3D bending simulation and mechanical properties of the OLED bending area

Liang Ma; Jinan Gu

doi:10.1515/phys-2020-0165

Article Open Access

3D bending simulation and mechanical properties of the OLED bending area

Liang Ma and Jinan Gu

Published/Copyright: August 3, 2020

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From the journal Open Physics Volume 18 Issue 1

Abstract

Due to the poor mechanical properties of traditional simulation models of the organic light-emitting device (OLED) bending area, this article puts forward a finite element model of 3D bending simulation of the OLED bending area. During the model construction, it is necessary to determine the viscoelastic and hyperelastic mechanical properties, respectively. In order to accurately obtain the stress changes of material deformation during the hyperelasticity determination, a uniaxial tensile test and a shear test were used to obtain data and thus to characterize the hyperelastic properties. In order to measure the viscoelasticity, a stress relaxation test was used to draw the stress relaxation curve, so as to characterize the viscoelastic properties. Then, the plane or axisymmetric stress–strain analysis was achieved, and the material parameters of the 3D model of the OLED bending area were obtained. Finally, the 3D model was applied to the 3D bending of the OLED bending area. Combined with the axisymmetric finite element analysis method, the 3D bending simulation finite element model of the OLED bending area was constructed by dividing the finite element mesh. Experimental results show that the mechanical properties of the proposed model are better than those of traditional OLED bending simulation models. Meanwhile, the proposed model has stronger application advantages.

Keywords: OLED; bending area; 3D bending simulation; mechanical property

1 Introduction

With the rapid development of information age, the information display technology has become an important branch of the information industry. As information carriers, display devices are attracting more and more attention [1]. People have higher requirements with respect to power consumption, volume, softness, and other aspects of display devices. Display devices originated from cathode ray tubes (CRTs). In a CRT, electron flow bombards the screen, so that R, G, and B phosphors give out light in proportion, thus producing different colors. Since the birth of the CRT technology in 1897, CRTs were applied in radar display and electronic oscilloscopes at first, and then they were popularized in TVs and computers, becoming the most mainstream display terminals in the twentieth century [2]. Although CRTs have strong advantages in terms of cost and image quality, their weight, volume, radiation, and energy consumption limit their development. The dominant position of CRTs is gradually replaced by flat panel displays (FPDs). Compared with the traditional CRTs, FPDs have many advantages, such as small size, light weight, and low energy consumption. In recent years, FPDs have developed rapidly. Liquid crystal displays (LCDs) and plasma display panels (PDPs) are the most representative display devices. A pixel in an LCD panel is composed of three LCD units. Each LCD unit contains a red filter, green filter, or blue filter. Different colors can be generated by controlling the light in different units [3]. An LCD is thinner than a CRT, which greatly saves space and avoids the radiation problem. In the aspect of screen refresh rate, a CRT kinescope adopts light-emitting materials. No matter how high the refresh frequency is, it will lead to the flicker problem. Direct imaging technology for LCDs does not cause flicker, so it is more suitable for human eyes. In addition, an LCD is a form of flat screen, and the display effect is much better than that of a CRT. However, LCDs also have some disadvantages in terms of resolution, viewing angle, color saturation, brightness, and reaction speed [4]. A pixel in a PDP is a plasma tube. The plasma gas discharges in the plasma tube, producing ultraviolet light and exciting the phosphor on the fluorescent screen. A PDP is a kind of self-luminous display technology without backlight, which overcomes the problems of visual angle and brightness of LCDs. It is easy to manufacture large-scale screens with excellent performance. However, PDPs have some problems in terms of service life, power consumption, and cost.

Although LCDs, PDPs, and other displays solve the problems of CRTs in terms of volume, weight, radiation, and screen refresh rate, they still need to be improved in the aspects of energy consumption, viewing angle, and brightness. In recent years, LCDs and PDPs have been unable to meet the growing demand for display functionality, especially flexible displays [5].

The display of an organic light-emitting device (OLED) is thinner (its thickness is less than 500 nm), and it has the advantages of self-illumination, short response time, large viewing angle, lifelike picture, high definition, and low energy consumption. It is a planar device and is highly compatible with plastic substrates. During its preparation, low-temperature technology is adopted to achieve a flexible display. Compared with other flexible displays, it has prominent advantages, as a result of which it gradually became the first choice of flexible displays. In addition, it is rated as the most potential FPD lighting technology. However, an OLED display is a composite structure composed of thin-film optical devices, and an optical clear adhesive (OCA) is used to make the bonding of all film layers more firm [6,7]. An OCA is a special adhesive used for cementing transparent optical elements. It is required to have colorless transparency, light transmittance above 90%, good cementing strength, curing at room temperature or medium temperature, and curing shrinkage. In the process of bending deformation, the bending radius of flexible OLED modules is small. Meanwhile, various thin-film devices cannot coordinate the deformation. The OCA adhesive material has viscous flow, leading to device stripping and permanent damage to the screen [8]. Therefore, a 3D bending simulation model of the OLED bending area was built to research the mechanical properties.

