Effect of Interlayer Stress on U Bends and Water Droplet Bends

­e interlayer stress (IS) analysis of the exible active-matrix organic light-emitting diode (AMOLED) panel is critical for decreasing the stress concentration and reducing the risk of overall screen failure. ­is article relies on the linear elastic models of ABAQUS to simulate nite element analysis of foldable panels. ­is article discussed three sensitive locations of the exible AMOLED panel caused by two dierent bending methods including U bends and water droplet bends.­e nite element method for simulating the layer analysis was constructed to analyze the eect of optically clear adhesive (OCA) lm thickness on the distribution of stress and strain. ­e module can be optimized by changing the thickness and shear modulus of OCA. With the decrease of OCA thickness and the increase of stiness, the maximum stress of the organic light-emitting diode (OLED) layer is decreased by 20% which is 55Mpa; meanwhile, the IS of the entire module is reduced by about 30%.


Introduction
With the popularity of smartphones, at-screen TVs, and laptops, display panels as a core component of electronics are best-in-class development. As the primary way to communicate with people, display performance is critical to the user experience [1]. Japan, South Korea, Taiwan, and China have spent great e ort in display technology development. Flexible active-matrix organic light-emitting diodes (AMOLED) with many attractive features, including high resolution, low power consumption, lightweight, and wide viewing angle, have a profound e ect on displays [2]. With the continuous development of personal smart terminals, exible OLED screens o er a wider range of applications. Compared to curved screens and full-screen mobile phones, foldable mobile phones can better meet people's requirements for communication [3]. Breakage and shedding as the common stress problems in folding screens have been bothering and hindering the promotion of the consumer market [4]. e main purpose is to compare and analyze technical solutions for exible AMOLED display modules.
Each functional lm layer contains only one layer of rstorder solid elements, which will result in a larger calculation error caused by the clipping self-lock e ect. erefore, it is di cult to simulate the transmission of pressure between functional lm layers [5]. In this paper, a hyperelastic model of OCA is proposed. e introduction of hyperelastic parameters has the e ect of scaling with strain to realize the correlation between the mechanical properties of materials and time [6]. e global pressure and pressure check the distribution of the folding panel [7][8][9][10]. Investigate the impact of the stacking structure further. Finally, the paper puts forward some suggestions to optimize the panel structure and operate e ectively. e most exible AMOLED display module folding scheme has been proposed by comparing and studying di erent laminate bending designs from the aspects of pressure and strain, material, process selection, and simulation optimization [11][12][13]. e 7-inch exible AMOLED module is produced by selecting di erent locations for the lm layer and process plan [14,15]. Reliability, optical, and mechanical testing of the nished screen is carried out through mechanical simulation and testing, and the panel is more effectively prevented from peeling or layering, and test results are given.

Geometric Model and Boundary Conditions.
e bending process of the collapsible AMOLED panel is simulated as a plane strain problem using nonlinear finite component software ABAQUS.
e common hard screen AMOLED module stacking technology mainly involving module optics, mechanics, heat, function, and appearance is very mature. Since stress and strain are associated with elastic modularity, strain is the main consideration. ABAQUS can calculate the change of stress by the elastic module. Modulus considers only the tensile stress during bending, regardless of the effect of shear slip. e flexible module stack design is mainly based on material process selection, film layer simplification, and simulation for scheme design. At present, the thickness of common polarizers (POL) is basically between 143 and 170 microns and generally includes two parts: linear polarizers and quarter-wave plates. e OLED device material is easily affected by water and oxygen, and its performance will be degraded. Although there is usually a layer of encapsulation on the surface of the OLED screen, in order to further improve its service life and reliability test results, a barrier film (barrier film) will be attached after encapsulation, which is also used to block water and oxygen. e barrier film is usually attached to the top surface of the screen. e thickness of the barrier film is between 50 and 150 microns. It is usually located on the top surface of the display screen to protect the screen. e cover film in the flexible AMOLED screen is similar to the cover glass in the ordinary AMOLED screen, and it is usually located on the uppermost surface of the display screen to protect the screen. e thickness of the protective sheet for flexible AMOLED is between 30 and 90 microns. e whole is a double-sided nonadhesive module material. e support film (back plate film) is usually only used for flexible AMOLED screens because the original glass substrate of the flexible AMOLED screen will be peeled off by laser during the production process, and then the support film will be attached to the other side of the PI substrate to realize the screen body in the production process. In the process of "flexibility," the stress on the upper end is balanced and the mechanical properties of the entire screen are enhanced. e thickness of the supporting film is selected between 50 and 75 microns. e whole is a single-sided adhesive module material.
According to industrial production, the thickness of the OCA layers is 25 μm, 25 μm, and 50 μm, respectively. In addition, the rest of the film materials are simplified as linear elastic materials. Both thickness of each film layer and specific parameters are shown in Table 1.
In the experiment, two auxiliary steel plates were used to bend the flexible screen. In this experiment, a separate module screen was used for the experiment without adding electronic devices. e length of the flexible screen is 146.7 mm, the width is 71.5 mm, the thickness is 338 μm, and the bending radius is 3 mm. We made a 180-degree U bend on the experimental object as shown in Figure 1(b). e steel plate covers a lot of the flexible screen, so it is difficult to see clearly. Figure 1(a) is a schematic diagram of the bending of the flexible screen during the experiment. Since the mechanical properties of the longitudinal section of the flexible screen are the same when it is bent, we used a two-dimensional model to replace the three-dimensional model of the experiment in the simulation. e initial state of the flexible screen and various parameters of the sample are shown in Figure 1(c). e schematic diagram in Figure 1(d) is the state and movement of the flexible screen after the U-shaped bending is completed.
ere are auxiliary instruments on both sides to finish. e coupling of the two reference points is set on both sides of the midpoint of the module, which drives the module to rotate. To form an arc shape when bending, the bending part will reduce the stress on the structure. e distance between the reference point and the axis of symmetry is πR/2 mm. When R � 3 mm, the distance is 4.71 mm. e structure and schematic diagram are shown in Figure 2. e coupled reference point RP-1 rotates clockwise at a speed of 1.57 rad/s and moves to the right at (π/2) R mm/s simultaneously. e figure after bending is shown in Figure 2(b), followed by static Set 300 s to simulate actual usage.

