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A new nonlinear elastic time reversal acoustic method forthe identification and localisation of stress corrosion cracking

in welded plate-like structures A simulation study

G. Zumpano a, M. Meo b,*

a Department of Engineering, Cambridge University, Trumpington Street, Cambridge CB2 1PZ, UKb Department of Mechanical Engineering, University of Bath, Bath BA2 7AY, UK

Received 21 February 2006; received in revised form 29 June 2006; accepted 11 October 2006Available online 17 October 2006

Abstract

In order to reduce the costs related to corrosion damage in aircraft structures, it is vital to develop new robust, accurateand reliable damage detection methods. A possible answer to this problem is offered by newly developed nonlinear ultra-sonic techniques, which monitors the nonlinear elastic wave propagation behaviour introduced by damage, to detect itspresence and location.

In this paper, a new nonlinear time reversal technique is presented for the detection and localization of a scattered zone(damage) in a multi-material medium. In particular, numerical findings on a friction stir-welded aluminium plate-likestructure are reported. Damage was introduced in the heat affected zone and modelled using a multi-scale material con-stitutive model (PreisachMayergoyz space).

Studies were conducted for two different transducer configurations. Particular attention was devoted to find the opti-mum time-reversed window to be re-emitted in the structures. The methodology was compared with traditional time-re-versal acoustics (TRA), showing significant improvements. While the traditional TRA was not able to clearly localisethe damage, the developed technique identified in a clear manner the faulted zone, showing its robustness to locate andcharacterize nonlinear sources, in presence of a multi-material medium. 2006 Elsevier Ltd. All rights reserved.

Keywords: Time-reversal acoustics; Stress-corrosion cracking; PM space; Nonlinear elastic wave spectroscopy

1. Introduction

Stress corrosion cracking (SCC) is cracking due to a process involving conjoint corrosion and straining of ametal due to residual or applied stresses (Cottis, 2000). SCC of in-service components has long been majorconcern for safety, operation time loss and material maintenance cost in major industries such as chemical(Rihan et al., 2005), nuclear power (Takaya and Miya, 2005; Yusa et al., 2005), aeronautic (Eliaz et al.,

0020-7683/$ - see front matter 2006 Elsevier Ltd. All rights reserved.

doi:10.1016/j.ijsolstr.2006.10.010

* Corresponding author. Tel.: +441225384224; fax: +441225386928.E-mail address:[email protected](M. Meo).

International Journal of Solids and Structures 44 (2007) 36663684

www.elsevier.com/locate/ijsolstr
mailto:[email protected]:[email protected]

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2005; Lynch et al., 1995), power (Turnbull et al., 2004), oil (Manfredi and Otegui, 2002; Rogante et al., 2005),space (Jha et al., 2003), gas distribution (Kim et al., 2004), off-shore (Leonard, 2003), and water supply (Prak-ash and Malik, 1999) industry. Moreover, cases of SCC on composites were reported for GFRP composites(Pauchard et al., 2002) (when exposed to the combined effects of fatigue loading and environmental ageing inhot and/or wet conditions), and for aluminium-based metal matrix composites (Monticelli et al., 1997). Sev-

eral methodologies in different industrial sectors were devised for the detection of corrosion related defects, themost common are ultrasonic (Silva et al., 2003), Eddy currents (Yusa et al., 2005; Kim et al., 2004), X-ray(Dunn et al., 2000), acoustic emissions (Kim et al., 2003), and electrochemical methods (Bosch, 2005), etc.Currently, particular effort of the scientific community is devoted to the implementation of linear acousticmethods (Silva et al., 2003; Kim et al., 2003) for structural health monitoring within a predictive maintenanceprogram. Linear acoustic methods analyze wave speed changes, reflections of waves due to damage presence,and/or amplitude changes to assess the presence and location of structural anomalies. However, a greater sen-sitivity to damage presence is offered by a promising new class of NDE techniques, based on the monitoring ofmaterial nonlinear elastic wave behaviour (Van Den Abeele et al., 2000; Guyer and Johnson, 1999; Johnson,1999), proving their effectiveness by detecting early signs of material degradation long before changes on thelinear acoustic properties, become identifiable. These novel NDE techniques are based on the concept of non-linear mesoscopic elasticity (Van Den Abeele et al., 2000; Guyer and Johnson, 1999), which analyse changes in

the material nonlinear elastic wave behaviour due to the presence of damage. This behaviour can manifest intwo main ways:

1. Under resonance conditions, if the excitation is increased, a resonance frequency shift is observed.2. Exciting a sample simultaneously with continuous waves of two separate frequencies, frequency-mixing

spectral components are generated such as harmonics and sidebands.

These effects are hardly measurable in undamaged materials, but are clearly visible in damaged materials.The localized damaged portion of the material acts as a multiplier and nonlinear mixer of the excitation fre-quencies. The monitoring of these phenomena can be an effective method to detect SCC due to their high sen-sitivity to the presence of structural changes. However, the studies on nonlinear elastic wave spectroscopy

(NEWS) do not give any information on damage location (Van Den Abeele and De Visscher, 2000; Cam-pos-Pozuelo and Gallego-Juarez, 2003; Van Den Abeele et al., 1999; Van Den Abeele et al., 2001a; VanDen Abeele et al., 2001b; Meo and Zumpano, 2005). In this paper, a new damage location imaging techniquebased on time-reversed mirror (TRM) is proposed.

