R.c. Addison, Jr. and A.D.W. McKie Rockwell Science Center Thousand Oaks, California 91358

Transcription

1 GENERATION AND DETECTION OF SINGLE MODE LAMB WA YES USING LASER-BASED ULTRASOUND R.c. Addisn, Jr. and A.D.W. McKie Rckwell Science Center Thusand Oaks, Califrnia INTRODUCTION Lamb waves have been successfully used fr the detectin f defects in and n the surfaces f plate-like structures fr many years [1-4]. In these applicatins, the Lamb waves have generally been generated and detected using angled-beam piezelectric transducers r EMAT transducers. In certain applicatins where nly the lwest rder symmetric r antisymmetric mde was needed, laser-based ultrasnic (LBU) techniques have been used fr generatin and/r detectin. The use f an LBU technique is attractive because f the ptential fr rapid inspectin f large areas and because it is nncntact with large stand-ff distances. The large stand-ff distance is particularly attractive fr the inspectin f structures with elements that prtrude slightly frm the surface that wuld interfere with the mvement ver the surface f an angled-beam transducer r an EMAT. Hwever, a ptential difficulty is that Lamb waves are a family f guided waves that exist in plate-like structures, and a large number f mdes f vibratin may c-exist in a given plate thickness. An essential element in establishing the feasibility f this technique is t demnstrate that LB U techniques can select and efficiently generate a single Lamb wave mde. The selected mde will ideally have an energy distributin within the plate wall that is ptimized fr detectin f specific defect types. Further, the dispersin characteristics f the waves depend n the specific mde and the perating pint n the frequency vs wavenumber dispersin curve. The slpe f the curve at the perating pint f the mde selected shuld be nearly cnstant ver the perating bandwidth. This implies that the grup velcity is nearly cnstant and a pulse will maintain its cmpact shape as it prpagates, i.e., it is nndispersive. This is especially imprtant fr the inspectin f large areas where the pulse might be required t prpagate ver lng path lengths. T btain efficient Lamb wave generatin, the mde and perating pint shuld be selected t have a lw mechanical admittance fr the cmbinatin f in-plane and ut-f-plane displacements prduced by the thermelastic surce. Further, fr an ptical detectr that is sensitive nly t ut-f-plane displacements, the mde must have a significant ut-f-plane displacement at the selected perating pint. Lamb wave mdes can be efficiently generated in thin metallic plates using lasers fr ultrasnic generatin at a single pint r line[5,6]. Hwever, this technique results in a Lamb wave surce that has a brad range f bth tempral and spatial frequencies and single pint generatin results in prpagatin utward frm the pint in all directins. Fr NDE applicatins, the ultrasnic energy must be cncentrated as much as pssible int a single mde that interacts ptimally with the expected types f defects. Excitatin f a single mde als facilitates unambiguus data interpretatin. The technique fr single mde generatin currently being investigated requires that a series f peridically spaced line surces be prjected nt a plate. The use f a line rather than a pint restricts the wave prpagatin Review f Prgress in Quantitative Nndestructive Evaluatin. Vl. 14 Edited by D.O. Thmpsn and D.E. Chimenti, Plenum Press, New Yark

2 directin t be perpendicular t the line. The resulting array has the effect f restricting the generated ultrasnic energy t a series f harmnically related spatial frequency bands which will be further described belw. If the line surces are then peridically pulsed in time (temprally mdulated), the ultrasnic energy will be further cncentrated int a series f harmnically related tempral frequency bands. METHOD FOR SINGLE MODE SELECTION Lamb Wave Dispersin Diagram The Lamb wave dispersin curves f the first six symmetric and antisymmetric mdes in aluminum are shwn in Fig. 1 calculated fr a plate thickness f 1.46 mm, a lngitudinal velcity f 6430 mis, and a shear wave velcity f 3180 mls. The dispersin curve fr the bulk lngitudinal wave is als shwn. It is f interest t select a specific perating pint n ne f the mde dispersin curves which has a specified wavenumber and frequency; fr example, an perating pint that is at the pint f intersectin f Lamb wave symmetric mde 2 with the bulk wave lngitudinal mde. The crssing f the lngitudinal mde and symmetric mde 2 ccurs at k = 4.90 mm-1 and f = 5.01 MHz. Althugh the values f A and f given abve specify the fundamental spatial and tempral frequencies f the arrays, the full spectral respnse must be calculated t gain insight int the ther mdes that might be generated. Selectin f the Mde Wavenumber A cnvenient methd fr reducing the spatial bandwidth f the bradband wavenumber excitatin prvided by a single line surce is t use a series f peridically spaced line surces n the plate being inspected. This will result in peridic passbands in the spatial frequency dmain whse spacing and width are dependent n the spacing and number f lines in the array f surces. As an example, assume that the laser is fcused t a line fcus which has a Gaussian prfile with a full-width half-maximum (FWHM) f 0.1 mm (Fig. 2a). This results in the bradband excitatin f wavenumbers extending frm 0 t mre than 60 mm-1 (Fig. 2b). The spatial array is assumed t cntain 16 elements with a L Mde6 MdeS Aluminum Plate Thickness = 1.46 mm.. ' Mde 4 Mde 3 Mde 2 Mdel Mde Symmetric Mdes - Slid Lines Antisymmetric Mdes - Dtted Lines Wavenumber, k (mm-1) 20 Figure 1. Lamb wave dispersin curves fr a 1.46 mm thick aluminum plate. 522

