due to their frequency dependence nature during

propagation, the dispersion curves are drawn showing the relationship between the wave

mode group velocities (Cg) and the product of the frequency and plate thickness ( fd ). At the

lower values of fd (< 1 MHz-mm), only the fundamental symmetric S 0 and anti-symmetric A 0

modes exist, with the S 0 mode being relatively less dispersive and having high group velocity

than the A 0 mode [5,3 ,18] . More detailed explanation of guided wave propagation theory and

dispersion curve plots for plate-like structures can be found in Ref. [18] .

The guided wave propagation in a structure depends on the excited wave mode and its ex-

citation frequency. In this numerical study, the fundamental S 0 mode is selected to identify

the asymmetrical delamination in the [0/90 3]S and [0/90] 2S composite plates, respectively.

The excitation frequency of the S 0 mode is 0.3 MHz. The motivation behind the selected

mode, excitation frequency, and cross-ply composite plates, is the experimental results re-

ported by Toyma et al. describing low velocity impact-induced delamination detection in

cross-ply composite plates (i.e. [0/90 3]S and [0/90] 2S) using the S 0 mode excited at 0.3 MHz

[3] . Another reason is to compare the numerical results with the experimental measurements

and then further use the FE model to investigate the propogating S 0 mode interaction with the

delamination.

In order to invoke the S 0 mode in the plates, a sinusoidal excitation signal s(t) of five cy-

cles with a central frequency of 0.3 MHz enclosed by the Hamming window is used. The ex-

citation signal s(t) can be described by

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sin(2 )[0.54 0.46cos(2 / )] /( )

0 /

ft ft N t N f s t

t N f

(1)

where f (in Hz) is the central excitation frequency, and N is the number of cycles within the

excitation signal.

For modeling the guided wave propagation in an elastic medium, the spatial and temporal

resolution of the finite element domain becomes critical for the convergence and accuracy of

the numerical results. For proper spatial resolution, the finite element size should be l e min

/20, where min is the minimum wavelength of the propagating guided wave mode, estimated

from min = C L / f max , where C L is the bulk longitudinal wave speed in the propagating medium.

For temporal resolution, the time step size should be t min( l e /C L, 1/(20 f max)) , where f max is

the highest frequency of interest, as recommended in Refs. [19,16] . The numerical simula-

tions are performed using a commercial finite element package ABAQUS EXPLICIT for

modeling the propagation of the S 0 mode excited at 0.3 MHz. In this paper, for all the simula-

tion cases, the finite element size of the discretized domain was 0.134 mm in the direction of

wave propagation, and 0.5 mm in the transverse direction of wave propagation, and the time

step size used was 110 -8 sec, which satisfies both the spatial and temporal resolution re-

quirements.

Modeling of the Guided Wave Propagation in an AluminumPlate

To validate the finite element modeling approach for the guided wave propagation prob-

lem, a numerical study is first performed for the S 0 mode travelling in an isotropic plate. An

aluminum plate (Al 6061-T6), under plane strain conditions ( z = 0), having length L = 500

mm and thickness d = 2 mm was modeled. The material properties used were Youngs mod u-

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lus E = 70.7 GPa, Poissons rati o = 0.3, and the bulk longitudinal wave speed at C L = 6313

m/sec. The excitation signal s(t) , described by Eq. (1), was applied in terms of an arbitrary

nodal displacement in region r of the plate (representing the transmitter position). The result-

ant propagating S 0 mode is observed at the nodal position A (at a distance of 90 mm) and

nodal position B (at a distance of 300 mm) away from the transmitter region, as shown in Fig.

1.

The wave structure of the aluminum plate is then analyzed by measuring the in-plane and

out-of-plane nodal displacements ( u and w, respectively) across the plate thickness at section

B- B at a distance of 300 mm from the excitation region. Fig. 1(d) shows that the S 0 mode

cannot be simply considered as a pure in-plane vibration mode; rather, it is a combination of

both u and w that varies across the plate thickness. Furthermore, the normalized magnitude of

u is relatively higher than that of w for an fd value of 0.6 MHz-mm. This observation is gen-

erally true for low values of fd (< 1 MHz-mm) and is consistent with findings described in

Ref. [18] .