Time reversal has been used in acoustics to exploit its ability to backpropagate the acoustic energy to ascattering target or a source. Time reversal has been demonstrated to hold for linear acoustics in a reciprocalmedium (Fink et al., 1989a; Jackson and Dowling, 1991; Fink, 1992), with inhomogeneous medium, multiplepaths and presence of scatterers (Derode et al., 1995). Typically, time reversal consists in sending a signal in amedium, collecting the acoustic wave that scatters from a target, time reverse this signal, and then retro-focus it onto the target. However, the presence of damaged areas (presence of absorption, nonlinear atten-uation, etc.) degrade the performance of retrofocused time-reversal systems (Dowling and Jackson, 1992;Dowling, 1993; Thomas and Fink, 1996) resulting in a loss of focusing ability with a broadening of the focalspot and a reduction of the peak pressure at the focus. A new technique called nonlinear elastic wave self-fo-cusing (NEWSF) was investigated in this paper to detect the presence and location of stress corrosion crackingin a friction stir-welded plate. The method was also compared to classical time reversal acoustics, showing therobustness of the proposed method and its capability to clearly detect the damage location for the caseinvestigated.

2. Material nonlinear elastic wave behaviour

Experimental evidences (Van Den Abeele et al., 2000; Guyer and Johnson, 1999; Johnson, 1999; Van DenAbeele and De Visscher, 2000; Campos-Pozuelo and Gallego-Juarez, 2003; Van Den Abeele et al., 1999; VanDen Abeele et al., 2001a; Van Den Abeele et al., 2001b; Meo and Zumpano, 2005) showed that classical non-

linear models (Landau and Lifshitz, 1959) cannot explain the nonlinear behaviour generated by local nonlin-

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ear forces due to damage presence (such as cracks, voids, and contacts). A theoretical description of thisbehaviour can be given by the nonlinear mesoscopic elastic material model, which contains terms that describeclassical nonlinearity, as well as hysteresis, and discrete memory (Van Den Abeele et al., 2000; Guyer andJohnson, 1999; Johnson, 1999). This is possible by adding to the nonlinear classical stressstrain relationship,a stress dependence on strain time derivative (Van Den Abeele et al., 2000; Guyer and Johnson, 1999; John-

son, 1999; Van Den Abeele and De Visscher, 2000; Campos-Pozuelo and Gallego-Jua

rez, 2003; Van Den Abe-ele et al., 1999; Van Den Abeele et al., 2001a; Van Den Abeele et al., 2001b; Meo and Zumpano, 2005)

r

Z Ee;_e de 1

where Eis the nonlinear and hysteretic modulus given by

Ee;_e E0f1bede2 aDeetsign_e g 2

where E0is the linear modulus, Deis the strain amplitude change over the last period, band dclassical non-linear coefficients, and a material hysteresis measure. It is worth mentioning that Eq. (2)is valid for signalshaving one pair of extrema per period, i.e., unipolar waves. Experimental and numerical evidences (VanDen Abeele et al., 2000; Guyer and Johnson, 1999; Johnson, 1999; Van Den Abeele and De Visscher,

2000; Campos-Pozuelo and Gallego-Juarez, 2003; Van Den Abeele et al., 1999; Van Den Abeele et al.,2001a; Van Den Abeele et al., 2001b; Meo and Zumpano, 2005) showed that:

(1) The 3rd harmonic is quadratic with the fundamental amplitude for a purely hysteretic material and cubicaccording to classical nonlinear theory.

(2) A second-order sidebandf2 2f1, generated by a bi-tone excitation (f1andf2) has amplitude proportion-al to aA1A2for a purely hysteretic material, in contrast with an amplitude dependence proportional toCb; dA21A2 for a classical nonlinear material, where Cis a constant function ofband d.

(3) For a classical nonlinear material, the first order sideband (f2f1) amplitude is linear with the excitationamplitudes bA1A2.

Due to the inadequacy of classical nonlinear material models to reproduce the behaviour of microcrackeddamaged materials, a new material constitutive model, based on Presaich and Mayergoyz (PM) space, capableof accurately describing the nonlinear, discrete memory, and hysteretic behavior of such materials, wasimplemented in the house FE code.

3. Presaich and Mayergoyz space

Non-classical nonlinear elastic material behavior (hysteresis and material memory) can be described by anonlinear mesoscopic elastic material model such as the PreisachMayergoyz (PM) (McCall and Guyer,1994; McCall et al., 1996). With this approach, the macroscopic behavior of damaged materials is describedby the contribution of a number of mesoscopic material cells (110 mm), which are composed of a statisticalcollection of microscopic units (1100 lm) with varying properties defining their stressstrain relation. Thestrain of these microscopic units is a combination of a classical nonlinear state relation (elastic componentcontribution), and a non-classical addition due to hysteretic effects (interface binding contribution). In partic-ular, the strain component of hysteretic mesoscopic elastic unity (HMEU) can be thought as the strain of amicro-crack when subject to an external pressure that produces its closing and opening. This two stage behav-ior is highlighted inFig. 1a in case of no classical nonlinear elastic behavior contribution.