3 Q) O.s 'C :E 0.6 Q. E 0.4 c( a) ~ 0.1 ::l.~ C C) ~.s b) Length (mm) O~-r~~~~~~-+~~~-r SO 100 Spatial Frequency, 2TC!'A (mm-1) Figure 2. this prfile. a) Spatial prfile f fcused laser beam. b) Spatial frequencies assciated with distance between them that is equal t the wavelength at the desired perating pint which is A == 21C / k == mm (Fig. 3a). The spatial frequency respnse f the array (Fig. 3b) shws that the energy is cncentrated int a series f hannnically related spatial frequency bands as expected. Nte that the first full band is centered at a wavenumber k == 4.90 mm'! as desired. The amplitudes f the ther bands are cntained within the envelpe f the spectrum f the individual line (Fig. 2b). Thus if the line fcus is made wider r narrwer, this envelpe will becme narrwer r wider in spatial frequency. The width f the spatial frequency bands prduced by the array can als be narrwed by using mre array elements. Selectin f the Mde Frequency A pulse wavefrm prduced by and: Y AG Q-switched laser (Fig. 4a) is used as the individual element f the tempral array. This has a FWHM f abut 20 ns. The spectra f the individual pulse (Fig. 4b) extends t abut 80 MHz. The tempral array is assumed t cntain 4 elements with a delay time, t = '" 00 /ls, between elements (Fig. Sa). The spectral respnse f the array (Fig. 5b) shws that the energy is cncentrated int a series f harmnically related frequency bands as expected. Nte that the first full band is centered at a frequency f 5.01 MHz, which is equal t the frequency f the desired perating pint. The amplitude and width f these bands are cntrlled by the analgus quantities t thse cited abve fr the spatial frequency bands. Superimpsing the frequency bands generated by the arrays n the Lamb wave dispersin mde graph (Fig. 1) reveals which f the ther mdes might be generated. The graph fr the allwed Lamb wave mdes in the plate having a thickness f 1.46 mm is shwn in Fig. 6. Lamb wave generatin is allwed nly in the rectangular areas where the r '!. mm., '0 2 I Q)O.s 'C :E 0.6 Q. EO.4 c( Q) 1.5 'C ::l -'c 1 C) C\l :E.s a) S 1 d Length (mm) ld 2 b) L II ~ ~ Spatial Frequency, 2rrl'A (mm-1) Figure 3. a) Spatial prfile f an array cntaining 16 f the elements shwn in Fig. 2a separated by 1.28 mm. b) Spatial frequency spectrum assciated with the 16 element array. 523

4 r t r ep 0.8 "t:j :::l :t: 0.6 c.. ~0.4 epo.015 "t:j :::l -'c 0.01 C) C'CI :::ii: b) O+~-r~~~~r-~+-~~~-r Time (I-Is) Frequency (MHz) Figure 4. a) Pulse wavefrm prduced by and: Y AG Q-switched laser. b) Tempral frequency spectrum f this pulse. spatial frequency bands and the tempral frequency bands crss. Clearly the use f spatial and tempral arrays significantly restricts the allwed mdes. Our chief cncern is with unwanted mdes within the same frequency band such as the antisymmetric mdes 0 and 1 in the first frequency band. Thse mdes that ccur in ther frequency bands can be filtered frm the utput signals f the array if necessary. EXPERIMENTAL RESULTS The experiments that have been perfrmed use a Q-switched Nd: Y AG laser fcused t a line t generate Lamb waves. A cw argn-in laser als fcused t a line in cnjunctin with a 0.5 m spherical Fabry-Pert interfermeter is used t detect the Lamb waves. A series f experiments have been perfrmed using an aluminum plate with a thickness f 1.46 mm. During an experiment, the separatin between the surce and receiver is incrementally increased, with the increment selected t simulate a specific array spacing (Fig. 7). This results in a series f wavefrms having increasing time delays befre the arrival f the ultrasnic Lamb waves. These individual wavefrms are then summed ff-line in a cmputer s that the ultrasnic respnse frm the simulated multiple line array f peridically spaced thermelastic surces may be bserved. The summatin prcedure fr N element generatin and detectin arrays requires the cllectin f 2N-1 wavefrms crrespnding t the 2N -1 different prpagatin paths that can exist between the elements f the tw arrays. The array respnse fr a single generating element, Gj and an N element receiving array is synthesized by first summing each f the N wavefrms, Ri, received by the detectin array elements frm the jth generatin array element. ep 0.8 "t:j :E 0.6 c.. E.4 <C -- a) 0 0 ~. 02 lis I I --,\ I,\ Time (I-Is) r-h-+...-r-h r-...-t ep g 0.05 :g 0.04 WO.03 :::ii: {l Frequency (MHz} 100 Figure 5 a) Tempral array cntaining 4 f the pulses shwn in Fig. 4a separated by 00 Jls. b) Tempral frequency spectrum assciated with the 4 element array. 524

