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Characterizing defects in multi-layer materials using guided ultrasonic waves
Optics and Lasers in Engineering 40 (2003) 371–378
Characterizing defects in multi-layer materials using guided ultrasonic waves R. Chona*, C.S. Suh, G.A. Rabroker Department of Mechanical Engineering, Texas A&M University, College Station, TX, USA
Abstract A brief description is given of a methodology that exploits guided ultrasonic waves, lasers and fiber optics, and simultaneous time–frequency analysis to interrogate the state of a material, component, or structure. This system offers a means by which surface-guided (Lamb and Rayleigh), broadband, ultrasound can effectively be generated and detected in a wide variety of materials in real time and in a non-contact, non-invasive fashion. The propagating ultrasound interrogates the host material in a manner providing a wealth of information when coupled with application of the Gabor wavelet transform to broadband dispersive waveforms. Recent results are presented pertaining to delamination detection within layered copper/ polymer films. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Defects; Multilayer materials; Ultrasound
1. Introduction The Photomechanics Laboratory at Texas A&M University is dedicated to the development and application of real-time, on-line, non-contact, non-invasive methods of material and component inspection and investigation. Applications are centered around the methodology termed TAP-NDE, or Thermal-Acousto-Photonic Non-Destructive Evaluation [1–3]. This method utilizes ultrasound that is both generated and detected by laser optic interactions with the material as a means of interrogation. A brief description of the system and methodology is provided first, followed by results from a recent application to demonstrate the merit and capabilities of the approach. *Corresponding author. E-mail address: [email protected] (R. Chona). 0143-8166/03/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 3 - 8 1 6 6 ( 0 2 ) 0 0 0 9 4 - 5
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R. Chona et al. / Optics and Lasers in Engineering 40 (2003) 371–378
2. System The system shown in Fig. 1 is best described in terms of the chronology of events required to generate, detect and analyze interrogating waveforms in the component material. The first step is to generate the interrogating wave. A short (E10 ns) pulse is fired from a Nd:YAG laser to the surface of the specimen, simultaneously triggering the oscilloscope. This pulse is typically focused down to illuminate a small spot on the specimen and is responsible for the generation of ultrasound in the material through rapid heating and subsequent expansion of the surface and subsurface material layers. As rapid and localized thermal expansion occurs, energy is released in the form of propagating ultrasound in all directions from the generation site guided by the free surface or surfaces causing in-plane as well as out-of-plane displacements. Sensing of the ultrasound is achieved by the Fiber Tip Interferometer (FTI). As the ultrasound passes the location of the FTI, which is positioned at a known distance from the generation site, the out-of-plane displacements are detected. The FTI system is a fiber-based Fizeau type interferometer. The coherent light source in this device is a HeNe laser that is coupled into one single mode fiber leg of a Fused Bi-Conical Taper Coupler (FBTC). The light coupled into this leg is split into two fibers after passing through the coupler itself, thus the FBTC is the analog of the beam-splitter in the classical Fizeau interferometer. The light in one of the output legs is routed to an index matching fluid to eliminate reflections from the termination face of the fiber. The remaining output leg, however, is routed to the specimen surface, where the Fizeau cavity is the standoff distance between the FTI and the specimen. This standoff is typically on the order of millimeters. At this point, the beam is divided into a reference and object beam. The reference beam is the portion of the beam that is internally reflected from the face of the stationary fiber and makes its way in the reverse direction towards a fiber-coupled photodetector. The object beam is that which exits the fiber tip, reflects from the specimen surface and re-enters the fiber. Superposed with the reference beam, the object beam too propagates to the photodetector. As the cavity dimension between the fiber tip and the specimen
optical termination
HeNe Laser
PC
Photodetector FTI
Oscilloscope
FBTC propagating wave
Nd:YAG Laser
≈10 ns generation pulse specimen
Fig. 1. Experimental system.
