FULL-FIELD STRAIN MEASUREMENT OF CARBON FIBER REINFORCED PLASTIC USING SAMPLING MOIRÉ FRINGES

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1 21 st International Conference on Composite Materials Xi an, th August 2017 FULL-FIELD STRAIN MEASUREMENT OF CARBON FIBER REINFORCED PLASTIC USING SAMPLING MOIRÉ FRINGES Q. Wang 1, S. Ri 1 and H. Tsuda 1 1 Research Institute for Measurement and Analtical Instrumentation, National Institute of Advanced Industrial Science and Technolog, Umezono, Tsukuba, Ibaraki Japan * wang.qinghua@aist.go.jp Kewords: Strain distribution, Microscale deformation, Image processing, Fringe analsis, CFRP ABSTRACT Microscale strain distributions are essential parameters for evaluating the mechanical properties and instabilit behaviours of composite materials. In this work, a recentl-developed reconstructed multiplication moiré method from 2-pixel sampling moiré fringes was used to investigate the deformation performance of a carbon fiber reinforced plastic (CFRP) specimen. The full-field distributions of two-dimensional displacements, normal strains and shear strains of CFRP were measured under different three-point bending loads. The deformation features of CFRP were analsed, which is helpful to stud its potential damage mechanism. 1 INTRODUCTION Carbon fiber reinforced plastic (CFRP) has been widel used in industrial fields of automobiles, aerospace, railwas and infrastructures owing to the advantages of low densit and high strength-toweight ratio. To evaluate its mechanical propert and instabilit behaviour, microscale strain distributions of CFRP under mechanical loading are necessar to be measured experimentall. Optical techniques have drawn great attention in both scientific and engineering fields owing to the merits of non-destructive testing and high sensitivit. In recent ears, the commonl used optical methods for microscale deformation measurement include electronic speckle pattern interferometr (ESPI) [1], digital image correlation (DIC) [2], geometric phase analsis (GPA) [3] and moiré methods [4]. Each method has its advantages and disadvantages, and is mainl used according to its own appropriate applications. Among these methods, the moiré methods impress the authors due to the advantages of deformation visualization, a large field of view and the strong noise resistance abilit. In this stud, a recentl-developed moiré method [5], i.e., the reconstructed multiplication moiré method from 2-pixel sampling moiré fringes was chosen as the research methodolog. It has the same wide field of view as the microscope scanning moiré method, and both the displacement and strain measurement sensitivities are doubled. Two-dimensional (2D) strain distributions are simpl measurable without rotating the sample stage or the scanning lines, no matter whether the scanning resolution is adjustable or not. The full-field displacement and strain distributions of a CFRP specimen was non-destructivel investigated under different three-point bending loads. 2 PRINCIPLE OF RECONSTRUCTED MULTIPLICATION MOIRE METHOD The used deformation measurement method was the reconstructed multiplication moiré method with advantages of high deformation sensitivit and a large field of view. Two groups of 2-pixel sampling moiré fringes were first generated from a grid image at each load, and then used to reconstruct multiplication moiré fringes (Fig. 1) to double the deformation measurement sensitivit [5]. Both the normal strains in the x and direction as well as the shear strain were able to be accuratel measured without rotating the sample stage or the microscope scanning lines. The detailed implementation procedure was introduced in [6]. To make the field of view as large as possible, the specimen grating pitch p can be as small as around 2 pixels in the recorded image. Since the microscope scanning pitch is 1 pixel, both the specimen grating and the

