- November, 7, Xiamen, China Detectability of pulsed infrared thermography of delaminations in carbon fiber composites More info about this article: http://www.ndt.net/?id=7 Peiqi JIANG, Xingwang GUO School of Mechanical Engineering and Automation, Beihang University, Beijing,China Corresponding author: Peiqi Jiang, e-mail: jpqpercy@3.com Abstract Pulsed thermography (PT) has been increasingly used in the inspection of composite materials, especially in aerospace industries. The detectability limit of the technique is often a question being concerned by end users. However, the detectability limit is not well defined up to now, because it cannot be described only by a simple parameter, and is affected by many factors associated with the defect, material, excitation, camera and signal processing algorithm. To completely describe the detectability limits of PT for delaminations in carbon fiber composites, a map of testing difficulty contours is newly proposed. The influences of defect size and defect depth on the defect informative parameters are studied by using the finite element method (FEM) based on D modeling. An experiment is conducted to verify the results of numerical simulation and to evaluate the noise level in practice. Eventually, a map of testing difficulty contours is presented to provide a guideline for the pulsed thermography of the carbon fiber composite. Keywords: Detectability limits, Pulsed thermography, Delamination, Carbon fiber composite. Introduction Carbon fiber reinforced polymer (CFRP) is widely used in aerospace industries due to its high specific strength and modulus, low density and heat resistance, however, internal delaminations in the material cannot be completely avoided by only controlling the production process, so the inspection of the defects is necessary. Ultrasonic inspection is usually used in the detection of delaminations even if it suffers from low productivity and contact operation. A severe drawback of the ultrasonic technique is that it needs coupling medium such as water or gel, which is banned in some cases. X-ray method is not applicable for delaminations in plates and shells. During the last decade, active infrared thermography (IRT) has evolved into a powerful nondestructive testing (NDT) method, which is particularly suitable for the detection and imaging of near surface and in-plane defects such as delaminations in composite materials or debondings between two layered materials [-]. IRT is fast, non-intrusive and safe for both the inspected object as well the operator. The history of the IRT NDT is reported in the review by Vavilov and Burleigh [3]. According to the thermal stimulation schemes, there are different kinds of infrared thermographic approaches, including pulsed thermography (PT), long pulse thermography, lock-in thermography, frequency modulated thermal wave imaging [] and other non-stationary forms of thermal excitation technique [5]. PT is one of the mostly accepted approaches due to its fast and simple features, and has been widely used, especially in the inspection of composite materials in aviation and aerospace industries, where subsurface defects might lead to catastrophic consequences. To improve the signal-to-noise ratio or characterize the defect size and depth more accurately, many post signal processing algorithms, such as Dynamic Thermal Tomography [], Polynomial Fitting [7], Pulse Phase Thermography [], and Thermographic Signal Reconstruction (TSR) [9-], etc. have been proposed by different researchers in the development history of PT []. The detectability limit of the technique has always been a question concerned by end users. However, the detectability limit is not well defined up to now, because it cannot be described only by a simple parameter, and is affected by many factors associated with the defect, material, excitation, camera and post signal processing methods.
- November, 7, Xiamen, China In this paper, the detectability limits of delaminations in carbon fiber composites are researched based on the basic principle of PT. A map of testing difficulty contours is newly proposed to describe the detectability limits. The influences of the defect size, defect depth and heating energy on the defect informative parameters are analyzed by using the finite element method (FEM) based on D modeling. An experiment is conducted to verify the results of numerical simulation and to evaluate the noise level in practice.. Numerical simulation. modeling The mathematical model for a body containing defects involves solving a 3D Cartesiancoordinate transient heat conduction problem []. The body under inspection is being heated on the front surface, whereas both front and rear surfaces exchange energy with ambient. Considering the simulation efficiency, each defect is modeled separately. A three-dimensional circular model with axial symmetry is used to describe the heat conduction in the composite plate containing a circular delamination, as shown in Fig. (a), where the circular defect area is filled with air. Because of the axial symmetry of the 3D model, it can be converted into a D model, as shown in Fig. (b), where R is the model radius, H is the model thickness, r denotes the defect radius or the axis in radius direction, is the defect thickness, h is the defect depth (i.e. the distance from the inspection surface to the defect), is ambient temperature, point D and N denote the centre of the defect and the typical non-defect area on the inspection surface respectively. The model radius is large enough comparing with the defect radius, and the side surface (r = R) is an adiabatic boundary. The thermal properties of materials are listed in Table. (a) 3D simulation model (b) D simulation model Fig. Numerical simulation models Table Thermal properties of materials Material Density ρ /kg m -3 Specific heat c /J kg - K - Thermal conductivity k /W m - k - CFRP 9 77. (in r-direction). (in z-direction) Air.5 5.59 The detectability of defects can be evaluated using defect informative parameters including: () temperature difference : the excess temperature difference between defect point D and nondefect point N; () maximum temperature difference : the maximum value of the temperature difference; (3) time of maximum temperature difference : the time when the maximum temperature difference occurs; () contrast C: the ratio of the temperature difference to the temperature at non-defect point N; (5) maximum contrast : the maximum value of the contrast; () time of maximum contrast : the time when the maximum contrast occurs.
