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

Abstract

The invention relates to a method and a device for predicting deformation of a rectangular thin substrate after deformation and variable curvature of a stress state in the technical field of precision measurement and analysis. The prediction method comprises the following steps: establishing a three-dimensional coordinate system XYZ; according to the method, a deflection model that the curvature of the thin substrate changes along with the change of position coordinates is established, an original deflection model with the same curvature at each position is abandoned, and strain models of the rectangular thin substrate at coordinates (x, y and z), namely X-axis direction strain epsilon x, Y-axis direction strain epsilon y and shear strain gamma xy, are obtained by establishing the variable-curvature deflection model. A method adopted by strain models of epsilon x, epsilon y and gamma xy is as follows: new # imgabs0 # omega, especially omega, is designed, a calculation model of deflection omega is designed to be omega = ax4 + by4 + cx2y2 + dx2 + ey2, at the moment, the curvature of the thin substrate is changed along with the change of position coordinates, and the curvature of the thin substrate is changed along with the change of position coordinates. A rectangular thin substrate deflection calculation model # imgabs1 # in a traditional thin substrate everywhere curvature equal model is completely abandoned, and the technical problem that in the prior art, prediction of the stress state of the rectangular thin substrate is not accurate is solved.

Description

Technical Field

[0001] The present invention 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 that implements the function of the prediction method, and a computer-readable storage medium that stores a program that implements the function of the prediction method, and in particular, it relates to a method for predicting the curvature change of the deformation and stress state of a rectangular thin substrate after deformation, 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 that implements the function of the prediction method, and a computer-readable storage medium that stores a program that implements the function of the prediction method. Background Art

[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 skins. Among thin plates, rectangular thin plates are one of the most widely used types. During the processing of thin plates, subsurface damage may occur on the thin plates. Usually, the thickness of this damaged layer is small, much lower than the thickness of the undamaged layer. Therefore, the subsurface damaged layer can be regarded as a thin film layer, which together with the undamaged layer forms a thin film substrate system. In addition, a coated thin plate is a thin film coated on a 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 flattening or coating the rectangular thin plate has been widely used in many fields.

[0003] For example, in solar photovoltaic panels, the core component is the solar panel, which is usually made of monocrystalline or polycrystalline silicon materials and is in the shape of a rectangular thin plate. During the production process, the thin film substrate system plays an important role in solar cells. Due to the damage layer that may appear on the surface during the flattening process of the panel, the panel is deformed, which in turn affects the efficiency of collecting sunlight. Therefore, the deformation caused by residual stress needs to be reduced during the processing. The damage layer mainly corresponds to the thin film layer part in the thin film substrate system, and the rest belongs to the substrate layer. In order to effectively improve the performance of photovoltaic panels, predicting the stress state and deformation in the thin film substrate system is crucial to guiding the flattening process of the panel. Similarly, when producing optical components such as lenses, filters, and reflectors, thin film layers are usually deposited on the substrate material to accurately control the reflection, transmission, and absorption of light to achieve the desired optical effect. These optical components also form a thin film substrate system. If the stress in the thin film layer is too high, it may cause the optical component to deform, which in turn affects the final optical performance. Therefore, predicting and analyzing the stress state and deformation in the thin film substrate system can help designers optimize the deposition process of thin film materials and the selection of substrate materials, thereby avoiding excessive stress, reducing the risk of failure of optical components, and ensuring their quality and stability. When studying thin film substrate systems, the deformation of the system is usually regarded as a spherical deformation, and its deformation is represented by a single fixed curvature. However, this assumption is only applicable to small deformations of the system in the linear domain. When the system undergoes a large deformation, the assumption of using a single curvature to represent the deformation of the system will deviate from the actual situation. The deformation of the system will no longer be a spherical deformation with a fixed curvature, and its curvature will change according to the change of its coordinate position. Summary of the invention

[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 invention provides a method for predicting the deformation and variable curvature of the stress state of a rectangular thin substrate after deformation, a device for predicting the deformation and variable curvature of the stress state of a rectangular thin substrate after deformation corresponding to the prediction method, an instrument for predicting the deformation and variable curvature of the stress state of a rectangular thin substrate after deformation using the prediction method, a computer terminal for realizing the function of the prediction method, and a computer-readable storage medium for storing a program for realizing the function of the prediction method.

