Direct Visualization of Cross-Sectional Strain Distribution in Flexible

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Functional Inorganic Materials and Devices

Direct Visualization of Cross-Sectional Strain Distribution in Flexible Devices Tae-Ik Lee, Woosung Jo, Wansun Kim, Ji-Hye Kim, Kyung-Wook Paik, and Taek-Soo Kim ACS Appl. Mater. Interfaces, Just Accepted Manuscript • DOI: 10.1021/acsami.9b01480 • Publication Date (Web): 21 Mar 2019 Downloaded from http://pubs.acs.org on March 23, 2019

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ACS Applied Materials & Interfaces

Direct Visualization of Cross-Sectional Strain Distribution in Flexible Devices

Tae-Ik Lee†, Woosung Jo†, Wansun Kim†, Ji-Hye Kim‡, Kyung-Wook Paik‡, and Taek-Soo Kim*,† †Department

of Mechanical Engineering, ‡Department of Materials Science and Engineering,

Korea Advanced Institute of Science and Technology (KAIST), 291 Daehak-ro, Yuseong-gu, Daejeon 34141, Korea; *E-mail: [email protected]

Keywords: flexible electronics; mechanical reliability; multiple neutral planes; stress concentration; digital image correlation.

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ABSTRACT For flexible devices that inevitably undergo repetitive deformations, it is important to evaluate and control the mechanical strain imposed on the flexible systems for enhancing the reliability. In this paper, a novel experimental method to directly visualize cross-sectional strain distribution in the thin flexible devices is proposed. Digital image correlation (DIC) is effectively adapted by using microscopic images of the cross-section for accurate analysis of the micro-scale deformations. To conduct the DIC strain analysis, speckle patterning is accomplished by using micro-particles from diamond abrasive suspensions with optimized fabrication conditions. First, the cross-sectional micro-DIC analysis is performed successfully for 100 𝜇𝑚-thick substrates. Full-field strain quantification and easy inspection of a neutral plane are demonstrated and compared with results of finite element analysis simulation. Using the presented method, generation of multiple neutral planes is clearly visualized for a tri-layer structure with a very soft adhesive mid-layer, where strain decoupling occurs by severe shear deformation of the soft adhesive layer. Furthermore, bending strain distribution in a flexible fabric-reinforced polymer (FRP) substrate is also investigated to analyze and predict the fatigue fracture in a complex inner structure under repetitive bending loading.


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 INTRODUCTION For flexible devices that undergo repetitive deformations, mechanical reliability is a significant bottleneck for commercializing the flexible system. To enhance the reliability, evaluating and controlling the degree of deformations in the flexible devices are crucial because the imposed strain on each component serves as essential parameters for both design reliability and failure analysis. It is most important to minimize the strain imposed on functional inorganic materials which are brittle and fragile, such as electrodes including indium-tin-oxide, graphene, and alumina encapsulated by various thin film layers, to prevent premature failures under bending.1-4 An effective mechanical approach to reduce the imposed strain on such components is to place the brittle functional layers close with the mechanical neutral plane where the strain is free under bending. This neutral plane (NP) strategy has been widely used to enhance the bending reliability of flexible devices.5-8 As a promising expansion of the NP strategy, a novel laminated structure has recently been proposed, which generates multiple neutral planes (MNP) in a device by adopting very soft interlayers. The soft layers take severe shear distortion in the multilayered system and decouple the continuous axial strain gradient along the throughthickness direction. Therefore, the MNP enable protection of multiple functional layers by exploiting the structural advantages. In recent studies, highly flexible and more reliable devices that do not damage the brittle materials have been demonstrated by applying the MNP method.9-12 Analytical and numerical solutions have been established to meet the growing needs for understanding the strain mechanics in the thin laminated structure.13-17 Despite the increasing applications of the NP and MNP strategies, it is difficult to thoroughly evaluate the internal strain in the multi-layered flexible devices. For example, depth-dependent strain could not be evaluated because existing indirect methods can only examine the intactness