Elastic Properties of Orthotropic Materials.
e Mooney-Rivlin model is based on rubber isotropy and approximate incompressible volume assumption. In engineering, the strain energy density function is generally Journal of Engineering used for rubber to characterize the superelasticity of the material. e polynomial strain energy function in the analysis has been more widely used in finite element analysis [16]. For rubber in terms of similar incompressible physical nonlinear materials, the Mooney-Rivlin strain energy function is the most common choice. Its constitutive relationship is as follows [17]: (1) U is the strain energy density; N is the class of the function; C ij is a material constant, usually obtained by experimental tests; I 1 and I 2 are the first-order and the second-order strain invariants [18,19]; D i is the material constant, which is related to the pressure of the material shrinkage correlation; J is the volume; and λ 3 are the main extension rate [20]. Based on the above constitutive relationship, the strain energy function of the incompressible material is established and is as follows: (2) C 10 and C 01 are the material constants obtained from the experiment, and D 1 is the material constant and is related to the compressibility of the material. Studies have shown that the Mooney-Rivlin model is a superelastic model type, which can better simulate the application of rubber materials' time-changing characteristics. e OCA hyperelastic model in this article is used in the simulation. To get more reliable superelastic parameters of OCA, we did a uniaxial tensile test and biaxial tensile and plane tensile test OCA to determine the parameters of OCA in the Mooney-Rivlin model as shown in Figures 2(c)-2(e). e single-layer board presents orthotropic anisotropy on a macroscopic scale. As shown in Figure 3, the direction parallel to the fiber of the single-layer board is called the longitudinal direction (or 1 direction), and the direction perpendicular to the fiber is called the transverse direction, along the thickness direction is 3 directions [20]. Generally, materials can show the strongest performance along the longitudinal direction, while the performances along the transverse and thickness directions are low and approximately equal.

