SH ultrasonic guided waves for the evaluation of interfacial adhesion.

ULTRAS 4785

No. of Pages 16, Model 5G

22 March 2014 Ultrasonics xxx (2014) xxx–xxx 1

Contents lists available at ScienceDirect

Ultrasonics journal homepage: www.elsevier.com/locate/ultras 4 5

SH ultrasonic guided waves for the evaluation of interfacial adhesion

3 6

Q1

7 8 9

Michel Castaings ⇑ Univ. Bordeaux, I2M, UMR 5295, F-33400 Talence, France CNRS, I2M, UMR 5295, F-33400 Talence, France Arts et Métiers ParisTech, I2M, UMR 5295, F-33400 Talence, France

10

a r t i c l e

1 4 2 2 13 14 15 16 17

i n f o

Article history: Received 2 August 2013 Received in revised form 11 February 2014 Accepted 5 March 2014 Available online xxxx

18 19 20 21 22 23

Keywords: Ultrasounds SH guided waves Interfacial adhesion NDE

a b s t r a c t Shear-Horizontally (SH) polarized, ultrasonic, guided wave modes are considered in order to infer changes in the adhesive properties at several interfaces located within an adhesive bond joining two metallic plates. Specific aluminium lap-joint samples were produced, with different adhesive properties at up to four interfaces when a glass–epoxy film is inserted into the adhesive bond. EMAT transducers were used to generate and detect the fundamental SH0 mode. This is launched from one plate and detected at the other plate, past the lap joint. Signals are picked up for different propagation paths along each sample, in order to check measurement reproducibility as well as the uniformity of the adhesively bonded zones. Signals measured for four samples are then compared, showing very good sensitivity of the SH0 mode to changes in the interfacial adhesive properties. In addition, a Finite Element-based model is used to simulate the experimental measurements. The model includes adhesive viscoelasticity, as well as spatial distributions of shear springs (with shear stiffness KT) at both metal–adhesive interfaces, and also at the adhesive–film interfaces when these are present. This model is solved in the frequency domain, but temporal excitation and inverse FFT procedure are implemented in order to simulate the measured time traces. Values of the interfacial adhesive parameters, KT, are determined by an optimization process so that best fit is obtained between both sets of measured and numerically predicted waveforms. Such agreement was also possible by adjusting the shear modulus of the adhesive component. This work suggests a promising use of SH-like guided modes for quantifying shear properties at adhesive interfaces, and shows that such waves can be used for inferring adhesive and cohesive properties of bonds separately. Finally, the paper considers improvements that could be made to the process, and its potential for testing the interfacial adhesion of adhesively bonded composite components. Ó 2014 Published by Elsevier B.V.

25 26 27 28 29 30 31 32 33 34 35 36 37 38 39 40 41 42 43 44 45 46 47

48 49

1. Introduction

50

Adhesive bonding of primary structures is increasingly attractive as a direct alternative to riveting, especially in aircraft constructions [1] but also in many other industries [2,3]. However, the degradation of the adhesive layer over time remains an issue and inspecting the adhesive layer is complex since sub-surface information must be extracted. Fracture tests or other mechanical tests can be performed on adhesively bonded specimens [4], and supported by mechanical modelling or energy-failure based analysis [5], but the tested samples must satisfy specific shapes and sizes to conform to norms, thus making it impossible to test real structures. Extensive destructive testing must then be carried out for statistical analysis in order to estimate the probable state of

51 52 53 54 55 56 57 58 59 60 61

⇑ Address: Univ. Bordeaux, I2M, UMR 5295, F-33400 Talence, France. Tel.: +33

Q2

540002463; fax: +33 540006964. E-mail address: [email protected]

the real structure. This is a time-consuming and expensive process, which involves the risk that some of the tested samples may be different from the real structure. Consequently, non-destructive testing (NDT) is of great importance for evaluating the quality of adhesive bonds, especially if this can be performed directly on the real structure without the need to dismantle it. Among all existing NDT techniques used to inspect adhesive bonds, ultrasound-based methods seem to be the most suitable because they mechanically interrogate the bonds, contrary to electromagnetic wave -based methods, e.g. X-rays, thermography, etc. [6,7]. However, one major difficulty lies in establishing a direct link between measured ultrasonic data and the mechanical strength of the adhesive bond, as well as being able to distinguish between weaknesses at the adhesive-adherent interfaces (adhesion) and within the adhesive bond-line (cohesion). A huge amount of work has been produced on the general topic of ultrasonic non-destructive evaluation (NDE) of adhesive bonds, using either longitudinal or shear bulk waves [8–13], Lamb or Shear-Horizontal (SH) guided

http://dx.doi.org/10.1016/j.ultras.2014.03.002 0041-624X/Ó 2014 Published by Elsevier B.V.

Please cite this article in press as: M. Castaings, SH ultrasonic guided waves for the evaluation of interfacial adhesion, Ultrasonics (2014), http://dx.doi.org/ 10.1016/j.ultras.2014.03.002

62 63 64 65 66 67 68 69 70 71 72 73 74 75 76 77 78 79

ULTRAS 4785


22 March 2014 2 80 81 82 83 84 85 86 87 88 89 90 91 92 93 94 95 96 97 98 99 100 101 102 103 104 105 106 107 108 109 110 111 112 113 114 115 116 117 118 119 120 121 122 123 124 125 126 127 128 129 130 131 132 133 134 135 136 137 138 139 140 141 142 143 144 145

M. Castaings / Ultrasonics xxx (2014) xxx–xxx

waves [14–17], and in linear or non-linear regimes [18,19]. Whether the interface adhesion or the bond-line cohesion is being examined, the following objectives are usually considered: (1) detection of localized defects, e.g. lack of adhesive [20], porosity [21], disbond [22], kissing bond [23,24], etc., and (2) measurement of mechanical properties either during the adhesive curing [11,13,25–27] or at any time during the life of the adhesivelybonded component [28–30,10,31–33]. Both experimental and numerical studies have been carried out in the above-mentioned publications, to investigate the sensitivity of ultrasonic waves to either mechanical properties or the presence of local defects. The ratio between normal and shear reflection coefficients at normal incidence was shown to be a good way to discriminate between types of interfacial imperfections, such as kissing, partial or slip bonds [32]. However, no real solution is available today for evaluating separately the adhesive and cohesive properties from the acoustic signature of an adhesive bond. It is therefore of interest to explore both numerically and experimentally those from ultrasonic waves, which may discriminate between the mechanical characteristics of the adhesive-adherent interfaces and those of the adhesive layer. Bonded joints are often submitted to shearing loads, and breaking, when it occurs, is often in the shearing mode, usually at the adhesive-adherent interfaces, since it is more difficult to build a good and reliable interfacial adhesion than it is to make a strong cohesion of the bond. This is mainly due to the fact that cohesion depends on the choice of two usually mixed-up components and on the way they are cured together, whereas adhesion relies upon complex and multi-parameter-dependent chemical and/or physical processes. For instance, alcohol may be used for cleaning the surfaces to be assembled, adhesion promoter may be applied for reinforcing the molecular connection, abrasion or sand-blasting can be used for preparing the surfaces of the adherents to be assembled, etc. Shear resistance of adhesive–adherent interfaces is then often a critical parameter for adhesive bonds, and its nondestructive evaluation is of great interest, especially in the Aeronautic or Aerospace context, for safety reasons. Thus a nondestructive technique for assessing the shear properties at the adhesive–adherent interfaces and those of the adhesive layer separately could be very useful as these may be good indicators of the shear strength of these parts of an adhesive bond. Many studies have investigated ultrasonic shear waves, which accumulate information about the shear properties of the medium they propagate through. However, such waves are not easy to generate or to detect because they require a strong mechanical coupling between the surface of the structure to be tested and the ultrasonic transducer used, when this is a standard piezoelectric shearing element; this makes scanning the structure difficult and, like any contact technique, it requires the tested bond to be perfectly parallel to the surface(s) where the transducer(s) is (are) attached. If not, the wave reflected from/transmitted past the tested interface is deviated in a different direction from the incident one, thus causing difficulties for finding the optimal position of the ultrasonic receiver, especially in a scanning process. One alternative may be to use two fluid-coupled transducers, oriented at specific angles to the tested component, but this implies quite complex processing to identify the various echoes detected by the receiving transducer [33,34]. A more promising technical alternative is to use EMAT transducers, which are suitable for the contact-less generation and detection of ultrasonic shear waves [13,26]. Depending on the magnetomechanical properties of the test specimen, a strip of highly magnetostrictive material may have to be bonded onto it to improve transmitter and receiver efficiency and to ensure sufficiently high signal-to-noise ratio [35]. Moreover, specific EMATs made of meander coils can generate and detect SH guided waves, which have been shown to be of interest because their displacement