The pressure-displacement of microcracks is characterised by a rectangular loop defined by two couples ofparameters: the two equilibrium lengths (lo,lc) and a pair of pressure (Pc,Po) withPcP Po. According to therectangular loop (Fig. 1a), the equilibrium length of the interface binding remains constant (o) until the pres-sure load equals the closing pressure Pc(c), therefore, the only length changes of the HMEU are those of itselastic component. For pressure loads above the closing pressure Pc, once again, the only length changes arethose of the HMEU elastic component. Then, decreasing the pressure load P, the HMEU length changes are

only due to the HMEU elastic component until the pressure Preaches the opening pressure Po, where the

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HMEU interface binding elongates to o, and remains constant until the pressure is reversed and increases to

Pc. The HMEU distribution of a material is represented in a stressstress space ( Pc, Po), commonly termedPM-space. This representation is defined analytically by specifying its density distribution l(Pc, Po) (seeFig. 1b for a Gaussian distribution). The PM space representation of real materials can be derived using quasi-static measurements of the material strain according to specifically designed protocol loads (McCall andGuyer, 1994; McCall et al., 1996). From the HMEU properties above described and their PM space distribu-tion, it is clear that the actual number of HMEUs closing or opening, at every instant, depends on the previousload history of the material and on the sign of the applied pressure DP. Once the number of the HMEU unitsclosed is known, the non-classical correction K1of the classical nonlinear elastic modulus Kcan be evaluatedas follows:

1

K1

1

LP

LP DP LP

DP ; P!PDP

1

K1

1

LP

LP LP DP

DP ; P!PDP

3

where Pis the applied pressure and the term L(P) (Eq.(4)) is the length of the specimen

LP ncP lc N ncP lo

LP DP ncP DP lc N ncP DP lo

LP DP ncP DP lc N ncP DP lo

4

where Nis the total number of HMEU, nc(P) is the number of HMEU closed when the pressure is P, and lcand loare the equilibrium lengths of HMEU. Therefore, considering only the contribution of the HMEU tothe material deformation, the strain generated by a stress Pis given by the following expression:

eL0LP

L05

whereL0is the initial length of specimen. For example, if the load history represented inFig. 2a is applied tothe material described inFig. 1b, the resulting stressstrain curve is shown inFig. 2b.

4. Nonlinear FE code

The material constitutive law, described above, was implemented in our in-house FE code to simulate thepresence of damage in structures. Because the material stressstrain behavior is nonlinear the equation ofmotion for a FE discretised structure can be written as:

Fig. 1. (a) Behaviour of HMEU; (b) example of PM-space.


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Mfdgn Df _dgn Knfdgn fRextgn

M Xe

ZVe

qNT

N dV; D Xe

ZVe

jdNT

N dV

Kn Xe

ZVe

qBT

EnB dV

6

where [M] and [D] are, respectively, the mass and damping matrix of the structure, [K]nis the stiffness matrix atthe nth time step, [E]n is the stress strain matrix for the finite element e at the nth time step, {d}n is the dis-placement vector at thenth time step, {Rext}nis the external force vector at the nth time step, [N] is the matrixof shape functions, [B] is the strain displacement matrix, jdis the material damping parameter for the finite

element e, q is material density, Veis the element volume. Therefore, according to the FE problem described

Fig. 2. (a) Load protocol. (b) Stressstrain curve.


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by Eq.(6), the stiffness matrix has to be evaluated at every time step. In order to avoid this cumbersome for-mulation, the stiffness contribution into the equation of motion can be rewritten as the sum of a linear elasticterm and a nonlinear perturbation force {Rint}n

Knfdgn Klinfdgn fRintgn 7

where a finite element contribution to the nonlinear perturbation force is evaluated as

fRinte gn

ZVe

BT

fDrgn dV

fDrgn En Elinfeegn

8

with [E]linmaterial linear elastic stressstrain matrix and {ee}nelement strain vector evaluated at the time stepn. The evaluation of the stressstrain matrix at the nth time step ([E]n) consists in a three step process that, inthis paper, was illustrated for a 2D plane strain case for an anisotropic material. The first step consists in theevaluation of the strain vector

fegn Bfdgn feing 9

with {ein}n pre-strain and/or thermal strain contribution. In the second step, the stress contribution for eachcoefficient of the stress strain matrix is evaluated:

r11 Q11e11; r12 Q12e22; r22 Q22e22; r66 Q66e12

En1

Q11 Q12 0

Q12 Q22 0

0 0 Q66

264

375; feegn

e11

e22

e12

8>:

9>=>; 10

where [E]n1is the stress strain matrix for the finite elementeat the (n1)th time step. In the last step, the fourindependent coefficients of [E]nare evaluated by inputting their stress contributionsrijin their respective PMspaces together with their previous load histories. As results of such procedure, the FE equation of motion

assumes the following shape

Mfdgn Df_dgn Klinfdgn fR

extgn fRintgn 11

The Newmark time integration scheme together with a conjugate gradient solver was used to solve Eq. (11)(Konhke, 2001; Bathe, 1982; Cook et al., 1989).