of the functional layers, such as by measuring the electrical resistance of conductive electrodes under bending. Therefore, the inspection is limited to certain locations where the additional functional layers are embedded. For the MNP case, in particular, it is even hard to identify whether the MNP are generated. Because the analytical solutions are only valid for simple structures under small deformation assumption of classical bending theories, complex strain analysis is hard to be accomplished in the flexible systems under large deformation. For the same reason, the numerical prediction method using finite element analysis (FEA) simulation is unreliable because the results significantly varies with different boundary conditions, which are hard to reproduce the actual configuration. For multi-component, non-homogeneous devices, evaluation of the strain distribution in areas of interest is crucial because stress concentration may occur due to the imperfections of mechanical integrity or the complex internal structures. For example, fabric-reinforced laminates, which is a promising candidate for flexible substrates, naturally possess the microstructural heterogeneity.18-21 The composite materials typically fails by fatigue loading of bending or thermal cycling, leading to fiber/resin delamination, fiber breakage, or resin cracking.22-24 These fatigue failures are usually investigated by fractography and FEA simulation where the fatigue mechanisms are speculated after the fracture has occurred.25-27 However, evaluation of the small and local fatigue strain is also impractical for both analytical solution and numerical simulation due to difficult implementation of the complex inner structure. Even if the microscopic modeling is successful, all of the material properties and adhesion properties between each components are necessarily known for the analysis. In this study, a direct strain evaluation method that accurately quantifies and visualizes the cross-sectional strain distribution in a flexible device under bending is proposed. Digital image correlation (DIC) method is adapted by taking advantage of the full-field analysis capability.


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Images from scanning electron microscopy (SEM) are utilized for the non-contact strain evaluation method for the micro-scale deformation analysis. Based on successful development of the SEM-DIC methods28-31, we show that the SEM-DIC can be effectively applied to the full cross-section of a thin and flexible device, not only to a local surface point of a bulk object in the conventional applications. Analyzing bending of the full cross-section is especially important to characterize the depth-dependent strain gradient or stress concentration for advanced flexible devices such as foldable, rollable displays. First, formation of speckle pattern is optimized for a well-polished cross-section of a 100 μm-thick PET film. Diamond polishing suspension is used as the micro-particle source, making this methodology low-cost and available for materials without any natural surface textures. Then, the cross-sectional micro-DIC analysis is performed using two consecutive SEM images that are taken at both flat and bent state. FEA simulation is also conducted and its results are compared with the experimental results. Using the proposed method, the bending strain is accurately quantified for the full-field cross-section and location of a neutral plane is easily identified. Generation of the MNP is clearly visualized for a tri-layer structure with a very soft adhesive mid-layer. For fundamental understanding of the strain decoupling phenomenon, severe shear deformation of the soft adhesive layer is characterized. Furthermore, strain concentration is effectively examined within a complex inner structure of flexible fabricreinforced substrate. The visualized fatigue strain is utilized to predict the actual position of fatigue fracture.



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 RESULTS AND DISCUSSION Figure 1a illustrates experimental procedure for the strain visualization method for thin cross-section of a flexible substrate. First, fine cross-section was formed using mechanical grinding and polishing machine with help of supporting plates that prevent the thin specimen from folding. Next, micro-patterning was conducted for the DIC analysis using 0.5 μm-sized diamond particles in a polishing suspension. Two cross-sectional microscopic images are taken for a specific position before and after bending which are compared by tracking the speckle pattern. The full-field strain evaluation is finally conducted using DIC algorithm based on the microscopic images. Detailed procedure of each step is summarized in the experimental section. Figure 1b shows the micro-DIC result for 100 μm-thick PET substrate with bending radius of 6 mm. The full-field bending strain contour was successfully obtained, where a neutral plane was clearly found at the central height of the substrate specimen that is under symmetric tensile/compressive axial strain distribution. Another merit of the presented method is to analyze various strain components simultaneously, which is found in Figure 1c that shows the strain maps for both x and y axis from the DIC and FEM simulation. The strain distribution was almost identical for the DIC analysis and FEM simulation, with the maximum x strain of ± 0.85 % and maximum y strain of ± 0.56 % for the tensile/compressive strain, respectively. Because the cross-section of interest is in a plane strain condition (εz = 0), the stress along the depth direction (𝜎𝑧) contributes to the resultant x and y strains. The state of 3D stress was identified with the FEM simulation. As an example, at the top of the PET substrate, 3D stress components were as follows: σx = 40.3 MPa, σy = ―0.001 MPa, σz = 16.1 MPa. Then, the strain components are calculated by the generalized Hooke’s law in the following Equation (1). (Modulus E=4 GPa, Poisson’s ratio 𝜈=0.4) 1