and stress are oriented parallel to the adhesive–adherent interface, and they can therefore be used to evaluate interface properties as they accumulate information while propagating along the bond [36]. In this case, the period of the meander coil controls the wavelength of the desired guided wave mode [37]. Recent work shows the potential of such transducers to launch and detect SH guided waves through lap joints, as well as the sensitivity of the low-order SH0 mode to changes in interfacial and cohesive conditions [38]. However, in order to solve the inverse problem, i.e. correlating changes in the measured SH-wave signals to quantitative changes in the mechanical (shear) properties of an interface and/or of an adhesive layer, a reliable and efficient numerical model is necessary. Such a model should take into account the properties of the interfaces as well as the properties of the adhesive layer, and of course those of the substrates. Several types of numerical model have been developed to understand or to predict the behaviour of ultrasonic waves when propagating through adhesively bonded materials, e.g. matrixbased models [16,27,39], Finite Element-based models [20,41,42], semi-analytical models [43,44], spring-based or mass-springbased models [45–54]. The latest spring representation is particularly appropriate for modelling adhesion at the adhesive–adherent interfaces, because interfacial normal or transverse stiffnesses can be correlated to the micromechanics and topography of two contacting surfaces [55]. This is of particular interest for completing the available solutions used on industrial or manufacturing plants, which are so far restricted to detecting extreme defects in the adhesive, e.g. lack of adhesive, severe change in bond thickness or high concentration of porosities. Indeed, assuming strength correlates with stiffness [52,56], a reliable technique for the evaluation of interfacial stiffnesses would be very helpful in the testing process of the mechanical strength of interfaces, which is often highlighted by industrial partners as a weak point of adhesive joints. Spring models associated to experimental measurements have so far been used successfully for evaluating normal and/or transverse stiffnesses distributed along an interface between two known substrates, or for environmentally degraded adhesive bonds prepared such that mainly interface properties were modified [47–49]. However, in these works the ultrasonic waves were bulk modes incident either normal or at an oblique angle with respect to the tested interface, measurements required quite a complex set-up and were made for interrogating a very local zone with no easy way to scan the tested interface. A successful experiment was carried out in the 1990s using guided Lamb waves to evaluate interfacial normal or transverse stiffnesses with an air-coupled ultrasonic receiver, which made measurements very reproducible, and part of the component could be scanned [53,54]. However, the structure was adhesive-less and the tested interface was a ‘‘simple’’ intimate contact between a glass plate and an elastomer block under variable loading to change the interfacial conditions. Although current studies have attempted to infer either the normal stiffness or both normal and transverse stiffnesses, transverse stiffness alone is sufficient to address the shear state of interfaces. Recent works reinforce the importance of investigating SH waves and shear-spring modelling to examine the shear state of interfacial joints [56,57]. The current paper utilizes a contact-less technique for generating and detecting SH-guided wave modes that propagate along aluminium lap-joint samples with different interfacial conditions. Measured temporal signals are first investigated to demonstrate the high sensitivity of the SH0 wave mode to these interfacial changes. They are then used for solving an inverse problem based on a finite element (FE) model, separately inferring shear stiffnesses at various interfaces of the adhesive bond (adhesive/adherent interfaces and adhesive/inner film interfaces), as well as the shear moduli of the adhesive layer itself. The aim of this paper is to


146 147 148 149 150 151 152 153 154 155 156 157 158 159 160 161 162 163 164 165 166 167 168 169 170 171 172 173 174 175 176 177 178 179 180 181 182 183 184 185 186 187 188 189 190 191 192 193 194 195 196 197 198 199 200 201 202 203 204 205 206 207 208 209 210 211

ULTRAS 4785


22 March 2014 M. Castaings / Ultrasonics xxx (2014) xxx–xxx

3

increasing the risk of bad interfacial adhesion. This will be investigated later in the paper. This sample is marked as SBI-T for ‘‘SandBlasted Interface & Tissue’’.

260

214

supplement previously published work by proposing a promising way to distinguish and evaluate non-destructively the adhesive and cohesive properties of adhesive bonds.

215

2. Experiments

2.2. Set-up and measurement process

263

216

226

2.1. Samples

227

Four samples are used in this study. These are made of two 3 mm thick, 250 mm long and 200 mm wide aluminium plates. The overlapping zone runs along the 200 mm long side and is 50 mm wide, as shown in Fig. 1. The structural adhesive film AF3109 used for assembling three pairs of aluminium plates is a thermosetting modified epoxy adhesive film [58]. This layer has a well-calibrated thickness of 0.2 mm. For the fourth sample, the chosen adhesive is slightly softer than the AF3109, and is referred to as PR1750B2. A thin self-supported film is integrated into this adhesive to control bond thickness. For each sample, the aluminium surfaces are prepared in a specific way before assembling the plates. For sample 1, sand-blasting is applied to the aluminium; this is a common industrially used surface treatment method applied prior to bonding [59]. It makes the substrate surfaces rough, which is supposed to enhance the adhesive joint strength [60]. This sample is then considered as the reference sample and is noted throughout the paper as SBI for ‘‘Sand-Blasted Interface’’. The same process is used for sample 2 as for sample SBI, except that no sand-blasting is applied to the aluminium surfaces, but only careful cleaning and degreasing. This sample is then identified as NSBI for ‘‘No Sand-Blasted Interface’’. For sample 3, sand-blasting is applied but an oily polluting agent is deposited on both sand-blasted aluminium surfaces before the adhesive is used. This sample is then marked as SBI-OP for ‘‘Sand-Blasted Interface & Oil Pollutant’’. The fourth and last sample has sand-blasted aluminium plates; no pollutant is applied but a 0.2 mm thick glass–epoxy self-supported film, also called tissue in the following, is inserted within the adhesive layer. This process is sometimes used for easier control of the joint thickness, however, this results here in a thicker bond, i.e. 0.5 mm thick joint including 0.2 mm tissue plus twice 0.15 mm adhesive (on each side of the tissue). In addition to expanding the joint thickness, this process increases the number of interfaces within the joint, thus also

Two EMAT transducers are used: one for launching the desired SH0 mode along one aluminium plate and propagating towards the lap joint, and one for detecting the SH0 mode transmitted past that joint, on the other aluminium plate. Both elements are placed so that the mode propagates along a direction normal to the lap joint (see Fig. 1). A specific plastic holder is used throughout the measurement process to keep both EMATs perfectly aligned, and at a constant distance apart of 80 mm, and so that each is 15 mm away from the edges of the aluminium plates contiguous to the lap joint (N.B. this holder is not shown in Fig. 2 because it hides the EMAT transducers). These EMAT elements are manufactured by SONEMAT Ltd. [61]. They use a periodic arrangement of permanent magnets, producing a bias magnetic flux density with a period (along the desired direction of propagation) equal to the desired acoustic wavelength k. A straight wire is placed between the magnets and the plate, and the current sent along the wire induces eddy currents in the plate. The interaction of the currents with the magnetic flux produces a pattern of alternating body forces, or Lorentz’ forces, normal to the direction of propagation, and parallel to the plate. This results in the generation of SH wave modes along the plate [35]. When an SH wave propagates underneath a receiving EMAT, the horizontally polarized stress field that it produces interacts with the local bias magnetic flux density, thus generating currents in the wire, which is placed between the plate and the magnets. The EMATs used here are designed so that they can launch and detect SH-guided waves with a wavelength equal to (or close to) 12 mm, within a frequency bandwidth running from about 110 kHz to 2.5 MHz, down to 6 dB (and up to 8 MHz, down to 15 dB). As shown in Fig. 3a, SH-like modes that may propagate along the 3 mm thick aluminium plate, with a wavelength equal to 12 mm, are SH0 and SH1 at frequencies close to 260 kHz and 580 kHz, respectively. Fig. 3b shows the group velocity dispersion curves for all possible plate modes within the [1] MHz frequency range; this demonstrates that SH0 is absolutely non-dispersive while SH1 is quite dispersive around 580 kHz. Consequently, the actual study focuses on the generation and detection of SH0 around 260 kHz, its sensitivity to changes in adhesion quality, and its use in inferring properties representative of that adhesion. Nevertheless, this does not mean that SH1 or other high-order modes should not be investigated for better evaluation of adhesion. These dispersion curves were predicted using Propag software developed by the late Bernard Hosten [40], using the following values as input data: q = 2780 kg/ m3, E = 72.4 GPa, m = 0.34 (VL = 6347 m/s, VT = 3116 m/s). An arbitrary function generator, Agilent 33120, is used to produce an 8-cycle, Hanning-windowed, toneburst as the excitation

264

225

The geometry of the investigated samples is that of lap-joint components. The aim is to propagate the guided, fundamental, shear-horizontally polarized mode, SH0, across the adhesively bonded zone for various states of the interfacial adhesion, to monitor its sensitivity to these different states, and to set the interfacial mechanical parameters in the numerical model so that predicted waveforms are as close as possible to the measured signals. Fig. 1 shows a schematic diagram of the samples together with the EMAT transducers used to generate and detect the SH0 wave mode.

212 213

217 218 219 220 221 222 223 224

228 229 230 231 232 233 234 235 236 237 238 239 240 241 242 243 244 245 246 247 248 249 250 251 252 253 254 255 256 257 258 259

Fig. 1. Schematic diagram of EMAT transducers used for generating and detecting SH0 wave mode propagating past adhesive lap-joint.


261 262

265 266 267 268 269 270 271 272 273 274 275 276 277 278 279 280 281 282 283 284 285 286 287 288 289 290 291 292 293 294 295 296 297 298 299 300 301 302 303 304 305 306 307 308 309

ULTRAS 4785


22 March 2014 4


Fig. 2. Photo of experimental set-up.

(a)

20

(b)

6

18

5 16

SH0

SH1

Group velocity (mm/µs)

Wavelength (mm)

14

= 12 mm

12 10 8

4

SH0 3

2

4 2 0

0

0.1

0.2

260 kHz

260 kHz

6

1

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency (MHz)

0

0

0.1

0.2

SH1

0.3

0.4

0.5

0.6

0.7

0.8

0.9

1

Frequency (MHz)

Fig. 3. Dispersion curves for SH guided wave modes propagating along 3 mm thick aluminium plate; (a) wavelengths and (b) group velocities – operating point is shown by the large dot.

310 311 312 313 314 315 316 317 318 319 320

signal. The centre frequency of this signal is equal to 260 kHz and Q3 its amplitude is 2 Vpp. This is sent to a Ritec 2500 GA power amplifier, which produces an output voltage of around 600 Vp-p through a 1 kWrms power. This level of power is required for driving the transmitting EMAT to ensure a good signal-to-noise ratio after propagation along the plate sample and through an adhesive lap joint. The receiving EMAT is plugged into a low-noise pre-amplifier/filter, Panametrics 5058PR, to get rid of any noise outside the frequency range of interest and amplify the measured signals before sending them to the scope, LECROY 9310. A Macintosh machine and Propag software are also used to send a digitized excitation

signal to the generator, and to capture signals visualized on the scope, via ENET interface. As indicated in Fig. 1 and seen in Fig. 2, five tracks are considered for each sample, along which the SH0 mode is propagated and measured; this is to verify the consistency of the measured signals, and thus ensure the uniformity of each adhesive bond (both in thickness and in mechanical properties), as well as the reproducibility of the measuring process when moving from one track to another and back to a previous position for checking. Fig. 4 gives examples of time traces measured for the NSBI sample. Fig. 4a clearly shows the good signal-to-noise ratio obtained for real-time


321 322 323 324 325 326 327 328 329 330 331

ULTRAS 4785


22 March 2014 5


(a)

(b)

0.1

Amplitude (V)

1

2

3

0

-0.1 30

45

60

75

90

105

120

Time (µs)

Fig. 4. Measured time responses for NSBI sample; (a) real-time signal over long time scale showing electrical component, echoes transmitted past lap-joint and echoes reflected by end of plate sample; (b) 20-times averaged signals showing reproducibility of measured echoes transmitted past lap-joint: EMATs are generating and detecting along path c () and path e (- - -) shown in Fig. 1.