5. Time reversal mirrors

Time reversal mirror (TRM) (Fink, 1999; Fink et al., 2000; Wu et al., 1992; Fink et al., 1989b; Chakrounet al., 1995) is based on the concept of optical phase-conjugate mirrors (PCM) (Pepper, 1982; Bunkin et al.,1986), where monochromatic signals are substituted by large bandwidth pulses in order to obtain high focus-ing properties. Basically, TRM is an array of transmit-receiver transducers, capable of emitting a broadbandpulse and, then, recording the arrival of incident waves, reverse it and, finally, re-emit it (last in, first out).TRM major advantage, compared (Wu et al., 1992; Fink et al., 1989b; Chakroun et al., 1995) to PCM, isthe possibility to select any time window of the recorded signals. This ability gives the possibility to work withmany reflective targets by concentrating on one target per time. Moreover, the time reversal process can beiterated in order to focus on the most reflective target or to increase the identifiably of the most faint one.

The selection of the time window to reverse into the structure is identified by the localisation of inhomo-geneity (defect) into the structure dynamic response between the pulse echo of the nearest structure edge andthe pulse echo of the furthest structure edge.

Although, TRM was used quite successively for non-destructive testing (NDT) (Chakroun et al., 1995) isclear that the traditional transducer array configuration is capable of highlighting defects only through struc-

ture thickness and, therefore, complete inspections of large structure can be carried out only using a series of


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scans, similarly to a C scan approach. Therefore, the authors proposed a new imaging technique with alter-native transducer configurations and an optimum time signal window to reverse was also analysed.

6. Nonlinear elastic wave time reversal mirror

The temporal approach of traditional TRM was an important breakthrough with respect to the PCM, how-ever, no indications for a reliable and efficient way for the selection of the time window to reverse, in case ofdamage presence, was found in literature. The present work aims to set-up a clear procedure to detect damagepresence through an optimum selection of the time window signal to reverse. In order to sort out the abovehighlighted TRM issues, two improvements were carried out to the methodology. The first advancement con-sisted in to place the transmitter array directly on the structure so as that a large portion of the structure canbe inspected with just one scan, because perturbation waves, generated by the transducer array, travels in anydirection through the structure and, so, information on damage presence, location, and severity can beobtained. Moreover, larger perturbation energy can be introduced in the structure, since there is no needof a coupling medium, which introduces additional damping and dispersion. With such configuration, cheapertransducers can be used such as piezoelectric patches and micro fiber composites (MFC). Drawback of thisnew transducer configuration is an increase of scattering phenomena due to the difficulty in generating unidi-

rectional perturbation waves, although, studies in this direction have been carried out with good results (Hayand Rose, 2002; Viktorov, 1967). However, in this paper, the generation of perturbation waves was supposedto be bidirectional.

Fig. 3. Proposed NEWTRM: (a) Damage (target) far from structure boundary; (b) damage (target) next to structure boundaries.

NEWTRM output: (c) damage (target) far from structure boundary; (d) damage (target) next to structure boundaries.


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The second improvement to the TRM exploited the non-classical nonlinear material behaviour (2) intro-duced by damage presence for the selection of the optimum time window to reverse. The presence of damageintroduces in the dynamic structure response high order harmonics of the excitation pulse central frequency,which otherwise would be negligible or totally absent for the undamaged structure. Therefore, only the reflect-ed or refracted waves by the damage can have this high frequency energy content (Fig. 3). The 3rd harmonic

was selected because it is the lowest harmonic predicted by all nonlinear material models, therefore, it has alarger energy content of higher order harmonics (Meo and Zumpano, 2005). Consequently, filtering therecorded time signals with a pass band frequency filter centred at the third harmonic of the excitation pulsecentral frequency, the arrival of the first wave packet reflected by the defect is highlighted and the time optimaltime window to reverse is identified.

This solution not only exemplifies the selection of the time window to reverse, but also allows the user toidentify structural defects next or on the structure boundaries (Fig. 3b), which reflected perturbation waveswould enclose. By re-emitting the Reversed time window signal (RTW) in the damaged structure, the structuredynamic response focus on the damage location and, therefore, the TRM output 3D plot shows coming wavescentred on the damage location (Fig. 3c and d).

Concluding, the proposed nonlinear elastic wave time reversal mirror (NEWTRM) consists in:

(1) The illumination of a structural defect through a pulse excitation carried out by a transducer arrayattached to the structure under investigation.

(2) The selection of the time window to reverse, which is achieved by a pass band filter centred on the 3rdharmonic of the central frequency of the excitation pulse.

