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Accurate measurement of composite laminates deflection using digital speckle pattern interferometry
G Model IJLEO-52851; No. of Pages 3
ARTICLE IN PRESS Optik xxx (2013) xxx–xxx
Contents lists available at SciVerse ScienceDirect
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Accurate measurement of composite laminates deflection using digital speckle pattern interferometry Guoqing Gu, Kaifu Wang ∗ , Keyin Zhou, Xing Xu College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
a r t i c l e
i n f o
Article history: Received 10 June 2012 Accepted 10 December 2012 Keywords: Composite laminate deflection DSPI Phase-shifting method PDM DPM
a b s t r a c t The modern digital speckle pattern interferometry (DSPI) technique is applied for the accurate measurement of the full-field deflection distribution of a bent composite laminates. Two kinds of powerful phase-shifting methods, phase of differences method (PDM) and difference of phases method (DPM), are described briefly and employed in DSPI to quantitatively extract the phase information, respectively. A comparison of the deflection distributions measured by DPM and PDM indicates that the former has a better measurement accuracy than the latter in laminate’s static test experiment. © 2013 Elsevier GmbH. All rights reserved.
It is well known that the composite laminates are increasingly applied in aerospace, naval, constructional engineering and automotive industries due to their excellent mechanical properties such as high strength-to-weight ratio, high stiffness-to-weight ratio and high impact resistance [1–4]. It is the fact that the stability of the surface shape of the composite laminated structures is very important for their mechanical performance and the out-of-plane displacement fields are directly related to the stress and strain distributions of these deformed structures. However, these composite structures are often suffered from the external excitation, such as static loads, bird strike and severe temperature changes. Therefore, the resultant deflection information must be seriously taken into consideration during the design and development of such composite structures. Various modern optical measurement techniques have been applied for the determination of the out-ofplane deformation of the composite laminates in the past decades (see, for instance, Refs. [5–8]). Digital speckle pattern interferometry (DSPI) is a popular non-destructive, full-field and high-precision experimental technology to measure whole-field displacement and strain fields [9], and it is more convenient to implement in practice than using photoelasticity technology, requires less surface preparation than moiré interferometry, and needs fewer precise devices than projection grating technique and 3D DIC. However, quantitative measurement of composite laminates deflection field by DSPI has been rarely reported. In this short note, we make use of DSPI technique for measuring the deflection fields of a bent thin
CFRP laminated plate, and two kinds of classical phase-shifting method, phase of differences method (PDM) and difference of phases method (DPM) [10], are both applied for quantitative phase extraction. A comparison of accuracy between PDM and DPM for whole-field deflection measurement is also presented. The producing real-time DSPI fringe patterns can be obtained by digital subtraction of the two specklegrams, one before and the other after object deformation. The PDM deals with the formation of DSPI correlation fringes along with phase-shifting device. In this method, a single frame in the undeformed state and four phase-shifted frames (each /2) in the deformed state are captured to generate phase-shifted images with correlation fringes. Four phase-shifted correlation fringe patterns are generated by a digital subtraction of the undeformed frame from each of the four phase-shifted deformed frames. The modulation phase change ı due to the object deformation can be obtained as follows
−1
ı = tan
2 − I2 IF2 F4
where IF is the intensity of the speckle fringe pattern. On the other hand, the DPM deals with the phase pattern rather than speckle fringe pattern. In this method, phase maps are calculated for both undeformed and deformed states using phaseshifting techniques. These phase maps are subtracted to obtain the desired phase change ı, which can be calculated as follows ı = + ı − = tan−1
∗ Corresponding author. E-mail address: [email protected] (K. Wang).