332 333 334 335 336 337 338 339 340 341 342 343 344 345 346 347 348 349 350 351 352 353

measurements, and also displays the electric component, which traditionally is obtained with EMATs at the very beginning of time traces, a strong direct transmission past the lap-joint, plus a couple of echoes from several reflections between the aluminium edges surrounding the lap joint, and finally reflections by the righthand-side of the sample of all the wave-packets transmitted past the joint. It is clear that SH0 only propagates along the 3 mm thick aluminium components, because of the frequency range of the excitation, but modes propagating along the adhesive joint can be SH0 and SH1-like modes according to the dispersion curves (not shown here but these have been calculated using Propag software) of that multi-layered zone. No investigation has been carried out here into measuring their respective amplitudes, for instance, and the dependence of these amplitudes on the quality of the adhesion, but this is likely to be studied later on. Only the shape and amplitude of the wave-packet transmitted past the various lap-joints have been investigated in the current study. Nevertheless, it is shown later that these carry quite a lot of information about adhesion quality. Before showing how these wave-packets are modified as the adhesion changes, let us check the consistency of the measurements, i.e. the reproducibility of the measuring process and the uniformity of the adhesive bonds. Fig. 4b shows an

example of two 20-time averaged wave-packets measured past the joint of the NSBI sample, for two different tracks. It is clear that they resemble each other very closely. To complete this investigation into the reproducibility of measurements, Table 1 provides amplitude and position-along-time data picked up from the three main packets, noted 1, 2 and 3 in Fig. 4, of signals measured for each of the five tracks. The table also shows values for amplitude ratios, time differences, mean values and standard deviations and these quantitatively confirm the good reproducibility of the measured signals, with standard deviations between 8% and 16% for the amplitude measurements, and close to 1% for the time measurements. When evaluating amplitude ratios or differences in time between wave-packets, the standard deviations obtained increase but never exceed 22% or 14%, respectively. Very similar comparisons have been possible between signals measured for any track of any of the four samples. This indicates that each adhesive bond has fairly uniform thickness and mechanical properties, at least so far as the ultrasonic SH0 mode is sensitive to changes in these parameters. Data in Table 1 and more specifically relative standard deviations (frames outlined in bold in the table) for the amplitude and time position of the 1st wave-packet, A1 and t1, respectively, for

Table 1 Picked-up amplitude and time data (plus amplitude ratios, time differences, means and standard deviations) from experimental signals measured along lanes (a), (b), (c), (d) and (e) of NSBI sample. The relative standard deviations (std. dev./mean), in frames outlined in bold (—), indicate typical reproducibility of measured data and represent targets for further comparisons between measured and FE simulated waveforms.


354 355 356 357 358 359 360 361 362 363 364 365 366 367 368 369 370 371 372 373 374 375

ULTRAS 4785


22 March 2014 6


387

both amplitude ratios between 2nd or 3rd wave-packets and 1st wave-packet, A2/A1 and A3/A1, and for both time shifts between 2nd or 3rd wave-packets and 1st wave-packet, t2 t1 and t3 t1 (or less wave-packets if appropriate) represent quantitative targets for further comparisons between measured and FE simulated waveforms. This means that the six above-mentioned quantities will be used as quantitative indicators to compare measured signals and FE simulated signals obtained during or after the adhesive and/or cohesive property optimization process. The aim is that the six FE quantities should not exhibit relative differences with measured data that are greater than the relative standard deviations of the reproducibility measurements provided in Table 1.

388

2.3. Sensitivity of SH0 mode to adhesion quality

376 377 378 379 380 381 382 383 384 385 386

Fig. 5 displays four typical signals measured past each lap-joint. We focus on the time domain of interest, i.e. that displaying echoes

390

(a)

Measured SH0 waveform past lap joint (V)

0.3

0.2

1

0.1

2

(b)

0.3


389

transmitted past the joints only, thus removing the electrical component and the reflections from the free edge of the sample. Fig. 5a shows nicely separated echoes occurring within the lapjoint of the SBI sample (well-bonded sample), with a fairly regular decay in amplitude from the first to the last visible echo. As explained before, this measurement was reproducible for any track along that sample. Such series of well-separated wave-packets can be recognized as a typical signature of the well-bonded lapjoint, i.e. with no damage or weakness along the interfaces or along the adhesive that may modify the shape and/or amplitude of the echoes, which indicate easy-going propagation and multi-reflections between the edges of the lap-joint. Fig. 5b shows that the transmitted signal is considerably modified when being measured for the NSBI sample. The echoes are no longer well separated, and the whole amplitude is almost divided in two compared with previous signals measured for the SBI sample. As surface roughness (which varies according to whether

3

0

-0.1

-0.2

-0.3

0.2

1

0.1

2

0

-0.1

-0.2

-0.3 40

60

80

100

120

140

40

60

Time (µs)

(c)

100

120

140

1 0.2

0.1

2

(d)

0.3



80

Time (µs)

0.3

3

0

-0.1

-0.2

-0.3

0.2

0.1

1

2

3

0

-0.1

-0.2

-0.3 40

60

80

Time (µs) Q6

3

100

120

140

40

60

80

100

120

140

Time (µs)

Fig. 5. Measured transmitted waveforms past lap-joint for (a) SBI, (b) NSBI, (c) SBI-OP and (d) SBI-T samples.


391 392 393 394 395 396 397 398 399 400 401 402 403 404 405 406 407

ULTRAS 4785


22 March 2014 7

M. Castaings / Ultrasonics xxx (2014) xxx–xxx 408 409 410 411 412 413 414 415 416 417 418 419 420 421 422 423 424 425 426 427 428 429 430 431 432 433 434 435 436 437 438 439 440 441 442 443 444 445 446 447 448 449 450 451 452 453 454 455 456 457 458 459 460 461 462 463 464 465 466 467 468 469 470 471 472 473

sandblasting treatment is applied or not) is known to affect adhesion characteristics and to modify the adhesive joint strength [59,60], then changes in the measured ultrasonic signal when going from SBI to NSBI samples indicate that the SH0 guided mode propagating from one plate to the other via the joint, is sensitive to changes in adhesion at the interfaces between the aluminium substrates and the adhesive bond, which is the main significantly different parameter between SBI and NSBI samples. It is likely that the SH-like modes propagating along the lap-joint, i.e. SH0 and SH1 -like modes, do not keep the same amplitude depending on the interfacial conditions existing between the adhesive layer and the aluminium plates. In such conditions, their interference is different for each sample, thus making it different the resulting time traces measured past the two joints. Fig. 5c indicates that almost no multi-reflections (or only multireflections with very little amplitude) occur for the SBI-OP sample. Surprisingly, the amplitude of the direct wave is higher than that of any SH0 mode transmitted past the four lap-joints. This may be explained by the fact that the energy (or part of the energy) which was transferred to multiple echoes, like those which are visible for the SBI and NSBI samples (Fig. 5a and b), is now kept (or partially kept) by the wave, which is directly transmitted past the joint. Although the aluminium plates are sand-blasted for this SBI-OP sample, the oil pollutant, which was deposited on each aluminium surface before the adhesive was applied, is likely to alter the interfacial conditions at both aluminium-adhesive interfaces of the lap-joint. However, the very different time responses measured for both SBI-OP and NSBI samples indicate that the interfacial conditions are not modified in the same way if there is no sandblasting or addition of oil pollutant. This confirms the good sensitivity of the SH0 mode to the interfacial adhesion. Finally, Fig. 5d shows two echoes in the signal detected past the SBI-T lap-joint sample. No specific procedure was followed to deliberately degrade the interfacial adhesion, but the measured signal (well reproducible over the 5 tracks) contains one echo less than that measured past the SBI joint (no third wave-packet is visible either because it is so small that it is totally lost in the noise, or because it is not produced by the propagation through that bond), and the amplitudes of both remaining echoes are significantly smaller (3–4 times smaller) than those shown in Fig. 5a. Although no pollutant was added to that sample and sand-blasting was properly applied to the aluminium plates before assembling, the glass–epoxy tissue inserted in that adhesive bond to control its thickness has a strong effect on the detected SH0 signal. In a preliminary approach, this can be easily justified by the extra 0.2 mm thickness, which is added by the tissue itself, as well as by its mechanical properties. Moreover, this tissue adds two more interfaces to the bond line, and the following section will demonstrate that the mechanical stiffness of these interfaces significantly affects the SH0 time waveform measured past the lap-joint. During these measurements, there was no room in our set-up for positioning the receiving EMAT between the transmitting one and the lap joint; this would have allowed the incident SH0 mode to be picked up and its amplitude to be used for normalizing these modes for all signals transmitted past the lap-joint. In this way, transmission coefficients would have been evaluated, thus providing a sensible parameter for comparing measured and numerically simulated data. Since EMAT transducers send/detect waves in/ from both directions aligned with their active axis, very long samples would have been necessary to avoid unwanted reflections from plate edges, and to resolve in time the incident and reflected wave modes. Our samples are too short for such measurements to be made, so an alternative was chosen consisting of normalizing our simulated data so that measured and predicted signals could be compared. Noting that the time-trace measured for the SBI-OP sample has the biggest amplitude among all experimental

measurements, the normalizing factor was chosen so that the simulated signal corresponding to that case has the same amplitude as that measured. All simulated signals presented in the next section are normalized by that factor, and all measured signals are kept unchanged.

474

3. Modelling

479

The purpose of this model is to mimic the experiments described previously, using all known material properties as input data, and to set up an optimization process consisting of determining unknown properties, so that predicted waveforms fit those measured as much as possible. Comsol Multiphysics software [58] is used in the general Partial Differential Equation mode, so that the following equations, boundary conditions, absorbing conditions, excitation, etc. are implemented according to procedures already described in other publications [43,63–65].

480

3.1. Description of the model

489

This is a two-dimensional anti-plane shear deformation problem, so only one non-zero displacement component, u3, can be considered as a function of spatial coordinates x1, x2 shown in Fig. 6. In the time domain this component can therefore be written as:

490

0 B Uðx1 ; x2 ; tÞ ¼ @

1

0

0

0

1

C B C 0 A ¼ @ 0 Aeiðxtkx1 Þ u3 ðx1 ; x2 ; tÞ u3 ðx2 Þ

2

~3 @ u ~3 @ u G þ @x21 @x22

1

0

!