The both in-plane and out-of-plane nodal displacements can be used to represent the prop-

agating S 0 mode. However, in-plane nodal displacement, due to its relatively higher magni-

tude, is selected for estimation of the S 0 mode velocity. As illustrated in Fig. 1(c), the wave

form of the S 0 mode observed at nodal positions A and B remains nearly unchanged, which

represents its low dispersion characteristic. The S 0 mode velocity is calculated by dividing the

travelled distance X AB = 210 mm by the difference in arrival times of the first peak of the S 0

mode arriving at the nodal positions A and B. The calculated group velocity is 5398 m/sec,

comparable to the group velocity of 5363 m/sec estimated from the plotted dispersion curve

for the aluminum plate, shown in Fig. 1(b). This result confirms that the given excitation sig-

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nal s(t) , applied as an arbitrary in-plane displacement, invokes the S 0 mode, and the observed

propagating mode is, indeed, the S 0 mode.

Fig. 1 (a) S0 mode excitation in an aluminum plate, (b) dispersion curve plot, (c) the measurement of S 0 mode

velocity, and (d) In-plane u and out-of-plane w displacements across plate thickness

Modeling of the Guided Wave Propagation in the Cross-ply

Composite Plates

Composite material attenuation

Guided waves attenuation is caused by the geometry and material damping of the elastic

media. For the geometric attenuation, no energy dissipates, and it occurs when a propagating

wave mode interacts with the geometrical attributes of a damage region and/or the end

boundary of a plate. However, the material attenuation is associated with the wave energy

dissipation, and is inherently present in all structures. In the composites, the material attenua-

tion causes a significant reduction in the guided wave amplitude and becomes no longer neg-

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ligible [18] . It is strongly dependent on factors such as the viscoelastic behavior of the matrix,

the properties of the constituent layers, the fiber direction and the stacking sequence. The ef-

fect of the material attenuation can be incorporated into the simulations by using the Rayleigh

proportional damping model available in ABAQUS [20] :

c m k (2)

Eq. (2) shows that the material damping coefficient c can be described by a linear combina-

tion of the mass m and the stiffness k along with the relevant mass and stiffness proportionali-

ty constants ( and , respectively). For modeling the material attenuation effect caused by

the viscoelastic behavior of the composites, both and should be known. Ramadas et al. [7]

showed that these proportionality constants can be expressed in terms of the attenuation coef-

ficient, group velocity, and the central excitation frequency. It is called the Lamb wave A t-

tenuation Constants (LACS) and is described below:

2w w w2 ; /i g k C (3)

where C g is the group velocity of the propagating mode, is the angular frequency of excita-

tion, and k i is the viscoelastic material attenuation coefficient.

The propagating mode group velocity in a composite plate can be determined if the ply-level

properties, the stacking sequence, and direction of the Lamb wave is known. The value of k i

is evaluated from the experiment using the following relation [7] :

1 2 1 2/ exp( ( ))i A A k x x (4)

where A1 and A2 are the amplitudes of the propagating wave mode observed at positions x1

and x2, respectively.

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FEM Simulations of Guided Wave Propagation in the Cross-ply Composite

Plate

In this work, we simulated the experimental results describing the delamination detection

caused by low-velocity impact using the S 0 mode excited at 0.3 MHz in the [0/90 3]S and

[0/90] 2S carbon fiber-reinforced ( T800H/3631) composite plates (each 300 mm 15 mm

1.072 mm) as reported by Toyama et al. [3] . The detected delaminations were of elliptical

form (i.e. 45mm 28 mm for the [0/90 3]S plate and 60 mm 12 mm for the [0/90] 2S plate,

respectively) with their major axis oriented along the 0 o fiber direction, for more detail see

[3] .

To avoid the high computational cost associated with modeling of the entire plate domain,

a volume of 300 mm 15 mm 1.072 mm was modeled with 3-dimensional solid finite ele-

ments, and the appropriate boundary conditions were applied. The element type used was

CP3D8R, which is an 8-node, linear brick element with reduced-integration and hour-glass

control, available in ABAQUS [20] . The FE models used for analysis of the S 0 mode propa-

gation in the cross-ply composite plates, before and after impact, are shown in Fig. 2(a-b). It

should be noted that the propagation direction of the S 0 mode is along the 0 o fiber direction of

the [0/90 3]S and [0/90] 2S plates .

