# Interlaminar Shear Behavior of Laminated Carbon Fiber Reinforced Plastic from Microscale Strain Distributions Measured by Sampling Moiré Technique

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## Abstract

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_{4s}laminated carbon fiber reinforced plastic (CFRP) specimen is investigated, by utilizing microscale strain mapping in a wide field of view. A three-point bending device is developed under a laser scanning microscope, and the full-field strain distributions, including normal, shear and principal strains on the cross section of CFRP, in a three-point bending test, are measured using a developed sampling Moiré technique. The microscale shear strain concentrations at interfaces between each two adjacent layers were successfully detected and found to be positive-negative alternately distributed before damage occurrence. The 45° layers slipped to the right relative to the −45° layers, visualized from the revised Moiré phases, and shear strain distributions of the angle-ply CFRP under different loads. The absolute values of the shear strain at interfaces gradually rose with the increase of the bending load, and the sudden decrease of the shear strain peak value implied the occurrence of interlaminar damage. The evolution of the shear strain concentrations is useful in the quantitative evaluation of the potential interlaminar shear failure.

## 1. Introduction

_{2s}CFRP [8] and the shear performance of [±45°]

_{4s}CFRP [9]. These strain distributions refer to the deformation on the front surface of the laminate, rather than the deformation on the cross section of the laminate, which is also important for instability evaluation. The normal and shear strain distributions across the thickness on the cross sections of [0°/±45°/90°] CFRP laminates [10] have been investigated by DIC, and shear strain localizations have been observed at several interfaces in an uniaxial tension test. Nevertheless, DIC measurement is easily affected by noise as the deformation carrier is speckle. Shear strain measurement of laminated CFRP by ESPI [11] has also been reported; however, ESPI is very sensitive to vibration and difficult to measure large deformation. To the authors’ knowledge, there are few reports on the interlaminar shear strain measurement of [±45°] CFRP by the Moiré methods, the grid method and GPA, since a periodic pattern is necessary to be fabricated. However, with the development of grid fabrication techniques, it becomes easy to fabricate a grid on CFRP. The Moiré methods [12,13] have been widely used in the deformation measurement of composite materials [14], including CFRP [15,16,17,18]. Due to the advantages of deformation visualization, high noise resistance and large field of view, the Moiré methods are at the center of attention, and expected to be used to visualize the shear strain concentration of CFRP.

_{4s}laminated CFRP specimen. To ensure in-situ strain measurement of CFRP in a three-point bending test, a mechanical loading device is developed under a laser scanning microscope. The evolution of the measured shear strain distributions is used to evaluate the interlaminar shear behavior and compared with the damage characteristic of the angle-ply CFRP under three-point bending.

## 2. Principle of Strain Measurement

#### 2.1. Phase Extraction from Sampling Moiré Method

_{y}, the grating intensity can be expressed as

_{y}-pixels down-sampling and linear or 2nd-order or 3rd-order intensity interpolation, where T

_{y}expresses the sampling pitch close to the grating pitch. The intensity of phase-shifting Moiré fringes can be represented by

_{my}is the phase of the Moiré pattern when k

_{y}= 0 in the y direction, and k

_{y}means the starting point of the down sampling [27].

_{my}in the y direction can be calculated from the phase-shifting method using a discrete Fourier transform (DFT) algorithm using the following expression [27]:

_{mx}in the x direction can also be obtained using the above equations by changing the direction symbol y to x.

_{mx}and φ’

_{my}stand for the Moiré phases after deformation in the x and y directions, respectively.

#### 2.2. Strain Measurement Using Local Phase Unwrapping Algorithm

## 3. Materials and Experiments

#### 3.1. Specimen Preparation and Grid Fabrication

_{4S}laminated CFRP with the width of 11.6 mm, length of 52.4 mm and thickness of 2.2 mm (Figure 3a). The materials were T700SC/2500 carbon/epoxy (Toray Co., Ltd., Tokyo, Japan) prepregs [34]. There were 16 layers (16-ply prepregs) and the thickness of each layer was 0.14 mm. First, 8 layers were alternately stacked with the stacking sequence of +45° and −45°. Then, another 8 layers were symmetrically stacked with the stacking sequence of −45° and +45° from the 9th layer to the bottom layer (Figure 3b), to form a balanced structure with less coupling effect [35]. The prepregs were cured in an autoclave at a preheating temperature of 90 °C for 1h followed by heating at 130 °C at a pressure of 0.2 MPa for 3.5 h, and the cured laminate was cut to the specimen with the desired size using a composite material cutting machine (AC-300CF, Maruto Testing Machine Co., Tokyo, Japan) [35].

