Shape Effect on Blind Frequency for Depth Inversion in Pulsed Thermography

Transcription

1 Shape Effect on Blin Frequency for Depth Inversion in Pulse Thermography M. Genest 1, E. Grinzato 2, P. Bison 2, S. Marinetti 2 C. Ibarra-Castaneo 1, X. Malague 1 1 Electrical an Computing Eng. Dept., Université Laval, Quebec City (Quebec) Canaa 1 2 ITC-CNR, Paova (Venice) Italy 2 Abstract In this paper, a stuy is presente inicating that the specimen shape, for orientation smaller than about 30, oes not affect the blin frequency obtaine in Pulse Phase Thermography processing. Therefore, it makes this measurement suitable for epth inversion in the case of non-flat shape specimens. Theory an experimental results are iscusse. 1. Introuction Infrare (IR) pulse thermography (PT) [1] experiences a fast eployment in NonDestructive (NDE) evaluation nowaays. In some instances, the part to be inspecte is of complex shape. Little stuies have been evote to those cases, especially if quantitative epth retrieval is of interest (see for instance [2, 3, 4]). In fact it is easily conceive that, with respect to a situation where a specimen is flat, the case of a complex shape - let say a tilte for now specimen will provie a ifferent temperature measurement if all other parameters are the same. This is ue to the local orientation of the surface (Fig. 1, left). Figure 1 Flat an tilte plate (left), experimental set-up for IR thermography NDE (right). We recall that in pulse thermography, the specimen is submitte to a thermal pulse which causes its surface temperature to rise. Assuming a photo-thermal pulse of energy, the specimen surface temperature rises an then ecays ue to natural cooling (Fig. 1, right). The temperature ecay is of interest since thermal waves launche into the specimen by the heating pulse reveal efects at a time which epens on efect epth [1]. 1 malagx@gel.ulaval.ca 2 ermanno.grinzato@itc.cnr.it, paolo.bison@itc.cnr.it, sergio.marinetti@itc.cnr.it 215

2 Pulse Phase Thermography (PPT) is a signal processing in which the specimen behaviour in PT is analyse not in the time omain but rather in the frequency omain [4]. PPT stuies were foun particularly helpful if phase is consiere. Moreover, recent stuies showe that epth inversion can be easily performe by extracting blin frequencies [5]. In this paper, the effect of shape orientation (that is local orientation ) is consiere in regars of epth inversion with blin frequency. 2. Theory 2.1 On orientation Pulse heating of a semi-infinite homogeneous specimen (Fig. 1-a, left) causes the surface temperature to rise an then ecay. Assuming a simple 1-D case, the temperature ecay T can be efine as [1, eq. 9.8]: Q T (1) e t where Q is the amount of energy absorbe by the specimen, t is the time an e is the thermal effusivity of the specimen efine as k C with k the thermal conuctivity, the mass ensity an C the specific heat. If we suppose a PPT subsequent processing [5], the temperature ecay recore by the IR camera (Fig. 1, right) will be subject to a iscrete Fast Fourier Transform (FFT) so that ata is move from the time omain (iscretize here as N ata per image pixel along the time axis) to the frequency omain leaing to: T(k) F(n) (2) F N 1 k 0 T ( k) e 2 ikn / N Re i Im n n where F is the FFT of T, i is the imaginary number ( 1 ), Re an Im are the real an imaginary parts of the transform, k stans for the time increment an the n esignates the frequency increment. The phase an amplitue images are finally obtaine from the known relationships: 2 2 Imn An Ren Imn an n arctan( ). (4) Ren Now, in the case of a tilte component an assuming a uniform surface heating Q of the surface, we have to consier the surface orientation. Angle affects the measurement in two ways. First, assuming orthographic heating, only cos of the energy contributes to the heating (this comes from the projection in the heating irection). Secon for a lambertian surface, only cos of the subsequent surface heating will be emitte in the (3) 216