(1)
2 − I2 IF3 F1
I − I A4 A2 IA3 − IA1
− tan−1
I − I B4 B2 IB3 − IB1
(2)
where the first and second arctangent terms represent the phase distributions corresponding to deformed state and undeformed
0030-4026/$ – see front matter © 2013 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2012.12.028
Please cite this article in press as: G. Gu, et al., Accurate measurement of composite laminates deflection using digital speckle pattern interferometry, Optik - Int. J. Light Electron Opt. (2013), http://dx.doi.org/10.1016/j.ijleo.2012.12.028
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ARTICLE IN PRESS G. Gu et al. / Optik xxx (2013) xxx–xxx
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Fig. 1. Real-time digital speckle fringe pattern.
state, is the random speckle noise phase term and IA , IB are the intensity of the speckle patterns related to deformed state and undeformed state. In this case, no fringes can be observed from the calculated phase maps. According to the direction of illumination and observation, the phase difference ı, arising due to object deformation, can be given by [11] ı=
4 w(x, y)
Fig. 2. Measured results using PDM: (a) raw wrapped phase map, (b) filtered wrapped phase map, and (c) and (d) unwrapped 2D plots and 3D plots.
(3)
where is the wavelength of the incident light and w(x, y) is the z direction out-of-plane displacement. The experimental specimen is taken from a piece of CFRP aircraft fuselage skin, which was made from carbon fiber (T-300) with epoxy resin as the matrix. The tested specimen was clamped along its edge by using two pieces of bolted circular ring steel plate which has an internal diameter of 60 mm and statically loaded at the center. In the experiment, the specimen was subjected to a maximum out-of-plane displacement of 2.3 m. The Michelson DSPI configuration was used to measure the out-of-plane displacement fields of a bent CFRP laminated plate. The process of speckle fringe patterns acquisition with phase-stepping is carried on with the support of commercial software. For the comparative study, we have recorded 4 phase-shifted images (each /2) before object deformation and 4 phase-shifted images (each /2) after deformation. The PDM deals with formation of speckle correlation fringes. Fig. 1 shows a typical real-time speckle subtraction correlation fringe pattern which represents the contours of the out-of-plane displacement fields. It can be obviously seen that the shape of contours corresponding to dark fringes becomes an elliptical shape, instead of circular shape corresponding to isotropic materials. This can be explained by the fact that the tested CFRP laminated plate has an orthotropic property. The raw phase map as obtained using Eq. (1) is shown in Fig. 2(a). Since the raw phase map is noisy, hence we have used a windowed Fourier filtering (WFF) method [12] to reduce noise. The evaluated filtered wrapped phase map is shown in Fig. 2(b). Fig. 2(c) and (d) shows the unwrapped 2D plots of phase distribution and 3D plots of deflection profile. However, the DPM deals with phase correlation rather than speckle fringe correlation. Fig. 3(a) and (b) shows the reconstructed phase maps related to undeformed state and deformed state. The subtracted raw phase map as obtained using Eq. (2) is shown in Fig. 3(c), and Fig. 3(d) shows the filtered wrapped phase map with WFF method. It is observed that the subtracted phase map obtained by DPM produces a better phase map for unwrapping as the phase term due to the random speckle noise is eliminated completely by the subtraction process. Fig. 3(e) and (f) shows the 2D plots of unwrapped phase distribution and 3D plots of deflection profile.
Fig. 3. Measured results using DPM: (a) and (b) calculated phase maps before and after object deformation, (c) and (d) subtracted raw and filtered wrapped phase maps, and (e) and (f) unwrapped 2D plots and 3D plots.
For comparison purpose, we take the deflection distribution along the fiber direction into consideration in PDM and DPM, respectively. The deflection data at the horizontal central crosssection of both Figs. 2(d) and 3(f) are selected for comparison. Fig. 4 shows the comparison of the PDM and DPM measurement deflection results. For a clear illustration, it is noted that only the
Please cite this article in press as: G. Gu, et al., Accurate measurement of composite laminates deflection using digital speckle pattern interferometry, Optik - Int. J. Light Electron Opt. (2013), http://dx.doi.org/10.1016/j.ijleo.2012.12.028
G Model IJLEO-52851; No. of Pages 3
ARTICLE IN PRESS G. Gu et al. / Optik xxx (2013) xxx–xxx
3
Acknowledgements This work was supported by the Fundamental Research Funds for the Central Universities and the Funding for Outstanding Doctoral Dissertation in NUAA under Grant No. BCXJ11-01. References
Fig. 4. Comparison of PDM and DPM measurement results.