(3) The reversed emission of the time window selected and the acquisition of the structure dynamic response,which allows the damage localisation knowing the perturbation wave propagation speed.

Another possibility arises if a validated undamaged FE model of the structure is available: the damagelocation can be identified by reversing the selected time window on it. As result of the numerical TRM onthe undamaged structure, the discrepancies introduced by the damage presence in the RTW self-focus onits location.

7. Case study

In this work, a friction stir-welded plate (Fig. 4) composed by two aluminium alloy plates (AA7075T7351and AA6056), 0.35 m long, 0.4 m wide and 5 mm thick, joined by 20 mm of weld (Bala Srinivasan et al., 2005)(Table 1), was analyzed.

According to experimental evidences (Bala Srinivasan et al., 2005), SCC tends to locate at welding interfac-es. Therefore, the SCC area was located at the welding interface (Fig. 4, 20 mm long and 8 mm wide) and sim-ulated using a PM space model with uniform HMEU distribution l(Pc,Po) = 1 between +/5 MPa andl(Pc,Po) = 0 everywhere else, for a maximum strain a = 0.001. Data relative to the characterization of PM spacesfor aluminum alloys were retrieved by analogue studies present in literature (Van Den Abeele et al., 2003,

2004). Because of the lack of information on the nature of the tensorial hysteresis, the damage introduced

Fig. 4. Transducers configurations: (a) 1st configuration; (b) 2nd configuration.


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on the welded plate structure was considered isotropic, and independent by eventual preferential directions.Therefore, the PM space for all the plane directions was assumed to be the same.

Two different transducer configurations were analyzed as shown inFig. 4: the sensor array was located oneither the actuator line (at one forth of the welded plate lengthFig. 4a) or symmetric to it sensors (at threeforth of the welded plate lengthFig. 4b).

The pulse excitation was assumed to be as follows:

Pressuret A sin2pfte

tt02

2p2

A 2 MPa; f 100 kHz; p 0:25f

; t0 3p12

The element size eL(13)of the FE model used is given by the ratio between the pulse wavelength WLand thenumber of elements, NoEWL, used to describe it

eL WLf

NoEWL

0:063 m

25 0:00252 mffi 2:5 mm 13

For wavelengthWL(14)is meant the space traveled by a pressure wave Poscillating with a frequencyf(pulsecentral frequency) with a wave speed cmax. Where cmax (15) is the maximum Pwave speed, in the structureunder investigation (AA7075T7351) (Cook et al., 1989).

WLf

cmax

f

6286 ms

100 kHz 0:063 m 14

cmax

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiE1 m

q1m1 2m

s

ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi ffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi72 GPa10:33

2700 kgm310:331 0:66

s 6286

m

s 15

Finally, the time integration step dt, used for the carried out investigations, was estimated as the time em-ployed by the quickest Pwave (cmax) to cross a finite element (eL), times a safe factor SF

dt SFeL

cmax0:25

0:0025 m

6286 ms

9:94 108 s 16

8. Results

To show the improvement of nonlinear elastic wave time reversal mirror (NEWTRM) with respect to thetraditional TRM, two different approaches were used to detect and localize the introduced SCC using bothconfigurations described inFig. 4. First stage of the comparison was the reversed time window (RTW) selec-tion, then, the re-emission output were compared and, finally, the SCC localization capabilities were observedusing the damage self-focusing approach. Before analyzing the results, it must be said that the effect of thewelds on the wave propagation, as wave scattering source, was almost unnoticeable because of three mainfactors: (1) material properties were very close, the largest difference in terms of elastic modules was closeto 10% of the AA7075T7351, (2) The pulse wavelength (WL= 6.3 cm) was larger than twice the weld width,(3) due to damage presence in the structure, large changes of the elastic modulus in the damaged area may beexperienced as those illustrated inFig. 5evaluated for a 200 kPa amplitude pulse (Eq.(12)) for the considered

case.

Table 1Material properties

Material Density [kg/m3] Elastic modulus [GPa]

AA7075T7351 2700 72.0AA6056 2700 68.4Weld 2700 65.0


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8.1. Reversed time window selection

The RTW selection methodology of both techniques was illustrated in 6, where the TRM selectionapproach was based on the identification of the presence of wave packets reflected by the damage betweenthe main pulse and its echo reflected by the structure furthest boundary from the sensor line. Instead, theNEWTRM exploited the damage nonlinearity response to univocally identify the damage presence by using

a pass band filter centred on the 3rd harmonic of the pulse central frequency.

8.1.1. 1st configuration

The first transducer configuration (Fig. 6), with a defect approximately positioned at half length of thewelded plate, is one of the worst scenario, because of the waves reflected by the damage overlap with wavesreflected by the left boundary (Figs. 7a and 8a). As result, an inexpert user might be brought to consider, asreflected pulse by the damage, the reflected pulse mirrored back by the left plate edge (Figs. 7a and 9a), leadingto a wrong defect localization. Therefore, in some case the wave reflected by the damage cannot be easily iden-tified. On the other hand, the solution offered by the NEWTRM RTW selection gets rid of any possible mis-interpretation of the recorded signals by highlighting their nonlinear elastic content introduced by the damagepresence (Figs. 7b and 9b). Consequently, the linear contributions to the structure dynamic response is filteredout, leaving only nonlinear elastic waves reflected/refracted by the defect, which curvature is focused at the

Fig. 5. Nonlinear elastic modulus (PM-Space).