3 irection of the IR camera (this comes from the projection in the observation irection). Hence, the observe tilte surface temperature T will be reuce by a factor: T ' cos 2 T. (5) Following eq. (3), knowing that the Fourier transform is a linear operator, an since 2 cos is a constant here (it oes not epen upon time), we see that: 2 ' ' cos Imn An cos Ren cos Imn an n arctan( ). (6) 2 cos Ren Here symbol was use since such an analysis is only approximative ue to the particular irraiation eploye. Clearly, in PPT, amplitue A images will be affecte by surface orientation while phase images shoul not be much since parameter cos 2 cancels out in the ivision process of eq. (6). Before terminating this section, the following table shows the value of cos 2 for several orientation. It is seen than for orientations of less than about 30 surface orientation shoul not affect much the ata assuming a common level of uncertainty (Table 1). Table 1. Values of cos 2 as function of cos 2 cos On epth inversion with blin frequency f b In PPT, the blin frequency f b is the frequency at which the phase value of a efect of given epth z merges with the phase value of the soun material [7]. It was emonstrate that f b an z can be relate using the following relationship for epth inversion [6]: z C (7) 1 C 2 fb Where C 1 an C 2 are regression coefficients C 1 being relate to material properties an is the thermal iffusivity ( k / C ). This equation is irectly erive after the thermal iffusion length C / f ) ( b 1/ 2. In fact in [8], author mentions a value of 217

4 3. Experiments In orer to verify the previous iscussion, several experiments where conucte on two ifferent specimens, ientical in all respect but Specimen 1 was mae of CFRP (Carbon Fiber Reinforce Plastic) while Specimen 2 was mae of GFRP (Glass Fiber Reinforce Plastic). Both samples have the shape of a cyliner with a curvature raius of 27.5 cm an several efects (square Teflon inserts of ifferent sizes: 5 rows of 5 square efects of size: 3, 5, 7, 10, 15 mm an of ifferent epths from 0.2 to 1 mm) locate between plies uring fabrication. Furthermore, uring the experiments, the specimens were tilte with respect to the heating/observation axis (Fig. 1) to get more orientations to analyse (Fig. 2). Fig. 2 Specimen tilte with various orientations. The specimen was teste by pulse thermography (Fig. 1, right). Figure 3 confirms what was sai in Section 2 (eq. (6)): phase is relatively insensitive to orientation while amplitue is. Fig. 3 Effect of orientation on phase an amplitue for Specimen 1 mae of CFRP with orientation of (a): 0 an (b): 20. Secon iscrete frequency (0.167 Hz). Plots along image row are also shown. Interestingly, a simple normalization of the temperature can remove most of the unwante effects of shape variation (an uneven heating since uniform heating is harly achieve). The normalization function consists in the ivision of each frame (k) of the temporal temperature T sequence by the first frame after the heating pulse. This can be expresse by the following equation (Fig. 4 shows some results): 218

5 Tk Tk /T 1 (8) normalize Following Section 2.2, blin frequencies were then extracte. Since ata was subject to noise (as shown on the plots of Fig. 3 an 4), smoothing was performe by fitting the phase ata with a logarithmic polynomial (as in temperature reconstruction [9]). Fig. 5 shows the phase for the five ifferent efect epths of the specimen. phase amplitue phase amplitue (a) Fig. 4 Effect of orientation on phase an amplitue for Specimen 1 with orientation of (a): 0 an (b): 20. Secon iscrete frequency (0.167 Hz). Plots along image row are also shown. Phase an amplitue after normalization of temperature sequence. (b) Fig. 5 Typical phase evolution from the shallowest to the eepest efect ranking (0.2 mm increment): 3, 2, 4, 5, 1 an ata 6 is the selecte reference area (non-efect). Results were obtaine using 400 frames at an acquisition spee of 25 Hz, allowing a minimum frequency of Hz an maximum frequency of 12.5 Hz. Specimen orientation was 0. Specimen 1. Several tests were performe over efects of ifferent sizes yieling to similar blin frequencies. In fact, provie the efect was large enough (size-on-epth ratio >> 1), size oes not affect blin frequency (at least as long as the efect can be etecte!). In the present stuy, size-on-epth ratio varies from 3 (minimum) to 75 (maximum). Table 2 summarizes the results for ifferent epths with orientation 0. Table 2. Experimental average blin frequencies for ifferent epths (here we refer to epths by specimen plies), Specimen 1. Orientation: 0 5 th an 6 th 4 th an 5 th 3 r an 4 th 2 n an 3 r 1 st an 2 n blin frequency