It is well-known that a low-velocity impact causes a major delamination at the lowest ply

interface away from the impact side, and such a delamination has an elliptical form with its

major axis oriented along the fiber direction as analytically and experimentally reported in

Refs. [21-26] . Therefore, the delamination in each plate is modeled only at the lowest ply-

interface, and damage at the other interfaces is ignored. Using symmetry conditions, the size

(ab/2 ) of the modeled delamination is 45 mm 14 mm for the [0/90 3]S plate and 60 mm 6

mm for the [0/90] 2S plate, respectively. The center of the delamination is positioned at the

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distance X= 130 mm, which is consistent with the experiment described in Ref. [3] . The de-

lamination is modeled by de-merging the local nodes in the delaminated region (i.e., generat-

ing zero-volume delamination). The inner mating surfaces at the delamination were defined

with a hard contact pressure over-closure relationship using the default master-slave algo-

rithm in ABAQUS [20] . The FE model of the impacted plates having elliptical delamination

is shown in Fig. 2(b).

Fig. 2 FE model for S 0 mode propagation in (a) the intact and (b) the impacted cross-ply composite plates, re-

spectively

In order to excite the required S0 mode, a sinusoidal signal s(t) , described by Eq. (1), is ap-

plied at region r , in terms of arbitrary in-plane nodal displacement. The length of the excita-

tion region r is 25 mm, approximately the size of the piezoelectric element of the Panametric

V414-SB angle beam transducer used in the experiment [3] . The propagating S 0 mode is then

observed in the form of the in-plane displacements u at 21 nodes, each 10 mm apart, covering

the plate inspection length of 210 mm in the x-direction.

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Free boundary conditions are imposed for sides FG,EH and v(y) = x = z = 0 for sides EF ,

GH , where v(y) is the nodal displacement in the y-direction and x and z are the rotational

degrees of freedom about the x and z-axes, respectively. The mechanical properties of a uni-

directional T800H/3631 ply are used, with the longitudinal modulus E 1= 157.6 GPa, trans-

verse modulus E 2 = 8.67 GPa, shear modulus G12 = 3.83 GPa, Poissons ratio v = 0.38, ply

thickness t ply = 0.134 mm and density = 1571 Kg/m3 [3] .

For modeling the material damping effect of [0/90 3]S and [0/90 2]S plates, the LACs values

are need. These can be expressed in terms of the central excitation frequency f , S 0 mode

group velocity C g and the viscoelastic material attenuation coefficient k i. The value of cen-

tral frequency is 0.3 MHz. The C g values are estimated from the dispersion curves of the

propagating S o mode through the composite plates, and are 5424 m/sec for the [0/90 3]s plate

and 7304 m/sec for [0/90 2]S plate, respectively (see Fig. 8). The k i values are determined us-

ing Eq. (4), and the experimental results are shown in Fig. 3.

Fig. 3 The normalized amplitude of the propagating S 0 mode measured during experiment for the intact [0/90 3]S

and [0/90] 2S plates [3]

The estimated k i value is 5.25 Nepers per meter (Np/m) for the [0/90 3]S plate and 3.17 Np/m

for the [0/90] 2S plate. Using Eqs. (3) and (4), the calculated LAC values ( w /2, w/2), which

are used as inputs to the Rayleigh proportional damping model, are (28,471 rad/s and 8.01e-9

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s/rad) for the [0/90 3]S plate and (23,183 rad/s and 6.53e-9 s/rad) for the [0/90] 2S plate, re-

spectively.

Results and discussion

Effects of composite material attenuation

During the simulation, the first peak arrival time and the maximum amplitude of the

propagating S 0 waveform in the cross-ply composite plates are observed. Fig. 4 (a-b) illus-

trates the waveform of the S 0 mode travelling through the intact [0/90 3]S and [0/90] 2S plates,

respectively, observed at a distance of 150 mm away from the excitation region. The dash-dot

line describes the case without material damping, and the solid line describes a case with ma-

terial damping incorporated. It can be clearly seen that a significant reduction in the maxi-

mum amplitude of the waveform (approx. 61% for [0/90 3]S plate and approx. 37% for

[0/90] 2S plate, respectively, at a distance of 150 mm away from excitation region) occurs for

the damping case. However, the first peak arrival time of the waveform remains unchanged.