0 Te 1 Be C B @ T2 A ¼ @ 0 r~ 13 Te 3

~3 ¼ qx2 u

0 0 ~ r23

481 482 483 484 485 486 487 488

491 492 493 494

495

498 499 500 501 502 503 504 505 506 507 508 509

510

512

1

0

n1 r~ 13 B C B r~ 23 C A@ n2 A ¼ @ n3

1

r~ 13 n3 C r~ 23 n3 A ~ ~ r13 n1 þ r23 n2

513 514 515 516 517 518 519

520

ð3Þ 522

where n is a unit vector outward to a domain X and normal to its ~ is the Fourier-transform of the stress tensor. boundary dX, and r At the outer or internal surfaces of the lap-joint samples studied here, the unit outward vector is defined along the x2 direction (or opposite) so the stress vector is reduced to only one non-zero component, the third one:

~ @u ~ 23 n2 ¼ Galu 3 n2 Te 3 ¼ r @x2

478

ð2Þ

10

0

477

497

where q and G are the mass density and shear modulus, respectively, of the material. G can be either real or complex, depending on whether the material is elastic (e.g. aluminium) or viscoelastic (e.g. adhesive). Later in the paper, G may be noted either Galu or Gadh, according to the material considered. ~ 3 , the expresIn such a case of single displacement component u e ¼r ~ n is: Q4 sion of the stress vector, T

0

476

ð1Þ

where t is the time variable, x is the circular frequency, equal to 2pf with f being the frequency, k is the guided mode wavenumber (k = 2p/k with k representing the mode wavelength), x1 is the position along the direction of propagation, x2 is the position across the wave-guide thickness, and finally i2 = 1. To speed up the numerical computations and properly take into account the viscoelastic properties of the adhesive, the equation of motion is written and solved in the frequency domain [62]. Consequently, the Fourier transform (FT) of the above displacement com~ 3 (x1, x2, x) = FT[u3(x1, x2, t)]. In these ponent is considered, i.e. u conditions, the equation of equilibrium for such motion in isotropic materials can be written as 2

475

ð4Þ


523 524 525 526 527 528

529 531

ULTRAS 4785


22 March 2014 8


Fig. 6. Schematic diagram of FE model used for predicting the propagation of SH-like wave modes along the lap-joint samples.

532 533 534 535 536 537 538 539 540 541 542 543 544

where n2 is the second component of n and is equal to ±1 when n is parallel to x2. The outer boundaries of the system, i.e. the surfaces of the three-layered joint, as well as those of the aluminium plates, are e 3 is equal to zero. At the inner interface between free of stress, so T the aluminium plates and the adhesive layer, the boundary condie 3 is continuous, but there tions are defined so that the stress T might be a jump of displacements in the x3 direction. A shearspring model is then used to ensure these interfacial conditions [45–54]. Its role consists in modelling changes in adhesion and, in the current study, predicting the effects of such changes on e 3 stress is then writthe propagation of SH-like wave modes. The T ten in the form:

545 547

548 549 550 551 552 553 554 555 556 557 558 559 560 561 562 563 564 565 566 567 568 569

~3 Te 3 ¼ kT Du

ð5Þ 3

where kT represents a uniform density of shear springs (N/m ) along the interface joining two adjacent materials, which in our study are the adhesive and the aluminium or the tissue, so that or tissue ~3 ¼ u ~ 3adhesiv e u ~ alu Du is the displacement jump between the 3 adhesive and either the aluminium or the tissue, the sign of the difference depending on the material this jump is considered from. As shown in a previous publication [53], such an interface could also be modelled as a very thin material layer with a thickness hinterface, a mass density and an elastic shear modulus Ginterface ¼ kT hinterface . Such a layer model would involve no extra equation or boundary conditions to be implemented in the FE model; however, it would be much more demanding in terms of number of degrees of freedom because very small finite elements would be required for meshing the various interfacial thin layers (up to four of them) of the lap joints. The interface spring model has already shown excellent efficiency in the way it produces the same results as the layer model while saving a very significant number of degrees of freedom [53]. The four plate edges and both edges of the adhesive layer, shown in Fig. 6, are also stress free. These are normal to direction x1 so that the stress vector is again reduced to only one non-zero component:

570 572

573 574

~ @u ~ 13 n1 ¼ G 3 n1 ¼ 0 Te 3 ¼ r @x1

ð6Þ

where n1 is the first component of n and is equal to ±1 when n is parallel to x1. G equals either Galu or Gadh, accordingly.

3.2. Specific recent absorbing regions

575

As illustrated in Fig. 6, absorbing regions are implemented in the FE model to suppress unwanted reflections from the edges of the sample, i.e. those not belonging to the overlapping zone. In this way, both aluminium plates are simulated as semi-infinite, each having one reflecting edge adjacent to the lap-joint. In the frequency domain, either PML (Perfectly Matched Layers) or gradually increasing viscoelastic regions may be used [64]. The former require a length equal to about one wavelength of the propagating mode to be absorbed, and need the equation of motion to be added a specific damping term, which is not always possible depending on the software/code being used; moreover, PMLs are known to become inefficient when inverse modes (modes where phase and energy velocities have opposite signs) are incoming, and it may not be possible to avoid the propagation of such modes when scattering problems are investigated. Indeed, mode conversion is a physical phenomenon, and the choice of scattered modes can usually not be controlled. Absorbing material regions with gradually increasing viscoelastic properties may be an alternative since they can easily be implemented in almost any software/code, and they can absorb any type of wave modes including inverse modes. However, such regions are known to be demanding in length, i.e. about three times the wavelength of the propagating mode to be absorbed. Recently, an original mathematical formulation was proposed for varying the material properties within such absorbing regions in such a way that they become more efficient, i.e. so that they can be significantly reduced in length while still absorbing all types of guided waves [65]. Traditionally, the imaginary parts of the elastic moduli are gradually increased as penetrating into the region. In the new expression, this is still true but the real part of the moduli, i.e. the material stiffness, is gradually decreased so that the mode wavelengths decrease, thus shortening the required length of the absorbing region, and the mass density is gradually rendered complex in such a way that the acoustic impedance remains as close as possible to that of the material, which constitutes the medium of interest. This model is presented in reference [65] but a specific paper is being prepared to explain in detail how these new absorbing regions are defined and to demonstrate their efficiency for various types of guided waves (Lamb, SH, inverse modes, etc.) at different frequency regimes, for both two-dimensional and three-dimensional cases, where modes may penetrate the absorbing region with various incident angles. The principal mathematical elements for using such absorbing regions in the current study are recalled below:

576


577 578 579 580 581 582 583 584 585 586 587 588 589 590 591 592 593 594 595 596 597 598 599 600 601 602 603 604 605 606 607 608 609 610 611 612 613 614 615 616 617 618

ULTRAS 4785


22 March 2014 9


Table 2 Selection of FE simulated data (dashed frame: – – –) for their best fitting with measured records (solid bold frame: —), i.e. so that relative differences (dotted frame: jjj) with measured amplitudes (or amplitude ratios) and time shifts for individual first three wave-packets (or two or one if less than three packets) are within the experimental reproducibility intervals (or as close as possible to these) indicated in Table 1.

621 622 623 624 625 626 627 628 629 630 631 632 633 634 635 636 637 638 639 640 641

GAR ¼ Galu ð1 aÞ and qAR ¼

qalu ð1 aÞ

ð7Þ

3 jx xAR j with a ¼ 1 b þ ib and b ¼ b 1LAR1 , where x1 is the position along and within the absorbing region, xAR 1 is a specific value of x1 corresponding to the starting position of the absorbing region, i.e. the junction position between the propagating domain and the absorbing region, LAR ¼ 1:5kSH0 is the length of the absorbing region, b is a coefficient fixing the rate in changes of the material parameters as penetrating within the absorbing region (usually, b is between 0.5 and 2 depending on the modes to be absorbed and the frequency; here, b was set equal to 1.5). kSH0 is the wavelength of the SH0 mode to be absorbed, qalu and qAR are the mass densities in the propagating medium and absorbing region, respectively, Galu and GAR are the shear moduli for the same media, respectively. Unlike traditional absorbing regions, which must have a length equal to or greater than three times the maximum wavelength, the length of the above-defined absorbing regions can be reduced to 1.5 times the maximum wavelength. In our study, as only the SH0 mode propagates along the aluminium plate components, and as it is absolutely non-dispersive (see Fig. 3), that maximum wavelength is determined by the lowest frequency in the spectrum of the excitation signal.

642

3.3. Temporal excitation and response via frequency modelling

643

The excitation applied to the FE domain is a volume force oriented along the x3 direction. It tends to simulate the Lorentz force, which is applied by the EMAT transmitter to the aluminium plate. This excitation is therefore defined within a 1 mm deep region located underneath the top surface of one of the aluminium plates. In the FE model, this starts immediately at the right of the left-handside absorbing region (Fig. 6). Although the Lorentz force produced by the EMAT transmitter varies according to a spatial period (set by the arrangement of the magnets) equal to the desired acoustic

644 645 646 647 648 649 650 651

wavelength k, along the x1 direction and over a few periods, the above-mentioned simulated excitation extends only 2 mm along x1, in the FE model. As SH0 is the sole SH-like mode that can propagate along the 3 mm thick aluminium plates in the frequency range of interest, there is no need to define a spatially mode-selecting source. The orientation along x3 of the volume force is sufficient

Absolute value of out-of-plane displacement, w (a.u.)

619

2.1

Gadhesive = 0.6 GPa Gadhesive = 0.8 GPa

1.8

Gadhesive = 1.0 GPa 1.5

1.2

Gadhesive = 1.2 GPa 0.9

0.6

0.3

0 0

3 101 4

6 101 4

9 101 4

1.2 10 1 5

1.5 10 1 5

3

Interfacial stiffness KT (N/m ) Fig. 7. Displacement produced past the adhesive bond by SH0 wave mode versus aluminium/adhesive interfacial stiffness values, for several values of adhesive shear modulus (not shown in the figure, this shear modulus has in fact an imaginary part equal to 3% of the value shown near each curve) – Frequency = 260 kHz.