Sensors

Time

Actuation

Left Plate Edge Reflected Pulse

Damage Reflected Pulse

Right Plate Edge Reflected

Pulse

Fig. 6. 1st configuration. Time-space localisation of wave packet arrivals at sensor locations.


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damage location (see the two thin black lines inFigs. 79). In both considered TRM methodologies, the bestRTW should contain the damaged reflected pulse (Fig. 8). In this study, all three wave group arrivals high-lighted inFigs. 7 and 10were re-emitted in the structure, in order to find the optimum time-reversed window.

8.1.2. 2nd configuration

The 2nd transducer configuration (Fig. 11) encloses the SCC defect, since the sensors are opposite to theactuators with respect to the defect position, therefore, the main damage reflected pulse does not exist as inthe previous case. This means that the discrepancies introduced by the damage presence are hidden into

the pulse (pulse arrival inFig. 12a) as it can be clearly seen inFig. 13a. Therefore, once again there is no mean

-4

Time[sec]

Sensor Location [m] Sensor Location [m]

Left Plate Edge Reflected Pulse + Damage Reflected Pulse

Right Plate Edge Reflected Pulse

Damage Reflected Pulse mirrored back by the Left Plate Edge

Damage location

along plate width

TRM NEWTRM

3rd

Harmonic of Recorded Signal

Pulse

10

Recorded Signal3

2.5

2

1

1.5

0.5

0.05 0.1 0.15 0.2 0.25 0.350.3 0.05 0.1 0.15 0.2 0.25 0.350.3

a b

Fig. 7. 1st configuration RTW selection: (a) TRM, (b) NEWTRM.

10-5

Time[sec]



TRM

Recorded Signal

NEWTRM

3rd Harmonic of Recorded Signal

Damage Reflected Pulse

0 .0 5 0 .1

8.2

8

7.8

7.6

7.4

7.2

6.8

6.6

6.4

6.2

7

0.15 0.2 0.25 0.350.3 0.05 0.1 0.15 0.2 0.25 0.350.3

a b

Fig. 8. 1st configuration Left plate edge reflected pulse + damage reflected pulse: (a) TRM; (b) NEWTRM.

10-4

Time[sec]


TRM

Recorded Signal

NEWTRM

3rd


0.05

0.44

0.42

0.4

1.38

1.36

1.34

1.32

1.3

1.28

0.1 0.15 0.2 0.25 0.350.3 0.05 0.1 0.15 0.2 0.25 0.350.3

a b

Fig. 9. 1st configuration Damage reflected pulse mirrored back by the Left plate edge: (a) TRM; (b) NEWTRM.


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to find out the defect presence unless its size and characteristic are such to be observed by a zoom of the pulsearrival wave. On the contrary, the NEWTRM RTW selection highlights the fault presence by eliminating thelinear dynamic response of the welded plate by using a pass-band filter. As for the 1st configuration, althoughthe first wave arrival should be the most suitable for structure re-emission, because of its larger amplitude, thethree first wave arrivals were re-emitted in the welded plate.

8.2. Re-emission of time-reversed signal

The chosen time window signal was reversed and re-emitted into the structure using the sensor array as anactuator array and, then, acquiring the structure dynamic responses at the sensor array. This process shouldallow a clear identification of damage location.

10-4

Time[sec]



Pulse Discrepancy due to Damage

TRM

Recorded Signal

NEWTRM

3rd


0.05

2.16

2.14

2.12

2.1

2.08

2.06

2.04

2.02

0.1 0.15 0.2 0.25 0.350.3 0.05 0.1 0.15 0.2 0.25 0.350.3

a b

Fig. 10. 1st configuration Right plate edge reflected pulse: (a) TRM; (b) NEWTRM.

Sensors

Time

Actuation

Pulse Arrival


Right Plate Edge ReflectedPulsePulse

Fig. 11. 2nd configuration. Time-space localisation of wave packet arrivals at sensor locations.

10-4

Time[sec]




Pulse Arrival

Damage location along plate width

TRM

Recorded Signal

NEWTRM

3rd


0.05

3

2.5

2

1.5

1

0.5

0.1 0.15 0.2 0.25 0.350.3 0.05 0.1 0.15 0.2 0.25 0.350.3

a b

Fig. 12. 2nd configuration RTW selection: (a) TRM; (b) NEWTRM.