Fig. 4 Effect of material damping on the S 0 mode amplitude for the intact: (a) [0/90 3]S plate, (b) [0/90] 2S plate,

respectively

The distribution of the normalized maximum amplitude of the S 0 mode observed from simu-

lation (with and without material damping) and those experimentally measured for the intact

plates (i.e. [0/90 3]S and [0/90] 2S ) is shown in Fig. 5(a-b). The normalized maximum ampli-

tude of the propagating waveform along the inspection length of the plate decreases gradually

as the distance from the excitation region increases. Since the wave attenuation is strongly

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dependent on the directional stiffness properties of the plate, the wave attenuation rate ob-

served in the [0/90 3]S plate is higher than that of the [0/90] 2S plate. It can be seen that the

simulation results without material damping incorporated significantly deviate from the ex-

perimental measurements. However, when the material damping effect is included, good

agreement is found between the simulation and the experiment results for both the plates.

Since the material damping causes a considerable amplitude reduction for composites, simu-

lation of the NDI technique using the change in the amplitude of the propagating mode to

identify the delamination should include the material damping effect.

Fig. 5 Normalized maximum amplitude of the S0 mode observed from simulation and measured from experi-

ment for the intact plates: (a) [0/90 3]S and (b) [0/90] 2S , respectively

Velocity increment at delamination

To study the effect of delamination on the propagating S 0 mode, the waveform signal

is observed at a distance of 170 mm and 210 mm away from the excitation region along the

plate length, as illustrated in the schematic of Fig. 6(a). For the intact [0/90 3]S plate, the S 0

waveform observed at a distance of 170 mm, is well maintained, see Fig. 6(b). However, for

the impacted [0/90 3]S plate the S 0 waveform at a distance of 170 mm is no longer preserved;

see Fig. 6(c). The observed waveform is well-attenuated due to the local stiffness reduction

caused by the presence of asymmetrical delamination. It consists of two wave packets. The

leading wave packet shows the transmitted S 0 signal through the delaminated 0 o layer (i.e.,

the region below the delamination) that arrives earlier due to the velocity increase. The cause

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of the velocity increase at the delaminated 0 o layer is its high fiber direction stiffness as com-

pared to the rest of plate (i.e. the region above the delamination). The following wave packet

corresponds to the transmitted signal through the region above the delamination. Both wave

packets begin to comingle with the passage of time at a distance away from the delamination,

as shown in Fig. 6(c). Similar waveform responses are also observed for the S 0 mode propa-

gating in the intact and impacted [0/90 2]S plate, but are not described here for brevity .

Fig. 6 (a) The schematic of observed propagating S 0 mode waveform in the composite plate; The waveform

results for the [0/90 3]S plate (b) the intact case observed at 170 mm, and (c-d) for impacted case at observed 170

mm and 210 mm away from the excited region, respectively

Estimation of the delamination length and location

The velocity increase at the delamination region causes a decrease in the arrival time of the

S0 mode for the impacted plate, and provides information regarding the length of the delami-

nation present in that plate, which can be calculated from the following relation [3] :

0 0/ ( )i ia V V V V t (5)

where t is the difference in the arrival times of the first peak of the S 0 waveform propagating

in the intact and impacted plates, and V 0 and V i are the S 0 mode wave velocities in the delam-

inated 0 o layer and the intact plate, respectively.

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The S 0 mode wave velocities for the delaminated 0 o layer, intact [0/90 3]S and [0/90] 2S

plates are determined in order to establish the baseline data. For each plate, the arrival times

of the first peak of the transmitted waveform are determined at the nodes 30-150 mm away

from the transmitter in steps of 30 mm. The wave velocities are calculated from dividing the

travelled distances of the S 0 mode by the relevant time durations. The average estimated value

is then taken as the S 0 mode velocity in the relevant plate. The propagating wave velocities of

the intact plates corresponding to an fd value of 0.3 MHz-mm are also determined from the

dispersion curves shown in Fig. 7. There is a good agreement between the S 0 mode velocity

observed from FE simulations, the plotted dispersion curves, and the experiment, as shown in

Table 1.