[0005] The present invention is implemented by the following technical solution: A method for predicting the curvature variation of a rectangular thin substrate after deformation and stress state, comprising the following steps:

[0006] Establishing 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 of the rectangular thin substrate respectively, and the Z-axis is perpendicular to the plane where the X-axis and the Y-axis are located;

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

[0008]

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

[0010] Among them, for ε x , ε y , γ xy Optimize and establish a deflection model in which the curvature of the thin substrate changes with the position coordinates. The optimized ε x , ε y , γ xy The strain models are:

[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 intermediate surface.

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

[0016] First, ω is designed as:

[0017]

[0018] ω=ax 4 +by 4 +cx 2 y 2 +dx 2 +ey2

[0019] At this point, a, b, c, d, e, a1, a2, a3, b1, b2, and b3 are all unknowns;

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

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

[0022] First, the strain energy density V of the rectangular thin substrate without the damaged layer is obtained. d1 :

[0023]

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

[0025] Secondly, the strain energy density V of the damaged layer of the rectangular thin substrate is obtained. d2 :

[0026] V d2 =σ0ε x +σ0ε y

[0027] Where σ0 is the residual stress in the damaged layer;

[0028] Next, the strain energy density V in the Z-axis direction is obtained by integrating in the Z-axis direction. dz :

[0029]

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

[0031] Then, continue to integrate in the X-axis and Y-axis directions to obtain the total strain energy density V of the rectangular thin substrate. total :

[0032]

[0033] Wherein, l1 is the length of the rectangular thin substrate, 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, and b3 are calculated to be zero, which is the solution to the minimum energy state of the rectangular thin substrate:

[0035]

[0036] Furthermore, Q 11 , Q 12 , Q 13 , Q 66 Calculated by the following formula:

[0037] From the above steps, we can get the expressions of a1, a2, a3, b1, b2, and b3:

[0038]

[0039]

[0040] Substituting the expressions of a1, a2, a3, b1, b2, and b3 into the equations, we can get the expressions of a, b, c, d, and e. The expressions of each coefficient are too long and are not shown. The expressions of each coefficient are too complicated, so an iterative method is used for prediction. Compared with direct prediction of nonlinear equations, it is more intuitive and simple, and does not require complex derivation and calculation.

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

[0042] The stress state σ in the X-axis direction of the rectangular thin substrate at the coordinate (x, y, z) is calculated by the following stress state model: x , stress state in the Y-axis direction σ y , shear stress state τ xy :

[0043]

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

[0045] The present invention also provides a device for predicting the curvature variation of the deformation and stress state of a rectangular thin substrate after deformation, which adopts any of the above-mentioned methods for predicting the curvature variation of the deformation and stress state of a rectangular thin substrate after deformation. The device for predicting the curvature variation of the deformation and stress state comprises:

[0046] A three-dimensional coordinate system establishment module, which is used to 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 of the rectangular thin substrate respectively, and the Z axis is perpendicular to the plane where the X axis and the Y axis are located; the rectangular thin substrate includes a base and a film laid on the base;

[0047] The strain stress calculation module is used to obtain the X-axis strain ε of the rectangular thin substrate at the coordinate (x, y, z) through the following strain model x , Y-axis strain ε y , shear strain γ xy :

[0048]

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

[0050] The strain stress calculation module also calculates ε x , ε y , γ xy Optimize and establish a deflection model in which the curvature of the thin substrate changes with the position coordinates. The optimized ε x , ε y , γ xy The strain models are:

[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 the stress state calculation models are:

[0055]

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

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

[0058] The present invention also provides an instrument for predicting the curvature change of a rectangular thin substrate after deformation and the state of stress, the instrument comprising:

[0059] A processor is used to predict ε according to the above-mentioned method for predicting the curvature of any rectangular thin substrate after deformation and stress state. x , ε y , γ xy ;

[0060] A display 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 invention also provides a computer terminal, which includes a memory, a processor, and a computer program stored in the memory and executable on the processor. When the processor executes the program, the steps of the above-mentioned method for predicting the variable curvature of deformation and stress state of any rectangular thin substrate after deformation are implemented.