1

εx = 𝐸(𝜎𝑥 ― 𝜈(𝜎𝑦 + 𝜎𝑧)) = 4 𝐺𝑃𝑎(40.3 ― 0.4( ―0.001 + 16.1)) 𝑀𝑃𝑎 = 0.847 (%)


(1a)

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1

1

εy = 𝐸(𝜎𝑦 ― 𝜈(𝜎𝑥 + 𝜎𝑧)) = 4 𝐺𝑃𝑎( ―0.001 ― 0.4(40.3 + 16.1)) 𝑀𝑃𝑎 = ―0.564 (%) 1

(1b)

1

εz = 𝐸(𝜎𝑧 ― 𝜈(𝜎𝑥 + 𝜎𝑦)) = 4 𝐺𝑃𝑎(16.1 ― 0.4(40.3 ― 0.001)) 𝑀𝑃𝑎 = 0.000 (%) (1c)

Again, the calculated strain components were equal to the DIC measurement result. Therefore, it is meaningful that the proposed DIC method accurately measures the resultant strain components caused by the complex stress effect. Figure 1d shows graphs of x and y strain along the thickness direction for a linear section within the 100 μm-thick PET film. When comparing the results from the DIC and FEM simulation, the two graphs for the thickness-dependent bending strain coincide well each other with the same magnitude and slope throughout the substrate thickness. It is noted that the SEM should be elaborately measured, otherwise it would lead to large error in the DIC analysis.28,29 In this study, sufficient dwell time was taken to reduce image noise. Low acceleration voltage was applied to reduce thermal damage of the polymer specimen and image drift from surface charging. Correction of spatial distortion at the low magnification would lead to more reliable analysis. It is especially important for the crosssectional micro-DIC analysis that the image is precisely in-focused for the entire area because out-of-focused image of tilt cross-section would lead to large artificial strain. Large error can be involved from this drawback of 2D-DIC for measurement of the small bending strain under low magnification. Therefore, care must be taken for specimen fixation to reduce environmental disturbances including vibration and to obtain parallel cross-section image plane with respect to the electron detector. Alternatively, although restricted to low magnification, optical microscopy (OM) is also effective for this application because it is easier to obtain the entirely in-focused image due to short depth of focus of the light source compared to the SEM.



Figure 1. (a) Experimental procedure of the cross-sectional micro-DIC analysis for direct strain evaluation in a flexible device. (b) Visualization of bending strain for 100 𝜇𝑚-thick PET substrate under 6 mm radius of bending. (c) Comparison of x and y axial strain results from the DIC method and FEM simulation. (d) Graph of through-thickness strain for both x and y axial strain from the DIC method and FEM simulation. In order to examine strain decoupling effect by the soft adhesive, two types of tri-layer specimen were prepared with size of 11 × 7 mm2 containing hard and soft adhesive mid-layer. Figure 2a, 2b summarize the micro-DIC results for the tri-layer specimens under bending radius of 6 mm. Figure 2c and 2d compares the x axial strain map for the tri-layered specimen with hard and soft mid-layer, respectively. Figure 2e and 2f show accurate strain distribution through the whole thickness for the hard and soft mid-layered specimen, respectively. As shown in Figure 2a, the tri-layer specimen with hard adhesive contains a single neutral plane because strain decoupling has not occurred by the stiff interlayer. The maximum tensile/compressive strain was 2.5 %/-1.5 %, respectively. It is observed that the neutral plane forms at lower height