5 L MdeG Mde _ 10 N l: ~ >- 8 t.i c: QI S. 6 ~ L.I Aluminum Plate Thickness = 1.46 mm 1- Symmetric Mdes - Slid Lines Antisymmetric Mdes - Dtted Lines Mde 4 Mde 3 Mde 2 Mde 1 Mde Wavenumber, k (mm-1) Figure 6. Lamb wave dispersin curves fr a 1.46 mm thick aluminum plate with the allwed spatial frequency and tempral frequency bands superimpsed. Thus: (1) The N cmpsite wavefrms, Gj, resulting frm this peratin are summed t btain the ttal wavefrm, W, resulting frm the N element generating array and N element receiving array. Thus: (2) Q-Swltched Nd:YAG Leser CW Ar-In Laaer Receiving Arrey Figure 7. Schematic diagram f the experimental methd used t acquire data fr the synthesis f the spatial array used fr restricting the spatial bandwidth f the laser beams. 525

6 Frming the array in the cmputer is advantageus since it enables great flexibility in array spacing and tempral mdulatin and thus allws the cnfiguratin t be tested and ptimized befre designing a laser beam array system using hardware techniques. In the experiments, a series f ultrasnic Lamb wavefrms are acquired t simulate a 16 x 16 element generating and receiving laser array. Separatin between clsest elements f the simulated array is - 23 mm, and the spacing is increased by fixed increments crrespnding t the desired array spacing. The element spacing in the arrays that have been simulated ranges frm 0.50 mm t 1.30 mm, with crrespnding values f k fr the 1 st rder spatial frequency band ranging frm 4.S mm-1 t 12.6 mm-l. Figure Sa shws the tempral wavefrm assciated with the bradband excitatin f many mdes by a single line surce. The frequency spectrum (Fig. Sb) that is assciated with this wavefrm is distributed ver the detectin bandwidth f abut 1-15 MHz with n clearly identifiable peaks that can be assciated with specific Lamb wave mdes. In cntrast, Fig. 9b shws the frequency spectrum resulting frm the synthesized generatin and detectin arrays having a line spacing f 1.10 mm. Clearly the cncentratin f the ultrasnic energy in a few spatial frequency bands has prduced the excitatin f well-reslved Lamb wave mdes. Of these mdes, a single mde may then be preferentially selected by temprally mdulating the array at the apprpriate frequency. Althugh this has als been demnstrated with cmputer summatin, it is nt shwn since digital filtering f the spectrum prduced acceptable results. Using this methd f synthesizing the utput f a generatin and detectin array, the spacing between the array elements was systematically varied frm 0.50 t 1.30 mm in 0.05 mm increments. Fr each f the resulting 17 arrays, the peaks f the spectra were pltted in a frequency vs wavenumber diagram verlying the dispersin curves fr the Lamb wave mdes. In general this resulted in a series f data pints that matched up with the numerically calculated dispersin curves. As shwn in Fig. 9, multiple rder symmetric (S) and antisymmetric (A) mdes were detected as well as harmnics f the zerth rder symmetric and antisymmetric mdes, ns and na, where n dentes the rder f the harmnic. The excitatin f harmnics f the zerth rder symmetric and antisymmetric mdes (identified as 2A, 3A in Fig. 9) causes sme ambiguity in interpretatin, but this can be reslved by adjusting the assumed wave number assciated with the frequency peak t be a higher harmnic f the spatial frequency spectrum. When the crrect rder fr the wavenumber is used, the pints align clsely with the calesced curves fr the S and A mdes. The peaks in the frequency spectrum were tabulated fr the 17 different arrays. These results are shwn graphically in Fig. 10, which als shws the numerically calculated dispersin curves fr bth symmetric and anti symmetric mdes. Figure 10 shws very gd agreement between the experimental and theretical data. The zerth rder symmetric and antisymmetric mdes were the nly nes detected ver the full wavenumber range. There is a regin ver which the 1 st rder symmetric mde was nt detected between the wavenumber ,.-,c-..-, :-y-...,..~..., :l >' 1S.0 a) E 10.0 ';' s. -g 0.0 E----"\r'IWI\MII'lIII~MMII~MMIIIIIIIIII/ I"'.. U... -:a -s. E c( -1S "-'---'-... S...-'-1'-0...L. 1 "'-S--'-'-'-...,20 Time (ljs) Uj'1 0.0,...,...~... "T"""'c r ,..., ,...,."!:: C :::I 8.0..ci ~ ~ 4.0 ::l ;g 2.0 m CIS b) :E 0.0 0~-'-... ~S......,1,1:,O:...::l"""~1S=-... ~20 Frequency (MHz) Figure S. a) Tempral wavefrm resulting frm bradband excitatin f multiple Lamb wave mdes. b) Frequency spectrum assciated with this wavefrm. 526