deflection profile along the horizontal centerline is plotted in the figure. It can be seen from the comparison curve that the measured deflection distributions obtained from two phase-shifting approaches are in good agreement, and the relative errors between the preassigned value and the measured value at the central point’s deflection are, respectively, only 2.3% corresponding to PDM and 1.1% corresponding to DPM. It is also noticed from the figure that the profile at the vicinity of the central point measured by DPM become lower than that measured by PDM. This can be explained by the fact that the random speckle noise phase term can be eliminated completely in DPM. In conclusion, DSPI has been demonstrated as an effective, robust and powerful technique for measuring the full-field deflection of the composite laminated plate. Comparison of experimental obtained deflection distributions has also shown that DPM has a much better measurement accuracy than PDM in static testing experiment for composite laminate.
[1] A.K. Bledzki, W. Zhang, A. Chate, Natural fiber-reinforced polyurethane microfoams, Compos. Sci. Technol. 61 (2001) 2405–2411. [2] W.V. Paepegem, A. Shulev, A. Moentjens, J. Harizanova, J. Degrieck, V. Sainov, Use of projection moiré for measuring the instantaneous out-of-plane deflections of composite plates subject to bird strike, Opt. Laser Eng. 46 (2008) 527–534. [3] X.F. Yao, L.B. Meng, J.C. Jin, H.Y. Yeh, Full-field deformation measurement of fiber composite pressure vessel using digital speckle correlation method, Polym. Test. 24 (2005) 245–251. [4] S.J. Huang, Y.F. Liu, Slope of the out-of-plane deflection measurement of composite sandwich plate with a fully potted insert by using digital phase-shifting shearography, Strain 47 (2011) 189–195. [5] T. Franz, Photoelastic study of the mechanic behaviour of orthotropic composite plates subjected to impact, Compos. Struct. 54 (2001) 169–178. [6] J.H. Lim, M.M. Ratnam, H.P.S. Abdul Khalil, An experimental and finite element analysis of the static deformation of natural fiber-reinforced composite beam, Polym. Test. 22 (2003) 169–177. [7] C.M. Liu, L.W. Chen, Using the digital phase-shifting projection moiré method and wavelet transformation to measure the deformation of a PMMA cantilever beam, Polym. Test. 24 (2005) 576–582. [8] X.F. Yao, L.B. Meng, G.C. Jin, H.Y. Yeh, 3D full-field deformation monitoring of fiber composite pressure vessel using 3D digital speckle correlation method, Polym. Test. 25 (2006) 42–48. [9] P.K. Rastogi, Digital Speckle Pattern Interferometry and Related Techniques, Wiley, England, 2001. [10] B. Bhaduri, M.P. Kothiyal, N.K. Mohan, A comparative study of phaseshifting algorithms in digital speckle pattern interferometry, Optik 119 (2008) 147–152. [11] K.F. Wang, A.K. Tieu, Volume-grating phase-shifting digital speckle pattern interferometry used for measurement of out-of-plane displacement field, Opt. Laser Technol. 36 (2004) 117–120. [12] K.M. Qian, Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations, Opt. Laser Eng. 45 (2007) 304–317.
