Method and device for predicting deformation and stress state curvature of a rectangular thin substrate after deformation

Abstract

The present application relates to the field of precision measurement and analysis technology, and relates to a rectangular thin substrate deformation and stress state variable curvature prediction method and device. The prediction method comprises: establishing a three-dimensional coordinate system XYZ; establishing a deflection model of the variable curvature of the thin substrate with the change of the position coordinates, abandoning the original deflection model with the same curvature everywhere, and obtaining the strain model of the rectangular thin substrate at the coordinates (x, y, z) by establishing the variable curvature deflection model: X-axis direction strain ε x , Y-axis direction strain ε y , and shear strain γ xy . The strain model of the present application ε x , ε y , and γ xy adopts the method of designing a new ω, especially ω, and the calculation model of the deflection ω is designed as ω=ax 4 +by 4 +cx 2 y 2 +dx 2 +ey 2 . At this time, the curvature of the thin substrate changes with the change of the position coordinates, and the traditional model of the rectangular thin substrate deflection calculation model with the same curvature everywhere is completely abandoned. The present application solves the technical problem of inaccurate prediction of the stress state of the rectangular thin substrate in the prior art.

Description

TECHNICAL FIELD

[0001] The present application relates to a deformation and stress state prediction method in the field of precision measurement and analysis technology, a deformation and stress state prediction device corresponding to the prediction method, a deformation and stress state prediction instrument using the prediction method, a computer terminal realizing the function of the prediction method, and a computer readable storage medium storing the program realizing the function of the prediction method, in particular to a rectangular thin substrate deformation and stress state variable curvature prediction method after deformation, a rectangular thin substrate deformation and stress state variable curvature prediction device corresponding to the prediction method, a rectangular thin substrate deformation and stress state variable curvature prediction instrument using the prediction method, a computer terminal realizing the function of the prediction method, and a computer readable storage medium storing the program realizing the function of the prediction method. BACKGROUND

[0002] Thin plates are one of the common structural forms in industrial production, and are widely used in many fields such as civil engineering, transportation, aerospace and electronic equipment, such as railways, circuit boards, automobile manufacturing and aircraft skin. Among the thin plates, the rectangular thin plate is one of the most widely used types. In the processing of thin plates, sub-surface damage may occur in the thin plates, and the thickness of the damage layer is usually small, much lower than the thickness of the undamaged layer. Therefore, the sub-surface damage layer can be regarded as a thin film layer, which forms a thin film substrate system together with the undamaged layer. In addition, coated thin plates are coated with a thin film on the rectangular thin plate, so that the rectangular thin plate is used as a substrate structure, and a composite thin film substrate system can also be formed. Due to its excellent performance, the thin film substrate system formed by the rectangular thin plate after flattening or coating treatment is widely used in many fields.

[0003] For example, in solar photovoltaic panels, the core component is the solar panel, which is usually made of single-crystal or multi-crystal silicon material in the form of a rectangular thin sheet. During the production process, the thin film substrate system plays an important role in the solar cell. Due to the flattening process of the panel, a damage layer may appear on the surface, causing the panel to deform, which in turn affects the collection efficiency of sunlight. Therefore, it is necessary to reduce the deformation caused by residual stress during the processing. The damage layer mainly corresponds to the thin film layer part of the thin film substrate system, and the rest belongs to the substrate layer. In order to effectively improve the performance of the photovoltaic panel, it is crucial to predict the stress state and deformation of the thin film substrate system to guide the flattening process of the panel. Similarly, when producing optical elements such as lenses, filters, and mirrors, a thin film layer is usually deposited on the substrate material to precisely control the reflection, transmission, and absorption of light, thereby achieving the desired optical effect. These optical elements also form a thin film substrate system. If the stress in the thin film layer is too high, it may cause the optical element to deform, which in turn affects the final optical performance. Therefore, predicting and analyzing the stress state and deformation of the thin film substrate system can help designers optimize the deposition process of the thin film material and the selection of the substrate material, thereby avoiding excessive stress, reducing the risk of failure of the optical element, and ensuring its quality and stability. In the study of thin film substrate systems, the deformation of the system is usually considered as spherical deformation, and a single fixed curvature is used to represent its deformation. However, this assumption only applies to small deformations of the system in the linear domain. When the system undergoes large deformation, the assumption of single curvature to represent the deformation of the system deviates from the actual situation, and the deformation of the system is no longer a spherical deformation with a fixed curvature, but its curvature changes with the change of its coordinate position. SUMMARY

[0004] In order to solve the technical problem of inaccurate prediction of the stress state of a rectangular thin substrate in the prior art, the present application provides a method for predicting the deformation and stress state variable curvature of a rectangular thin substrate after deformation, a device for predicting the deformation and stress state variable curvature of a rectangular thin substrate after deformation corresponding to the prediction method, an instrument for predicting the deformation and stress state variable curvature of a rectangular thin substrate after deformation using the prediction method, a computer terminal implementing the function of the prediction method, and a computer readable storage medium storing the program implementing the function of the prediction method.

[0005] The present application realizes the following technical scheme: a method for predicting the deformation and stress state variable curvature of a rectangular thin substrate after deformation, which comprises the following steps:

[0006] A three-dimensional coordinate system is established, with the origin of the coordinate system being the center of the middle surface of the rectangular thin substrate, the X-axis and Y-axis being parallel to the length and width directions of the rectangular thin substrate, and the Z-axis being perpendicular to the plane of the X-axis and Y-axis.