Table 1 Measurement of the S 0 mode velocity for the intact T800H/3631 cross-ply plates

Plate type

Wave velocity (m/sec) observed from

FEM simulation dispersion curves plots Experiment [21]

0o layer 10058 10820 10144

[0/90 3]S 5385 5424 5420

[0/90] 2S 7317 7304 7344

Fig. 7 Dispersion curve plots for the 0 o delaminated layer, [0/90 3]S and [0/90] 2S plates, respectively

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Table 2 Measurement of delamination length

Plate typeFirst peak arrival time ( sec ) Delamination length (mm)

Intact case Delaminated case FEM simulation Experiment [21] [0/90 3]S 39.5 35.8 42.9 42

[0/90] 2S 29.6 27.4 59.1 61

After estimating the arrival time of the first peak of the transmitted S 0 waveform observed

at a distance of 210 mm away from the excitation region for intact and impacted plates, the

delamination length a is then calculated using Eq. (5), and is shown in Table 2. It can be seen

that the length of the delamination present in each impacted plate is well-predicted by the

FEM-based numerical simulations.

For estimation of the delamination of the front-edge location, the normalized amplitude of

the transmitted S 0 mode is observed along the inspection length of the impacted plates. Fig. 8

shows the distribution of the normalized maximum amplitude of the S 0 mode observed from

the simulation with damping incorporated and from experiment [3] for the impacted plates.

Good agreement can be seen between the simulation results for the impacted plates

with material damping incorporated and the experiment measurements. As the distance from

the excitation region increases, the normalized amplitude of the S 0 mode gradually decreases.

However, a sudden drop in the amplitude occurs while reaching the delamination region,

which is then approximately maintained even beyond the delamination region. The distance

at which the amplitude transition occurs indicates the location of the delamination front-end.

The estimated front-end locations from the simulation, with material damping incorporated,

are approximately 10.83 cm and 10.5 cm away from the excitation region for the impacted

[0/90 3]S and [0/90] 2S plates, respectively, which are consistent with the experimental results

[3] .

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The sudden drop in the amplitude over the delamination area can be partly attributed

to wave scattering at the delamination boundaries, wave reflections at the edges, and mode

conversion to generate extra modes. The S 0 mode propagation depends on the fd value of a

plate, and at the delamination region it is subjected to travel through two layers of different

thicknesses with an interfacial discontinuity between them. Consequently, the energy of the

transmitting S 0 mode is divided, also causing amplitude reduction at the delamination.

Fig. 8 Comparison of the normalized maximum amplitude of the S 0 mode observed from simulation with

damping implemented and from the experiment [3] for the impacted plates: (a) [0/903]

S and (b) [0/90]

2S plates,

respectively

Delamination mouth opening

In order to understand the delamination response during the passing of the S 0 mode, the

wave structure of the impacted plates is analyzed. The transmitted and reflected modes repre-

sented by S 0T and S 0R , respectively, are observed in the form of an in-plane and out-of-plane

nodal displacement time histories at node A on the top edge BC and at node A on the bottom

edge DE of the plate at section A- A (across the middle of delamination) as shown in Fig. 9

(a). Although both nodes A and A are located at the same distance of 130 mm away from the

excitation region but the in-plane displacement histories for the [0/90 3]S plate and the [0/90] 2S

plate, as illustrated in Fig. 9 (b-c) and Fig. 9 (f-g) respectively, shows that the transmitted S 0T

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mode arrives earlier at the bottom node A than at the top node A due to the velocity increase

at the 0 o delaminated layer. The estimated arrival time reduction due to the velocity increase

for the [0/90 3]S plate and the [0/90] 2S plate is approximately 3 sec and 5.8 sec , respective-

ly. The arrival time reduction for the [0/90] 2S plate is larger than the [0/90 3]S because the 0 o

delaminated layer length for the [0/90] 2S plate is higher than that of [0/90 3]S.

Due to the complex interaction between the passing S 0 mode and the boundaries of

the delamination region, several extra modes can be generated. Hu et al. [6] showed that

when the S 0 mode passes through a delamination, four modes are generated at each delami-

nation end (i.e., the front and rear ends): two transmitted modes and two reflected modes. In

this work, to identify the generated modes the in-plane nodal displacement histories are used.