652 653 654 655 656 657

ULTRAS 4785


22 March 2014 10

662 663 664 665 666 667 668 669 670 671

0.3

(a)

1 0.2

0.1

2

3

0

-0.1

-0.2

-0.3 40

60

80

100

120

(b)

0.3

Simulated SH0 waveform past lap-joint

661

mode and its echoes; this mode has uniform displacement across the plate, so any position monitored through the plate thickness would show the same output data. After all these considerations the size of the FE model can be significantly reduced. For the excitation signal a Gaussian-windowed, 8-cycle, toneburst is chosen with centre frequency equal to 260 kHz according to explanations given in Section 2.2. The length chosen for the temporal domain is 200 ls, long enough to contain several echoes that may occur within the bonded joints, as experienced in the measured signals. This makes the frequency spectrum of the excitation run from 170 kHz to 400 kHz, down to 40 dB, with frequency step equal to 5 kHz. The FE model is then solved for each of these 47 frequency components, considering the corresponding complex ~ 3 displacement is amplitudes of this excitation spectrum. The u

140

1

0.2

0.1

2

3

0

-0.1

-0.2

-0.3

Time (µs)

40

60

80

100

120

140

Time (µs)

(c)

0.3

1

0.2

0.1

2

3

0

-0.1

-0.2

-0.3

(d)

0.3


660

to launch SH0 only, as long as the frequency remains below the SH1 frequency cut-off, which is always the case in our study, for the aluminium plates (not for the three-layered lap-joint zone). Note, however, that having EMAT elements, which reproduce the desired mode wavelength over 3–4 times that wavelength, could be useful in situations where mode selection is required, e.g. for different plate samples or higher operating frequencies for which there would be more than one SH-like mode (e.g. above 500 kHz in Fig. 3). This lack of need for spatial mode selection in the low frequency regime is also true for the monitoring region located past the overlapping zone, which is therefore reduced to a single ~ 3 displacement component at point in the model. Picking up the u any point on the second aluminium plate, past the lap-joint and before the absorbing region of course, shows the transmitted SH0


659


658


0.2

1 2

0.1

3 0

-0.1

-0.2

-0.3 40

60

80

100

Time (µs)

120

140

40

60

80

100

120

140

Time (µs)

Fig. 8. FE-predicted transmitted waveforms past lap-joint for KT Alu-Adh = 1.5 PPa/m and GAdh = (a) 0.6 (1 + i0.03), (b) 0.8 (1 + i0.03), (c) 1.0 (1 + i0.03) or (d) 1.2 (1 + i0.03) GPa.


672 673 674 675 676 677 678 679 680 681 682 683 684 685

ULTRAS 4785


22 March 2014 11


691

monitored past the joint, at the monitoring point shown as a large dot in Fig. 6, for each of these frequencies. An inverse FFT is then applied to the set of these monitored displacements so that the temporal response of the lap-joint sample can be reconstructed for comparison purposes with the measured waveforms shown in Fig. 5.

692

3.4. Determination of adhesive and cohesive properties

693

Taking the above criteria, the model is made of two 83 mm long aluminium plates including two absorbing regions of 26 mm in length (1.5 kmin 1.5 17 mm). It is meshed by 4655 secondorder (quadratic), triangular elements with maximum size of 0.76 mm (a fifth of the minimum wavelength) and 31062 degrees

690

694 695 696 697

0.3

0.3

(a) Simulated SH0 waveform past lap-joint

689

of freedom. On an Intel Core i7 machine with 3.4 GHz processor and 16 Gb of RAM, the computation job takes 25 s for the 47 frequency components. The extra post-processing done with Matlab ~ 3 displacements at the monitoring point, consists of loading the u for all these frequencies, then of calculating properly the inverse Fourier transform so that the temporal response of the simulated sample can be constructed. This processing step lasts about 8 s on the same i7 machine. This optimized model is therefore suitable for running large series of numerical simulations with variable values for the shear modulus of the adhesive, Gadh, and for the shear stiffnesses, KT, considered at the several interfaces of the lap-joint. The final aim is to determine values of these parameters, so that all predicted waveforms fit those measured as well as possible (Fig. 5). Quantitative comparison between experimental and FE-simulated

0.2

1 0.1

2

3

0

-0.1

-0.2

-0.3

(b)

0.2

1 2

0.1

3

0

-0.1

-0.2

-0.3 40

60

80

100

120

140

40

60

Time (µs)

(c)

0.3

0.2

1

0.1

80

100

120

140

Time (µs)

2

3

0

-0.1

-0.2

-0.3

(d)

0.3


688


687


686

1

0.2

0.1

2

3

0

-0.1

-0.2

-0.3 40

60

80

100

Time (µs)

120

140

40

60

80

100

120

140

Time (µs)

Fig. 9. FE-predicted transmitted waveforms past lap-joint for GAdh = 1.0 (1 + i0.03) GPa and KT Alu-Adh = (a) 0.01, (b) 0.03, (c) 0.1 or (d) 0.3 PPa/m.


698 699 700 701 702 703 704 705 706 707 708 709 710 711

ULTRAS 4785


22 March 2014 12 712 713 714 715 716 717 718 719 720 721 722


temporal signals is considered to be satisfactory when differences (in percentage, the measured data being the reference) between the following measured and predicted quantities become smaller than (or as close as possible to) the corresponding relative standard deviations obtained for the reproducibility measurements discussed in Section 2.2 and presented in Table 1: – amplitude A1 and time t1 for 1st wave-packet, – amplitude ratios between 2nd or 3rd wave-packets and 1st wave-packet, A2/A1 and A3/A1, – time shifts between 2nd or 3rd wave-packets and 1st wavepacket, t2-t1 and t3-t1

723

726 727 728 729 730 731 732 733 734 735 736 737 738 739 740 741 742 743 744 745 746 747 748 749 750 751

0.3

0.2

0.1

2

3

0

-0.1

-0.2

-0.3

40

60

0.3

(a)

1


725

As explained in Section 2.2, these six quantities are picked up on the three main wave-packets (or less if appropriate) of signals, and constitute criteria of acceptability for comparisons between measured and FE simulated signals. Table 2 presents numerical data obtained from the measured signals and from signals simulated at several stages of the adhesive properties optimization process. This table shows four sets of data, i.e. one per sample. Each set displays data picked up from the experimental signals and from various simulated signals obtained at different stages of the optimization process for the adhesive properties. Experimental quantities t1, t2 t1, t3 t1, A1, A2/A1 and A3/A1, are framed by solid bold lines, while those predicted for the most suitable parameters (adhesive shear moduli and/or interfacial stiffness) are framed by dashed bold lines. In order to make predicted signals as close as possible to measured ones, the following procedure is applied: a/The reference sample, SBI, is considered first. For this sample, the shear stiffness, KT, at the aluminium/adhesive interface is supposed to have a nominal value above which any further change (in KT) has no effect or only a negligible effect on wave propagation. Also in this sample, the shear modulus of the adhesive, Gadh, is likely to have a value close to that given in the supplier’s data sheet [58]. To evaluate these parameters, the model is run for several values ~ 3 , is plotted versus KT. of Gadh, and the anti-plane displacement, u Fig. 7 shows these plots, which clearly indicate that increasing the shear stiffness KT when this is greater than 1015 N/m3 has no significant effect on the SH0 propagation, for any values of Gadh between 0.6 GPa and 1.2 GPa, which are chosen as extreme values for representing adhesives that are not fully cured and perfectly


724

cured, respectively [27,43,44]. Therefore, KT is set at 1.5 1015 N/ m3, a value chosen to match the plateau reached by the displacement produced by the SH0 mode transmitted past the lap-joint, for any sensible value of Gadh. For convenience, in the following the unit for KT will be changed from N/m3 to PPa/m, where PPa/ m stands for 1015 Pa/m or 1015 N/m3 (capital ‘P’ for peta, which is 1015). Consequently, 1.5 PPa/m is considered here as representative of a good quality aluminium/adhesive interface, as that resulting from all the attention, which was given to make sample SBI. Next, still for that sample, the value of Gadh is tuned so that the transmitted signal predicted at the monitoring point becomes as similar in shape as possible to that measured and shown in Fig. 5a, and also so that all six simulated quantities t1, t2 t1, t3 t1, A1, A2/A1 and A3/A1 conform as closely as possible to the corresponding measured data. Fig. 8 shows four waveforms predicted with the four values attributed above to Gadh, i.e. 0.6, 0.8, 1.0 and 1.2 GPa. Comparing each of these graphs with Fig. 5.a clearly indicates that Gadh is rather close to 1 GPa. Indeed, for the three echoes measured through the SBI sample to be properly predicted, i.e. with similar temporal and amplitude data as mentioned above, Gadh has to be set close to 1 GPa in the FE model (Fig. 8c). As seen in Table 2, the relative differences with experimental data for all three predicted time quantities, and also for the A2/A1 ratio, fit well within the experimental reproducibility intervals given in Table 1. Amplitude A1 and ratio A3/A1, however, exhibit differences from the measured data, which are outside the corresponding experimental reproducibility intervals, but close enough for the whole predicted signal to be considered as an acceptable match with the measured waveform. Such a value for the shear modulus (1 GPa) is very standard for well-cured, epoxy-based adhesive [44] and especially for the current AF3109 adhesive [58]. Note that this shear modulus is systematically rendered complex in the model, by adding an imaginary part equal to 3% of its real part. This is supposed to be more representative of the real adhesive, which is viscoelastic; however, viscoelasticity has been checked to have negligible effect on wave propagation and on the waveforms predicted past the lap-joints because the frequency here is very low, i.e. between 170 and 400 kHz. Nevertheless, the model is kept unchanged and will thus be ready for dealing with other cases in the future, e.g. if higher frequencies and/or higher-order modes more sensitive to viscoelastic properties are investigated.

80

100

Time (µs)

120

140

(b)

1 0.2

0.1

2

3

0

-0.1

-0.2

-0.3

40

60

80

100

120

140

Time (µs)

Fig. 10. FE-predicted transmitted waveforms past lap-joint for KT Alu-Adh = 0.3 PPa/m and GAdh = (a) 0.75 (1 + i0.03) or (b) 0.5 (1 + i0.03) GPa.