[0062] The present invention also provides a computer-readable storage medium, in which computer program instructions are stored. When the computer program instructions are read and executed by a processor, the steps of the above-mentioned method for predicting the variable curvature of deformation and stress state of any rectangular thin substrate are executed.

[0063] Compared with the prior art, the advantages of the present invention are as follows:

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

[0065] (2) The present invention x , ε y , γ xy The strain model adopts the method of designing a new ω, especially ω, the calculation model of deflection ω is designed to be 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 position coordinates, completely abandoning the traditional thin substrate curvature equal model of rectangular thin substrate deflection calculation model

[0066] (3) In the field of rectangular thin substrates, there are not only technical problems such as large amount of calculation and difficult prediction due to the high order of the ω calculation model, but also technical problems such as inaccurate prediction due to the thin substrate being rectangular. The present invention establishes a model in which the curvature of the thin substrate varies with the position coordinates, abandons the original assumption that the curvature of the thin substrate is equal at all locations, establishes a new deflection mathematical model, and 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 middle surface through the minimum energy method to solve these problems. The prediction process is clear and can also make ε x , ε y , γ xy The strain model is consistent with the actual situation. BRIEF DESCRIPTION OF THE DRAWINGS

[0067] Figure 1 It is a flow chart of the method for predicting the variable curvature of the strain and stress state of a rectangular thin substrate provided in Example 1 of the present invention.

[0068] Figure 2 This is a comparison diagram of the displacement change along the Y-axis of the rectangular thin substrate after deformation provided by Example 2 of the present invention.

[0069] Figure 3 This is a stress state diagram of the Y-direction stress component of the rectangular thin substrate obtained by ANSYS simulation along the Y-axis in Example 2.

[0070] Figure 4 It is a state diagram of the Y-direction stress component of the rectangular thin substrate in Example 2 obtained according to the calculation method in this article when the thin substrate changes along the Y-axis.

[0071] Figure 5 This is a state diagram of the Y-direction stress component of the rectangular thin substrate obtained by the constant curvature assumption method along the Y-axis in Example 2.

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

[0073] Figure 7It is the Y-direction strain distribution diagram of the rectangular thin substrate in Example 2 obtained according to the calculation method in this article when the thin substrate changes along the Y-axis.

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

[0075] Fig. 9 This is a stress state diagram of the stress component in the X direction of the rectangular thin substrate obtained by ANSYS simulation along the X axis in Example 2.

[0076] Fig.10 This is a state diagram of the stress component in the X direction of the rectangular thin substrate in Example 2 obtained according to the calculation method in this article.

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

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

[0079] Fig.13 This is the X-direction strain distribution diagram of the rectangular thin substrate along the X-axis obtained according to the calculation method in this article for the thin substrate in Example 2.

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

[0081] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0082] The method for predicting the variable curvature of the deformation and stress state of a rectangular thin substrate after deformation of the present invention mainly comprises the following steps: establishing a three-dimensional coordinate system XYZ; establishing a deflection model in which the curvature of the thin substrate changes with the position coordinates, abandoning the original deflection model in which the curvature is the same at all locations, and obtaining the strain model of the rectangular thin substrate at the coordinates (x, y, z) by establishing the variable curvature deflection model: the strain ε in the X-axis direction is x , Y-axis strain ε y , shear strain γ xyThe present invention establishes ε by re-establishing the variable curvature model. x , ε y , γ xy The strain model solves the technical problem of inaccurate prediction of the stress state of a rectangular thin substrate in the prior art. x , ε y , γ xy The strain model adopts the method of designing a new ω, especially ω, the calculation model of deflection ω is designed to be 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 position coordinates, completely abandoning the traditional thin substrate curvature equal model of rectangular thin substrate deflection calculation model Rectangular thin substrates can be used in optical components, such as thin film substrate systems for solar photovoltaic panels. The present invention can be used to predict the stress state and deformation in the thin film substrate system (mainly the surface film of the solar photovoltaic panel), which can effectively improve the performance of the solar photovoltaic panel and is crucial for guiding the flattening process of the panel. Rectangular thin substrates can also be used in the production of optical components such as lenses, filters and reflectors. For example, as a thin film substrate system for optical components, the present invention can be used to predict and analyze the stress state and deformation in the thin film substrate system, which can help designers optimize the deposition process of thin film materials and the selection of base materials, thereby avoiding excessive stress, reducing the risk of failure of optical components, and ensuring their quality and stability.