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changes with passage of ultrasound beneath the fiber tip, the object and reference beams interfere in a dynamic fashion thus generating a dynamic voltage in the photodetector that is proportional to the out-of-plane displacements (within the limits of quadrature). The voltage from the photodetector is recorded in a digitizing oscilloscope and transferred to a computer for signal analysis via Fast Fourier Transform (FFT) and/or wavelet analysis. It is important to mention that this type of ultrasound generation most effectively produces guided waves on free surfaces or layers while injecting very little acoustic energy into the bulk of the material. The chronology of events described above occurs within a matter of microseconds, excluding the transfer of data to the computer and the subsequent signal analysis. The latter processes have always been comparatively slow. However, recent developments have improved the efficiency and effectiveness of the transfer and, more importantly, the ability to extract desired information from the waveforms. These developments will be described next.
3. The wavelet transform The primary improvement in TAP-NDE methodology involves the method by which waveforms are analyzed. Unless methods are employed to narrow the signature, laser generated ultrasound is broadband. This characteristic combined with the dispersive nature of waveforms generated in components such as plates and films poses a challenge to many methods of signal processing. In many applications, a measure of ultrasound group velocity is required while working with a dispersive signal. If this signal is broadband, a particular frequency component or components must be isolated and tracked from within the broadband waveform. In other words, a joint time–frequency analysis method is needed. This has led to exploration into the possibilities of the wavelet transform [4]. The Gabor wavelet transform (GWT) has been chosen and employed with good results. The Gabor wavelet lends itself well to time–frequency analysis because the resulting wavelet coefficient matrix is generated directly in terms of time and frequency as opposed to time and scale. The coefficient matrix contains elements analogous to Fourier coefficients except each element corresponds to a specific temporal location within the signal as well as a frequency. Rather than go into great detail on the properties of the GWT, its application and effectiveness at analyzing experimental dispersive waveforms will be described in the following sections.
4. Delaminations in layered media Layered media is becoming increasingly common in many applications including electronics. The dimensional uniformity of layers as well as the integrity of bond quality at the layer interfaces is often of critical importance [5,6]. The description that follows is of recent work that deals with a three-ply laminate composed of a polymer film (5 mm) sandwiched between two copper films (25 mm). The goal of the
374
R. Chona et al. / Optics and Lasers in Engineering 40 (2003) 371–378
study was to use TAP-NDE to detect and locate regions where delaminations were present between film layers. The data will be used here for two purposes: (1) as a platform for discussion on broadband dispersive waveform characteristics that can be effectively quantified by the wavelet transform; (2) to demonstrate that TAPNDE can be employed to characterize bond quality of interfaces beneath the visible surface of a layered specimen. Fig. 2 shows the configuration of the layers and the two different types of delaminations being detected. The inspection process has two goals: (1) to identify the existence of a delamination in the region being tested, (2) to quantify the size of the delaminated region. Successfully accomplishing these goals requires the ability to correlate propagation velocity to the number and configuration of contiguous lamina. The sequence of experimental data shown below establishes the ability of TAP-NDE to make such distinctions. Figs. 3–5 each show three waveforms generated in a two-ply laminate (Type 2 defect) region. These signals were recorded from FTIs located at 1, 2 and 3 cm from the generation site, respectively. Figs. 3–5 also illustrate the effects of dispersion very well. Since the generation mechanism was unaltered for the different waveforms, the frequency content in waveforms over all three propagation lengths is the same. It is evident, however, that the packet of energy that is initially excited does not travel along unaltered. The higher frequencies propagate at a higher velocity than the lower frequencies and therefore tend to broaden the packet as it propagates. This is a trait of dispersive waveforms. This effect is quantified in terms of time–frequency analysis through the use of the wavelet transform. The results from a GWT analysis for one of the waveforms in each of Figs. 3–5 are shown in Figs. 6–8, respectively. The best way to interpret the information contained in the transform is in terms of the frequency-dependent group velocity. Each contour peak in the plots marks a local maximum of the wavelet coefficient, thus pinpointing
Inspection Side 25 µm (Cu) 5 µm (Poly) 25 µm (Cu) Type 1 Defect
Type 2 Defect Fig. 2. Cu/Poly/Cu laminate and defect types.