752 753 754 755 756 757 758 759 760 761 762 763 764 765 766 767 768 769 770 771 772 773 774 775 776 777 778 779 780 781 782 783 784 785 786 787 788 789 790 791 792

ULTRAS 4785


22 March 2014 13


797 798 799 800 801 802 803 804 805 806

0.3

1

0.2

0.1

2

3

0

-0.1

-0.2

-0.3

40

60

0.3

(a) Simulated SH0 waveform past lap-joint

796

a relative difference from the experimental data, which does not fit inside the experimental reproducibility intervals given in Table 1. The achieved value for KT shows a very significant drop when compared with that obtained for the SBI sample, indicating that the absence of sand-blasting is likely to severely decrease the quality of the aluminium/adhesive interfaces. c/Next, sample SBI-OP is considered. For this sample, the adhesive was prepared and the assembly was made in exactly the same conditions as those used for sample SBI, including sand-blasting, except that an oil pollutant was deposited onto the aluminium surfaces to be assembled. This is supposed to cause weakness in the interfacial adhesion. First, the KT value is adjusted so that the predicted waveform is as similar as possible to the measured result (Fig. 5c). However, large series of computations show that

80

100

120

(b)

0.2

1

0.1

2 3

0

-0.1

-0.2

-0.3

140

40

60

Time (µs)

(c)

0.3

0.2

0.1

1

2

0

-0.1

-0.2

-0.3

40

60

80

100

Time (µs)

80

100

120

140

Time (µs)

120

140

(d)

0.3


795

b/Next, sample NSBI is considered. For this, the adhesive was prepared and the assembly was made in exactly the same conditions as those used for sample SBI, except that sand-blasting was not applied. There is then no reason for the shear modulus of the adhesive, Gadh, to be different from that established in a/. This parameter therefore remains unchanged in the FE model but the value of KT is changed over a large range of values from 0.01 to 1.5 PPa/m (i.e. following the curve with plain-circle dots in Fig. 7). Fig. 9 shows a sketch of predicted waveforms with four different values of KT. As indicated in Table 2, KT has to be given a very low value, very close to 0.03 PPa/m corresponding to Fig. 9.c, for five of the six simulated quantities t1, t2 t1, t3 t1, A1, A2/A1 and A3/A1 to match the corresponding experimental data as closely as possible. As seen in Table 2, only the predicted A3/A1 ratio shows


794


793

0.2

0.1

1

2

0

-0.1

-0.2

-0.3

40

60

80

100

120

140

Time (µs)

Fig. 11. FE-predicted transmitted waveforms past lap-joint for GAdh = 1.0 (1 + i0.03) GPa, KT Alu-Adh = 1.5 PPa/m and KT Tissue-Adh = (a) 1.5, (b) 0.01, (c) 0.0006 PPa/m; (d) KT Tissue-Adh = 1.5 PPa/m but air-bubbles have been distributed all along both Tissue/Adhesive interfaces.


807 808 809 810 811 812 813 814 815 816 817 818 819 820

ULTRAS 4785


22 March 2014 14 821 822 823 824 825 826 827 828 829 830 831 832 833 834 835 836 837 838 839 840 841 842 843 844 845 846 847 848 849 850 851 852 853 854 855 856 857 858

859 860 861 862 863 864 865 866 867 868 869 870 871 872 873 874 875 876 877 878 879 880 881 882 883 884 885 886


adjusting this parameter is not sufficient to obtain a satisfactory correlation between simulated and measured waveforms. For instance, no waveform shown in Fig. 9, representing different values of KT, corresponds to that shown in Fig. 5c, and many more jobs than these four, varying the KT value, were run unsuccessfully, i.e. they all provided simulated waveforms but which did not match the measured signal for the SBI-OP sample. In fact, the adhesive shear modulus, Gadh, also has to be tuned for good agreement to be obtained. This parameter has to be decreased to 0.5 GPa, while the KT value has to be set very close to 0.3 PPa/m, for the desired agreement to be reached. This decay in Gadh may be explained by a diffusion of the oil pollutant into the adhesive during the curing process, thus altering the adhesive shear stiffness. Fig. 9d shows that the predicted signal is very different from the measured one when Gadh = 1.0 GPa and KT = 0.3 PPa/m (the final KT value for SBI-OP). Fig. 10.a shows that the agreement improves when KT is kept equal to 0.3 PPa/m and Gadh is reduced to 0.75 GPa, and even better if Gadh is given a value close to 0.5 GPa (Fig. 10b). Table 2 confirms quantitatively the very good agreement between measured and simulated quantities t1, t2 t1, A1 and A2/A1; note this time that t3 t1 and A3/A1 are not considered as comparative criteria because no 3rd wave-packet was present in the measured signals. d/Finally, sample SBI-T is considered. Because of the thin glass– epoxy tissue which was inserted into the adhesive in this sample (see Section 2.1), two extra interfaces (between adhesive and tissue) have to be considered in the FE model, in addition to both aluminium/adhesive interfaces. The sample was very carefully prepared, i.e. sand-blasting was applied to the aluminium, no pollutant was used and careful cleaning was carried out before assembling. The value given to KT for modelling both aluminium/ adhesive interfaces is the same as that previously established for the SBI sample, i.e. 1.5 PPa/m. However, the model is modified so that two 0.15 mm thick layers of the adhesive are considered on each side of the 0.2 mm thick glass epoxy tissue, according to the way the sample was made. This is illustrated in Fig. 6 (see small lower diagram). This tissue is supposed to be homogeneous at the frequency 260 kHz, and its mechanical properties, i.e. density qTissue and shear modulus GTissue, are set at 1800 kg/m3 and GTissue = (3.5 + i0.3) GPa, respectively, which correspond to standard data for such material [66]. Stiffness KT at both tissue/adhesive interfaces is naturally first given the same value as that obtained for the good-quality aluminium/adhesive interfaces (SBI sample), i.e. 1.5 PPa/m. In this case, as shown in Fig. 11a, the predicted waveform is very different from that measured for the SBI-T sample (Fig. 5d). The KT stiffness at both tissue/adhesive interfaces has to be reduced to much lower values than 1.5 PPa/m for the predicted signal to begin looking like the measured one. To distinguish between both types of interfacial stiffness, i.e. between the aluminium and adhesive components and between the tissue and adhesive components, these will be further noted KT Alu-Adh and KT Tissue-Adh, respectively. Since the adhesive used in this case is supposed to be slightly softer than that used for the three previous samples (see Section 2.1), a numerical investigation was carried out to quantify the effect of varying Gadh between 0.7 and 1.0 GPa, for a few arbitrary values of KT Tissue-Adh, on the transmitted wave mode. The effects were shown to be negligible, probably due to the presence of the self-supported film (tissue), which brings a high shear stiffness (3.5 GPa) over a significant thickness (0.2 mm), and which thus has a determinant effect on the global shear stiffness of the cohesive component of the bond. The value chosen for Gadh in the model is then equal to 1.0 GPa, as for the previous cases a/ and b/. Fig. 11b shows that the predicted signal is beginning to be similar to the measured signal (Fig. 5d) if KT Tissue-Adh is set equal to 0.01 PPa/m, but still the stiffness has to be reduced to 0.6 TPa/m (0.0006 PPa/m) for the simulation (shown

in Fig. 11c) to become very close to the experimental waveform, and for the simulated quantities t1, t2 t1, A1 and A2/A1 to match the measured ones. Table 2 shows that predicted A1 and A2/A1 present differences from the experimental data, which are outside the experimental reproducibility intervals given in Table 1, but the global shapes of measured and predicted waveforms are nevertheless very similar, so the bond properties can be considered acceptable in a first approximation. In fact, there are only two wave-packets of small amplitudes in the measured signal (Fig. 5d) and the best-fitting simulated signal also displays only two wave-packets (i.e. A3 = 0) with small amplitudes. Finally, Fig. 11d displays an interesting simulated waveform obtained by setting KT Tissue-Adh = 1.5 PPa/m, i.e. a nominal value corresponding to good adhesion, but where series of holes simulating air-bubbles have been distributed along both tissue/adhesive interfaces. It can be seen that using such total discontinuities of displacements and stresses along about two thirds of the whole interface length results in the simulated signal being fairly similar to the measured signal (Fig. 5d). It is also similar to that obtained with no bubbles but with KT Tissue-Adh = 0.6 TPa/m (Fig. 11c), except that the amplitude is not equal to zero in between both main echoes, as is the case in Fig. 11.c. This is likely to be due to multiple scattering occurring between the various air bubbles, thus causing dispersion of the temporal signal. Nevertheless, such an effect does not seem to occur in the experimental measurement (Fig. 5d), thus making the low-valued KT Tissue-Adh model more appropriate than the air-bubble model for the current investigation, which is a good point because it is much simpler to adjust a value for KT Tissue-Adh than to implement empty cavities in the FE model. However, the fact that the measured waveform is similar to both predictions obtained either with 66% of the adhesive/tissue interfaces being disconnected, or with an extremely low value of KT Tissue-Adh, indicates a severe weakness of both adhesive/tissue interfaces, probably due to inappropriate preparation of the tissue surfaces before the adhesive assembly was made, and/or to a poor match between the physicochemical properties of the adhesive and the tissue.