6 The next step was to stuy the effect of orientation on blin frequency. Results are presente in Table 3. Table 3. Experimental average blin frequencies for ifferent epths an orientations. Specimen 1. Orientation 5 th an 6 th 4 th an 5 th 3 r an 4 th 2 n an 3 r 1 st an 2 n * * position * suspecte ata! From Table 3, we notice the orientation oes not affect significatively the blin frequency, at least if the orientation is reasonable ( < 30, Table 1). In fact, if values of Table 3 are average (Table 4), we obtaine similar values as liste in Table 2. Table 4. Blin frequency for ifferent epths (average values of Table 3). Specimen 1. 5 th an 6 th 4 th an 5 th 3 r an 4 th 2 n an 3 r 1 st an 2 n Mean * st * * Removing the value of 8.00 at 40, a mean of 6.98 an stanar eviation of are obtaine. On Fig. 6 the evolution of blin frequency as function of epth is plotte after ata of Table 4, such a curve can be use for calibration purpose (eq. 7). Fig. 6 Blin frequency for ifferent epths. Specimen

7 Specimen 2 (GFRP) was similarly teste without application of any paint. Since this material is partly transparent (in both visible an infrare spectra), mitigate results were obtaine an a threshol ha to be applie to the phase contrast (ifference of phase between point of interest an reference area) ue to the high noise level. The high noise level prevents the full analysis of efects at all epths. Nevertheless, results from the shallowest efect inicate orientation oes not affect the blin frequency, at least for reasonable orientations ( < 30, Table 1). Table 5 list the experimental frequencies as function of epth for the 0 orientation case. Table 5 Average blin frequency for ifferent epths with 0 orientation. Specimen 2. Orientation: 5 th an 6 th 4 th an 5 th 3 r an 4 th 2 n an 3 r 1 st an 2 n 0 Mean Conclusion In this paper, a stuy of the blin frequency as function of surface orientation was performe. We conclue that, for reasonable orientations ( < 30 ), blin frequencies are not affecte by orientation. Moreover, we note blin frequencies are also size invariant provie that efect size-on-epth ratio is sufficiently high (>> 1). Results were obtaine on both CFRP an GRFP. It is recommene to ap a coating on GFRP ue to the semi-transparent nature of this material. 5. Acknowlegements The support of Ministère es affaires étrangères u Québec an from Ministri Affari Esteri of Italy is acknowlege. 6. References [1] Malague X.P.V., Theory an Practice of Infrare Technology for Non Destructive Testing, John-Wiley & Sons, 684 p., [2] X. Malague, E. Barker, A. Nouah, E. Boisvert, B. Dufort, L. Fortin, On methos for shape correction an reconstruction in thermographic NDT, II n Workshop on Avances in signal processing for NDE of Materials, Kluwer Acaemic Pub., E 262: , [3] J.F.Pelletier, E. Grinzato, R. Dessì, X. Malague: Shape an uneven heating correction for NDT on cyliners by thermal methos, QIRT 96: , [4] V.P.Vavilov, S.Marinetti: Pulse Phase Thermography an Fourier-Analysis Thermal Tomography, Russian Journal of Nonestructive Testing, 35: 2, pp , (from Defectoscopyia No.2, pp , Russia), [5] X. Malague, S. Marinetti, Pulse Phase Infrare Thermography, J. Appl. Phys, 79(5): , [6] C. Ibarra-Castaneo, N. P. Aveliis, X. Malague Quantitative Pulse Phase Thermography Applie to Steel Plates, Thermosense XXVII, 5782: ,

8 [7] Bai W., Won B. S. Evaluation Defects in Composite Plates uner Convective Environments using Lock-In Thermography, Meas. Sci. Technol.s 12: , [8] Busse G. Optoacoustic Phase Angle Measurement for Probing a Metal, Appl. Phys. Lett., 36(10): , [9] Shepar S. M. Avances in Pulse Thermography, Thermosense XXIII, 4360: ,