[0083] Example 1

[0084] The method for predicting the curvature variation of the deformation and stress state of a rectangular thin substrate after deformation provided in this embodiment mainly includes three steps.

[0085] 1. 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 of the rectangular thin substrate respectively, and the Z-axis is perpendicular to the plane where the X-axis and the Y-axis are located.

[0086] The rectangular thin substrate comprises a base and a film laid on the base. The middle plane refers to a plane parallel to the rectangular plane of the thin substrate and equidistant from the upper and lower rectangular planes.

[0087] 2. The X-axis strain ε of the rectangular thin substrate at the coordinate (x, y, z) is obtained by the following strain model: x , Y-axis strain ε y , shear strain γ xy :

[0088]

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

[0090] 3. Calculate the stress state σ of the rectangular thin substrate in the X-axis direction at the coordinates (x, y, z) by the following stress state model: x , stress state in the Y-axis direction σ y , shear stress state τ xy :

[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] In the second step, ε x , ε y , γ xy Optimize and establish a deflection model in which the curvature of the thin substrate changes with the position coordinates. The optimized ε x , ε y , γ xy The strain models are:

[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] 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 intermediate surface.

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

[0099] The strain energy density of the rectangular thin substrate after the damaged layer is removed:

[0100]

[0101] The strain energy density of the damaged layer of a rectangular thin substrate:

[0102] V d2 =σ0ε x +σ0ε y

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

[0104]

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

[0106]

[0107] Where h is the thickness of the thin plate and t is the thickness of the damaged layer.

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

[0109]

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

[0111] 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 middle surface are calculated to make them zero, which is the solution to the minimum energy state of the system:

[0112]

[0113] In summary, in this embodiment, please refer to Figure 1 , which is a flow chart of the method for predicting the deformation and stress state variable curvature of a rectangular thin substrate after deformation provided by this embodiment. The method for predicting the deformation and stress state variable curvature of a rectangular thin substrate after deformation may include the following steps: S11 to S14.

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

[0115] S12. The strain and stress state prediction formula of the rectangular thin substrate is derived from the strain formula and physical equation. The strain formula is obtained from the following strain formula:

[0116]

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

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

[0119]

[0120] Among them, a1, a2, a3, b1, b2, and b3 are the deformation coefficients of the assumed intermediate surface.

[0121] The strain of the mid-surface and the deflection model used: ω = ax 4 +by 4 +cx 2 y 2 +dx 2 +ey 2 Substitute into the strain formula to obtain the strain formula.

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

[0123]

[0124] Substituting the obtained strain formula into the physical equation, the stress formula of the rectangular thin substrate is obtained as follows:

[0125]

[0126] S13. Obtain 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, and use the minimum energy method to predict them. The minimum energy method means that the system will always tend to the state of minimum energy.

[0127] S14, substituting the obtained curvature coefficient and the mid-plane deformation coefficient into the strain calculation formula and the stress state. The calculation formula obtains the strain and stress state of the thin substrate.

[0128] When this embodiment is applied, the method for predicting the variable curvature of the stress state of a rectangular thin substrate after deformation can be set in the form of software, such as a device for predicting the variable curvature of the stress state of a rectangular thin substrate after deformation corresponding to the prediction method, which can be specifically designed as an independent non-embedded software, or an embedded software that can be called at any time (such as embedded in a stress state prediction instrument, as an application software of the stress state prediction instrument, controlling the stress state prediction instrument to achieve the function of stress state prediction). Whether it is non-embedded or embedded software, it can be summarized as a corresponding device for predicting the stress state of a rectangular thin substrate after deformation. 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 formulas through deformation formulas, etc.; 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 middle 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; 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 may include a memory, a processor, and a computer program stored in the memory and running on the processor. The computer terminal may also be a smart phone, a tablet computer, a laptop computer, etc. that can execute a program. The processor may be a central processing unit (CPU), a controller, a microcontroller, a microprocessor, or other data processing chips in some embodiments. The processor is generally used to control the overall operation of a computer device. In the present embodiment, the processor is used to run the program code stored in the memory or process data. When the processor executes the program, the steps of the function of the method for predicting the curvature of the strain and stress state after deformation of a rectangular thin substrate of the present invention can be realized.