Please cite this article in press as: G. Gu, et al., Accurate measurement of composite laminates deflection using digital speckle pattern interferometry, Optik - Int. J. Light Electron Opt. (2013), http://dx.doi.org/10.1016/j.ijleo.2012.12.028
ARTICLE IN PRESS Optik xxx (2013) xxx–xxx
Contents lists available at SciVerse ScienceDirect
Optik journal homepage: www.elsevier.de/ijleo
Accurate measurement of composite laminates deflection using digital speckle pattern interferometry Guoqing Gu, Kaifu Wang ∗ , Keyin Zhou, Xing Xu College of Aerospace Engineering, Nanjing University of Aeronautics and Astronautics, Nanjing 210016, China
a r t i c l e
i n f o
Article history: Received 10 June 2012 Accepted 10 December 2012 Keywords: Composite laminate deflection DSPI Phase-shifting method PDM DPM
a b s t r a c t The modern digital speckle pattern interferometry (DSPI) technique is applied for the accurate measurement of the full-field deflection distribution of a bent composite laminates. Two kinds of powerful phase-shifting methods, phase of differences method (PDM) and difference of phases method (DPM), are described briefly and employed in DSPI to quantitatively extract the phase information, respectively. A comparison of the deflection distributions measured by DPM and PDM indicates that the former has a better measurement accuracy than the latter in laminate’s static test experiment. © 2013 Elsevier GmbH. All rights reserved.
It is well known that the composite laminates are increasingly applied in aerospace, naval, constructional engineering and automotive industries due to their excellent mechanical properties such as high strength-to-weight ratio, high stiffness-to-weight ratio and high impact resistance [1–4]. It is the fact that the stability of the surface shape of the composite laminated structures is very important for their mechanical performance and the out-of-plane displacement fields are directly related to the stress and strain distributions of these deformed structures. However, these composite structures are often suffered from the external excitation, such as static loads, bird strike and severe temperature changes. Therefore, the resultant deflection information must be seriously taken into consideration during the design and development of such composite structures. Various modern optical measurement techniques have been applied for the determination of the out-ofplane deformation of the composite laminates in the past decades (see, for instance, Refs. [5–8]). Digital speckle pattern interferometry (DSPI) is a popular non-destructive, full-field and high-precision experimental technology to measure whole-field displacement and strain fields [9], and it is more convenient to implement in practice than using photoelasticity technology, requires less surface preparation than moiré interferometry, and needs fewer precise devices than projection grating technique and 3D DIC. However, quantitative measurement of composite laminates deflection field by DSPI has been rarely reported. In this short note, we make use of DSPI technique for measuring the deflection fields of a bent thin
CFRP laminated plate, and two kinds of classical phase-shifting method, phase of differences method (PDM) and difference of phases method (DPM) [10], are both applied for quantitative phase extraction. A comparison of accuracy between PDM and DPM for whole-field deflection measurement is also presented. The producing real-time DSPI fringe patterns can be obtained by digital subtraction of the two specklegrams, one before and the other after object deformation. The PDM deals with the formation of DSPI correlation fringes along with phase-shifting device. In this method, a single frame in the undeformed state and four phase-shifted frames (each /2) in the deformed state are captured to generate phase-shifted images with correlation fringes. Four phase-shifted correlation fringe patterns are generated by a digital subtraction of the undeformed frame from each of the four phase-shifted deformed frames. The modulation phase change ı due to the object deformation can be obtained as follows
−1
ı = tan
2 − I2 IF2 F4
where IF is the intensity of the speckle fringe pattern. On the other hand, the DPM deals with the phase pattern rather than speckle fringe pattern. In this method, phase maps are calculated for both undeformed and deformed states using phaseshifting techniques. These phase maps are subtracted to obtain the desired phase change ı, which can be calculated as follows ı = + ı − = tan−1
∗ Corresponding author. E-mail address: [email protected] (K. Wang).