^{2}surface was polished by sandpaper with size of #800 and polishing solutions (DP-Spray P 15 μm followed by P 1 μm). On the polished surface, a 3-μm-pitch grid was fabricated in an ultraviolet (UV) nanoimprint lithography device (EUN-4200, Engineering System Co., Ltd., Matsumoto, Japan). The grid fabrication process of UV nanoimprint lithography is illustrated in Figure 4a. The used nanoimprint mold was a commercial grid mold from SCIVAX Corporation (Kawasaki, Japan). The used resist was PAK01, the UV wavelength was 375 nm and the exposure time was 30 s. The fabricated grid image is shown in Figure 4b observed with a laser scanning microscope (Lasertec Hybrid Optelics, Yokohama, Japan). The grid contains two orthogonal gratings, which are respectively parallel and perpendicular to the specimen axial direction.

#### 3.2. Three-Point Bending Test

## 4. Results and Discussion

#### 4.1. Normal, Shear and Principal Strain Distributions

_{4s}angle-ply CFRP specimen investigated in this study, a three-point bending test was performed to another [±45°]

_{4s}CFRP, which was manufactured using the same curing and cutting processes, but no grid was fabricated on. During the bending test, the surface of CFRP without grid was observed using the laser microscope at different magnifications, and it was found that the most vulnerable part (crack and delamination locations) was not directly below the loading head, but slightly deviated from the extension line of the load. Therefore, in this study, an area near the bottom surface of the CFRP specimen, which slightly deviates from the load extension line was selected as the observation area (Figure 6a). A region with the size of 600 × 550 µm

^{2}in the observed grid image was chosen as the region of interest (ROI), as seen in Figure 6b. The axial direction of CFRP was defined as the x direction, as shown in Figure 6a. The normal, shear and principal strain distributions under different bending loads were measured using the developed sampling Moiré method.

#### 4.2. Visualization of Relative Slip Direction of Different Layers

_{x}is the grid phase and φ

_{mx}is the calculated Moiré phase in the x direction. A revised sampling pitch T

_{rev}= 4.5 pixels is adopted to get the revised Moiré phases in the x direction, as shown in Figure 8, for visualization of the slip deformation under different loads, i.e., the maximum bending stresses at the bottom surface are 127 MPa, 199 MPa, 238 MPa, 258 MPa, 272 MPa, 292 MPa, 313 MPa, and 327 MPa, respectively.

#### 4.3. Evolution of Shear Strain Distribution

_{1}is still close to 90° at 327 MPa (Figure 11c) and the angle change is near zero, suggesting that the shear strain is near zero in accord with the measured shear strain in Figure 9h. At the (45°/−45°) layer interface, the grid angle θ

_{2}is close to 82.5° at 327 MPa (Figure 11d) and the angle reduction is near 7.5°, i.e., 0.13 in rad. It means that the shear strain at (45°/−45°) layer interface is around 0.13, the magnitude order of, which is the same to that of the measured shear strain in Figure 9h and Figure 10.

#### 4.4. Discussion

_{4s}CFRP found in this study agrees well with the results in other experimental [10] and numerical studies [37]. The shear strain distributions across the thickness of [0/−45°/45°/90°] and [0/90°/45°/−45°] laminates in an uniaxial tension test were measured by DIC in [10], and the highest interlaminar shear strain occurred at the interfaces between −45° and 45° layers. The distribution trend of the shear strain of [±45°]

_{4s}laminate under three-point bending in this study is similar to that of the [0/−45°/45°/90°] laminate under tensile bending in [10], i.e., the shear strain is positive at the (45°/−45°) layer interface and negative at the (−45°/45°) layer interface (Figure 9 and Figure 10). Whereas this distribution trend is opposite to that of the [0/90°/45°/−45°] laminate, i.e., the shear strain of the [0/90°/45°/−45°] laminate under tensile bending in [10] is negative at the (45°/−45°) layer interface and positive at the (−45°/45°) layer interface. Whatever, it is known that the shear strain tends to concentrate at the (45°/−45°) and (−45°/45°) layer interfaces, and the combined effect of the interface stiffness and shear lag leads to the shear strain localizations at the interfaces. The research results may provide useful information for the optimal design of CFRP laminates.