R. Chona et al. / Optics and Lasers in Engineering 40 (2003) 371–378
0.4 0.3 Voltage
0.2 0.1 0 −0.1 −0.2 0
30
60
90
120
150
180
Time [microseconds] Fig. 3. Waveforms in Cu/Poly after 1 cm of propagation for a type 2 defect.
0.04 0.03
Voltage
0.02 0.01 0 −0.01 −0.02 −0.03 −0.04 0
50
100 150 Time [microseconds]
200
Voltage
Fig. 4. Waveforms in Cu/Poly after 2 cm of propagation for a type 2 defect.
0.05 0.04 0.03 0.02 0.01 0 −0.01 −0.02 −0.03 −0.04 −0.05 0
50 100 Time [microseconds]
150
Fig. 5. Waveforms in Cu/Poly after 3 cm of propagation for a type 2 defect.
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145 110 75
192
176
160
144
128
96
112
80
64
48
32
0
16
40
Frequency [kHz]
(48 µs, 40 kHz)
5
Time [microseconds] Fig. 6. GWT in Cu/Poly (1 cm propagation).
145 110 75
192
176
160
144
128
112
96
80
64
48
32
0
16
40
Frequency [kHz]
(98 µs, 40 kHz)
5
Time [microseconds] Fig. 7. GWT in Cu/Poly (2 cm propagation).
145 110 75
192
176
160
144
128
112
96
80
64
48
32
0
16
40
Frequency [kHz]
(156 µs, 40 kHz)
5
Time [microseconds] Fig. 8. GWT in Cu/Poly (3 cm propagation).
an arrival time of the corresponding frequency component from within the broadband signal. This information together with the known propagation path length is easily used to compute a frequency-dependent group velocity. Dispersion is represented by the curvature of the trace of peaks on the plots and, more specifically, the relative change in the trace curvature between figures. Thus, the information in the GWT plots show the progression of the full broadband frequency spectrum contained within the wave packets propagating through the film. As expected, each transform shows that the signal contains the same overall frequency content, but the trace of the peaks on the wavelet contour plot evolve and separate with increased propagation length. It is important to mention that a particular frequency within a particular mode will travel at a constant velocity. This can be demonstrated by tracking the arrival
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377
Table 1 Group velocity extraction of 40 kHz component in Cu/Poly Propagation length (cm)
Arrival time (ms)
Velocity (m/s)
1 2 3
47–49 97–99 155–157
209–204 206–202 194–191
0.004 0.003
Voltage
0.002 0.001 0 −0.001 −0.002 −0.003 0
30
60 90 120 Time [microseconds]
150
180
Fig. 9. Waveforms in Cu/Poly/Cu after 3 cm of propagation (defect free).
time and computing the corresponding group velocity of a chosen frequency component through a sequence of wavelet transforms. The 40 kHz component has been labeled on Figs. 6–8. These velocities are tabulated in Table 1. The small differences in calculated velocity stem from the coarse discretization used for both the time and frequency domain within the wavelet algorithm, and should not be misinterpreted as indicative of inaccuracy of the methodology. To demonstrate that TAP-NDE is capable of differentiating between defect free and material with Type 2 defects, a waveform generated in a defect free Cu/Poly/Cu specimen after propagating over 3 cm is shown in Fig. 9. Differences can clearly be seen between this data and that of the data taken in the region containing the defect. Comparison of the GWT of this signal given in Fig. 10 with that in Fig. 8 (same propagation length) clearly shows that the velocities for all frequencies within the spectrum of the wave packet are greater than in the region containing the defect. Group velocity can be used as the indicating parameter in the determination of the number of contiguous layers beneath the exposed surface on which ultrasound is generated and detected. The following calculations show that there is a substantial difference between group velocities in delaminated and defect free specimens, and that this characteristic can certainly serve as a diagnostic. For the defect free (Cu/ Poly/Cu) waveform propagating over a distance of 3 cm, the 40 kHz component arrived at the FTI location after 114 ms. The group velocity is therefore vg ¼ 3 cm/ 114 ms=263 m/s. The 40 kHz component in the waveform recorded in the
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196
182
168
154
140
126
98
112
84
70
56
42
28
0
14
40
Frequency [kHz]
110
5
Time [microseconds]
Fig. 10. GWT of the Cu/Poly/Cu (3 cm propagation) waveform of Fig. 9.
delaminated region arrived at 156 ms after propagating over a distance of 3 cm, making the group velocity vg ¼ 3 cm/156 ms=192 m/s.