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than the geometric center. The downward shift of the neutral plane is explained with plastic deformation of the PET substrate that generate the asymmetric tensile/compressive strain by tensile yielding of the polymeric substrate. In Figure 2e, some discrepancy was found between the FEM prediction and the micro-DIC results for the hard adhesive specimen where plasticity was involved. This is attributed to lack of accurate mechanical properties adopted in the FEM analysis, especially for plastic behavior of the polymeric materials. In contrast, two neutral planes were clearly found for the tri-layer specimen with the soft interlayer (Figure 2b). The multiple neutral planes (MNP) are easily identified by the alternating colors of the strain map along the thickness direction. It is noted that the soft adhesive region was excluded from the DIC analysis because the speckle pattern was lost by surface distortion with out-of-plane squeezing of the soft layer. In Figure 2f, the cross-sectional strain graph for the soft adhesive case shows the effect of strain reduction of the MNP strategies distinctly. The strain range was from 1.0 % to -0.4 % for the upper substrate and from 0.4 % to -0.9 % for the lower substrate, respectively. The micro-DIC results verified the existence of multiple neutral plane effectively and accurately, and coincided with the FEM simulation results.



Figure 2. (a, b) DIC results for bending deformation (R=6 mm) of tri-layer specimens with mid-layer of hard adhesive and soft adhesive, respectively, with the thickness of 30 𝜇𝑚. (c, d) x axial strain field for the specimen with hard adhesive and soft adhesive, respectively, for the DIC (left) and FEM simulation (right). (e, f) Graph of through-thickness strain for x strain for the tri-layer specimens with hard adhesive and soft adhesive, respectively. In practical application of the multiple neutral plane strategy, longer and larger specimen should be used. The tri-layer specimen with the soft mid-layer was prepared with size of 25 × 10 mm2 in order to conduct spatial analysis in length position and bending fatigue test. Patterned indium tin oxide (ITO) was deposited on top of the tri-layer specimen as electrode for inspection of electrical failure by bending fatigue loading (Figure 3a). Figure 3b shows x axial strain under the bending with radius of 4 mm for three different X position of left, center, and right (X=-5, 0, 5 mm, respectively). On the whole, the strain


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decoupling effect is diminished by observing the z position of the neutral planes which approaches to the soft mid-layer. Most importantly, the maximum tensile strain at the top surface was the largest at central position (X=0 mm) with value of 1.9 %, while the maximum strain was ~1.1 % at both left and right position (X= ± 5 mm). Figure 3c summarizes quantitative results for the axial strain at each X position. Only at the central position (X=0 mm), ITO cracks were observed for exceeding the fracture strain of ITO of 1.4 % [8]. In order to understand the largest bending strain at the central position, local curvature was also measured using the DIC method as illustrated in Figure 3d. Curves for Y displacement is obtained from the Y displacement contour before and after the bending. The measured bending radius at the central position was less than half of the left or right position with value of 8.1, 4.0, and 8.5 mm for X=-5, 0, 5 mm, respectively. Light emitting diode (LED) demonstration showed fatigue failure of the ITO electrode at the central position after 1,000 bending cycles with radius of 4 mm (Figure 3e). Analysis of large shear strain at the mid-layer is crucial because it determines both the degree of strain decoupling and the mechanical reliability of the adhesive. The shear strain could be simply calculated under the assumption of shear lag model for constant shear strain through the thickness direction. Calculation procedure for the shear strain is illustrated in Figure 3g. The global shear distortion of the mid-layer adhesive is quantified by tracking the lateral displacement between the upper and lower side pattern. The resulting shear strain can be assumed as constant through the whole thickness. Figure 3f shows the DIC analysis for shear strain: Shear strain was fully carried by the soft adhesive layer while zero-shear was induced in the two PET substrates. No shear strain was induced in the soft layer as well for the central location where longitudinal symmetry is achieved. Positive shear strain of 0.70 was measured at the left side and negative shear strain of -0.70 was found at the right side. These experimental



results well validate, for the first time, the theoretical studies presented by Li et al. that clarified the significance of shear deformation of the soft adhesive13 and dependence of MNP splitting on the length of the laminated flexible structure14.