(1)
2 − I2 IF3 F1
I − I A4 A2 IA3 − IA1
− tan−1
I − I B4 B2 IB3 − IB1
(2)
where the first and second arctangent terms represent the phase distributions corresponding to deformed state and undeformed
0030-4026/$ – see front matter © 2013 Elsevier GmbH. All rights reserved. http://dx.doi.org/10.1016/j.ijleo.2012.12.028
Please cite this article in press as: G. Gu, et al., Accurate measurement of composite laminates deflection using digital speckle pattern interferometry, Optik - Int. J. Light Electron Opt. (2013), http://dx.doi.org/10.1016/j.ijleo.2012.12.028
G Model IJLEO-52851; No. of Pages 3
ARTICLE IN PRESS G. Gu et al. / Optik xxx (2013) xxx–xxx
2
Fig. 1. Real-time digital speckle fringe pattern.
state, is the random speckle noise phase term and IA , IB are the intensity of the speckle patterns related to deformed state and undeformed state. In this case, no fringes can be observed from the calculated phase maps. According to the direction of illumination and observation, the phase difference ı, arising due to object deformation, can be given by [11] ı=
4 w(x, y)
Fig. 2. Measured results using PDM: (a) raw wrapped phase map, (b) filtered wrapped phase map, and (c) and (d) unwrapped 2D plots and 3D plots.
(3)
where is the wavelength of the incident light and w(x, y) is the z direction out-of-plane displacement. The experimental specimen is taken from a piece of CFRP aircraft fuselage skin, which was made from carbon fiber (T-300) with epoxy resin as the matrix. The tested specimen was clamped along its edge by using two pieces of bolted circular ring steel plate which has an internal diameter of 60 mm and statically loaded at the center. In the experiment, the specimen was subjected to a maximum out-of-plane displacement of 2.3 m. The Michelson DSPI configuration was used to measure the out-of-plane displacement fields of a bent CFRP laminated plate. The process of speckle fringe patterns acquisition with phase-stepping is carried on with the support of commercial software. For the comparative study, we have recorded 4 phase-shifted images (each /2) before object deformation and 4 phase-shifted images (each /2) after deformation. The PDM deals with formation of speckle correlation fringes. Fig. 1 shows a typical real-time speckle subtraction correlation fringe pattern which represents the contours of the out-of-plane displacement fields. It can be obviously seen that the shape of contours corresponding to dark fringes becomes an elliptical shape, instead of circular shape corresponding to isotropic materials. This can be explained by the fact that the tested CFRP laminated plate has an orthotropic property. The raw phase map as obtained using Eq. (1) is shown in Fig. 2(a). Since the raw phase map is noisy, hence we have used a windowed Fourier filtering (WFF) method [12] to reduce noise. The evaluated filtered wrapped phase map is shown in Fig. 2(b). Fig. 2(c) and (d) shows the unwrapped 2D plots of phase distribution and 3D plots of deflection profile. However, the DPM deals with phase correlation rather than speckle fringe correlation. Fig. 3(a) and (b) shows the reconstructed phase maps related to undeformed state and deformed state. The subtracted raw phase map as obtained using Eq. (2) is shown in Fig. 3(c), and Fig. 3(d) shows the filtered wrapped phase map with WFF method. It is observed that the subtracted phase map obtained by DPM produces a better phase map for unwrapping as the phase term due to the random speckle noise is eliminated completely by the subtraction process. Fig. 3(e) and (f) shows the 2D plots of unwrapped phase distribution and 3D plots of deflection profile.
Fig. 3. Measured results using DPM: (a) and (b) calculated phase maps before and after object deformation, (c) and (d) subtracted raw and filtered wrapped phase maps, and (e) and (f) unwrapped 2D plots and 3D plots.