887

4. Conclusions

924

The SH0 guided-wave mode was successfully generated and detected in aluminium plates forming adhesively-bonded lap joint samples, using efficient EMAT transducers. Three samples were investigated, each with the aluminium/adhesive interfaces prepared differently (with or without sand-blasting applied to the aluminium plates for two samples, and the third was polluted using an oily agent), plus one sample with a thin glass–epoxy self-supported film (called tissue) inserted within the adhesive bond. Signals transmitted past the various lap-joints revealed good signal-to-noise ratio, good uniformity in the adhesive bonds, and high sensitivity of the investigated transmitted SH0 mode to the adhesion quality. A finite element-based model was developed to simulate the Lorentz force produced by the EMAT transmitter, the propagation along the plates and lap-joints, and the reception by the EMAT receiver. This model was written in the frequency domain, taking the adhesive viscoelasticity into account and including specific shear spring stiffnesses distributed along the interfaces to model the strength or weakness of the various interfaces of the lap-joint samples. For the first three samples, the two aluminium/adhesive interfaces were considered. For the fourth sample, four interfaces were modelled: two aluminium/adhesive interfaces and two adhesive/tissue interfaces. The models were solved for a series of frequencies corresponding to the frequency components of a toneburst temporal excitation, and inverse Fourier transform was applied to series of anti-plane

925


888 889 890 891 892 893 894 895 896 897 898 899 900 901 902 903 904 905 906 907 908 909 910 911 912 913 914 915 916 917 918 919 920 921 922 923

926 927 928 929 930 931 932 933 934 935 936 937 938 939 940 941 942 943 944 945 946 947 948 949

ULTRAS 4785


22 March 2014 M. Castaings / Ultrasonics xxx (2014) xxx–xxx

1009

displacements monitored past the lap-joints to reconstruct temporal responses at a given observation point. Optimized absorbing regions were implemented in the models, allowing a significant number of degrees of freedom to be saved. Both shear modulus of the adhesive and shear stiffness of the aluminium/adhesive interfaces were successfully quantified so that predicted signals became very similar to signals measured for the first three samples. For the last sample, extra tuning of the shear stiffness at both adhesive/tissue interfaces was successfully achieved. The very good correlations obtained between predicted and measured signals demonstrate the possibility of using the SH0 guided-wave mode to quantify the adhesive shear modulus and interfacial shear stiffnesses separately, as they are good indicators of the quality of adhesive bonds. However, looking carefully at the whole set of simulated signals, it appears that some of them are very similar despite being predicted using quite different sets of values for the material parameters sought. This means that the sets of values proposed in this paper do not constitute unique solutions for the various samples investigated. Nevertheless, given the procedure used to obtain these values, i.e. first tuning the adhesive shear modulus while being almost 100% sure that the shear interfacial stiffness is correct, and then adjusting the shear interfacial stiffness while being almost 100% sure that the adhesive shear modulus is the same as in first step, etc., the results are likely to be quite reliable. However, this was possible only because we had a good knowledge of the careful preparation of the various samples. Moreover, the substrates were aluminium plates with well-known mechanical properties and thickness, presenting no dispersion that could affect the ultrasonic wave propagation or mask the effect of the adhesive properties on this propagation. Thus conditions were perfect to reach sensible values for adhesive shear modulus and shear interfacial stiffness. In real cases, knowledge of the components and adhesive joints to be tested would not be as good as in this laboratory investigation. However, the current study has clearly demonstrated the potential of the SH0 guided-wave mode for evaluating separately the adhesive shear modulus and the interfacial shear stiffness of lap-joint structures. Further studies will investigate high-order SH-like modes, e.g. SH1 or SH2 in addition to the SH0 mode, to provide more information about the adhesive and cohesive properties sought, and ensure the uniqueness of the solutions obtained. The propagation and modal conversion occurring at the lap-joint should also be carefully investigated and analyzed to check whether it could provide extra information. Also, composite substrates will be considered soon, using an original trick for efficiently coupling EMAT transducers with polymer and/or carbon-based material plates, for instance. However, another difficulty may arise with the use of composite samples, due to our incomplete knowledge of their mechanical properties and more specifically to the possible dispersion of these properties over space. Indeed, this may have non-negligible effects on the ultrasonic waves, compared with the effects produced by the adhesive/cohesive properties, and using several SH-like wave modes may help to overcome this difficulty. It is hoped that this challenging project will lead to success in the non-destructive evaluation of adhesive shear modulus and interfacial shear stiffness for adhesively bonded composite structures. To check final estimations of material/ interface parameters, destructive mechanical tests are also planned.

1010

Acknowledgement

1011

This work was supported technically and financially by ASTRIUM-ST, St Médard en Jalles, France.

950 951 952 953 954 955 956 957 958 959 960 961 962 963 964 965 966 967 968 969 970 971 972 973 974 975 976 977 978 979 980 981 982 983 984 985 986 987 988 989 990 991 992 993 994 995 996 997 998 999 1000 1001 1002 1003 1004 1005 1006 1007 1008

1012

15

References

1013

[1] A. Higgins, Adhesive bonding of aircraft structures, Int. J. Adhes. Adhes. 20 (2000) 367–376. [2] T.A. Barnes, I.R. Pashby, Joining techniques for aluminium spaceframe used in automobiles. Part II – adhesive bonding and mechanical fasteners, J. Mater. Process. Technol. 99-1 (2000) 72–79. [3] R.D. Adams (Ed.), Adhesive Bonding, Science, Technology and Applications, Woodhead Publishing Limited, Cambridge, 2005. [4] J.Y. Cognard, P. Davies, B. Gineste, L. Sohier, Development of an improved adhesive test method for composite assembly design, Compos. Sci. Technol. 65–3 (2005) 359–368. [5] Z. Chen, R.D. Adams, L.F.M. da Silva, Prediction of crack initiation and propagation of adhesive lap joints using an energy failure criterion, Eng. Fract. Mech. 78–6 (2011) 990–1007. [6] C.C.H. Guyott, P. Cawley, R.D. Adams, The nondestructive testing of adhesively bonded structure: a review, J. Adhes. 20 (1986) 129–159. [7] R.D. Adams, B.W. Drinkwater, Nondestructive testing of adhesively-bonded joints, NDT&E Int. 2–30 (1997) 93–98. [8] S.I. Rokhlin, D. Marom, Study of adhesive bonds using low-frequency obliquely incident ultrasonic waves, J. Acoust. Soc. Am. 2–80 (1986) 585–590. [9] A. Pilarski, J.L. Rose, Ultrasonic oblique incidence for improved sensitivity in interface weakness determination, NDT Int. 21-4 (1988) 241–246. [10] F.J. Margetan, R.B. Thompson, J.H. Rose, T.A. Gray, The interaction of ultrasound with imperfect interfaces: experimental studies of model structures, J. Nondestruct. Eval. 11 (1992) 109–125. [11] B.W. Drinkwater, P. Cawley, Measurement of the frequency dependence of the ultrasonic reflection coefficient from thin interface layers and partially contacting interfaces, Ultrasonics 35 (1997) 479–488. [12] R.J. Freemantle, R.E. Challis, Combined compression and shear wave ultrasonic measurements on curing adhesive, Meas. Sci. Technol. 9 (1998) 1291–1302. [13] S. Dixon, D. Jaques, S.B. Palmer, G. Rowlands, The measurement of shear and compression waves in curing epoxy adhesives using ultrasonic reflection and transmission techniques simultaneously, Meas. Sci. Technol. 15 (2004) 939– 947. [14] P.B. Nagy, L. Adler, Non-destructive evaluation of adhesive joints by guided waves, J. Appl. Phys. 66 (1989) 4658–4663. [15] M.J.S. Lowe, R.E. Challis, C.W. Chan, The transmission of Lamb waves across adhesively bonded lap joints, J. Acoust. Soc. Am. 107–3 (2000) 1333–1345. [16] R. Seifried, L.J. Jacobs, J. Qu, Propagation of guided waves in adhesive bonded components, NDT&E Int. 35 (2002) 317–328. [17] F. Lanza di Scalea, P. Rizzo, Propagation of ultrasonic guided waves in lap-shear adhesive joints: case of incident A0 Lamb wave, J. Acoust. Soc. Am. 115 (2004) 146–157. [18] D. Donskoy, A. Sutin, A. Ekimov, Nonlinear acoustic interaction on contact interfaces and its use for nondestructive testing, NDT&E Int. 34 (2001) 231– 238. [19] D. Yan, B.W. Drinkwater, S.A. Neild, Measurement of the ultrasonic nonlinearity of kissing bonds in adhesive joints, NDT&E Int. 42 (2009) 459– 466. [20] N. Quaegebeur, P. Micheau, P. Masson, M. Castaings, Methodology for optimal configuration in Structural Health Monitoring of composite bonded joints, Smart Mater. Struct. 21-10 (2012) 105001–105012. [21] P. Mylavarapu, E. Woldesenbet, Non-Destructive characterization of bondlines in composite adhesive joints, J. Adhes. Sci. Technol. 20–7 (2006) 647–660. [22] D. Cerniglia, N. Montinaro, V. Nigrelli, Detection of disbonds in multi-layered structures by laser-based ultrasonic technique, J. Adhes. 84 (2008) 811–829. [23] P. Nagy, Ultrasonic detection of kissing bonds at adhesive interfaces, J. Adhes. Sci. Technol. 5–88 (1991) 619–630. [24] T. Kundu, A. Maji, T. Ghosh, K. Maslov, Detection of kissing disbonds by Lamb waves, Ultrasonics 35 (1998) 573–580. [25] S.I. Rokhlin, D.K. Lewis, K.F. Graff, L. Adler, Real-time study of frequency dependence of attenuation and velocity of ultrasonic waves during the curing reaction of epoxy resin, J. Acoust. Soc. Am. 79–6 (1986) 1786–1793. [26] S. Dixon, D. Jaques, S.B. Palmer, The development of shear and compression elastic moduli in curing epoxy adhesives measured using non-contact ultrasonic transducers, J. of Physics D: Appl. Phys. 36–6 (2003) 753–759. [27] M.K. Budzik, B. Mascaro, J. Jumel, M. Castaings, M. Shanahan, Monitoring of crosslinking of a DGEBA-PAMAM adhesive in composite/aluminium bonded joint using mechanical and ultra-sound techniques, Int. J. Adhes. Adhes. 35 (2012) 120–128. [28] H. Wang, M.L. Qian, W. Liu, Laser ultrasonic characterization of adhesive bonds between epoxy coating and aluminum substrate, Ultrasonics 44 (2006) 1349– 1353. [29] A.I. Lavrentyev, S.I. Rokhlin, Ultrasonic spectroscopy of imperfect contact interfaces between a layer and two solids, J. Acoust. Soc. Am. 103 (1998) 657– 664. [30] S. Rokhlin, M. Hefets, M. Rosen, An ultrasonic interface-wave method for predicting the strength of adhesive bonds, J. Appl. Phys. 52–4 (1981) 2847– 2851. [31] A.K. Moidu, A.N. Sinclair, J.K. Spelt, Non-destructive characterisation of adhesive joint durability using ultrasonic reflection measurements, Res. Nondestruct. Eval. 11 (1999) 81–95. [32] P. Nagy, Ultrasonic classification of imperfect interfaces, J. Nondestruct. Eval. 11–3 (4) (1992) 127–139.