Figure 3. (a) Schematic of 25 mm-long tri-layer specimen with the soft mid-layer. Patterned ITO is deposited on top of the tri-layer specimen as electrode. (b) Spatial micro-DIC strain analysis for x axial strain under bending radius of 4 mm, for three different X position of left, center, and right (X=-5, 0, 5 mm, respectively). (c) Through-thickness x axial strain distribution and the maximum strain for the center and the left position. Microscopic image shows ITO cracks at the center position after the single bending. (d) Local curvature measurement using the DIC displacement analysis at the different X position. (e) LED demonstration with the laminated specimen shows failure at the central LED after cyclic bending of 1,000 cycles with the radius of 4 mm. (f) Spatial micro-DIC analysis for shear strain for the three different X position. (g) Shear strain measurement method using the DIC method at the different X position for the large shear strain of the soft mid-layer. Strain analysis within a flexible device with complex inner structure is of critical importance because the actual strain distribution is basically difficult to examine. Furthermore, stress concentration at a complex shaped position or a weak interface is rarely predicted by FEM


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simulation. As an example, the micro-DIC analysis was performed for a flexible glass fabricreinforced polymer (GFRP) substrate. Figure 4a is an optical microscopic image of the flexible composite substrate for the cross-section, showing internal woven fabric and resin structure. Figure 4b shows the results of axial strain under bending with the radius of 6 mm. First, concentrated deformation was clearly observed at the epoxy resin part. The deformation is expanded to the interface with the glass fabric in both left (red square) and right (green square) direction (Figure 4b). For the interface at the right side, the deformation expansion is thoroughly prevented by the reinforcing glass fabric in the parallel alignment. For the interface at the left side, on the contrary, large deformation of the resin permeated through small gap between the outermost fibers. The strain concentration was clearly observed in the micro-DIC analysis using SEM image with magnification × 2000. After slide bending fatigue for 50 k cycles with the radius of 6 mm, fatigue cracks were found at the strain concentration position as predicted from the developed method (Figure 4c). Fatigue cracks were not found at the interface with fabric in reinforcing direction (right) but at the interface with fabric in perpendicular direction (left). Initiation and propagation at the interface of resin and fiber was obvious in the magnified SEM image (Figure 4d). As seen in the tilt view of fractured surface (Figure 4e), the fatigue fracture occurred not only at the edge side but along full width of the specimen, where the fracture pattern is well matched with the internal configuration of the woven fabric (Figure 4f).



Figure 4. Cross-sectional micro-DIC strain analysis of a flexible glass fabric-reinforced polymer (FRP) substrate. (a) Cross-sectional image of a flexible FRP substrate showing the internal woven fabric and resin structure (Scale bar: 100 μm). (b) The micro-DIC results of axial strain under bending with the radius of 6 mm. (c) SEM cross-section image of the flexible substrate after cyclic bending of 50 k cycles. (d, e) SEM cross-section and 45° tilt image, respectively, of the typical fatigue fracture under bending at the interfaces of fibers. (f) Top image of the flexible composite laminate that shows a regular pattern of the woven fabric structure.