2 Q. Wang, S. Ri and H. Tsuda traditional multiplication moiré fringes with frequenc of (2/p -1/p scan_ ) will be recorded [7], where p scan_ represents the scanning pitch in the direction. The intensit of the recorded image can be expressed as 2 1 Irecorded Acos(2π ) + Bcos[2π ( )] + C (1) p p p scan_ where A and B stand for the modulation amplitudes, and C contains the background and higher-frequenc intensit of the recorded image. Due to the mutual disturbance, both the specimen grating and the multiplication moiré fringes in the recorded image are not distinct, see Fig. 1(b). If the recorded intensit image is thinned out ever 2 pixels [8] followed b linear or high-order intensit interpolation shown in Fig. 1(c), two 2-pixel down-sampling moiré patterns can be generated with intensities of 1 1 k k Im, Acos[2π ( ) + 2π ] + Bcos[2π ( ) + 2π ] + C p T T p p T T scan_ 1 1 k Acos[2π ( ) + 2π ] + D ( k 0, 1 pixel) p T T Because k0, 1 pixel and T 2 pixels, the intensities of the two sampling moiré patterns can also be represented b 1 1 Im, 1 Acos[2π ( )] + D p T 1 1 Im, 2 -Acos[2π ( )] + D p T If the microscope magnification remains unchanged and the scanning resolution in the direction is changed to half, the microscope scanning pitch will be approximatel equal to the specimen grating pitch, and the traditional scanning moiré will emerge with intensit of I m,scan_acos[2π(1/p -1/T )]+E. From Eq. (3), one of the 2-pixel sampling moiré patterns is the same to the traditional scanning moiré pattern. As the microscope magnification does not change, the field of view of the 2-pixel sampling moiré is also the same to that of the scanning moiré. (2) (3) Figure 1: Formation principle of 2-pixel sampling moiré and reconstructed multiplication moiré patterns, where m is the fringe order.

3 21 st International Conference on Composite Materials Xi an, th August 2017 To achieve higher deformation measurement accurac b using both of the two sampling moiré patterns, a distinct multiplication moiré pattern can be reconstructed from the multiplicative interference between the two sampling moiré patterns using the following equation [5] A 1 1 A I I I D multi m, 1 m, 2 cos[4π ( )] 2 p T 2 + (4) From Eq. (4) and Fig. 1(d), the frequenc of the multiplication moiré is twice that of the sampling moiré. Both the displacement and strain measurement sensitivities in the reconstructed multiplication moiré method are twice as high as in the scanning moiré method [5]. Based on the fringe centering method, the displacement of the specimen relative to the sampling pitch in the direction can be acquired from u mt ( m 0, 0.5, 1, 1.5, 2, 2.5,...) (5) where m indicates the fringe order of the reconstructed multiplication moiré fringes in the direction. Similarl, the relative displacement in the x direction can be calculated using u xm xt x, where m x means the fringe order of the reconstructed multiplication moiré fringes in the x direction, and T x is the sampling pitch in the x direction. The x-direction, -direction and shear strain components are obtainable from the partial differentials of the displacements in the x and directions u ε x x u ε ( mt) x ( mt) x x x u u ( ) ( ) x mt mt x x γ x + + x x (6) 3 EXPERIMENTS AND RESULTS 3.1 Specimen preparation and three-point bending test The CFRP specimen was made up of epox resin and K13D carbon fibers with diameters of 10~11 μm. The thickness, the width and the length of the specimen were 1 mm, 4 mm and 22 mm, respectivel, see Fig. 2(a). All fiber directions were perpendicular to the 1 22 mm 2 surface to be observed, which was polished using sand papers and polishing solutions on an automatic polishing machine. A strain gauge was pasted on a 4 22 mm 2 surface to monitor the maximum tensile strain during the following bending test, as shown in Fig. 2(b). A cross grating with pitch of 3 μm was fabricated on the polished surface b ultraviolet nanoimprint lithograph (EUN-4200), the process of which is presented in Fig. 3(a). The used resist was PAK01 and the UV wavelength was 375 nm. The three-point bending test was carried out using a self-developed automatic mechanical loading device under a laser scanning microscope (Lasertec OPTELICS HYBRID). The three-point bending experimental setup is displaed in Fig. 2(c). The support span was 16 mm, and the span-to-depth ratio was 16 according to the American Societ for Testing and Materials (ASTM) standards. During the bending test, a series of grid images were recorded using the microscope. 3.2 Displacement and strain distributions of CFRP Under different three-point bending loads, the grid images were collected when the magnification of the objective lens was 5 and the image resolution was In this case, the grid pitch was around 2 pixels, and the developed reconstructed multiplication moiré method was able to be used for deformation measurement in a large field of view. The CFRP surface image, the recorded 3-μm-pitch grid fabricated according to the process in Fig. 3(a) and the region of interest are shown in Fig. 3(b).