Meshing and Accuracy Verification.
In this paper, the implicit dynamic viscoelastic analysis step has been used for analysis and calculation. To be consistent with the real force, plane strain grids have been applied in this model. When dividing the grid, quadrilateral grids are used to facilitate convergence and calculation.
In the thickness direction, all membrane materials and OCA adhesive materials are divided into three layers. e grid-type used in this paper is plane strain, hybrid, and reduced integral CPE8RH element. e accuracy of meshing usually affects the accuracy of the results. Generally speaking, the finer the meshing is, the more accurate the result will be. However, if the mesh is too dense, the computational overhead and the calculation time will increase obviously. For display dynamics algorithms, computer memory consumption and calculation time consumption are proportional to the number of grid cells.
e computational cost increases with the increase in the fineness of the grid division. It can be more directly predicted that the grid refinement will cause cost changes. But for the implicit dynamics algorithm used in this article, the computer memory consumption and computing time consumption will have an exponential relationship with the number of grid cells. erefore, using a reasonable mesh density can greatly optimize the calculation cost the same with the same accuracy to verify whether the mesh density of the current model can meet the accuracy requirements, a more refined model is used for the comparison of calculation results. e original model is in the length direction, and the grid size is 0.025 mm. In the thickness direction, all layers are divided into 3 layers. We use the implicit viscoelastic analysis step to reduce the calculation time and reduce the probability of grid distortion. Each film layer is divided from three layers to six layers to transmit longitudinal stress to reduce the value of residual stress. We also changed the mesh size to reduce the mesh size without losing experimental data and without increasing the simulation time, minimizing the error caused by mesh errors on the simulation. e results of partial model division are shown in Figure 4. For comparison, the refined model is used in the length direction, and the grid size is 0.0125 mm. In the thickness direction, all layers are divided into 6 layers, and the results of partial model division are shown in Figure 4.
Since the full integration unit may have a shear selflocking problem, the commonly used eight-node hexagonal contraction overall reduction unit is C3D8R. e appropriate element type, the secondary reduction, and integration element C3D20R are determined by comparing the influence of stress on IS. Figure 4 shows each lamination sequence. When each functional film layer is divided into 3 layers of grid cells, the stresses of the three layers of grid cells  are superimposed along the thickness direction. e neutral layer represents the integrity of the grid layer stress of the membrane layer.

Global Stress and Strain Distribution in Folding Panels.
During the U-shaped bending, the bending stress of each film layer changes proportionally with time, as shown in Figure 5. As shown in Figure 5(a), the distribution of cloud images in each field shows a certain symmetry. Among them, the displacement field cloud distribution with only some angle changes is clear and stable. It can be seen that the displacement field in the x-direction is approximately symmetrical with the y-axis. Cloud images change rapidly at the beginning of loading. When the tensile displacement of the module reaches about 5 mm, the cloud image begins to form a stable distribution. Figure 5(b) shows the stress changes of the eight functional film layers in the process of stretching and compression. e cover film layer and the backplane bear the greatest tensile pressure, which is also in line with our design of the two functional film layers in the flexible screen. Based on the above, it can be seen that because the cover film is far from the display layer, the buffering effect of the OCA glue layer and the effect of the thickness change on the display area can be ignored. e backplane is closer to the display layer when the thickness changes. It will affect the strain of the display area so that the maximum compressive strain will increase, the maximum tensile strain will decrease, and the device will be damaged. When the strain of the OCA adhesive layer rises, the risk of adhesive layer peeling increases as well.
erefore, the authenticity of the simulation can be verified. e maximum stress of the Backplane layer reaches 357 MPa, which shows that the risk of failure is also in the backplane layer, and the strength of the backplane should be improved during production. During the bending process, it can be reasonably assumed that the upper part of the screen body is compressed when the lower part is stretched.

Fold Multiple Neutral Planes in the Panel.
When the flexible display module is in a bent state, the most important thing is to ensure the integrity of the brittle TFT layer, above the PI substrate, and the easily debonded organic light- +9.649e+05 (Avg: 75%) S, S11  emitting layer. ere are multiple neutral layer positions (the x-coordinate is equal to 0) in the lamination structure because OCA has a very small elastic modulus compared with the adjacent film layer, resulting in a shielding effect. When the influence between the two layers becomes weak, the structural relationship between the two neutral layers can be analyzed independently. It is vital to keep the position nearing the neutral layer of the module. It is usually achieved by changing the type and thickness of the laminated materials to adjust the position of the neutral layer or to manufacture multiple neutral layers. In this section, the neutral surfaces in the folding panel and the effect of tensile stress on the panel were examined. e locations where the maximum tensile stress is generated at the three U-shaped bends are also the areas with the most serious fatigue fracture. In Figure 6(d), the tensile stress of the pet rear plane and the POL film layer is maximum, and the deformation on the X-axis is the largest. e tensile force between them and the upper and lower film layers is in a dangerous state.
In Figure 7, the cover film and touch panel have the highest tensile force. When the interface between layers of the same type is located at different thickness locations, the distribution trend of IS is similar, but the magnitude is different. In addition, the magnitude and distribution of normal stress between layers are very different, especially the angle corresponding to the peak value also has a certain deviation. However, the magnitude and distribution of interlayer shear stress are almost the same. e difference in position of the interface in the x-direction of the same layer does not affect the distribution trend of IS, but only its size and thickness corresponding to the peak value. Among them, IS is greatly affected, and interlayer shear stress is slightly affected. en explore the relationship between the size of normal stress in the S22 direction and thickness and neutral layer.
As can be seen from Figure 7, the IS on both sides of y-0 changes in the same pattern with the thickness of 193 nm as the dividing line. e size of the dividing line is the same on both sides of the line, but the size of τ z and τ x is different, which is related to the laying characteristics and boundary conditions of laminates. Because laminates are centrally symmetrical in the plane, the change of the stratification stresses is the same on both sides of the dividing line. In addition, when the fixed constraints are applied to one end of the laminate and the stretch load is applied to the other +2.776e+08 (Avg: 75%) S, Mises +2.544e+08 +2.313e+08 +2.082e+08 +1.850e+08 +1.619e+08 +1.388e+08 +1.157e+08 +9.252e+08 +6.939e+08 +4.626e+08 +2.313e+08 +3.145e+08 (a) +2.776e+08 (Avg: 75%) S, Mises +2.544e+08 +2.313e+08 +2.082e+08 +1.850e+08 +1.619e+08 +1.388e+08 +1.157e+08 +9.252e+08 +6.939e+08 +4.626e+08 +2.313e+08 +3.145e+08 end of the plane, the stress difference between the layers on both sides of the dividing line will occur. For the distribution of stress in the subsequent layer, only the part on the other side of the y-0 needs to be studied. As can be seen from Figure 7, when the interface between layers of the same type is located at different thickness locations, the distribution trend of IS is similar, but the magnitude is different. e magnitude and distribution of the normal stress between the various layers are very different, especially the angle corresponding to the peak value also has a certain deviation. Moreover, the value of the transverse strain of the film grid does not change appearance, and the magnitude and distribution of the interlaminar shear stress are almost the same. erefore, the differences in interface positions between layers along the same thickness direction do not affect the distribution trend of IS, but only their size and the angle corresponding to the peak value. us, the force will be greatly affected, while the shear stress between the pull skins is also slightly affected.