2 Construction of a finite element model of 3D bending simulation of the OLED bending area

2.1 Parameter measurement and fitting of the OCA material

An OCA is a kind of viscoelastic material. It is necessary to measure its viscoelastic and hyperelastic mechanical properties separately. In the determination of hyperelasticity, the elastic modulus of the OCA material is too small, and the stress changes little with deformation. The measurement scheme is suitable for traditional hyperelastic materials, such as rubber, but it cannot be completely suitable for the OCA material due to the measurement accuracy. In order to accurately find the stress changes during the material deformation, it is necessary to adopt appropriate instruments and measurement schemes. For example, a uniaxial tensile test and a simple shear test are used to obtain data and thus to characterize the hyperelastic properties. When determining the viscoelasticity, we can use the stress relaxation test to get the stress relaxation curve, so as to characterize the viscoelastic properties. Thus, the plane or axisymmetric stress–strain analysis is carried out [9].

2.1.1 Determination and fitting of hyperelastic material parameters

The uniaxial tensile test and simple shear test were used to determine the hyperelasticity of materials. Dynamic mechanical analysis (DMA) was applied to the uniaxial tensile test. A rotational rheometer was applied in the simple shear test.

The thickness h of the specimens prepared by two tests is 1 mm. The measurement method is the same as the viscoelastic measurement. The OCA samples are stacked and pasted, and then the specimens are cut as per the requirements of the chucking appliance [10]. Table 1 shows the size and instrument models of uniaxial tensile specimens. Table 2 shows the specifications and instrument models of simple shear specimens. When DMA is adopted for the tensile test, the tensile rate refers to ASTM D412. When the rotary rheometer is adopted for the simple shear test, the shear strain rate is 0.01 s⁻¹.

Table 1

Specimen size and instrument model of the uniaxial tension test

Serial number	Instrument type	DMA TA RSA-G2
1	Sample shape and size	Long strip sample, l = 60 mm, B = 6 mm
2	Testing accuracy	0.02 mN

Table 2

Specimen size and instrument model of the simple shearing test

Serial number	Instrument type	Rotational rheometer TA DHR-2
1	Sample shape and size	Disc specimen, radius r = 40 mm
2	Testing accuracy	0.01 mN

The original data obtained from the experiment are shown in Tables 1 and 2. After processing the data, we can get the stress data and strain data. The specific calculation is shown below.

In the uniaxial tensile test, the formula for processing stress σ _T and strain ε _T is as follows:

(1) ε T = l − l 0 l 0 σ T = f b h ,

where l ₀ is the original length of the specimen, l is the length of the specimen after stretching, f is the tensile load, h is the thickness of the specimen, and b is the tensile rate.

In the simple shearing test, the formula for processing stress σ _S and strain γ _S is as follows:

(2) γ S = r ϕ h σ S = 2 τ π r 3 ,

where r is the torque of the parallel plate, φ is the rotational displacement of the parallel plate, r is the radius, and τ is the shear strain rate.

The stress and strain formulas of different strain energy density function models under uniaxial tension mode and simple shearing mode are obtained by derivation. The derivation formulas are comparable with experimental data, and the hyperelastic parameter fitting can be achieved [1].

Through the mathematical software 1Stopt, the formula of stress–strain constitutive relation can be derived. Combined with the experimental data, the fitting results under different strain energy density functions are obtained [11]. After the comparison of the fitting quality and the judgment of simulation convergence, the reduced polynomial model with N = 3 order is adopted. The fitting results are shown in Figure 1.

Figure 1

Fitting results.

We can see that the simple shear test data are basically consistent with the simple shear fitting result. There is a slight difference between the data of the uniaxial tensile test and the uniaxial tensile fitting results, but they are consistent in the overall trend. On the whole, the fitting effect is very good. After the fitting, relevant parameters of the strain energy density function are obtained. The fitting parameters are shown in Table 3 [12].