- November, 7, Xiamen, China. Simulation results The model is solved numerically by the finite element method by applying the software ANSYS. The initial temperature is equal to the ambient temperature, i.e. =. In heating stage, the heat flux loaded on the inspection surface is set to =. W m with a heating duration =.s. In radiating stage, the convection heat transfer occurring on the top and bottom surfaces of the model is considered with a heat convection coefficient h = W (m K). The radiating time is set to = s. Set the structure parameters as the followings: R = 5 mm, H = mm, r = 5mm, h = mm, =.mm. The simulation results are shown in Fig.. 5 5 Temperature T D / C 5 5 5 Zoom in the details.. Temperature T N / C 5 5 5 Zoom in the details.. 5 5 (a) Temperature evolution of defect point D 5 5 (b) Temperature evolution of non-defect point N Temperature difference ΔT / C.5.5 -.5 5 5 (c) Temperature difference between point D and N (d) Contrast between point D and N Fig. Numerical simulation results In Fig., the following results can be seen: () The temperature of defect area and non-defect area reaches its maximum at the end of heating stage, which is about 5, and decreases rapidly to about at the end of radiating stage, and then decreases steadily. () is positive because the air gap is a heat insulation defect, which hinders the conduction of heat in the model. (3) =.9s and =.s, so the best time for defect identification is between.9s and.s..3 Influence of defect radius on detectability -. 5 5 Many factors can affect the defect informative parameters. Firstly, the influence of the defect radius on the defect informative parameters is studied. Set the structure parameters as the followings: h = mm, =.mm. Vary the defect radius from.5mm to 35mm. The informative parameters vs. defect radius are shown in Fig. 3, which shows that the variation trends of the four curves are similar and divided into three stages. Contrast ratio C..5..3.. 3
- November, 7, Xiamen, China Temperature difference ΔT m / C.9..7..5..3.. 5 5 5 3 35 Defect radius r / mm (a) Maximum temperature difference.5. Time t m / s 3 9 7 5 5 5 5 3 35 Defect radius r / mm (b) Time of maximum temperature difference Contrast ratio C m.3.. Time t cm / s 5 5 5 3 35 Defect radius r / mm (c) Maximum contrast (d) Time of maximum contrast Fig. 3 Defect informative parameters vs. defect radius Stage one is a linear increasing stage, in which the four defect informative parameters are linearly increasing with the defect radius. Stage two is a transition stage, in which the increasing trends of the four parameters slow down gradually. Stage three is a saturation stage, in which the heat transfer in defect areas reaches a quasi-d behaviour, and less lateral diffusion occurs, therefore the four defect informative parameters are stabilized at fixed values ( =., =.s, =., =.5s).. Influence of defect depth on detectability 5 5 5 3 35 Defect radius r / mm A defect depth is the distance from the inspection surface to the defect. It has been noticed from the results of section.3 that the defect radius has important influence on the defect informative parameters. Two cases should be discussed respectively: when the defect radius is smaller and large enough. Take two values of the defect radius respectively: = 3mm and = 3mm. Change the defect depth from.5mm to mm. The simulation results are shown in Fig.. Temperature difference ΔT m / C.5.5.5 3 3.5 (a) Maximum temperature difference r = 3mm r = 3mm Time t m / s r = 3mm r = 3mm.5.5.5 3 3.5 (b) Time of maximum temperature difference
- November, 7, Xiamen, China Contrast ratio C m.5.5.5 r = 3mm r = 3mm Time t cm / s 5 5 r = 3mm r = 3mm.5.5.5 3 3.5 (c) Maximum contrast (d) Time of maximum contrast Fig. Variation law of defect informative parameters with defect depth As it s shown in Fig., the maximum temperature differences as well as the maximum contrasts are decreasing rapidly with increasing defect depth and showing an exponential downward trend. The fitting curves for the case r = 3mm are = 39.35 exp(.99h)( ) () =.exp (.9h) () The time of maximum temperature difference increases approximately linearly with the defect depth, so as too for the time of maximum contrast. 3. Experiment 3. Experimental setup and samples.5.5.5 3 3.5 The experimental set-up is presented schematically in Fig. 5. It consists of an IR camera, two flash lamps with total energy of J, a controller, a computer and an IR NDT software. The camera is equipped with a lens of 9 and an uncooled FPA detector with 3 pixels and thermal sensitivity of.k in the long wave infrared range (7.5 3 μm). Fig. 5 Schematic diagram of the experimental setup The sample is a CFRP plate with six flat-bottom hole defects, which are used to simulate delamination defect in engineering field, as shown in Fig.. Three defects on the upper row, named as A, B and C, are.9mm deep from the inspection surface, meanwhile the other three defects, named as A, B and C, are 3.5mm deep from the inspection surface. 5