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8.2.1. 1st configuration

The three wave packet arrivals identified at the sensor locations, shown inFig. 7, were time-reversed andinputted back into the structure in order to establish which RTW gave the clearest indication of damage pres-

ence and location. When the first wave packet (left plate edge reflected pulse + damage reflected pulse,Fig. 8)was re-emitted in the structure through the sensor array, not only the damage (see red oval in Fig. 14a), butalso, the pulse on the actuator array location (Fig. 14a) was refocused, hiding almost the damaged refocusedwave. On the contrary, by reversing only the 3rd harmonic (according to NEWTRM procedure, Fig. 8b) ofthe selected RTW (Fig. 8a), only the damage is refocused and, therefore, a clear damage localisation isobtainable (Figs. 14b and 15).

By reversing the damage reflected pulse mirrored back by the left plate edge, the traditional TRM was notcapable of highlighting any damage. In contrast, the NEWTRM reversion (Fig. 16) brought into light thepresence of damage, though, the eye (biconvex) shape of the incoming wave showed the overlap betweenthe 3rd harmonic damage refocused wave and the 3rd harmonic RTW reflected by the left plate edge. Con-sequently, the accuracy of the predicted damage location might be increased. For the last RTW selected inFig. 7(the right plate edge reflected pulse, Fig. 10), the pulse and the damage-induced signal distortions cannotbe separated using the TRM approach (Fig. 17a). Therefore, the damage discrepancy refocused wave resultedpartially overlapped with the RTW mirrored back by the left plate (Fig. 17a). A similar behaviour wasobserved reversing the 3rd harmonic of the selected RTW, though, the damage discrepancy refocused waveis clearly observable (Fig. 17a) and the front of the wave packet is clearly focused on the damage location.

8.2.2. 2nd configuration

For the second transducer configuration (Fig. 4b), the damage reflected pulse is not refocused, as for thefirst TRW selected for the 1st transducer configuration, but in this case, the damage introduced discrepancy

10-5

Time[sec]


Pulse Arrival

TRM

Recorded Signal

NEWTRM

3rd


Pulse Discrepancy due to Damage

0.05 0.1 0.15 0.2 0.25 0.350.3 0.05 0.1 0.15 0.2 0.25 0.350.3

a b

Fig. 13. 2nd configuration pulse arrival: (a) TRM; (b) NEWTRM.

10-5

Sensor Location [m]

Pulse Refocusing

TRM NEWTRM

Reversed Time Window

Sensor Location [m]

Damage Refocused wave

Time[sec]

0.05

12

10

8

6

4

2

0.1 0 .15 0.2 0.25 0.350.3 0.05 0.1 0.15 0.2 0.25 0.350.3

a b

Fig. 14. 1st configuration reversed time signal: (a) TRM; (b) NEWTRM. (For interpretation of the references to color in the text, the

reader is referred to the web version of this paper.)


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in the pulse and the pulse itself are refocused (Figs. 12a and 13a). Hence, for the traditional TRM (Fig. 18a),the excitation pulse and the damage discrepancy are refocused at the same time, causing a reduced visibility ofthe damage refocused wave. On the contrary, the NEWTRM refocused wave is composed only by the 3rd har-monic due to damage presence (Fig. 13b), allowing a simpler damage localisation (Fig. 18b). By reverting theother two RTW highlighted in Fig. 12a using TRM, a similar behaviour to that recorded inFig. 18a wasobserved and, therefore, they are not reported. Instead, if their 3rd harmonics are reversed (Fig. 12b,NEWTRM), a damage refocusing was observed in both cases (Fig. 19). However, a discontinuous wave frontwas observed (Fig. 19) seemingly to a destructive diffraction phenomenon (two optical waves of opposite

phase meet).

10-5

Left Plate Edge Reflected TRW

TRM

Sensor Location [m]

Time[sec]



0.05 0.1 0.15 0.2 0.25 0.350.3

12

10

8

6

4

2

Fig. 15. 1st configuration reversed time signal: damage reflected pulse TRM.

10-5

NEWTRM


Sensor Location [m]

Time[sec]

0.05

12

10

8

6

4

2

0.1 0 .15 0.2 0.25 0.350.3

Fig. 16. 1st configuration reversed time signal: damage reflected pulse from left plate edge NEWTRM.

10-5

Sensor Location [m]

Reversed Right Plate Edge Reflected Pulse reflected by Left Plate Edge

TRM NEWTRM


Sensor Location [m]


Time[sec]

0.05

12

10

8

6

4

2

0.1 0 .15 0.2 0.25 0.350.3 0.05 0.1 0.15 0.2 0.25 0.350.3

a b

Fig. 17. 1st configuration reversed time signal, right plate edge reflected pulse: (a) TRM; (b) NEWTRM.


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8.3. Damage self-focusing

Damage self-focusing consists in the re-emission of a RTW in a validated FE model of the undamagedstructure. As result, the damage-induced signal distortions in the recorded signal will focus into the damagelocations. Using the TRM process, the damage focusing phenomena overlap with the main focusing pulse(Figs. a2023a), determining a loss of clarity and the need of a re-iteration of the TRM process to separatethe excitation pulse from the damage generated waves. However, a clear refocusing to the damage locationwas obtained using the proposed NEWTRM TRWs (Figs. 20b, 21, 22, and 23b). The best damage refocusingwas obtained by the first selected RTW for both transducer configurations, since the related waves did notundergo any boundary reflection (Figs. 20b and 22b) and, therefore, the entire wave packet generated bythe damage presence converges in the damage location as in a funnel and, then, diverges in its way out.