[0007] The X-axis direction strain ε of the rectangular thin substrate at coordinates (x, y, z) is obtained by the following strain model x , Y-axis direction strain ε y , and shear strain γ xy :

[0008]

[0009] In the formula, and are the X-axis direction strain, Y-axis direction strain and shear strain ω of the middle surface respectively, and ω is the deflection of the rectangular thin substrate;

[0010] wherein, ε x , ε y , and γ xy are optimized, and the strain model of the optimized ε x , ε y , and γ xy of the deflection model of the thin substrate whose curvature changes with the position coordinates is respectively:

[0011] ε x = a1 + a2x 2 + a3y 2 - z (12ax 2 + 2cy 2 + 2d)

[0012] ε y = b1 + b2y 2 + b3x 2 - z (12by 2 + 2cx 2 + 2e)

[0013]

[0014] In the formula, a, b, c, d, and e are curvature coefficients of the rectangular thin substrate, and a1, a2, a3, b1, b2, and b3 are deformation coefficients of the middle surface.

[0015] As a further improvement of the above scheme, the strain model optimization method comprises the following steps:

[0016] First, ω is designed as:

[0017]

[0018] ω = ax 4 + by 4 + cx 2 y 2 + dx 2 + ey​2

[0019] At this time, a, b, c, d, e, a1, a2, a3, b1, b2, b3 are unknown numbers;

[0020] Secondly, the minimum energy method is used to predict a, b, c, d, e, a1, a2, a3, b1, b2, b3.

[0021] Further, the prediction method for predicting a, b, c, d, e, a1, a2, a3, b1, b2, b3 by using the minimum energy method comprises the following steps:

[0022] Firstly, the strain energy density V d1 :

[0023]

[0024] In the formula, Q 11 , Q 12 , Q 13 , Q 66 are elements in the elastic stiffness matrix;

[0025] Secondly, the strain energy density V d2 :

[0026] V d2 = σ0ε x + σ0ε y

[0027] In the formula, σ0 is the residual stress in the damage layer;

[0028] Then, the integral in the Z-axis direction is carried out to obtain the strain energy density V dz :

[0029]

[0030] In the formula, h is the thickness of the thin plate, and t is the thickness of the damage layer;

[0031] Then, the integral in the X-axis and Y-axis directions is carried out to obtain the total strain energy density V total :

[0032]

[0033] In the formula, l1 is the length of the rectangular thin substrate, and l2 is the width of the rectangular thin substrate;

[0034] Finally, the partial derivatives of a, b, c, d, e, a1, a2, a3, b1, b2, b3 are made to be zero, that is, the solution of the minimum energy state of the rectangular thin substrate is obtained:

[0035]

[0036] Further, Q 11 , Q 12 , Q 13 , Q 66 The expressions of a1, a2, a3, b1, b2, b3 are obtained by the following formula:

[0037] The expressions of a1, a2, a3, b1, b2, b3 are obtained by the above steps:

[0038]

[0039]

[0040] The expressions of a, b, c, d, e are obtained by substituting the expressions of a1, a2, a3, b1, b2, b3, respectively, and the expressions of the coefficients are too long to be displayed. The expressions of the coefficients are too complex, so the iterative method is used for prediction. Compared with directly predicting the nonlinear equation set, it is more intuitive and simple, and does not need complex derivation and calculation.

[0041] As a further improvement of the above scheme, the deformation and stress state variable curvature prediction method further comprises:

[0042] The X-axis direction stress state σx, the Y-axis direction stress state σy and the shear stress state τxy of the rectangular thin substrate at coordinates (x, y, z) are calculated by the following stress state model: x , Y-axis direction stress state σ y , shear stress state τ xy :

[0043]

[0044] In the formula, E is the elastic modulus of the rectangular thin substrate, and μ is the Poisson's ratio of the rectangular thin substrate.

[0045] The application also provides a rectangular thin substrate deformation and stress state variable curvature prediction device, which adopts any rectangular thin substrate deformation and stress state variable curvature prediction method described above, and the deformation and stress state variable curvature prediction device comprises:

[0046] A three-dimensional coordinate system establishing module is configured to establish a three-dimensional coordinate system, wherein an origin of the coordinate system is a center of a middle surface of the rectangular thin substrate, an X-axis and a Y-axis are parallel to a length direction and a width direction of the rectangular thin substrate respectively, and a Z-axis is perpendicular to a plane in which the X-axis and the Y-axis are located; and the rectangular thin substrate comprises a substrate and a thin film laid on the substrate;

[0047] A strain stress calculating module is configured to obtain X-axis direction strain ε x , Y-axis direction strain ε y and shear strain γ xy of the rectangular thin substrate at a coordinate (x, y, z) by a strain model as follows:

[0048]

[0049] In the formula, ε , ε and γ are X-axis direction strain, Y-axis direction strain and shear strain of the middle surface respectively, and ω is deflection of the rectangular thin substrate;

[0050] Wherein, the strain stress calculating module further optimizes ε x , ε y and γ xy , establishes a deflection model in which curvature of the thin substrate changes with the coordinate, and the strain models of the optimized ε x , ε y and γ xy are as follows:

[0051] ε x = a1 + a2x 2 + a3y 2 - z(ax 2 + b)

[0052] ε y = b1 + b2y 2 + b3x 2 - z(cy 2 + d)

[0053]

[0054] And stress state calculating models are as follows:

[0055]

[0056] In the formula, σ x is X-axis direction stress state, σ y is Y-axis direction stress state, and τ xy is shear stress state.