For comparison purpose, we take the deflection distribution along the fiber direction into consideration in PDM and DPM, respectively. The deflection data at the horizontal central crosssection of both Figs. 2(d) and 3(f) are selected for comparison. Fig. 4 shows the comparison of the PDM and DPM measurement deflection results. For a clear illustration, it is noted that only the
Please cite this article in press as: G. Gu, et al., Accurate measurement of composite laminates deflection using digital speckle pattern interferometry, Optik - Int. J. Light Electron Opt. (2013), http://dx.doi.org/10.1016/j.ijleo.2012.12.028
G Model IJLEO-52851; No. of Pages 3
ARTICLE IN PRESS G. Gu et al. / Optik xxx (2013) xxx–xxx
3
Acknowledgements This work was supported by the Fundamental Research Funds for the Central Universities and the Funding for Outstanding Doctoral Dissertation in NUAA under Grant No. BCXJ11-01. References
Fig. 4. Comparison of PDM and DPM measurement results.
deflection profile along the horizontal centerline is plotted in the figure. It can be seen from the comparison curve that the measured deflection distributions obtained from two phase-shifting approaches are in good agreement, and the relative errors between the preassigned value and the measured value at the central point’s deflection are, respectively, only 2.3% corresponding to PDM and 1.1% corresponding to DPM. It is also noticed from the figure that the profile at the vicinity of the central point measured by DPM become lower than that measured by PDM. This can be explained by the fact that the random speckle noise phase term can be eliminated completely in DPM. In conclusion, DSPI has been demonstrated as an effective, robust and powerful technique for measuring the full-field deflection of the composite laminated plate. Comparison of experimental obtained deflection distributions has also shown that DPM has a much better measurement accuracy than PDM in static testing experiment for composite laminate.
[1] A.K. Bledzki, W. Zhang, A. Chate, Natural fiber-reinforced polyurethane microfoams, Compos. Sci. Technol. 61 (2001) 2405–2411. [2] W.V. Paepegem, A. Shulev, A. Moentjens, J. Harizanova, J. Degrieck, V. Sainov, Use of projection moiré for measuring the instantaneous out-of-plane deflections of composite plates subject to bird strike, Opt. Laser Eng. 46 (2008) 527–534. [3] X.F. Yao, L.B. Meng, J.C. Jin, H.Y. Yeh, Full-field deformation measurement of fiber composite pressure vessel using digital speckle correlation method, Polym. Test. 24 (2005) 245–251. [4] S.J. Huang, Y.F. Liu, Slope of the out-of-plane deflection measurement of composite sandwich plate with a fully potted insert by using digital phase-shifting shearography, Strain 47 (2011) 189–195. [5] T. Franz, Photoelastic study of the mechanic behaviour of orthotropic composite plates subjected to impact, Compos. Struct. 54 (2001) 169–178. [6] J.H. Lim, M.M. Ratnam, H.P.S. Abdul Khalil, An experimental and finite element analysis of the static deformation of natural fiber-reinforced composite beam, Polym. Test. 22 (2003) 169–177. [7] C.M. Liu, L.W. Chen, Using the digital phase-shifting projection moiré method and wavelet transformation to measure the deformation of a PMMA cantilever beam, Polym. Test. 24 (2005) 576–582. [8] X.F. Yao, L.B. Meng, G.C. Jin, H.Y. Yeh, 3D full-field deformation monitoring of fiber composite pressure vessel using 3D digital speckle correlation method, Polym. Test. 25 (2006) 42–48. [9] P.K. Rastogi, Digital Speckle Pattern Interferometry and Related Techniques, Wiley, England, 2001. [10] B. Bhaduri, M.P. Kothiyal, N.K. Mohan, A comparative study of phaseshifting algorithms in digital speckle pattern interferometry, Optik 119 (2008) 147–152. [11] K.F. Wang, A.K. Tieu, Volume-grating phase-shifting digital speckle pattern interferometry used for measurement of out-of-plane displacement field, Opt. Laser Technol. 36 (2004) 117–120. [12] K.M. Qian, Two-dimensional windowed Fourier transform for fringe pattern analysis: principles, applications and implementations, Opt. Laser Eng. 45 (2007) 304–317.
Please cite this article in press as: G. Gu, et al., Accurate measurement of composite laminates deflection using digital speckle pattern interferometry, Optik - Int. J. Light Electron Opt. (2013), http://dx.doi.org/10.1016/j.ijleo.2012.12.028