Several modes are generated in the presence of delamination. The amplitude of the generated

modes lowers not only because of the material damping, but also due to the reduced localized

stiffness at the damage area. Moreover, wave overlapping makes it hard to clearly isolate and

identify the generated modes at the delamination boundaries. Only the S 0R mode generated

due to the reflection of the transmitted S 0T mode from the plate rear-end, is identified. The

mode identification is done based on the group velocity estimated from the dispersion curves

and the time of flight (TOF) of the propagating modes. The transmitted S 0T mode and the re-

flected S 0R mode generated from the plate rear-end reflection for [0/90 3]S and [0/90] 2S plates

are shown in Fig. 9 (b-c) and Fig. 9 (f-g), respectively.

The out-of-plane displacement histories observed at section A- A were found to be more

useful in gaining insight on the delamination response to the passing S 0 mode. During propa-

gation of the S 0 mode, the delamination mouth is observed to open due to upward defor-

mation of region A and downward deformation of region B, as illustrated in Fig. 9 (d-e) for

the [0/90 3]S plate and Fig. 9 (h-i) for the [0/90] 2S plate. The delamination mouth remains open

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even after the passage of the S 0 mode. This transverse deformation can be attributed to the

reduced local bending stiffness at the delamination region. For both plates, region B experi-

ences more transverse deflection than region A because the bending stiffness of region B is

lower than that of region A. In case of the [0/90] 2S plate, there is excessive transverse deflec-

tion owing to the delamination length of 61 mm, in comparison to the [0/90 3]S plate where

the delamination length of 45 mm is present.

The delamination mouth is kept open after the passage of the S 0 mode because of the pres-

ence of standing waves, which are generated by the superposition of waves travelling in op-

posite directions and are described by the following equations [27] :

1 2( , ) cos( ); ( , ) cos( ),u x t A t kx u x t B t kx (6a)

1 2( , ) ( , ) ( , )

2 cos( )cos( ) ( ) cos( ),2 2

u x t u x t u x t

B kx t A B t kx

(6b)

where the term u(x,t) shows the superposition of waves u1(x,t) and u2(x,t) travelling in oppo-

site directions with amplitudes A and B, respectively; and k are the frequency and wave-

number, respectively, of the travelling waves, is the arbitrary phase, t and x represent time

and space coordinates and x is the zero-shifted coordinate given by x = x + /(2k ). The first

term of Eq. 6(b), containing cos( k x ) cos( t+ /2), describes the standing wave and the se-

cond term, containing cos( t - k x + /2) , is for the residual travelling wave.

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Fig. 9 (a) Schematic of the impacted plate with the top node A and bottom node A at section A -A ; In-plane

and out-of-plane displacement time histories for (b-e) the [0/90 3]S plate and (f-i) the [0/90] 2S plate, respectively

When the S 0 mode reaches the delamination region, it is bifurcated and propagates through

regions A and B independently, see Fig. 9 (a). A portion of the transmitted waves is reflected

from the delamination rear-end, which then travels back and is reflected again at the delami-

nation front-end. Due to multiple reflections at the delamination boundary, some part of the

wave energy is captured inside the delamination zone, resulting in the generation of standing

waves. The presence of these standing waves keeps the delamination mouth open. This effect

dissipates with the passage of time as the wave energy leaks out of the delamination bounda-

ries. Fig. 10 shows the out-of-plane nodal displacement observed along the plate-edges BC

(top edge) and DE (bottom edge) at 100 sec, long after the passage of the S 0 mode. It clearly

shows that the delamination mouth, which opened during the passing of the S 0 mode is still

open because of the presence of standing waves.

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Fig. 10 Observed out-of- plane nodal displacement at 100 s ec, showing the delamination mouth opening for the

impacted plates: (a) [0/90 3]S and (b) [0/90] 2S , respectively

Practically, this opening of the delamination mouth can be helpful for the identification of

subsurface delaminations using non-contact methods such as scanning laser vibrometry using

a laser vibrometer which is device widely used for vibration measurements in many

engineering applications [28] . In addition, the waveform signals from the laser vibrometer

can be processed further to obtain the guided wave field image of the composite structure to

locate the asymmetrical delamination.