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 EXPERIMENTAL SECTION Flexible substrates preparation. Three types of PET specimens were prepared as follows: A 100 μm-thick single PET layer and two PET/adhesive/PET tri-layer specimens with different mid-layer modulus. Two UV-curable adhesives of acrylated urethane were used: ‘Hard’ (Loctite 3321) and ‘soft’ (Dymax 9702) adhesives with elastic modulus of 255 MPa and 0.36 MPa, respectively. The acrylated urethanes were UV-cured using a UV LED lamp with condition of 3 W/cm2 at 365 nm for 15 seconds. The mid-layer thickness was controlled using film spacer of which the thickness corresponds to the resultant adhesive thickness. The procedure of specimen fabrication is as follow. Firstly, PET films and spacers were cleaned by using iso-propyl alcohol, acetone, and deionized water. Then, PET films were further treated with O2 plasma at 100 mW for 1 min to improve the surface wetting. Second, a PET film was put on the glass plate, and then spacers were put on the each edge of PET film. UV curable acrylated urethane were spread inside the spacers. The second PET film and glass plate covered on top to make the tri-layered structure. Finally, the specimens were UV-cured with clips for retaining the acrylated urethane thickness during UV curing process. For a flexible GFRP substrate, a commercial FR4 with thickness of 100 μm that consists of T glass fabric (#2116) and bismaleimide-triazine epoxy resin. A single-ply of the glass fabric was impregnated with the resin binder which was filled with some silica fillers. Flexural modulus of the flexible substrate was 14 GPa which was measured by three-point bending test.

Mechanical grinding of thin cross-section. Overall procedure follows the illustration in Figure 1a. The specimen was gripped in between two supporting polycarbonate substrates and fixed with a metal clip for stable grinding process. Because the specimen should be freely deformed after the specimen preparation, no epoxy molding materials were used. Grinding and



polishing was conducted with three-step process to obtain highly smooth cross-section: At speed of 40 rpm, four minutes using each abrasive types in FEPA standards of P1200 and P2400. Finally, four more minutes at speed of 80 rpm using P4000 abrasive paper. The specimen was dried with compressed air and then heated for two minutes at 140 ℃ in a convection chamber in order to quickly remove moisture on the cross-section.

Micro-pattern generation on thin cross-section. The micro-pattern generation was performed using a typical polishing suspension with 0.5 μm-sized polycrystalline diamond particles. The suspension solvent was a mixture of water and propylene glycol and the combination with different content was tested for optimization. After fine dispersion of the particles is achieved by mixing the suspension, 5 ml of the suspension was poured onto a glass plate that is to spin at 40 rpm. The specimen was tilted to hold the cross-section toward the spinning suspension to capture the particles onto the clean and activated cross-section. The spinning capture was conducted for two minutes. It is noted that O2 plasma treatment for 1 minute with power of 70 W and oxygen flow of 20 sccm helped good wetting of the suspension onto the cross-section. Finally, soft baking was conducted at 140 ℃ for two minutes to eliminate the solvent and leave the adhered diamond particles. To summarize, this speckle patterning on the thin cross-section requires following key factors: Smooth cross-section with high surface energy, particles with uniform distribution and high density, watery suspension, and fast drying. This micro-particle method is cheap, fast and also proper for large area application. Furthermore, this is a non-destructive patterning method so that any thermal damage or residual stress issues on the specimen surface are prevented.


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Micro-DIC analysis for bending. A field emission SEM was used to obtain high quality image of the cross-section (SU5000, Hitachi, Japan). Secondary electron detecting mode was used with following parameters: Working distance of 5.5 mm, accelerating voltage of 3 kV, and spot intensity of 10 for damage-free measurement. In order to avoid electron charging problem for the SEM imaging of the non-conducting specimen, 5 nm-thick Pt was coated by sputtering at conditions of 100 mW for 100 seconds. The procedure for image measurement is illustrated in Figure 1a. Two images, one in the flat state and the other in the bent state, were taken for the same location of a specimen in order to conduct the DIC analysis. First, a reference image was taken for the flat state, at central region with the same magnification of × 500. For more detailed analysis (Figure 4b, left and right), higher magnification of × 2000 was used. Next, the specimen was bent with the radius of 6 mm using a custom bending fixture that consists of two aluminum plates as both wall sides. The second SEM image was taken after searching the exact location of the reference image which is recognized by the specific speckle pattern. Finally, full-field DIC analysis was performed using the two consecutive images by tracking the speckle pattern of diamond particles. The full-field strain calculation was processed by using a commercial DIC software (ARAMIS professional, GOM mbH, Germany). The DIC analysis was conducted with a subset size of 100 pixel and a subset distance of 50 pixels that guarantee local strain accuracy of 0.08 % (= 2 × displacement error / subset step distance = 2 × 0.02 pixels / 50 pixels).32,33