1014 1015 1016 1017 1018 1019 1020 1021 1022 1023 1024 1025 1026 1027 1028 1029 1030 1031 1032 1033 1034 1035 1036 1037 1038 1039 1040 1041 1042 1043 1044 1045 1046 1047 1048 1049 1050 1051 1052 1053 1054 1055 1056 1057 1058 1059 1060 1061 1062 1063 1064 1065 1066 1067 1068 1069 1070 1071 1072 1073 1074 1075 1076 1077 1078 1079 1080 1081 1082 1083 1084 1085 1086 1087 1088 1089 1090 1091 1092 1093 1094 1095 1096


Q5

ULTRAS 4785


22 March 2014 16 1097 1098 1099 1100 1101 1102 1103 1104 1105 1106 1107 1108 1109 1110 1111 1112 1113 1114 1115 1116 1117 1118 1119 1120 1121 1122 1123 1124 1125 1126 1127 1128 1129 1130 1131 1132 1133 1134 1135 1136 1137 1138 1139 1140 1141 1142


[33] K. Vine, P. Cawley, A.J. Kinloch, Comparison of normal and oblique incidence ultrasonic measurements for the detection of environmental degradation of adhesive joints, NDT&E Int. 35 (2002) 241–253. [34] T. Pialucha, P. Cawley, The reflection of ultrasounds from interface layers in adhesive joints, in: D.O. Thompson, D.E. Chimenti (Eds.), Review of Progress in Quantitative NDE, vol. 10-B, Plenum, New York, 1990, pp. 1303–1309. [35] R. Ribichini, F. Cegla, P. Nagy, P. Cawley, Study and comparison of different EMAT configurations for SH wave inspection, IEEE Trans. Ultr. Ferroelectr. Freq. Control 58-12 (2011) 2571–2581. [36] F. He, S. Rokhlin, L. Adler, Application of SH and Lamb wave EMAT’s for evaluation of adhesive joint in thin plate, in: D.O. Thompson, D.E. Chimenti (Eds.), Review of Progress in Quantitative NDE, vol. 7-B, Plenum, New York, 1988, pp. 911–918. [37] H. Gao, S. Ali, B. Lopez, Efficient detection of delamination in multilayered structures using ultrasonic guided wave EMATs, NDT&E Intn. 43 (2010) 316– 322. [38] K. Arun et al., An EMAT-based shear horizontal (SH) wave technique for adhesive bond inspection, in: Review of Progress in Quant. Non Destruct. Eval. 31 – AIP Conf. Proc. 1430, 2012, pp. 1268–1275. [39] M.J.S. Lowe, Matrix techniques for modeling ultrasonic waves in multilayered media, IEEE Trans. UFFC 42 (1995) 525–542. [40] B. Hosten, M. Castaings, Surface impedance matrices to model the propagation in multilayered media, Ultrasonics 41–7 (2003) 501–507. [41] M.J.S. Lowe, R.E. Challis, C.W. Chan, The transmission of Lamb waves across adhesively bonded lap joints, J. Acoust. Soc. Am. 107 (2000) 1333–1346. [42] O. Voloshko, Y. Lapusta, V. Loboda, Analytical and numerical study of cohesive zones for a crack in an adhesive layer between identical isotropic materials, Eng. Fract. Mech. 77 (2010) 2577–2592. [43] B. Le Crom, M. Castaings, Shear horizontal guided wave modes to infer the shear stiffness of adhesive bond layers, J. Acoust. Soc. Am. 127–4 (2010) 2220– 2230. [44] Z. Fan, M. Castaings, M.J. Lowe, C. Biateau, P. Fromme, Feature-guided waves for monitoring adhesive shear modulus in bonded stiffeners, NDT&E Int. 54 (2013) 96–102. [45] J.P. Jones, J.S. Whitter, Waves in a flexible bounded interface, J. Appl. Mech. 34 (1967) 905–909. [46] S.I. Rokhlin, Y.J. Wang, Analysis of boundary-conditions for elastic wave interaction with an interface between two solids, J. Acoust. Soc. Am. 89 (1991) 503–515. [47] A. Baltazar, L. Wang, B. Xie, S.I. Rokhlin, Inverse ultrasonic determination of imperfect interface and bulk properties of a layer between two solids, J. Acoust. Soc. Am. 114 (2003) 1424–1434. [48] S. Biwa, S. Hiraiwa, E. Matsumoto, Stiffness evaluation of contacting surfaces by bulk and interface waves, Ultrasonics 47 (2007) 123–129. [49] T. Nam et al., Harmonic generation of an obliquely incident ultrasonic wave in solid–solid contact interfaces, Ultrasonics 52 (2012) 778–783.

[50] J.Y. Kim, A. Baltazar, S.I. Rokhlin, Ultrasonic assessment of rough surface contact between solids from elastoplastic loading–unloading hysteresis cycle, J. Mech. Phys. Solids 52 (2004) 1911–1934. [51] V. Vlasie Belloncle, M. Rousseau, Empirical rheological model for rough or grooved bonded interfaces, Ultrasonics 47 (2007) 10–14. [52] M.V. Golub, A. Boström, Interface damage modeled by spring boundary conditions for in-plane elastic waves, Wave Motion 48 (2011) 105–115. [53] B. Hosten, M. Castaings, Finite elements methods for modeling the guided waves propagation in structures with weak interfaces, J. Acoust. Soc. Am. 117 (2005) 1108–1113. [54] B.W. Drinkwater, M. Castaings, B. Hosten, The measurement of A0 and S0 Lamb wave attenuation to determine the normal and shear stiffnesses of a compressively loaded interface, J. Acoust. Soc. Am. 113–6 (2003) 3161–3170. [55] A. Baltazar, S.I. Rokhlin, C. Pecorari, On the relationship between ultrasonic and microstructural properties of imperfect interfaces in layered solids, in: D.O. Thompson, D.E. Chimenti (Eds.), Review of Progress in Quantitative NDE, vol. 18, Plenum, New York, 1999, pp. 1463–1470. [56] A. Boström, M. Golub, Elastic SH wave propagation in a layered anisotropic plate with interface damage modelled by spring boundary conditions, Q. J. Mech. Appl. Math. 62 (2009) 39–52. [57] A. Boström, O.V. Kvasha, Elastic SH wave propagation in a layered anisotropic plate with periodic interface cracks: exact versus spring boundary conditions, J. Mater. Struct. 5–1 (2010) 67–78. [58] http://multimedia.3m.com/mws/me diawebserver?m wsId=66666UF6EVsSy XTt4xTt4Xf_EVtQEVs6EVs6EVs6E666666–&fn=TDS_AF3109-2.pdf for adhesive reference (last viewed 25.01.14). [59] M. Asgharifar, F. Kong, B. Carlson, R. Kovacevic, An experimental and numerical study of effect of textured surface by arc discharge on strength of adhesively bonded joints, J. Mech. Eng. Automat. 2 (2012) 229–242. [60] A.F. Harris, A. Beevers, The effects of grit-blasting on surface properties for adhesion, Int. J. Adhes. Adhes. 19 (1999) 445–452. [61] http://www.sonemat.com for reference to EMATs manufacturer (last viewed 25.01.14). [62] http://www.comsol.com for reference to Comsol Multiphysics software (last viewed 25.01.14). [63] M. Castaings, C. Bacon, B. Hosten, M.V. Predoi, Finite element predictions for the dynamic response of thermo-viscoelastic material structures, J. Acoust. Soc. Am. 115–3 (2004) 1125–1133. [64] M. Drozdz, Efficient finite element modelling of ultrasound waves in elastic media, Ph.D. thesis, Mechanical Engineering, Imperial College, London, 2008. [65] W. Ke, M. Castaings, C. Bacon, 3D Finite Element simulations of an air-coupled ultrasonic NDT system, NDT&E Int. 42 (2009) 524–533. [66] M. Castaings, Measurement of viscoelastic modules, in: B.S.M. Bruneau, C. Potel (Eds.), Materials and Acoustics Handbook, ISTE-WILEY, London, 2009. ISBN 9781848210745.


1143 1144 1145 1146 1147 1148 1149 1150 1151 1152 1153 1154 1155 1156 1157 1158 1159 1160 1161 1162 1163 1164 1165 1166 1167 1168 1169 1170 1171 1172 1173 1174 1175 1176 1177 1178 1179 1180 1181 1182 1183 1184 1185 1186 1187 1188

Predicting bone strength with ultrasonic guided waves.

Amplitude Dispersion Compensation for Damage Detection Using Ultrasonic Guided Waves.

Ultrasonic guided interface waves at a soft-stiff boundary.

Transverse and Oblique Long Bone Fracture Evaluation by Low Order Ultrasonic Guided Waves: A Simulation Study.

3D modeling of circumferential SH guided waves in pipeline for axial cracking detection in ILI tools.

The anisotropic propagation of ultrasonic guided waves in composite materials and implications for practical applications.

Axial transmission method for long bone fracture evaluation by ultrasonic guided waves: simulation, phantom and in vitro experiments.

Influence of the Spatial Dimensions of Ultrasonic Transducers on the Frequency Spectrum of Guided Waves.

High-frequency guided ultrasonic waves for hidden defect detection in multi-layered aircraft structures.

The influence of temperature variations on ultrasonic guided waves in anisotropic CFRP plates.

Measurement of viscosity of highly viscous non-Newtonian fluids by means of ultrasonic guided waves.

Nondestructive measurement of neutral temperature in continuous welded rails by nonlinear ultrasonic guided waves.

Rainbow trapping of ultrasonic guided waves in chirped phononic crystal plates.

Numerical simulation of monitoring corrosion in reinforced concrete based on ultrasonic guided waves.

Symmetric low-frequency feature-guided ultrasonic waves in thin plates with transverse bends.

Reference-free corrosion damage diagnosis in steel strands using guided ultrasonic waves.

Design, development and evaluation of an automatic fruit-juice pasteurization system using microwave - ultrasonic waves.

Interaction of low-frequency axisymmetric ultrasonic guided waves with bends in pipes of arbitrary bend angle and general bend radius.

Dynamic interfacial trapping of flexural waves in structured plates.

Ultrasonic evaluation of the scrotum.

Ultrasonic evaluation of the heart.

Ultrasonic tracking of shear waves using a particle filter.

The reflection of guided waves from simple dents in pipes.

[The percutaneous ultrasonic-guided fluoroscopy-controlled drainage of pericardial fluids].