The remaining two RTWs (Figs. 21b and 23b), used for damage self-focusing, showed the previous highlightedbehaviour for the bulk of the reversed wave train, but leaving evident signs of their different propagationpaths. By comparing the two transducer configuration results, no apparent difference could be spotted, sincethe introduced damage lies almost at the centre of the plate and, therefore, the travelling paths of the reversedwave trains were almost identical.

9. Discussions

The TRM methodology based on NEWS presented in this paper differs from previous applications ( Sutinand Johnson, 2004; Ulrich et al., 2006) exploiting nonlinear elastic responses of structural defects in severalpoints. The NEWTRM re-emits a time-reversed signal previously filtered around the third harmonic of the

excitation central frequency (highlighting the time distortion due to the damage presence) in the acquired loca-

10-5

Sensor Location [m]

TRM NEWTRM


Sensor Location [m]


Tim

e[sec]

0 .0 5 0 .1

1

2

3

4

5

6

7

8

0.15 0.2 0.25 0.350.3 0.05 0.1 0.15 0.2 0.25 0.350.3

a b

Fig. 18. 2nd configuration time-reversed main pulse waves: (a) TRM; (b) NEWTRM.

10-5

Sensor Location [m]


Sensor Location [m]


Time[sec]

0 .0 5 0 .1

1

2

3

4

5

6

7

8

0.15 0.2 0.25 0.350.3 0.05 0.1 0.15 0.2 0.25 0.350.3

a b

Fig. 19. 2nd configuration NEWTRM time-reversed main pulse: (a) reversed right plate edge pulse; (b) reversed left plate edge pulse.


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tion, while literature reported approaches (Sutin and Johnson, 2004; Ulrich et al., 2006) re-emit a time-re-versed signal in the excitation source, but acquired on the opposite face of the structure. Moreover, these pro-posed nonlinear TRM are based on the observation that the amplitude second harmonic or first sideband ofthe time signal acquired after re-emission of the time-reversed signal is larger on the surface above the damage

location. Therefore, the localization of the damage is dictated by the number of points used to scan the struc-

Time steps= Time steps=a b

Fig. 20. 1st transducer configuration comparison of damage focusing by reversing left plate edge reflected pulse + damage reflectedpulse: (a) TRM; (b) NEWTRM.


Fig. 21. 1st transducer configuration comparison of damage focusing by reversing right plate edge reflected pulse: (a) TRM; (b)NEWTRM.


Fig. 22. 2nd transducer configuration comparison of damage focusing by reversing the Pulse arrival wave: (a) TRM; (b) NEWTRM.


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ture surfaces and possible only if these are accessible. While, the NEWTRM is capable of localizing damageson the structure by measuring the time arrivals of the nonlinear elastic response of the structure due to thedamage presence and, potentially, the number of sensors/actuators employed can be reduced to two by usingray-tracing algorithm techniques (Zumpano and Meo, 2005).

By re-emitting the time-reversed signal, the dynamic response of the structure focuses at the location of thedamage, giving larger amplitude at the sensor locations, deployed in front of the damage location ( Figs. 14band 16), decreasing rapidly (especially if compared with the behaviour recorded before re-emission, see Figs.810) with the distance from damage axis projection on the sensor array line, making easier the identificationof the damage location.

Finally, a further improvement of the NEWTRM can be obtained by coupling it to a space-temporal cor-relation technique (Dominguez et al., 2005), which will reduce shadowing effects of multi-damage locationsand increase the longitudinal resolution of the damage locations.

10. Conclusions

In this paper, a new nonlinear time reversal technique is presented for the detection and localization ofstress corrosion cracking damage in a friction stir-welded aluminium plate-like structure. The corroded areawas placed in the heat affected zone and modelled using a multi-scale material constitutive model (PreisachMayergoyz space).

A new nonlinear damage detection imaging technique based on time-reversal acoustics was developed.Compared to the traditional TRM, the newly developed time-reversal method takes into account the non-clas-sical nonlinear material behaviour introduced by the cracked area. In particular, the presence of damage intro-duces in the dynamic structure response high order harmonics of the excitation pulse central frequency.

Then, studies were conducted to select the optimum time window signal to reverse and to re-emit in thestructures. Subsequently, the selected time signals was filtered with a pass band frequency filter centred atthe third harmonic of the excitation pulse central frequency and re-emitted in the structure to have an imageof the faulted zone. The 3rd harmonic was selected because of its larger energy content.

The methodology was compared with traditional time-reversal acoustics (TRA) showing significantimprovements. While the traditional TRA was not able to clearly localise the damage, the developed techniqueidentified in a clear manner the faulted zone showing its robustness to detect and locate nonlinear sources inpresence of different materials.

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Fig. 23. 2nd transducer configuration comparison of damage focusing by reversing the right plate edge reflected pulse: (a) TRM; (b)NEWTRM.

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