[0057] Wherein, a, b, c, d, e are curvature coefficients of the rectangular thin substrate, a1, a2, a3, b1, b2, b3 are deformation coefficients of the intermediate surface.

[0058] The present application also provides a rectangular thin substrate deformation and stress state variable curvature prediction instrument, the deformation and stress state variable curvature prediction instrument comprises:

[0059] A processor is used for predicting ε x , ε y , γ xy according to any of the above rectangular thin substrate deformation and stress state variable curvature prediction methods.

[0060] A display is used for displaying the predicted ε x , ε y , γ xy , σ x , σ y , τ xy , or voice broadcast the predicted ε x , ε y , γ xy , σ x , σ y , τ xy .

[0061] The present application also provides a computer terminal, which comprises a memory, a processor and a computer program stored in the memory and executable on the processor, and the processor implements the steps of any of the above rectangular thin substrate deformation and stress state variable curvature prediction methods when executing the program.

[0062] The present application also provides a computer readable storage medium, which stores computer program instructions, and the computer program instructions are read and executed by a processor to perform the steps of any of the above rectangular thin substrate deformation and stress state variable curvature prediction methods.

[0063] Compared with the prior art, the present application has the following advantages:

[0064] (1) The present application establishes the strain model of ε x , ε y , γ xy by re-establishing the variable curvature deflection model, and solves the technical problem of inaccurate prediction of the stress state of the rectangular thin substrate in the prior art.

[0065] (2) The strain model of ε x , ε y , γ xy of the present application adopts the method of designing a new ω, especially ω, the calculation model of deflection ω is designed as ω=ax 4 +by 4 +cx 2 y 2 +dx 2 +ey 2 At this time, the curvature of the thin substrate changes with the change of the position coordinates, and the traditional thin substrate curvature equal model is completely abandoned

[0066] (3) In the field of rectangular thin substrates, not only the technical problems of large calculation amount and difficult prediction caused by high order of ω calculation model exist, but also the technical problems of inaccurate prediction caused by the rectangular thin substrate exist, and the present application establishes a model in which the curvature of the thin substrate changes with the change of the position coordinates, abandons the original assumption that the curvature of the thin substrate is equal everywhere, establishes a new deflection mathematical model, and solves these problems by predicting the curvature coefficients a, b, c, d, e of the rectangular thin substrate, the deformation coefficients a1, a2, a3, b1, b2, b3 of the middle surface, and the strain model of ε x , ε y , γ xy is clear and can make the strain model of ε BRIEF DESCRIPTION OF DRAWINGS

[0067] Figure 1 is the flow chart of the variable curvature prediction method for predicting the strain and stress state of the rectangular thin substrate provided by the embodiment 1 of the present application.

[0068] Figure 2 is the change comparison chart of the displacement of the deformed rectangular thin substrate along the Y axis.

[0069] Figure 3 is the stress state chart of the Y direction stress component of the thin substrate along the Y axis of the rectangular thin substrate obtained by ANSYS simulation in the embodiment 2.

[0070] Figure 4 is the stress state chart of the Y direction stress component of the thin substrate along the Y axis of the rectangular thin substrate obtained according to the calculation method in the embodiment 2.

[0071] Figure 5 is the stress state chart of the Y direction stress component of the thin substrate along the Y axis of the rectangular thin substrate obtained by the constant curvature assumption method in the embodiment 2.

[0072] Figure 6 is the Y direction strain distribution chart of the thin substrate along the Y axis of the rectangular thin substrate obtained by ANSYS simulation in the embodiment 2.

[0073] Figure 7is a Y-direction strain distribution diagram of the thin substrate according to the calculation method in the present disclosure along the Y-axis variation of the rectangular thin substrate in Example 2.

[0074] Figure 8 is a Y-direction strain distribution diagram of the thin substrate obtained by the constant curvature assumption method along the Y-axis variation of the rectangular thin substrate in Example 2.

[0075] Figure 9 is an X-direction stress component stress state diagram of the thin substrate obtained by the ANSYS simulation along the X-axis variation of the rectangular thin substrate in Example 2.

[0076] Figure 10 is an X-direction stress component state diagram of the thin substrate according to the calculation method in the present disclosure along the X-axis variation of the rectangular thin substrate in Example 2.

[0077] Figure 11 is an X-direction stress component state diagram of the thin substrate obtained by the constant curvature assumption method along the X-axis variation of the rectangular thin substrate in Example 2.

[0078] Figure 12 is an X-direction strain distribution diagram of the thin substrate obtained by the ANSYS simulation along the X-axis variation of the rectangular thin substrate in Example 2.

[0079] Figure 13 is an X-direction strain distribution diagram of the thin substrate according to the calculation method in the present disclosure along the X-axis variation of the rectangular thin substrate in Example 2.