- November, 7, Xiamen, China 3. Experimental analysis Fig. Shape and size of the sample (all dimensions in mm) In experiment, the frame rate was set to 7.5Hz, the number of frames before the flash heating was set to 5, a total of N=5 frames were collected during the whole dynamic process including the background, flash heating and cooling regime, an excess temperature sequence was obtained by subtracting the average of the background frames. The experimental results are as follows: the defects A, B, A and B can be observed clearly in the excess temperature image, and the defects C and C cannot be detected. Fig. 7 is the excess temperature images of defects A, B, A and B at the time of maximum temperature difference for the defect concerned, where the defects appears as hot areas. In most cases, an area of 9 9 pixels on the defect and an area of L (, ) pixels on the nearby non-defect zone were selected to calculate the informative signals. In each figures of Fig. 7, the larger marked rectangular area is the observation area, the smaller marked rectangular area is the non-defect area, and the cross denotes the centre of the defect area. As we can see, defect A and B share the same non-defect zone, moreover, defect A and B share the same non-defect zone. The informative signal evolutions are shown in Fig., where the signal-to-noise ratio is defined as = /, and denotes the standard deviation of the excess temperatures in the nondefect zone. In order to verify the numerical simulation, the simulation results were used to compare with the experimental results. The contrast, which is not affected by heat flux, was used to compare. Fig. 9 shows the comparison between the simulation result and the experimental result of defect A. (a) Defect A (b) Defect B
- November, 7, Xiamen, China (c) Defect A (d) Defect B Fig. 7 Excess temperature images of four defects Temperature difference ΔT / C.5.5 -.5 5 5 5 3 35 (a) Temperature difference Signal-to-noise ratio S 5 3 - defect A defect B defect A defect B Contrast ratio C..5..3.. -. 5 5 5 3 35 defect A defect B defect A defect B (b) Contrast defect A defect B defect A defect B - 5 5 5 3 35 (c) Signal-to-noise ratio Fig. Experimental informative signal evolutions..5 Contrast ratio C..3.. experimental result simulation result -. 5 5 Fig. 9 Comparison between simulation result and experimental result 7
- November, 7, Xiamen, China As it s shown in Fig. 9, the simulation results are basically consistent with the experimental results, so it can be explained that the numerical simulation is correct. The deviation of defect A s maximum contrast is 35.9%. The possible causes of deviation are as following: () the systematic error of experimental setup; () using flat-bottom hole defect to simulate delamination defect; (3) the inaccuracy of materials thermal properties; () the influence of adjacent defects; (5) the inaccuracy of model s heat convection coefficient.. Map of testing difficulty contours. detectability limit The criterion allowing one to distinguish a defect from the background area is >, i.e. > at the observation time. Usually, the time of maximum temperature difference is taken as the best observation time. For safety s sake, it is customary to specify a multiple (n) of the noise level ( ) as the minimum signal level for detectability, so the criterion becomes > = ( ) (3) where is the threshold of, is the safety factor which represents the reliability of the detection. In order to determine the detectability limits under the given conditions, should be set based on behaviors of properly. Fig. shows the standard deviation of the non-defect zone marked in section 3.. It can be seen that the standard deviation is about. in time interval 5s s where the four defects time of maximum temperature difference locate in, so it is taken =.. Standard deviation σ / C..7..5..3. non-defect area A&B non-defect area A&B. 5 5 5 3 35 Fig. Standard deviation of the excess temperature in the non-defect areas Considering the uneven heating and random noise, the threshold of maximum temperature difference was selected as., which meant the criteria to distinguish a defect is that the maximum temperature difference should be higher than the threshold =.. More numerical simulation calculations were performed to find out the minimum defect radius, i.e. the detection limit radius that could be detected at different defect depths. The results were shown in Table. Table Detection limit radii at different defect depths when =. Defect depth h/mm.5.5.5 3 3.5 Detection limit radius r/mm.3..5. 3. 5. 7. 5. Ratio of diameter to depth.... 3.7. 7. The regression equation of detection limit radii at different defect depths is Eq. (). The detection limit radius vs. defect depth is shown in Fig., where all the cases in the area above the curve are detectable. =.55 exp(9.h) +.997exp(.9h)(mm) ()