Table 3

Fitting parameters of the hyperelastic Yeoh model

Name	Fitting parameters
Name	C ₁₀	C ₂₀	C ₃₀	D ₁	D ₂	D ₃
Numerical value	0.01061	−0.00012	1.7318 × 10⁻⁶	4.79455	0	0

To be clear, the OCA material is an incompressible material. Poisson’s ratio v is 0.5. At this time, parameter D ₁ should be zero. In Abaqus, for materials whose Poisson’s ratio v is greater than 0.475, Poisson’s ratio v is considered to be 0.475. That is to say, the material is approximated as an incompressible material, rather than a completely incompressible material in theoretical sense [13].

2.1.2 Determination and fitting of viscoelastic material parameters

DMA is applied to the viscoelastic stress relaxation test. During the test, the specimens are prepared first. The thickness of specimens in the DMA test should not be less than 1 mm, while the thickness of the OCA specimen should be less than 0.05 mm. Therefore, it is necessary that the OCA sample should be cemented, so that the thickness can reach 1 mm. Then, we cut the shape of specimens according to the requirements of fixtures and then we can obtain the specimens for the experiments. The specification and instrument model are shown in Table 4.

Table 4

Specimen size and instrument model

Serial number	Instrument type	DMA TA RSA-G2
1	Sample shape and size	Long strip sample, l = 50 mm, B = 5 mm
2	Testing accuracy	0.01 mN

Then, the simple shearing experiment is carried out. A 5% instantaneous shear deformation is given to the specimen. It is unchanged, and the change of stress is recorded. The data are normalized using equation (3), and then the data are input into Abaqus for fitting. The result is shown in Figure 2 [14].

(3) g ( t ) = 1 − ∑ i = 1 N g i ( 1 − e − t / τ i ) ,

where g(t) is the relaxed modulus of elasticity after normalization, t is the relaxation time, N is the number of terms of the Prony series, g _i and τ _i are the parameters in the model, e is the shear threshold, and i is a constant.

Figure 2

Fitting results.

For the viscoelastic fitting process of the material, it is only necessary to nondimensionalize the experimental data of stress relaxation in Abaqus, and thus to achieve the plane or axisymmetric stress–strain analysis. After input, Prony parameters g _i and τ _i can be obtained by fitting. Finally, the viscoelastic properties are given to the materials.

It can be seen that the fitting curve basically coincides with the experimental data curve after the normalization. The fitting quality is very good. After fitting, Prony parameters g _i and τ _i are obtained (Table 5).

Table 5

Prony parameters based on viscoelastic fitting

_i	1	2	3	4	5
g _i	0.5902	0.1461	0.1115	0.0643	0.0352
τ _i	0.0188	0.2084	1.8675	19.167	233.07

2.2 Construction of the 3D model of the OLED bending area

2.2.1 Material parameters

The structure of the OLED bending area is mainly composed of an organic photoresist, metal wiring, and a polyimide (PI) substrate. The metal wiring at the end of the structure is deposited in the organic photoresist. The metal wiring at the end of the bending area is used to transmit and control the electric signal of the light-emitting diodes in the OLED display area. There are huge amounts of metal wires deposited in the organic photoresist [15]. The structure of the bending area is shown in Figure 3.

Figure 3

Structure of the OLED bending area.

According to the structural characteristics of the OLED bending area, OCA material parameters and membrane material parameters are obtained. The OCA material parameters are shown in Figure 4.

Figure 4

OCA rubber parameters.

The parameters of membrane materials are shown in Table 6.

Table 6

Parameters of membrane materials

Back panel material	Modulus of elasticity (GPa)	Poisson’s ratio
Protective cover plate	5.6	0.29
Touch layer	4.076	0.31
Polarizer	3.769	0.33
Display layer	49	0.30
Substrate	9.1	0.33
Backplane	4.2	0.32

2.2.2 Construction of the 3D model

In order to simplify the OLED bending area, meso-structure information is introduced to characterize the properties of the bending area. The micromechanics of materials are based on the relationship between the macromechanical properties of materials and the microstructure. Therefore, the macroproperties can be achieved by optimizing the design of the microstructure. The structure region at the end of the OLED has obvious periodic characteristics [16]. According to the characterization of the microstructure, the microstructure of the end structure of the OLED can be composed of an organic photoresist, single metal wire, substrate material, and PI substrate. Thus, the 3D model of the bending area is built as shown in Figure 5.

Figure 5

3D model of the bending area.

For the 3D model of the bending area, the geometric parameters of relevant metal lines and material layers are shown in Table 7.