5. Conclusions The usefulness of guided ultrasonic waves for the detection of delaminations in layered media has been demonstrated. This is due, in part, to the introduction of the wavelet transform into the post-processing algorithm for TAP-NDE. The simultaneous time–frequency resolution makes accurate interpretation of broadband dispersive waveforms possible and exploitable.
References [1] Burger CP, Dudderar TD, Gilbert JA, Peters BR, Smith JA, Raj B. Thermal acousto-optics for noncontacting NDE. Proceedings, 1986 Spring Conference on Experimental Mechanics, New Orleans, LA, 1986. p. 680–85. [2] Burger CP, Schumacher NA, Duffer CE, Knab TD. Fiber-optics techniques for generating and detecting ultrasonic waves for quantitative NDE. Opt Lasers Eng 1993;19:121–40. [3] Rabroker GA, Suh CS, Chona R. Laser induced stress wave thermometry applied to silicon wafer processing. Exp Mech 2002; in press. [4] Kishimoto K, Inoue H, Hamada M, Shibuya T. Time frequency analysis of dispersive waves by means of wavelet transform. J Appl Mech 1995;62:841–6. [5] Heller K, Jacobs LJ, Qu J. Characterization of adhesive bond properties using lamb waves. Int J NDT&E 2000;33:555–63. [6] Nagy PB, Alder L. Nondestructive evaluation of adhesive joints by guided waves. J Appl Phys 1989;66(10):4658–63.
Characterizing defects in multi-layer materials using guided ultrasonic waves R. Chona*, C.S. Suh, G.A. Rabroker Department of Mechanical Engineering, Texas A&M University, College Station, TX, USA
Abstract A brief description is given of a methodology that exploits guided ultrasonic waves, lasers and fiber optics, and simultaneous time–frequency analysis to interrogate the state of a material, component, or structure. This system offers a means by which surface-guided (Lamb and Rayleigh), broadband, ultrasound can effectively be generated and detected in a wide variety of materials in real time and in a non-contact, non-invasive fashion. The propagating ultrasound interrogates the host material in a manner providing a wealth of information when coupled with application of the Gabor wavelet transform to broadband dispersive waveforms. Recent results are presented pertaining to delamination detection within layered copper/ polymer films. r 2002 Elsevier Science Ltd. All rights reserved. Keywords: Defects; Multilayer materials; Ultrasound
1. Introduction The Photomechanics Laboratory at Texas A&M University is dedicated to the development and application of real-time, on-line, non-contact, non-invasive methods of material and component inspection and investigation. Applications are centered around the methodology termed TAP-NDE, or Thermal-Acousto-Photonic Non-Destructive Evaluation [1–3]. This method utilizes ultrasound that is both generated and detected by laser optic interactions with the material as a means of interrogation. A brief description of the system and methodology is provided first, followed by results from a recent application to demonstrate the merit and capabilities of the approach. *Corresponding author. E-mail address: [email protected] (R. Chona). 0143-8166/03/$ - see front matter r 2002 Elsevier Science Ltd. All rights reserved. PII: S 0 1 4 3 - 8 1 6 6 ( 0 2 ) 0 0 0 9 4 - 5
372
R. Chona et al. / Optics and Lasers in Engineering 40 (2003) 371–378
2. System The system shown in Fig. 1 is best described in terms of the chronology of events required to generate, detect and analyze interrogating waveforms in the component material. The first step is to generate the interrogating wave. A short (E10 ns) pulse is fired from a Nd:YAG laser to the surface of the specimen, simultaneously triggering the oscilloscope. This pulse is typically focused down to illuminate a small spot on the specimen and is responsible for the generation of ultrasound in the material through rapid heating and subsequent expansion of the surface and subsurface material layers. As rapid and localized thermal expansion occurs, energy is released in the form of propagating ultrasound in all directions from the generation site guided by the free surface or surfaces causing in-plane as well as out-of-plane displacements. Sensing of the ultrasound is achieved by the Fiber Tip Interferometer (FTI). As the ultrasound passes the location of the FTI, which is positioned at a known distance from the generation site, the out-of-plane displacements are detected. The FTI system is a fiber-based Fizeau type interferometer. The coherent light source in this device is a HeNe laser that is coupled into one single mode fiber leg of a Fused Bi-Conical Taper Coupler (FBTC). The light coupled into this leg is split into two fibers after passing through the coupler itself, thus the FBTC is the analog of the beam-splitter in the classical Fizeau interferometer. The light in one of the output legs is routed to an index matching fluid to eliminate reflections from the termination face of the fiber. The remaining output leg, however, is routed to the specimen surface, where the Fizeau cavity is the standoff distance between the FTI and the specimen. This standoff is typically on the order of millimeters. At this point, the beam is divided into a reference and object beam. The reference beam is the portion of the beam that is internally reflected from the face of the stationary fiber and makes its way in the reverse direction towards a fiber-coupled photodetector. The object beam is that which exits the fiber tip, reflects from the specimen surface and re-enters the fiber. Superposed with the reference beam, the object beam too propagates to the photodetector. As the cavity dimension between the fiber tip and the specimen
optical termination
HeNe Laser
PC
Photodetector FTI
Oscilloscope
FBTC propagating wave
Nd:YAG Laser
≈10 ns generation pulse specimen
Fig. 1. Experimental system.
R. Chona et al. / Optics and Lasers in Engineering 40 (2003) 371–378
373
changes with passage of ultrasound beneath the fiber tip, the object and reference beams interfere in a dynamic fashion thus generating a dynamic voltage in the photodetector that is proportional to the out-of-plane displacements (within the limits of quadrature). The voltage from the photodetector is recorded in a digitizing oscilloscope and transferred to a computer for signal analysis via Fast Fourier Transform (FFT) and/or wavelet analysis. It is important to mention that this type of ultrasound generation most effectively produces guided waves on free surfaces or layers while injecting very little acoustic energy into the bulk of the material. The chronology of events described above occurs within a matter of microseconds, excluding the transfer of data to the computer and the subsequent signal analysis. The latter processes have always been comparatively slow. However, recent developments have improved the efficiency and effectiveness of the transfer and, more importantly, the ability to extract desired information from the waveforms. These developments will be described next.
3. The wavelet transform The primary improvement in TAP-NDE methodology involves the method by which waveforms are analyzed. Unless methods are employed to narrow the signature, laser generated ultrasound is broadband. This characteristic combined with the dispersive nature of waveforms generated in components such as plates and films poses a challenge to many methods of signal processing. In many applications, a measure of ultrasound group velocity is required while working with a dispersive signal. If this signal is broadband, a particular frequency component or components must be isolated and tracked from within the broadband waveform. In other words, a joint time–frequency analysis method is needed. This has led to exploration into the possibilities of the wavelet transform [4]. The Gabor wavelet transform (GWT) has been chosen and employed with good results. The Gabor wavelet lends itself well to time–frequency analysis because the resulting wavelet coefficient matrix is generated directly in terms of time and frequency as opposed to time and scale. The coefficient matrix contains elements analogous to Fourier coefficients except each element corresponds to a specific temporal location within the signal as well as a frequency. Rather than go into great detail on the properties of the GWT, its application and effectiveness at analyzing experimental dispersive waveforms will be described in the following sections.