- November, 7, Xiamen, China Detection limit radius r / mm Simulation result Regression equation. Map of testing difficulty contours 3 Fig. Detection limit radius vs. defect depth By changing the threshold, for example =., another group of detection limit radii were obtained, as shown in Table 3. Table 3 Detection limit radii at different defect depths when =. Defect depth h/mm.5.5.5. Detection limit radius r/mm...3.. 5 Ratio of diameter to depth Ra.. 3.7.. 9.3 The regression equation of detection limit radii at different defect depths when =. is Eq. (5). =.79 (.77h) + 3.79 (3.9h)(mm) (5) In order to completely describe the detectability of defects in material, a map of testing difficulty contours was newly presented. The map of testing difficulty contours were derived by drawing the curves (e.g. Eq. () and Eq. (5)) of detection limit radius vs. defect depth for different thresholds of the maximum temperature difference in the same Cartesian coordinates, as shown in Fig.. Note, a big discrepancy exists near the origin (r=) for the regression equation. Defect radius r / mm 5 5 5.5.5.5 3 3.5 Fig. Map of testing difficulty contours The map of testing difficulty contours (Fig. ) has the following features. () The defects denoted by its radius and depth on one curve have the same detection degree of difficulty denoted by the threshold, and the space of the material is divided into different zones by the so called testing difficulty contours. () The diameter to depth ratio on each contour curve is not a constant, but increases with defect depth (see Table and Table 3), so the traditional diameter to depth ratio cannot reflect the 9 Simulation result for ΔT m =. C Simulation result for ΔT m =. C Fitting curve for ΔT m =. C Fitting curve for ΔT m =. C
- November, 7, Xiamen, China detection difficulties accurately. (3) The curve =. represents the limit of detection capability, the lower left area of the curve is non-detectable area. () The other testing difficulty contours are distributed in accordance with the same law as the two curves =. and =. on the upper right of the curve =.. The more upper right the testing difficulty contour is, the better detectable the defect is. (5)Since the maximum temperature difference is directly proportional to the heat flux, the map of testing difficulty contours can be extended as follows: when the heat flux is changed to k times, namely =. W m, the thresholds of the two curves will become =. and =. respectively. 5. Conclusions () The temperature difference between defect area and non-defect area as well as the contrast are always positive, and each one has a unique peak. The time period between the two peaks is the best time to observe defects theoretically. () The influence of defect radius on the defect informative parameters is divided into three stages: the linear increasing stage, the transition stage and the saturation stage. (3) The influence of defect depth on the defect informative parameters is as follows. With the increase of defect depth, the maximum temperature difference and the maximum contrast all show an exponential downward trend; the time of maximum temperature difference and the time of maximum contrast all increase approximately linearly with the defect depth. () The traditional diameter to depth ratio of a defect cannot reflect the detection difficulties accurately, while the map of testing difficulty contours can completely describe the detectability of defects in materials under given experimental conditions. The map of testing difficulty contours, as shown in Fig., can be a general tool in the IR NDT of materials. These conclusions provide a guideline for the pulsed infrared thermography of CFRP. Acknowledgment This work was supported by the National Natural Science Foundation of China under the projects: 57, U33. References. Almond DP, Angioni SL, Pickering SG. Long pulse excitation thermographic nondestructive evaluation. NDT&E International, 7; 7:7. Guo Xingwang, Zhang Nannan. A phase sensitive modulated thermography of debondings in the insulator of SRMs. Polymer Testing, 7; 57: -3 3. Vavilov VP, Burleigh DD. Review of pulsed thermal NDT: physical principles, theory and data processing. NDT & E International, 5;73: 5.. Ghali VS, Mulaveesala R, Takei M, Frequency-modulated thermal wave imaging for nondestructive testing of carbon fiber-reinforced plastic materials, Meas. Sci. Technol. () () e3 5. Silipigni G, Burrascano P, Hutchins DA, et al. Optimization of the pulse-compression technique applied to the infrared thermography nondestructive evaluation. NDT&E International, 7; 7:. Vavilov VP, Maldague X. Dynamic thermal tomography: new promise in the IR thermography of solids. In Proceeding of SPIE, Thermosense-XIV, 99; Vol.: 9 7. Vavilov VP, Grinzato E, Bison PG, Marinetti S. Nondestructive testing of delaminations in frescoes plaster using transient infrared thermography. Res. NDE, 99; 5(): 57-7
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