Table 7

Geometric parameters

Serial number	Material layer	Thickness (µm)
1	Organic photoresist	4.5
2	Metal alignment	0.73
3	Substrate material	1.5
4	PI substrate	15

2.3 Construction of the finite element model of 3D bending simulation of the OLED bending area

2.3.1 3D bending for the OLED bending area

The 3D model of the OLED bending area is combined with the axisymmetric principle, and the OLED bending area is bent in the 3D mode, so that the lower part of the screen is able to fit with the middle frame. Thus, the screen rotation is achieved. The middle frame can be regarded as a rigid body. In order to form a circular arc at the bending part and reduce the structure stress, the distance between the reference point and the symmetry axis is set as π 4 R mm . When R is 5 mm, the distance is 7.85 mm. The structure and size are shown in Figure 6 [17].

Figure 6

Bending structure and size.

In the first second, the rigid body rotates anticlockwise around the reference point, at a speed of 1.57 rad/s. At the same time, the rigid body moves to the left at a speed of ( π 4 − 1 ) R mm . The shape after bending is shown in Figure 7. After that, it is placed for 300 s to simulate the actual use.

Figure 7

Shape after bending.

When the bending radius R = 5 mm, the boundary condition is that in the first second, the rigid body rotates anticlockwise around the reference point at a speed of 1.57 rad/s, and then it moves to the left at a speed of 2.85 mm/s. Finally, it is placed for 300 s.

After bending, the 3D bending simulation model of the OLED bending area is built as shown in Figure 8.

Figure 8

3D bending simulation model of the OLED bending area.

2.3.2 Grid partition based on axisymmetric finite element analysis

According to the 3D bending simulation model of the OLED bending area, the finite element model of the three-dimensional bending process is built. First, the axisymmetric finite element analysis method is used to generate the finite element meshes. After bending, the difference between the internal metal wiring width in the OLED bending area and the overall size is large. It is more difficult to generate finite element meshes [18]. It is easy to ignore some characteristics of the metal wiring structure by using the whole grid division method, influencing the analysis of different metal wiring structures negatively. It is not able to reflect the structural differences of different metal wires. Combined with the principle of axisymmetric finite element analysis, the implicit dynamic viscoelastic analysis method was adopted for the grid division. In order to be consistent with the actual stress situation, the plane strain grids are adopted. During the mesh generation, the network is quadrilateral, which is convenient for convergence and calculation. The grid size is 0.025 mm. All the membrane materials and OCA materials are divided into three layers. The grid type includes the plane strain unit, hybrid unit, and CPE8RH reduced integration unit.

A HyperMesh platform with powerful finite element preprocessing ability is used for the OLED bending area. A hexahedron mesh method is used to divide the metal wires and other areas. This can effectively reduce the number of meshes. On this basis, progressive grid division is adopted to ensure the accuracy of the calculated structure and thus to reduce the calculation time. All units in the model are linear hexahedron elements with complete integration [19].

Generally, the accuracy of grid division directly influences the accuracy of the result. The finer the mesh division is, the more accurate the result is. When the grid is too dense, the computer overhead will increase and the computing time will also increase. For the explicit dynamics, the consumption of computer memory and computing time are directly proportional to the number of grid units. The computing cost increases with the improvement of grid subdivision, so that we can directly predict the cost change caused by grid subdivision. For the implicit dynamics, the computing cost is roughly proportional to the square of the number of freedom degrees. The consumption of memory and computing time will have an exponential relationship with the number of grid units. It is difficult to predict the cost. The change is obvious. On the basis of accuracy, a reasonable grid density can greatly optimize the computing cost. For the structure of the OLED bending area, on the premise of reflecting the structural features of the metal wire, we must refine the grid as much as possible, so that the grid size can ensure the computing accuracy without consuming too much computing resource [20]. Due to the ratio of the length and thickness of the OLED bending area after bending, the number of metal wiring meshes is still huge on the basis of accuracy, consuming too much computer resource. In order to improve the accuracy of calculation and analysis, a sub-model is used to divide the structure of the OLED bending area after bending. There are 26 × 30 divided finite element grids, as shown in Figure 9.

Figure 9

Finite element mesh.

On this basis, the finite element meshes are divided in detail. The specific results are shown in Figure 10.

Figure 10

Finite element meshes after the detailed division.

The details of the division of finite element meshes after the OLED bending are shown in Figure 11.

Figure 11

Details of the finite element mesh after the detailed division: (a) details of finite element mesh and (b) enlarged details.