4. Delaminations in layered media Layered media is becoming increasingly common in many applications including electronics. The dimensional uniformity of layers as well as the integrity of bond quality at the layer interfaces is often of critical importance [5,6]. The description that follows is of recent work that deals with a three-ply laminate composed of a polymer film (5 mm) sandwiched between two copper films (25 mm). The goal of the
374
R. Chona et al. / Optics and Lasers in Engineering 40 (2003) 371–378
study was to use TAP-NDE to detect and locate regions where delaminations were present between film layers. The data will be used here for two purposes: (1) as a platform for discussion on broadband dispersive waveform characteristics that can be effectively quantified by the wavelet transform; (2) to demonstrate that TAPNDE can be employed to characterize bond quality of interfaces beneath the visible surface of a layered specimen. Fig. 2 shows the configuration of the layers and the two different types of delaminations being detected. The inspection process has two goals: (1) to identify the existence of a delamination in the region being tested, (2) to quantify the size of the delaminated region. Successfully accomplishing these goals requires the ability to correlate propagation velocity to the number and configuration of contiguous lamina. The sequence of experimental data shown below establishes the ability of TAP-NDE to make such distinctions. Figs. 3–5 each show three waveforms generated in a two-ply laminate (Type 2 defect) region. These signals were recorded from FTIs located at 1, 2 and 3 cm from the generation site, respectively. Figs. 3–5 also illustrate the effects of dispersion very well. Since the generation mechanism was unaltered for the different waveforms, the frequency content in waveforms over all three propagation lengths is the same. It is evident, however, that the packet of energy that is initially excited does not travel along unaltered. The higher frequencies propagate at a higher velocity than the lower frequencies and therefore tend to broaden the packet as it propagates. This is a trait of dispersive waveforms. This effect is quantified in terms of time–frequency analysis through the use of the wavelet transform. The results from a GWT analysis for one of the waveforms in each of Figs. 3–5 are shown in Figs. 6–8, respectively. The best way to interpret the information contained in the transform is in terms of the frequency-dependent group velocity. Each contour peak in the plots marks a local maximum of the wavelet coefficient, thus pinpointing
Inspection Side 25 µm (Cu) 5 µm (Poly) 25 µm (Cu) Type 1 Defect
Type 2 Defect Fig. 2. Cu/Poly/Cu laminate and defect types.
R. Chona et al. / Optics and Lasers in Engineering 40 (2003) 371–378
0.4 0.3 Voltage
0.2 0.1 0 −0.1 −0.2 0
30
60
90
120
150
180
Time [microseconds] Fig. 3. Waveforms in Cu/Poly after 1 cm of propagation for a type 2 defect.
0.04 0.03
Voltage
0.02 0.01 0 −0.01 −0.02 −0.03 −0.04 0
50
100 150 Time [microseconds]
200
Voltage
Fig. 4. Waveforms in Cu/Poly after 2 cm of propagation for a type 2 defect.
0.05 0.04 0.03 0.02 0.01 0 −0.01 −0.02 −0.03 −0.04 −0.05 0
50 100 Time [microseconds]
150
Fig. 5. Waveforms in Cu/Poly after 3 cm of propagation for a type 2 defect.
375
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145 110 75
192
176
160
144
128
96
112
80
64
48
32
0
16
40
Frequency [kHz]
(48 µs, 40 kHz)
5
Time [microseconds] Fig. 6. GWT in Cu/Poly (1 cm propagation).
145 110 75
192
176
160
144
128
112
96
80
64
48
32
0
16
40
Frequency [kHz]
(98 µs, 40 kHz)
5
Time [microseconds] Fig. 7. GWT in Cu/Poly (2 cm propagation).
145 110 75
192
176
160
144
128
112
96
80
64
48
32
0
16
40
Frequency [kHz]
(156 µs, 40 kHz)
5
Time [microseconds] Fig. 8. GWT in Cu/Poly (3 cm propagation).