Conclusions

In this study, the composite material damping for the [0/90 3] S and [0/90] 2S plates is

effectively implemented in the numerical simulations using the Rayleigh damping model and

estimating the Lamb wave attenuation constants. The material damping causes considerable

wave attenuation of the propagating S 0 mode, and should be modeled in the simulations.

There is a good agreement between the distribution of the normalized maximum amplitude of

the S 0 mode along the plate length observed from simulation for the intact and impacted

[0/90 3]S and [0/90] 2S plate with material damping incorporated and the experiment measure-

ments.

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From the numerical simulations carried out in this paper, the estimated asymmetric

delamination length and its front edge location for both [0/90 3]S and [0/90] 2S using the S 0

mode also matches well with the experiment. The delamination length is estimated from the

S0 mode velocity increment in the 0 o delaminated layer present at the delamination region for

the impacted [0/90 3]S and [0/90] 2S plates, respectively. The wave velocity increases in the 0 o

delaminated layer due to its higher fiber directional stiffness than the rest of the plate. The

delamination front-edge location is determined from the sudden drop in the amplitude of the

S0 mode over the delamination region.

The wave structure analysis of the impacted composite plates shows the presence of

extra generated modes due to the interaction of the propagating S 0 mode with delamination

boundaries and plate ends. However, only the S 0R mode generated from the reflection of the

transmitted S 0T from the plate rear-end is identified using the TOF method. Other generated

modes are not identified either because of complicated wave overlaps or/and their low ampli-

tude as the material damping is incorporated in the simulations. Moreover, during the passing

of S 0 mode the mouth of the asymmetrical delamination in the [0/90 3]S and [0/90] 2S

composite plates opens up due to the reduced local bending stiffness. The delamination

mouth is kept open even after the passage of the S 0 mode because of the presence of standing

waves, which are generated from multiple reflections of the wave energy captured in the de-

lamination zone when the S0 mode passes through.

Future work will be focused on the study of the mouth opening of delamination oc-

curring at other ply interfaces in the composite plates with different layup sequences, during

the passing of the S 0 mode.

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References

1. Guo, N., Cawley, P.: The interaction of Lamb waves with delaminations in compositelaminates. The Journal of the Acoustical Society of America 94 , 2240 (1993).

2. Tan, K.S., Guo, N., Wong, B.S., Tui, C.G.: Experimental evaluation of delaminations incomposite plates by the use of Lamb waves. Composites science and technology 53 (1), 77-84 (1995).

3. Toyama, N., Takatsubo, J.: Lamb wave method for quick inspection of impact-induceddelamination in composite laminates. Composites science and technology 64(9), 1293-1300 (2004).

4. Ramadas, C., Hood, A., Padiyar, J., Balasubramaniam, K., Joshi, M.: Sizing ofdelamination using time-of-flight of the fundamental symmetric Lamb modes. Journal of

Reinforced Plastics and Composites 30 (10), 856-863 (2011).5. Hu, N., Li, J., Cai, Y., Yan, C., Zhang, Y., Qiu, J., Sakai, K., Liu, Y., Peng, X., Yan, B.:

Locating Delamination in Composite Laminated Beams Using the A 0 Lamb Mode.Mechanics of Advanced Materials and Structures 19(6), 431-440 (2012).

6. Hu, N., Shimomukai, T., Yan, C., Fukunaga, H.: Identification of delamination position incross-ply laminated composite beams using S 0 Lamb mode. Composites science andtechnology 68 (6), 1548-1554 (2008).

7. Ramadas, C., Balasubramaniam, K., Hood, A., Joshi, M., Krishnamurthy, C.V.: Modellingof attenuation of Lamb waves using Rayleigh damping: Numerical and experimentalstudies. Composite Structures 93 , 2020-2025 (2011).

8. Ramadas, C., Balasubramaniam, K., Joshi, M., Krishnamurthy, C.: Numerical andexperimental studies on propagation of A 0 mode in a composite plate containing semi-infinite delamination: Observation of turning modes. Composite Structures 93(7), 1929-1938 (2011).

9. Ramadas, C., Balasubramaniam, K., Joshi, M., Krishnamurthy, C.: Interaction of guidedLamb waves with an asymmetrically located delamination in a laminated composite plate.Smart Materials and Structures 19 , 065009 (2010).