4 Q. Wang, S. Ri and H. Tsuda The 2-pixel sampling moiré patterns and the reconstructed multiplication moiré pattern in a mm 2 square region are illustrated in Fig. 3(c) when the strain gauge value is 5330 µε. From the grid images when the strain gauge values were 0 µε, 2460 µε, 3500 µε, 4220 µε and 5330 µε, the displacement and strain distributions of CFRP were measured using the reconstructed multiplication moiré method mentioned above. The displacement distributions in the x and directions under different loads are presented in Fig. 4, and the distributions of the normal strains in the x and directions, and the shear strains under these different loads are listed in Fig. 5. Figure 2: (a) CFRP specimen size, (b) photo of specimen after bending, and (c) experimental setup of three-point bending test under a laser scanning microscope. Figure 3: (a) Process of UV nanoimprint lithograph, (b) CFRP surface image and 3-μm-pitch grid image, and (c) 2-pixel sampling moiré patterns and the reconstructed multiplication moiré pattern in the direction when the strain gauge value is 5330 µε.

5 21 st International Conference on Composite Materials Xi an, th August 2017 Figure 4: 2D displacement distributions of CFRP under different three-point bending loads Figure 5: Distributions of x-direction strain, -direction strain and shear strain of CFRP under different three-point bending loads From Fig. 4, the displacement in the x (axial) direction under each load is positive in the upper-left and bottom-right corners and negative in the other two corners, and the displacement in the (loading) direction is negative in all the area and minimum along the loading line, both of which agree well with the three-point bending feature. From Fig. 5, the strain in the x direction is compressive in the upper area and tensile in the lower area, while the strain in the direction is tensile in the upper region and

6 Q. Wang, S. Ri and H. Tsuda compressive in the lower region. The shear strain is negative in the left area, positive in the right area and almost zero in the middle area. With the increase of the bending load, the absolute values of the tensile and compressive (or positive and negative) strains graduall grow. The strain results are useful in finding the weak area on the specimen which is helpful to understand the potential damage mechanism. 4 CONCLUSIONS In conclusion, the microscale deformations including displacement and strain distributions of CFRP under different three-point bending loads were quantitativel investigated using the reconstructed multiplication moiré method from 2-pixel sampling moiré fringes. ACKNOWLEDGEMENTS This work was supported b Japan Societ for the Promotion of Science (JSPS) KAKENHI Grant Numbers JP16K17988, JP16K05996; and Structural Materials for Innovation of the Cross-ministerial Strategic Innovation Promotion Program (SIP) of Japan Science and Technolog (JST). REFERENCES [1] V. D. Madjarova, H. Kadono and S. Toooka, Dnamic electronic speckle pattern interferometr (DESPI) phase analses with temporal Hilbert transform, Optics express, 11(6), 2003, pp (doi: /OE ). [2] T.C. Chu, W.F. Ranson and M.A. Sutton, Applications of digital-image-correlation techniques to experimental mechanics, Experimental mechanics, 25(3), 1985, pp (doi: /BF ). [3] Z. Liu, H. Xie, D. Fang, F. Dai, Q. Xue, H. Liu and J. Jia. Residual strain around a step edge of artificial Al/Si(111)-7x7 nanocluster, Applied Phsics Letters, 87(20), 2005, pp (doi: / ). [4] S. Kishimoto, M. Egashira and N. Shina, Microcreep deformation measurements b a moiré method using electron-beam lithograph and electron-beam scan, Optical Engineering, 32(3), 1993, pp (doi: / ). [5] Q. Wang, S. Ri and H. Tsuda, Digital sampling moiré as a substitute for microscope scanning moiré for high-sensitivit and full-field deformation measurement at micron/nano scales, Applied Optics, 55(25), 2016, pp (doi: /AO ). [6] Q. Wang, S. Ri and H. Tsuda, Micro/nano-scale strain distribution measurement from sampling moiré fringes, Journal of Visualized Experiments, 123, 2017, pp. e55739 (doi: /55739). [7] Y. Li, H. Xie, P. Chen and Q. Zhang, Theoretical analsis of moiré fringe multiplication under a scanning electron microscope, Measurement Science and Technolog, 22, 2010, pp (doi: / /22/2/025301). [8] S. Ri, M. Fujigaki and Y. Morimoto. Sampling moiré method for accurate small deformation distribution measurement, Experimental Mechanics, 50(4), 2010, pp (doi: /s ).