[0080] Figure 14 is an X-direction strain distribution diagram of the thin substrate obtained by the constant curvature assumption method along the X-axis variation of the rectangular thin substrate in Example 2. DETAILED DESCRIPTION

[0081] The technical solutions in the embodiments of the present application will be clearly and completely described below with reference to the drawings in the embodiments of the present application. Obviously, the described embodiments are only a part of the embodiments of the present application, rather than all the embodiments. Based on the embodiments in the present application, all other embodiments obtained by those skilled in the art without creative labor fall within the protection scope of the present application.

[0082] The curvature prediction method for deformation and stress state of the rectangular thin substrate after deformation of the present application mainly includes the following prediction steps: establishing a three-dimensional coordinate system XYZ; a deflection model of the curvature of the thin substrate changing with the position coordinates is established, and the original deflection model with the same curvature everywhere is abandoned; the strain model of the rectangular thin substrate at the coordinates (x, y, z) is obtained by establishing the variable curvature deflection model: X-axis direction strain ε x , Y-axis direction strain ε y , shear strain γ xyThe present application establishes the strain model of epsilon x , epsilon y , and gamma xy by re-establishing the variable curvature model, and solves the technical problem of inaccurate prediction of the stress state of the rectangular thin substrate in the prior art. The strain model of epsilon x , epsilon y , and gamma xy of the present application adopts the method of designing a new omega, especially omega, and the calculation model of the deflection omega is designed as omega=ax 4 +by 4 +cx 2 y 2 +dx 2 +ey 2 At this time, the curvature of the thin substrate changes with the position coordinates, and the deflection calculation model of the rectangular thin substrate in the traditional model in which the curvatures at all places of the thin substrate are equal The rectangular thin substrate can be applied to optical elements, such as a thin film substrate system of a solar photovoltaic panel, and the stress state and deformation in the thin film substrate system (mainly the surface film of the solar photovoltaic panel) can be predicted by using the present application, which can effectively improve the performance of the solar photovoltaic panel and is crucial for guiding the flattening process of the panel. The rectangular thin substrate can also be applied to the production of optical elements such as lenses, optical filters, and mirrors, such as a thin film substrate system of an optical element, and the stress state and deformation in the thin film substrate system can be predicted and analyzed by using the present application, which can help designers optimize the deposition process of the thin film material and the selection of the substrate material, thereby avoiding the generation of excessive stress, reducing the failure risk of the optical element, and ensuring its quality and stability.

[0083] Embodiment 1

[0084] The rectangular thin substrate deformation and stress state variable curvature prediction method provided in this embodiment mainly includes three steps.

[0085] I. Establish a three-dimensional coordinate system: the origin of the coordinate system is the center of the middle surface of the rectangular thin substrate, the X-axis and the Y-axis are parallel to the length and width directions of the rectangular thin substrate respectively, and the Z-axis is perpendicular to the plane in which the X-axis and the Y-axis lie.

[0086] The rectangular thin substrate includes a substrate and a thin film laid on the substrate. The middle surface refers to a surface parallel to the rectangular surface of the thin substrate and equidistant from the upper and lower rectangular surfaces.

[0087] II. Obtain the X-axis direction strain epsilon x , Y-axis direction strain epsilon y , and shear strain gamma xy of the rectangular thin substrate at the coordinates (x, y, z) by the following strain model:

[0088]

[0089] wherein, and are the X-axis direction strain, Y-axis direction strain and shear strain of the middle surface respectively, and ω is the deflection of the rectangular thin substrate.

[0090] III. The X-axis direction stress state σ x , Y-axis direction stress state σ y and shear stress state τ xy of the rectangular thin substrate at coordinates (x, y, z) are calculated by the following stress state model:

[0091]

[0092] wherein, E is the elastic modulus of the rectangular thin substrate, and μ is the Poisson's ratio of the rectangular thin substrate.

[0093] wherein, in the second step, ε x , ε y and γ xy are optimized to establish a deflection model of the curvature of the thin substrate changing with the position coordinates, and the strain models of the optimized ε x , ε y and γ xy are respectively:

[0094] ε x = a1 + a2x 2 + a3y 2 - z(ax 2 + b)

[0095] ε y = b1 + b2y 2 + b3x 2 - z(cy 2 + d)

[0096]

[0097] wherein, a, b, c, d, e are respectively the curvature coefficients of the rectangular thin substrate, and a1, a2, a3, b1, b2, b3 are the deformation coefficients of the middle surface.

[0098] The prediction process of a, b, c, d, e, a1, a2, a3, b1, b2, b3 is as follows:

[0099] The strain energy density of the rectangular thin substrate removing the damaged layer part:

[0100]

[0101] Strain energy density of rectangular thin substrate damage layer:

[0102] V d2 = σ0ε x + σ0ε y

[0103] Wherein, σ0 is residual stress in damage layer; Q 11 , Q 12 , Q 22 , Q 66 The element in elastic stiffness matrix, is the coefficient in the relationship between stress and strain, which is calculated by the following formula:

[0104]

[0105] Integrating in Z-axis direction obtains strain energy density of system in Z direction:

[0106]

[0107] Wherein, h is thin plate thickness, t is damage layer thickness.

[0108] Continuing to integrate in X-axis and Y-axis directions obtains total strain energy density of rectangular thin substrate:

[0109]

[0110] Wherein, l1 is length of rectangular thin substrate, l2 is width of rectangular thin substrate.