7 3.0 en S.O AfIS 2.0 a) c - => 4.0 b) > _1.0.c:i -g ~.:;: 3.0 2A 0.0 [j' =: ~ 2.0 "Q. 1.0 :::I E ct 2.0 'c "0 CI «I..., 3.0..l A :E S 10 ls 20 S 10 ls 20 Time (I-Is) Frequency (MHz) Figure 9. a) Tempral wavefrm btained frm a spatial array with an element separatin f 1.10 mm. b) Frequency spectrum assciated with this wavefrm. values and the ther mdes, AI. S2, and A2 were nt detectable at the higher wavenumbers. In sme instances, the Lamb wave mde f interest was nt detectable because it was masked by the large amplitude harmnics f the antisymmetric mde. In ther instances, the admittance fr a particular mde may have been high, resulting in inefficient excitatin. This result demnstrates that LBU techniques can be used t generate bth symmetric and antisymmetric Lamb wave mdes at least up t mde 2. Any f the mdes shwn in Fig. 10 can be islated by filtering the utput signal, W, that is btained frm the synthesized arrays. As an example, the S2 mde fr an array spacing f 0.85 mm is shwn in Fig. 11. This is a cmpact pulse with a relatively narrw bandwidth that can be used fr varius NDE applicatins such as detectin f cracks and thinning f plates caused by crrsin Aluminum Plate Thickness = 1.46 mm _ 10.0 N l: :E ;: 8.0 () C G/ :::I ~ 6.0 u Al ~... A Wavenumber, k (mm-1) Figure 10. Lamb wave dispersin curves fr a 1.46 mm thick aluminum plate verlaid with the data pints btained frm experiments using 17 different array element spacings ranging frm mm

8 Generating Array Receiving Array #-#---U/;;:## L Sum ~ GI 'ti t.---ia ~ Q. E c( <l.1 Filler -<l.2 -<l Time (l.is) Figure 11. Tempral pulse resulting frm islatin f the S2 Lamb wave mde btained with an array element spacing f 0.85 mm. CONCLUSIONS In many situatins, the use f a laser t generate and detect Lamb waves results in a surce that is bradband in bth tempral and spatial frequencies which causes the simultaneus excitatin f many mdes. Althugh the zerth rder mdes can be islated by judicius chice f the frequency r the plate thickness, this des nt permit selectin f the ptimum Lamb wave mde fr many NDE applicatins and causes difficulties in data interpretatin. This paper has demnstrated that the restrictin f the spatial and tempral bandwidth by the use f arrays permits the generatin and detectin f a single Lamb wave mde. The generatin f bth symmetric and antisymmetric mdes f zerth thrugh secnd rder was demnstrated in an aluminum plate. Excellent agreement was btained between the frequency and wavenumber f these mdes and the numerically calculated Lamb wave dispersin curves fr aluminum. These results led t the feasibility f using LBU techniques t select and generate a single mde Lamb wave. ACKNOWLEDGMENTS This wrk was supprted by The Gas Research Institute and the Rckwell Internal Research and Develpment prgram. We thank T.A. Gray fr supplying the prgram used fr calculating the Lamb wave dispersin curves. REFERENCES 1. D.C. Wrltn, Nn-destructive Testing 15,218 (1957). 2. D.F. Ball and D. Shewring, Nn-destructive Testing 9, 13 (1976). 3. S.l. Rkhlin and F. Bendec, J. Acust. Sc. Am. 73, 55 (1983). 4. R.B. Thmpsn and D.O. Thmpsn Prc. IEEE 73,1716 (1985). 5. R. J. Dewhurst, C. Edwards, A. D. W. McKie, and S. B. Palmer, Appl. Phys. Lett (1987). 6. D. A. Hutchins, K. Lundgren and S. B. Palmer, J. Acust. Sc. Am. 85,1441 (1989). 528