Interlayer Stress.
e maximum stress of the module is located in the bending zone, reaching 705 MPa. It usually has good mechanical properties along the fiber direction, while the mechanical properties perpendicular to the fiber direction mainly depend on the properties of the matrix material and the bonding ability of the matrix and the fiber. Due to the bending curvature of the entire module, the maximum stress of S22 is on the backplane of the module. From Figure 8, we can see that the stress growth of S22 is relatively small when the module is just bent. As the bending process progresses, the stress transfer between the film layers becomes more intense, resulting in more and more intense changes in the stress experienced by the backplane. e way to solve the stress transfer is to change the OCA adhesive layer. Finally, the IS is effectively reduced by the OCA adhesive layer. is phenomenon is called the free edge effect. Furthermore, IS is singular at the free edge of the laminate. When the finite element method is used to analyze IS, the thinner the mesh near the edge, the greater the stress value +2.776e+08 (Avg: 75%) S, Mises +2.544e+08 +2.313e+08 +2.082e+08 +1.850e+08 +1.619e+08 +1.388e+08 +1.157e+08 +9.252e+08 +6.939e+08 +4.626e+08 +2.313e+08 +3.145e+08 within the layer, until infinity. Given the relatively weak internal strength of the laminate, it is likely that the decontamination and delayering at the free edge caused the premature failure and the inability to exert its original loadbearing capacity. e classical laminate theory commonly used in engineering is based on Kirchhoff's hypothesis that each single-layer plate in the composite laminate is in a plane stress state, only in-machine stress is considered and interlayer shear strain is not considered. However, this assumption is only valid in areas far from the free edge. e fault load of the composite laminate based on this theory is usually greater than the actual load measured in the experiment, which may be caused by local interlayer pressure. erefore, it is of great engineering practical significance to study the size and distribution of IS for predicting the final load and the displayer position and optimizing the laminate design.

Conclusions
An AMOLED model describing the nonlinear viscoelastic behavior of OCA is proposed. Based on the mechanical model, the IS distribution of AMOLED is discussed, and the finite element analysis of the touch layer in the folded state is performed. e bending state display module of the monitor device of the flexible panel has a plurality of neutral planes.
is is because the OCA layer affects protecting each functional layer and reduces stress and strain transmission. e insignificant interaction between adjacent films can help the AMOLED device maintain relatively low pressure. e maximum longitudinal stress of the AMOLED module is at the folding symmetry, and the thickness of the OCA and the position in the module have been improved to reduce the stress and strain of the functional layer. e maximum IS in the improved module is on the protective cover, reaching 600 MPa. After exploring several dangerous locations after bending, the strain of the OCA layer is improved by 5%. e stress concentration of the module with seven neutral layers has been well improved, removing the risk of delamination or fracture.
Data Availability e data collected and analyzed during this study are included in the paper and can also be accessed from the authors through a rational request.

Conflicts of Interest
e authors declare that they have no conflicts of interest.