[0111] Respectively, partial derivative of curvature coefficients a, b, c, d, e of rectangular thin substrate and deformation coefficients a1, a2, a3, b1, b2, b3 of middle surface is zero, that is, the solution of minimum energy state of system:

[0112]

[0113] As described above, in the embodiment, referring to Figure 1 It is a flow chart of rectangular thin substrate deformation and stress state variable curvature prediction method provided by the embodiment, and the rectangular thin substrate deformation and stress state variable curvature prediction method can include the following steps: S11-S14.

[0114] S11, obtain Young's modulus E, Poisson's ratio μ, thickness h, length l1, width l2 of the rectangular thin substrate, and obtain thickness t and residual stress σ0 in the damage layer of the thin film;

[0115] S12, derive rectangular thin substrate strain and stress state prediction formula from strain formula and physical equation. Wherein, the strain formula is obtained from the following strain formula:

[0116]

[0117] wherein and are the X-axis direction strain, Y-axis direction strain and shear strain of the middle surface respectively.

[0118] wherein the strain model of the middle surface is:

[0119]

[0120] wherein a1, a2, a3, b1, b2, b3 are the assumed deformation coefficients of the middle surface.

[0121] The strain of the middle surface and the deflection model used are substituted into the strain formula to obtain the strain calculation formula. 4 +by 4 +cx 2 y 2 +dx 2 +ey 2 The stress state calculation formula is obtained by the following physical equation:

[0122] The stress state calculation formula is obtained by the following physical equation:

[0123]

[0124] The obtained strain calculation formula is substituted into the physical equation to obtain the stress calculation formula of the rectangular thin substrate, and the obtained formula is as follows:

[0125]

[0126] S13, the curvature coefficients a, b, c, d, e of the rectangular thin substrate and the deformation coefficients a1, a2, a3, b1, b2, b3 of the middle surface are obtained, and the minimum energy method is used to predict them, that is, the system will tend to the state of minimum energy.

[0127] S14, the obtained curvature coefficients and the middle surface deformation coefficients are substituted into the strain calculation formula and the stress state. The calculation formula obtains the strain and stress state of the thin substrate.

[0128] The rectangular thin substrate deformation stress state variable curvature prediction method in the application can be set in the form of software, such as a rectangular thin substrate deformation stress state variable curvature prediction device corresponding to the prediction method. Specifically, the method can be designed as independent non-embedded software or embedded software that can be called at any time (such as embedded in a stress state prediction instrument as application software of the stress state prediction instrument to control the stress state prediction instrument to realize the function of stress state prediction). Whether it is non-embedded or embedded software, it can be summarized as a corresponding rectangular thin substrate deformation stress state prediction device. The device includes a prediction formula module, a curvature coefficient calculation module, a strain calculation module, and a stress state calculation module.

[0129] The prediction formula module predicts the strain and stress state calculation formula through the deformation formula; the curvature coefficient calculation module predicts the curvature coefficients a, b, c, d, e of the rectangular thin substrate and the deformation coefficients a1, a2, a3, b1, b2, b3 of the intermediate surface through the minimum energy method; the strain calculation module substitutes the predicted curvature coefficients into the strain calculation formula to predict the strain of the rectangular thin substrate; and the stress state calculation module substitutes the predicted curvature coefficients into the stress state calculation formula to predict the stress state of the rectangular thin substrate.

[0130] The software can be applied in a computer terminal, which can include a memory, a processor, and a computer program stored in the memory and executable on the processor. The computer terminal can also be a smartphone, tablet computer, notebook computer, etc. that can execute programs. The processor can be a central processing unit (CPU), controller, microcontroller, microprocessor, or other data processing chip in some embodiments. The processor is generally used to control the overall operation of the computer device. In this embodiment, the processor is used to run the program code or process data stored in the memory. The processor executes the program to implement the steps of the rectangular thin substrate deformation strain and stress state variable curvature prediction method.

[0131] The software can be stored in a computer readable storage medium, which stores computer program instructions. When the computer program instructions are read and executed by a processor, the steps of the thin substrate deformation strain and stress state variable curvature prediction method are executed. The computer readable storage medium, such as a U disk, can be inserted into a traditional stress state prediction instrument (which can also be a computer, mobile phone, or other electronic device) in the form of a U disk. The strain and stress state prediction instrument reads the computer program instructions in the U disk and executes them to predict the strain and stress state solution of the rectangular thin substrate of the corresponding size and material. The predicted results are accurate and consistent with the actual situation, and the prediction process is simple and easy to understand.

[0132] Example 2

[0133] This example 2 is a specific example of example 1. This example will introduce in detail how to predict the strain and stress state of the rectangular thin substrate through the strain formula, physical equation and minimum energy method, etc. For this purpose, the specific steps of this example will be described from the following aspects.

[0134] Please refer to Figure 1 , this example selects a thin substrate with thickness h = 400 μm, length l1 = 200 mm, width l2 = 150 mm for demonstration, in which Young's modulus E = 150 GPa, Poisson's ratio μ = 0.25, film thickness t = 1 μm, stress σ0 in the film = 1000 MPa.

[0135] The implementation includes the following steps:

[0136] Step one, the material characteristic parameters, size and stress σ0 in the film of the rectangular thin substrate are known, the material characteristic parameters include elastic modulus E = 150 GPa and Poisson's ratio μ = 0.25, the size parameters include the overall thickness of the thin substrate h = 400 μm, length l1 = 200 mm, width l2 = 150 mm, film thickness t = 1 μm.