Finite element analysis simulation. FEM simulation was conducted using a commercial software, Abaqus ver. 6.14. The specimen and guiding plates were implemented to be the same as experimental bending condition. Half model was used with a symmetrical boundary condition at the center of the specimen. Specimen surface of the end tip was tied with



the end surface of the guiding plates, and surface-to-surface contact interactions were assigned to the interface with the length of 0.5 mm. Then, a rotation boundary condition was imposed on the guiding plate in order to bend the specimen to the required bending radius (4 or 6 mm). An 8-node biquadratic plane strain quadrilateral, reduced integration elements (CPE8R) were used for each layer of the specimen. The guiding plate was modeled as a discrete rigid type, and linear line elements (R2D2) were used with refined mesh. Mechanical properties for the FEM simulation were measured for the PET substrate and derived from the manufacturer datasheet for the adhesives: The Young’s modulus (E), Poisson ratio (ν), yield stress (σY) assigned in the specimen were EPET = 4 GPa, νPET = 0.4, σY,PET = 40 MPa for the PET layer; EHard adhesive = 255 MPa and νHard adhesive = 0.4 for the PET layer; EHard adhesive = 255 MPa and ν Hard adhesive

= 0.4 for the hard adhesive layer; ESoft adhesive = 0.36 MPa and νSoft adhesive = 0.49 for

the soft adhesive layer.


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 CONCLUSION Full-field strain distribution of bent flexible substrates was directly and accurately evaluated using a cross-sectional micro-DIC method. Using the developed method, axial strain field of the bent substrate was successfully measured and visualized for both x and y directions. The bending strain gradient was precisely measured even though the maximum absolute strain values were less than 0.01. Generation of the multiple neutral planes (MNP) was first verified experimentally using a tri-layer specimen with a structure of PET/adhesive/PET, fabricated using a very soft adhesive with elastic modulus of 0.36 MPa. The developed method could be used for spatial strain analysis and local curvature measurement. Large shear deformation that is fully carried by the soft mid-layer was effectively measured with the value of 0.70 rad. The position-dependent shear deformation was measured along the laminate length direction, showing zero-shear at the central region and maximum degree of shear at the specimen edges. FEM simulation was also conducted and verified by the experimental results. The micro-DIC method was also applied to analyze stress concentration in a fabric-reinforced polymer substrate. The results indicated that not only the position of concentrated deformation but also the accurate magnitude of fatigue strain could be evaluated. For cases of multi-layered or complex inner structures, predicting the actual strain distribution is very challenging. This method directly provides accurate strain information in a flexible device so that systematic and in-depth study becomes possible regarding the MNP mechanics or bending fatigue analysis. We believe that this experimental inspection method will contribute to the commercialization of highly reliable electronics including flexible/rollable displays, energy storage devices, and various sensors.





NOTES

The authors declare no competing financial interest.

 ACKNOWLEDGMENTS This work was supported by the Wearable Platform Materials Technology Center (2016R1A5A1009926) funded by the National Research Foundation (NRF) under the Ministry of Science, ICT and Future Planning (MSIP), the Korea Institute of Energy Technology Evaluation and Planning (KETEP) (20183010014470) under the Ministry of Trade, Industry & Energy (MOTIE), and the Graphene Materials and Components Development Program (10044412) under MOTIE/KEIT of the Republic of Korea.

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Direct Visualization of Cross-Sectional Strain Distribution in Flexible

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