2.3.3 Finite element modeling

Refined finite element meshes are used to build the three-dimensional bending simulation finite element model of the OLED bending area. During the finite element simulation, the setting of boundary condition directly influences the success of simulation. This is also an extremely important part of finite element simulation. In the finite element simulation, there are two ways to realize the periodic boundary: (1) coupling corresponding surface nodes. This method has higher requirements for serial number of nodes, but it can reduce constraints and improve calculation accuracy. (2) A penalty function is introduced. The implementation of this method is simple, but it is easy to cause a numerical difference. Therefore, the periodic boundary constraints can be achieved by combining these two methods. The special boundary constraint needs to divide the whole model into two independent models: a global model and a sub-model. The global model includes a geometric constraint, displacement constraint, and boundary constraint. The sub-model is a part of the whole model, so we cannot analyze the global features of the model, such as cracks. In the global model, the displacement corresponding to the sub-model is the boundary condition of the sub-model. Therefore, the grid of the global model is relatively coarse. If the global model corresponds to the sub-model, the calculation results will be more accurate [21].

The basic implementation steps of special boundary constraints in the finite element analysis include the following:

global model analysis: the global model is divided with coarse meshes without considering the local structure details, and then the global structure is analyzed to calculate the displacement at a specific location (near the boundary of the sub-model).
establishment of the sub-model: according to the analysis target and the actual structure, the sub-model of a local fine mesh is built.
boundary condition interpolation value: the displacement boundary of the global model obtained in the first step is taken as the boundary condition. Then, it is automatically loaded to the corresponding position in the sub-model by the linear interpolation method (the displacement interpolation result determines the computing accuracy of the sub-model).
result analysis of the sub-model: the original boundary and load in the region of sub-models are unchanged, and then the finite element analysis is performed on sub-models. The global model is shown in Figure 12, and the sub-model is shown in Figure 13.

In the setting of boundary conditions, the efficiency of calculation can be improved by increasing the bending speed under the condition of a constant time step. If the bending speed is expanded n times, the calculation time will be shortened to 1 n of the original time. In order to ensure that the energy distribution in the simulation process is consistent with the actual situation, the simulation speed should be stable. Therefore, the bending speed is set as 3,000 mm/s, the optimal bending radius is 2 mm, and the time to complete the simulation is 2.444 s. Then, the amplitude curve of finite element analysis is obtained. The specific process is shown in Figure 14.

Figure 12

Global model.

Figure 13

Sub-model.

Figure 14

Specific process of obtaining the amplitude curve of finite element analysis.

According to the amplitude curve of finite element analysis, HyperMesh software is used to build the finite element model of three-dimensional bending simulation of the OLED bending area. The specific model is shown in Figure 15.

Figure 15

Finite element model of 3D bending simulation of the OLED bending area.

3 Research on mechanical properties

3.1 Experimental process

The mechanical properties in the bending process of the OLED bending area were researched using the 3D bending simulation finite element model of the OLED bending area [22–25]. First, the material parameters of each layer in the finite element model were calculated. The specific results are shown in Table 8.

Table 8

Parameters of each material layer in the finite element model

Material layer	Young’s modulus (Mpa)	Poisson’s ratio
PI substrate	9,200	0.35
Organic photoresist	3,400	0.35
Metal alignment	80,000	0.35
Inorganic substrate	1,10,000	0.17

In order to ensure the fairness and effectiveness of the experimental results, three traditional bending simulation models such as the model based on a periodic boundary condition algorithm, the model based on special boundary constraints, and the model based on bending mechanical response were used to compare the finite element model designed in this article. The mechanical properties of the proposed model were judged using the strain distribution [26,27]. The more tortuous the strain distribution curve is, the stronger the strain distribution performance is.

3.2 Research results

In this study, the mechanical properties of the bending region were analyzed by observing the motion states at different positions. The experimental results of the mechanical properties of three traditional OLED bending simulation models are shown in Figure 16.

Figure 16

Experimental results of mechanical properties of traditional models.

The experimental results of the mechanical properties of the finite element model of three-dimensional bending simulation of the OLED bending area are shown in Figure 17.

Figure 17

Experimental results of mechanical properties of the proposed model.

According to the verification results of mechanical properties, the performance of strain distribution of the finite element model of three-dimensional bending simulation of the OLED bending area is better than that of the traditional model, so that the effectiveness of the proposed model can be proved.

4 Conclusions

Due to the poor mechanical properties obtained in the traditional simulation models of the OLED bending area, a finite element model for three-dimensional bending simulation of the OLED bending area is proposed. This model effectively improves the mechanical properties, so it has great significance for the research on the bending properties of OLED screens.

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Received: 2019-11-27

Revised: 2020-05-27

Accepted: 2020-05-30

Published Online: 2020-08-03

This work is licensed under the Creative Commons Attribution 4.0 International License.

Articles in the same Issue

https://doi.org/10.1515/phys-2020-0165

Keywords for this article

OLED; bending area; 3D bending simulation; mechanical property

Creative Commons

BY 4.0