[0137] Step two, the strain and stress state calculation formula of the rectangular thin substrate is predicted by the deformation equation and physical equation, in which the strain formula is obtained from the following strain formula:

[0138]

[0139] In which And The X-axis direction strain, Y-axis direction strain and shear strain of the middle surface are respectively.

[0140] In which the strain model of the middle surface is:

[0141]

[0142] In which a1, a2, a3, b1, b2, b3 are the assumed deformation coefficients of the middle surface.

[0143] The strain of the middle surface and the deflection model used: ω = ax 4 +by 4 +cx 2 y 2 +dx 2 +ey 2 are substituted into the strain formula to obtain the strain formula.

[0144] The stress state formula is obtained from the following physical equation:

[0145]

[0146] Substituting the resulting strain equations into the physical equations gives the stress equations for the rectangular thin substrate, and given Young's modulus E = 150 GPa and Poisson's ratio μ = 0.25, the resulting equations are as follows:

[0147] σ x = -3.2 x 10 11 (μ(6by 2 + cx 2 + e) + 6ax 2 + cy 2 + d)z + 1.6 x 10 11 (μ(b2y 2 + b3x 2 + b1-8b 2 y 6 - 8(cx 2 + e)by 4 - 2(cx 2 + e)y 2 + 2(2by 3 + cx 2 y + ey) 2 ) + a2x 2 + a3y 2 + a1-8a 2 x 6 - 8(cy 2 + d)ax 4 - 2(cy 2 + d) 2 x 2 + 2(2ax 3 + cy 2 + dx) 2 )

[0148] σ y = -3.2 x 10 11 (μ(6ax 2 + cy 2 + d) + 6by 2 + cx 2 + e)z + 1.6 x 10 11 (μ(a2x 2 + a3y 2 + a1-8a 2 x 6 - 8(cy 2 + d)ax 4 - 2(cy 2 + d)x 2 + 2(2ax 3 + cy 2x + dx) 2 )+ b2y 2 +b3x 2 +b1-8b 2 y 6 -8(cx 2 +e)by 4 -2(cx 2 +e) 2 y 2 +2(2by 3 +cyx 2 +ey) 2 )

[0149]

[0150] Step three, using the minimum energy method to predict the curvature coefficient, get the rectangular thin substrate curvature coefficient a, b, c, d and the intermediate surface deformation coefficient a1, a2, a3, b1, b2, b3, using the minimum energy method to predict, the minimum energy method that the system tends to the state of minimum energy. The prediction process is as follows:

[0151] Strain energy density of rectangular thin substrate removing damage layer part:

[0152]

[0153] Strain energy density of rectangular thin substrate damage layer:

[0154] V d2 = σ0ε x + σ0ε y

[0155] Where σ0 is the residual stress in the damage layer; Q 11 , Q 12 , Q 22 , Q 66 The elements in the elastic stiffness matrix are calculated by the following formula:

[0156]

[0157] Integrating in the Z-axis direction to get the strain energy density in the Z direction of the system:

[0158]

[0159] Where h is the thickness of the thin plate, t is the thickness of the damage layer.

[0160] Continue to integrate in the X-axis and Y-axis directions to get the total strain energy density of the rectangular thin substrate:

[0161]

[0162] wherein li is the length of the rectangular thin substrate, and I2 is the width of the rectangular thin substrate.

[0163] Here V dz and V total It is too long to expand and inconvenient to show.

[0164] The partial derivatives of the curvature coefficients a, b, c, d, e of the rectangular thin substrate and the deformation coefficients a1, a2, a3, b1, b2, b3 of the intermediate surface are set to zero, i.e. the solution of the minimum state of the system energy:

[0165]

[0166] The final prediction is:

[0167] a = 0.5545655423

[0168] b = 1.0643768280

[0169] c = 0.7008098087

[0170] d = 0.0564656243

[0171] e = 0.0534134277

[0172] a1 = -4.4818993410 x 10 -6

[0173] a2 = 0.0003936159

[0174] a3 = -0.0049760819

[0175] b1 = -9.5843270320 x 10 -6

[0176] b2 = 0.0012440205

[0177] b3 = -0.0015744634

[0178] Step four, substituting the predicted curvature coefficients into the calculation formula:

[0179] ε z = (-6.655x 2 -1.402y 2 -0.1129)z + 0.0003936x 2 -0.004976y 2 -4.48210 -6

[0180] ε y= (-1.402x 2 - 12.77y 2 - 0.1068)z + 0.001244y 2 - 0.001574x 2 - 9.584 x 10 -6

[0181] γ xy = xy(-0.0010370 + 1.865x 4 + 8.789y 2 x 2 + 0.2897x 2 + 3.580y 4 + 0.5307y 2 - 5.606z)

[0182] σ x = -200x 6 + (100y 2 + 10)x 4 + (-1.121 x 10 12 z + 100y 4 )x 2 + (-7.352 x 10 11 z - 7.464 x 10 8 )y 2 - 2.234 x 10 10 z - 1.100 x 10 6

[0183] σ y = -40x 6 + (-4.905 x 10 11 z + 300y 4 - 2.362 x 10 8 )x 2 + (-2.099 x 10 12 z + 0.2)y 2 - 2.161 x 10 10 z - 1.713 x 10 6