## 5. Conclusions

_{4s}laminated CFRP specimen in a three-point bending test was investigated from microscale strain distributions measured by a developed sampling Moiré technique. The full-field normal, shear and principal strain distributions of CFRP were measured. The tensile strain concentration regions pointed out several micro damage locations along the loading direction. The shear strain concentrations at interlaminar interfaces indicated the large shear deformations of different layers. The shear strain was positive at (45°/−45°) layer interfaces and negative at (−45°/45°) layer interfaces, indicating that the relative slip direction of 45° layers was right and of −45° layers was left, which was also visualized from the revised Moiré phases. The shear strain went up and then dropped with the load increase at the bottom (45°/−45°) layer interface, attributed to an emerged interlaminar damage. The shear strain distributions under different loads enable quantitative evaluation of the shear behavior and prediction of interlaminar damage, such as delamination of CFRP. In summary, despite this Moiré method requires a uniformly distributed grid before deformation, it can visually measure the specimen deformation with strong noise-resistance ability and is useful in detection and evaluation of tiny damages in composite materials.

## Author Contributions

## Acknowledgments

## Conflicts of Interest

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**Figure 3.**Carbon fiber reinforced plastic (CFRP) specimen geometry: (

**a**) Specimen size and fiber directions; (

**b**) surface image and layer structure on cross section.

**Figure 4.**Microscale grid fabrication: (

**a**) Process of ultraviolet (UV) nanoimprint lithography; (

**b**) grid image fabricated on CFRP specimen.

**Figure 5.**Experimental setup: (

**a**) Developed three-point bending device under a laser microscope; (

**b**) enlarge image of the loading unit; (

**c**) loading size.

**Figure 6.**Surface images showing (

**a**) the observation area and (

**b**) the analysis area on CFRP specimen during three-point bending test.

**Figure 7.**Strain measurement process and results: Images of (

**a**) grid, (

**b**) Moiré x, (

**c**) Moiré y, (

**d**) Moiré phase x and (

**e**) Moiré phase y at 0MPa; Images of (

**f**) grid, (

**g**) Moiré x, (

**h**) Moiré y, (

**i**) Moiré phase x and (

**j**) Moiré phase y at 258 MPa; distributions of (

**k**) strain x, (

**l**) strain y, (

**m**) shear strain, (

**n**) maximum principal strain and (

**o**) minimum principal strain of CFRP. The phase range is −π–π, and the symbols x and y are abbreviations of ‘in the x direction’ and in the y direction’, respectively.

**Figure 8.**Visualization of the relative slip directions of different layers from revised Moiré phases in the x direction at (

**a**) 127 MPa, (

**b**) 199 MPa, (

**c**) 238 MPa, (

**d**) 258 MPa, (

**e**) 272 MPa, (

**f**) 292 MPa, (

**g**) 313 MPa, and (

**h**) 327 MPa.

**Figure 9.**Evolution of the shear strain distributions of CFRP at (

**a**) 127 MPa, (

**b**) 199 MPa, (

**c**) 238 MPa, (

**d**) 258 MPa, (

**e**) 272 MPa, (

**f**) 292 MPa, (

**g**) 313 MPa, and (

**h**) 327 MPa, where the arrows show the relative slip directions of different layers.

**Figure 10.**Shear strain of CFRP under different loads along the section line A-A’ labeled in Figure 9a.

**Figure 11.**Recorded 2D grid images in (

**a**) the analysis area and (

**b**) a local area near the lower (45°/−45°) layer interface, and enlarged views (

**c**) in the middle of 45° layer and (

**d**) at the (45°/−45°) layer interface on CFRP at 327 MPa in the three-point bending test.

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**MDPI and ACS Style**

Wang, Q.; Ri, S.; Tsuda, H.; Takashita, Y.; Kitamura, R.; Ogihara, S. Interlaminar Shear Behavior of Laminated Carbon Fiber Reinforced Plastic from Microscale Strain Distributions Measured by Sampling Moiré Technique. *Materials* **2018**, *11*, 1684.
https://doi.org/10.3390/ma11091684

**AMA Style**

Wang Q, Ri S, Tsuda H, Takashita Y, Kitamura R, Ogihara S. Interlaminar Shear Behavior of Laminated Carbon Fiber Reinforced Plastic from Microscale Strain Distributions Measured by Sampling Moiré Technique. *Materials*. 2018; 11(9):1684.
https://doi.org/10.3390/ma11091684

**Chicago/Turabian Style**

Wang, Qinghua, Shien Ri, Hiroshi Tsuda, Yosuke Takashita, Ryuta Kitamura, and Shinji Ogihara. 2018. "Interlaminar Shear Behavior of Laminated Carbon Fiber Reinforced Plastic from Microscale Strain Distributions Measured by Sampling Moiré Technique" *Materials* 11, no. 9: 1684.
https://doi.org/10.3390/ma11091684