an arrival time of the corresponding frequency component from within the broadband signal. This information together with the known propagation path length is easily used to compute a frequency-dependent group velocity. Dispersion is represented by the curvature of the trace of peaks on the plots and, more specifically, the relative change in the trace curvature between figures. Thus, the information in the GWT plots show the progression of the full broadband frequency spectrum contained within the wave packets propagating through the film. As expected, each transform shows that the signal contains the same overall frequency content, but the trace of the peaks on the wavelet contour plot evolve and separate with increased propagation length. It is important to mention that a particular frequency within a particular mode will travel at a constant velocity. This can be demonstrated by tracking the arrival
R. Chona et al. / Optics and Lasers in Engineering 40 (2003) 371–378
377
Table 1 Group velocity extraction of 40 kHz component in Cu/Poly Propagation length (cm)
Arrival time (ms)
Velocity (m/s)
1 2 3
47–49 97–99 155–157
209–204 206–202 194–191
0.004 0.003
Voltage
0.002 0.001 0 −0.001 −0.002 −0.003 0
30
60 90 120 Time [microseconds]
150
180
Fig. 9. Waveforms in Cu/Poly/Cu after 3 cm of propagation (defect free).
time and computing the corresponding group velocity of a chosen frequency component through a sequence of wavelet transforms. The 40 kHz component has been labeled on Figs. 6–8. These velocities are tabulated in Table 1. The small differences in calculated velocity stem from the coarse discretization used for both the time and frequency domain within the wavelet algorithm, and should not be misinterpreted as indicative of inaccuracy of the methodology. To demonstrate that TAP-NDE is capable of differentiating between defect free and material with Type 2 defects, a waveform generated in a defect free Cu/Poly/Cu specimen after propagating over 3 cm is shown in Fig. 9. Differences can clearly be seen between this data and that of the data taken in the region containing the defect. Comparison of the GWT of this signal given in Fig. 10 with that in Fig. 8 (same propagation length) clearly shows that the velocities for all frequencies within the spectrum of the wave packet are greater than in the region containing the defect. Group velocity can be used as the indicating parameter in the determination of the number of contiguous layers beneath the exposed surface on which ultrasound is generated and detected. The following calculations show that there is a substantial difference between group velocities in delaminated and defect free specimens, and that this characteristic can certainly serve as a diagnostic. For the defect free (Cu/ Poly/Cu) waveform propagating over a distance of 3 cm, the 40 kHz component arrived at the FTI location after 114 ms. The group velocity is therefore vg ¼ 3 cm/ 114 ms=263 m/s. The 40 kHz component in the waveform recorded in the
378
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196
182
168
154
140
126
98
112
84
70
56
42
28
0
14
40
Frequency [kHz]
110
5
Time [microseconds]
Fig. 10. GWT of the Cu/Poly/Cu (3 cm propagation) waveform of Fig. 9.
delaminated region arrived at 156 ms after propagating over a distance of 3 cm, making the group velocity vg ¼ 3 cm/156 ms=192 m/s.
5. Conclusions The usefulness of guided ultrasonic waves for the detection of delaminations in layered media has been demonstrated. This is due, in part, to the introduction of the wavelet transform into the post-processing algorithm for TAP-NDE. The simultaneous time–frequency resolution makes accurate interpretation of broadband dispersive waveforms possible and exploitable.
References [1] Burger CP, Dudderar TD, Gilbert JA, Peters BR, Smith JA, Raj B. Thermal acousto-optics for noncontacting NDE. Proceedings, 1986 Spring Conference on Experimental Mechanics, New Orleans, LA, 1986. p. 680–85. [2] Burger CP, Schumacher NA, Duffer CE, Knab TD. Fiber-optics techniques for generating and detecting ultrasonic waves for quantitative NDE. Opt Lasers Eng 1993;19:121–40. [3] Rabroker GA, Suh CS, Chona R. Laser induced stress wave thermometry applied to silicon wafer processing. Exp Mech 2002; in press. [4] Kishimoto K, Inoue H, Hamada M, Shibuya T. Time frequency analysis of dispersive waves by means of wavelet transform. J Appl Mech 1995;62:841–6. [5] Heller K, Jacobs LJ, Qu J. Characterization of adhesive bond properties using lamb waves. Int J NDT&E 2000;33:555–63. [6] Nagy PB, Alder L. Nondestructive evaluation of adhesive joints by guided waves. J Appl Phys 1989;66(10):4658–63.