[0184] τ xy = xy(-3.364 x 10 11 z - 6.222 x 10 7 + 1.119 x 10 11 x 4 + 5.274 x 10 11 y 2 x 2 + 1.738 x 10 10 x 2+2.148x10 11 y 4 +3.184x10 10 y 2 )

[0185] Please refer to Figures 2 to 14 . In the examples, Figure 2 shows the cross-section comparison diagram across Y axis, from which it can be observed that the deformation error obtained by the method of the present disclosure is significantly smaller than that obtained by the constant curvature method, and there is a significant progress; Figure 3 、 Figure 4 、 Figure 5 respectively show the layer diagrams of the y-direction stress components along the Y axis respectively obtained by ANSYS simulation, the method of the present disclosure and the constant curvature method, the variation trend of the stress obtained by the method of the present disclosure on each layer along the Y axis is the same as that of the ANSYS simulation, and the variation of the stress obtained by the constant curvature method is quite different from that of the ANSYS simulation. From the y-direction stress analytical expression, when the method of the present disclosure is used for prediction, there are coupling terms between y and z, and the slope of the variation along the z direction of each layer is affected by y, so the stress distribution obtained by the method of the present disclosure is more in line with the actual situation; Figure 6 、 Figure 7 、 Figure 8 respectively show the layer diagrams of the y-direction strain components along the Y axis respectively obtained by ANSYS simulation, the method of the present disclosure and the constant curvature method, the variation trend of the strain obtained by the method of the present disclosure on each layer along the Y axis is the same as that of the ANSYS simulation, and the variation trend of each layer obtained by the constant curvature method is the same as that of the ANSYS simulation, which is not similar to the result of the ANSYS simulation. From the y-direction strain analytical expression, when the method of the present disclosure is used for prediction, there are coupling terms between y and z, and the slope of the variation along the z direction of each layer is affected by y, so the stress distribution obtained by the method of the present disclosure is more in line with the actual situation; Figure 9 、 Figure 10 、 Figure 11 respectively show the layer diagrams of the x-direction stress components along the X axis respectively obtained by ANSYS simulation, the method of the present disclosure and the constant curvature method, and the y-direction stress components are similar, the variation trend of the stress obtained by the method of the present disclosure on each layer along the X axis is the same as that of the ANSYS simulation, and in particular, the variation trend of the stress values of the uppermost layer and the lowermost layer along the X axis is obviously closer to the ANSYS simulation result than that of the constant curvature method. From the x-direction stress analytical expression, when the method of the present disclosure is used for prediction, there are coupling terms between x and z, and the slope of the variation along the z direction of each layer is affected by x; Figure 12 、 Figure 13 、 Figure 14The layering diagrams of the x-direction strain components along the X-axis distribution obtained by ANSYS simulation, the method in this paper and the constant curvature method are shown respectively, and the y-direction strain components are similar. The variation trend of the strain obtained by the method in this paper along the X-axis direction on each layer is the same as that of the ANSYS simulation, and the variation trend of each layer of the constant curvature method is not similar to the result of the ANSYS simulation. According to the x-direction strain analytical expression, when the method in this paper is used for prediction, there are coupling terms between x and z, and the slope of the change along the z direction of each layer is affected by x, while when the constant curvature method is used for prediction, the slope of the change along the z direction of each layer is not affected by x, so the stress distribution obtained by the method in this paper is more in line with the actual situation. According to the above x-direction stress and strain components, y-direction stress and strain components and displacement along the Y-axis comparison diagrams, compared with the traditional constant curvature method for predicting the stress and strain of a rectangular thin substrate, the result obtained by the variable curvature method in this paper is more in line with the actual situation, can reflect the real variation trend, and has significant progressiveness.

[0186] The above-described embodiments only express several embodiments of the present application, and the description is more specific and detailed, but it should not be understood as limiting the scope of the application. It should be noted that for ordinary skilled in the art, without departing from the concept of the present application, several modifications and improvements can be made, which are all within the protection scope of the present application. Therefore, the protection scope of the present application should be subject to the appended claims.

Claims

1. A method for predicting deformation and stress state curvature of a rectangular thin substrate after deformation, comprising the following steps: establishing a three-dimensional coordinate system, wherein the origin of the coordinate system is the center of the middle surface of the rectangular thin substrate, the X-axis and the Y-axis are parallel to the length and width of the rectangular thin substrate, and the Z-axis is perpendicular to the plane in which the X-axis and the Y-axis lie; The X-axis direction strain ε x , Y-axis direction strain ε y , and shear strain γ xy of the rectangular thin substrate at coordinates (x, y, z) are obtained by the following strain model ε x = - (1 - v) (ε x + y ) - v (ε x - y ) ε y = - (1 - v) (ε x - y ) - v (ε x + y ) γ xy = 2 (1 - v wherein and are the X-axis direction strain, Y-axis direction strain and shear strain of the intermediate surface, respectively, and ω is the deflection of the rectangular thin substrate. The features are that ε x , ε y , γ xy are optimized, a deflection model of the curvature of the thin substrate changing with the position coordinates is established, and the strain models of the optimized ε x , ε y , γ xy are respectively: ε x = a1 + a2x 2 + a3y 2 - z(12a 2 x + 2c 2 y + 2d) ε y = b1 + b2y 2 + b3x 2 - z(12b y 2 + 2c x 2 + 2e) wherein a, b, c, d, and e are curvature coefficients of the rectangular thin substrate, and a1, a2, a3, b1, b2, and b3 are deformation coefficients of the middle surface.