10. Ramadas, C., Janardhan Padiyar, M., Balasubramaniam, K., Joshi, M., Krishnamurthy,C.: Delamination Size Detection using Time of Flight of Anti-symmetric (A o) and ModeConverted Ao mode of Guided Lamb Waves. Journal of Intelligent Material Systems andStructures 21 (8), 817-825 (2010).

11. Ramadas, C., Balasubramaniam, K., Joshi, M., Krishnamurthy, C.: Interaction of the primary anti-symmetric Lamb mode (A o) with symmetric delaminations: numerical andexperimental studies. Smart Materials and Structures 18 , 085011 (2009).

12. Hayashi, T., Kawashima, K.: Multiple reflections of Lamb waves at a delamination.Ultrasonics 40 (1), 193-197 (2002).

8/11/2019 ACMA-S-13-00078

27/28

13. Palacz, M., Krawczuk, M., Ostachowicz, W.: The spectral finite element model foranalysis of flexural-shear coupled wave propagation. Part 2: Delaminated multilayercomposite beam. Composite Structures 68 (1), 45-51 (2005).

14. Hayashi, T.: Guided wave animation using semi-analytical finite element method. In:

Proceedings of the 16th World Conference on Nondestructive Testing (WCNDT),Montreal, Canada 2004

15. Hayashi, T., Rose, J.L.: Guided wave simulation and visualization by a semi-analyticalfinite element method. Materials evaluation 61 (1), 75-79 (2003).

16. Moser, F., Jacobs, L.J., Qu, J.: Modeling elastic wave propagation in waveguides with thefinite element method. NDT AND E INTERNATIONAL 32 , 225-234 (1999).

17. Cho, Y., Rose, J.L.: A boundary element solution for a mode conversion study on theedge reflection of Lamb waves. The Journal of the Acoustical Society of America 99 ,

2097 (1996).18. Rose, J.L.: Ultrasonic waves in solid media. Cambridge University Press, (1999)

19. Bartoli, I., Marzani, A., Lanza di Scalea, F., Viola, E.: Modeling wave propagation indamped waveguides of arbitrary cross-section. Journal of Sound and Vibration 295 (3-5),685-707 (2006).

20. Abaqus User's Manual, Version 6.10.

21. Aslan, Z., Karakuzu, R., Okutan, B.: The response of laminated composite plates underlow-velocity impact loading. Composite Structures 59 (1), 119-127 (2003).

22. Choi, H.Y., Chang, F.K.: A model for predicting damage in graphite/epoxy laminatedcomposites resulting from low-velocity point impact. Journal of composite materials26 (14), 2134 (1992).

23. Choi, H.Y., Downs, R.J., Chang, F.K.: A new approach toward understanding damagemechanisms and mechanics of laminated composites due to low-velocity impact: Part I experiments. Journal of composite materials 25 (8), 992 (1991).

24. Jih, C.J., Sun, C.T.: Prediction of delamination in composite laminates subjected to lowvelocity impact. Journal of composite materials 27 (7), 684 (1993).

25. Li, C.F., Hu, N., Cheng, J.G., Fukunaga, H., Sekine, H.: Low-velocity impact-induceddamage of continuous fiber-reinforced composite laminates. Part II. Verification andnumerical investigation. Composites Part A: Applied Science and Manufacturing 33 (8),1063-1072 (2002).

26. Li, C.F., Hu, N., Yin, Y.J., Sekine, H., Fukunaga, H.: Low-velocity impact-induceddamage of continuous fiber-reinforced composite laminates. Part I. An FEM numericalmodel. Composites Part A: Applied Science and Manufacturing 33 (8), 1055-1062 (2002).

8/11/2019 ACMA-S-13-00078

28/28

27. Sohn, H., Dutta, D., Yang, J.Y., Park, H. J., DeSimio; M., Olson, S. Swenson, E.:Delamination detection in composites through guided wave field image processing.Composites science and technology 71 , 1250-1256 (2011).

28. Staszewski, W., Lee, B., Mallet, L., Scarpa, F.: Structural health monitoring using

scanning laser vibrometry: I. Lamb wave sensing. Smart Materials and Structures 13 , 251(2004).