2. The method of claim 1, wherein, The method for optimizing the strain model comprises the following steps: First, the ω are designed as follows: ω = ax 4 + by 4 + cx 2 y 2 + dx 2 + ey 2 At this time, a, b, c, d, e, a1, a2, a3, b1, b2, and b3 are all unknown numbers; Secondly, the minimum energy method is used to predict a, b, c, d, e, a1, a2, a3, b1, b2, and b3.

3. The method of claim 2, wherein, The prediction method for predicting a, b, c, d, e, a1, a2, a3, b1, b2, and b3 by using the minimum energy method comprises the following steps: First, the strain energy density V of the rectangular thin substrate removing the damage layer portion is acquired d1 : where Q 11 , Q 12 , Q 13 , Q 66 are elements in the matrix of elastic stiffness. Secondly, the strain energy density V of the rectangular thin substrate damage layer is acquired d2 : V d2 = σ0ε x + σ0ε y wherein σ0 is the residual stress in the damage layer; Next, the strain energy density V in the Z-axis direction is obtained by integrating in the Z-axis direction dz : wherein h is the thickness of the thin plate, and t is the thickness of the damage layer; Then, integration is continued in the X-axis and Y-axis directions to obtain the total strain energy density V of the rectangular thin substrate total : wherein l1 is the length of the rectangular thin substrate, and l2 is the width of the rectangular thin substrate; Finally, the partial derivatives of a, b, c, d, e, a1, a2, a3, b1, b2, and b3 are taken to be zero, which is the solution of the minimum energy state of the rectangular thin substrate:

4. The method of claim 3, wherein the rectangular thin substrate is a glass substrate. Q 11 , Q 12 , Q 13 , Q 66 respectively:

5. The method of claim 3, wherein, characterized in that a1, a2, a3, b1, b2, and b3 are respectively: 。 6. The method of claim 1, wherein, The method for predicting deformation and stress state curvature further comprises: The stress state model is used to calculate the stress state σ x , σ y , and τ xy in the X-axis direction of the rectangular thin substrate at coordinates (x, y, z) as follows: wherein E is the elastic modulus of the rectangular thin substrate, and μ is the Poisson's ratio of the rectangular thin substrate.

7. An apparatus for predicting the curvature of deformation and stress state of a rectangular thin substrate after deformation, which adopts the method for predicting the curvature of deformation and stress state of a rectangular thin substrate after deformation according to any one of claims 1 to 6, characterized by The device for predicting deformation and stress state curvature comprises: a three-dimensional coordinate system establishing module, which is configured to establish a three-dimensional coordinate system, wherein the origin of the coordinate system is the center of the middle surface of the rectangular thin substrate, the X-axis and the Y-axis are parallel to the length and width of the rectangular thin substrate, and the Z-axis is perpendicular to the plane in which the X-axis and the Y-axis lie; the rectangular thin substrate comprises a substrate and a thin film laid on the substrate; a strain stress calculation module for obtaining an X-axis direction strain ε x , a Y-axis direction strain ε y , and a shear strain γ xy of the rectangular thin substrate at coordinates (x, y, z) by the following strain model: wherein and are the X-axis direction strain, Y-axis direction strain and shear strain of the intermediate surface, respectively, and ω is the deflection of the rectangular thin substrate. Wherein, the strain stress calculation module also optimizes ε x , ε y , γ xy , establishes the deflection model of the curvature of the thin substrate changing with the position coordinates, and the strain models of the optimized ε x , ε y , γ xy are respectively: ε x = a1 + a2x 2 + a3y 2 - z(12a 2 + 2c 2 + 2d) ε y = b1 + b2y 2 + b3x 2 - z(12by 2 + 2cx 2 + 2e) The strain stress module also calculates σ x , σ y , τ xy with the following stress state model: In the formula, σ x , σ y , and τ xy are the stress states in the X-axis direction, the Y-axis direction, and the shear force direction, respectively, at the corresponding coordinates. wherein a, b, c, d, and e are curvature coefficients of the rectangular thin substrate, a1, a2, a3, b1, b2, and b3 are deformation coefficients of the middle surface, E is the elastic modulus of the rectangular thin substrate, and μ is the Poisson's ratio of the rectangular thin substrate.

8. An apparatus for predicting the curvature of a deformed and stressed state of a rectangular thin substrate after deformation, characterized by, The instrument for predicting deformation and stress state curvature comprises: a processor configured to predict ε x , ε y , γ xy , σ x , σ y , τ xy according to the rectangular thin substrate deformation and stress state curvature prediction method of any one of claims 1 to 6 a display for displaying the predicted ε x , ε y , γ xy , σ x , σ y , τ xy , or a voice announcement of the predicted ε x , ε y , γ xy , σ x , σ y , τ xy .

9. A computer terminal comprising a memory, a processor, and a computer program stored on the memory and executable on the processor, characterized in that, When the processor executes the program, the steps of the method for predicting deformation and stress state curvature of a rectangular thin substrate after deformation according to any one of claims 1-6 are implemented.

10. A computer-readable storage medium, characterized in that, The computer program instructions are stored in the computer readable storage medium, and when read and run by a processor, the steps of the method for predicting deformation and stress state curvature of a rectangular thin substrate after deformation according to any one of claims 1-6 are executed.

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