[0131] The software can be stored in a computer-readable storage medium, in which a computer program instruction is stored. When the computer program instruction is read and executed by a processor, the steps of the method for predicting the variable curvature of the strain and stress state of a thin substrate after deformation are executed. The computer-readable storage medium, such as a U shield, is made in the form of a U shield and can be plugged into a traditional stress state prediction instrument (or an electronic device such as a computer or a mobile phone) by electronic plug-in. The strain and stress state prediction instrument predicts the strain and stress state solution of a rectangular thin substrate of corresponding size and material by reading and executing the computer program instruction in the U shield. The predicted result is accurate and in line with the actual situation, and the prediction process is simple and easy to understand.

[0132] Example 2

[0133] This embodiment 2 is essentially a specific example of embodiment 1. This embodiment will introduce in detail how to predict the strain and stress state of a rectangular thin substrate by using strain formulas, physical equations, and the minimum energy method. To this end, the specific steps of this embodiment will be described from the following aspects.

[0134] See also Figure 1 In this embodiment, a thin substrate with a thickness of h = 400 μm, a length of l1 = 200 mm, and a width of l2 = 150 mm is selected for demonstration, wherein the Young's modulus E = 150 GPa, the Poisson's ratio μ = 0.25, the film thickness t = 1 μm, and the stress σ0 in the film = 1000 MPa.

[0135] Implementation includes the following steps:

[0136] Step 1: The material characteristic parameters, dimensions and stress in the film of the rectangular thin substrate σ0 = 1000MPa are known. The material characteristic parameters include elastic modulus E = 150GPa and Poisson's ratio μ = 0.25. The dimension parameters include the overall thickness of the thin substrate h = 400μm, length l1 = 200mm, width l2 = 150mm, and film thickness t = 1μm.

[0137] Step 2: The deformation and stress state calculation formula of the rectangular thin substrate is predicted by the deformation equation and the physical equation, wherein the strain formula is obtained by the following strain formula:

[0138]

[0139] in and They are the X-axis strain, Y-axis strain and shear strain of the middle surface respectively.

[0140] The strain model of the middle surface is:

[0141]

[0142] Among them, a1, a2, a3, b1, b2, and b3 are the deformation coefficients of the assumed intermediate surface.

[0143] The strain of the mid-surface and the deflection model used: ω = ax 4 +by 4 +cx 2 y 2 +dx 2 +ey 2 Substitute 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 obtained strain formula into the physical equation, the stress formula of the rectangular thin substrate is obtained. It is also known that Young's modulus E = 150 GPa and Poisson's ratio μ = 0.25, the obtained formula is as follows:

[0147] σ x =-3.2×10 11 (μ(6by 2 +cx 2 +e)+6ax 2 +cy 2 +d)z+1.6×10 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 +cxy 2 +dx) 2 )

[0148] σ y =-3.2×10 11 (μ(6ax 2 +cy 2 +d)+6by 2 +cx 2 +e)z+1.6×10 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 3: Use the minimum energy method to predict the curvature coefficient, obtain the curvature coefficients a, b, c, d of the rectangular thin substrate and the deformation coefficients a1, a2, a3, b1, b2, b3 of the middle surface, and use the minimum energy method to predict them. The minimum energy method means that the system will always tend to the state of minimum energy. The prediction process is as follows:

[0151] The strain energy density of the rectangular thin substrate after the damaged layer is removed:

[0152]

[0153] The strain energy density of the damaged layer of a rectangular thin substrate:

[0154] V d2 =σ0ε x +σ0ε y

[0155] Where σ0 is the residual stress in the damaged layer; Q 11 , Q 12 , Q 22 , Q 66 is an element in the elastic stiffness matrix and is calculated by the following formula:

[0156]

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

[0158]

[0159] Where h is the thickness of the thin plate and t is the thickness of the damaged layer.

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

[0161]

[0162] Wherein l1 is the length of the rectangular thin substrate, and l2 is the width of the rectangular thin substrate.

[0163] Here V dz and V total The expansion is too lengthy and inconvenient to display.

[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 middle surface are calculated to make them zero, which is the solution to the minimum energy state of the system:

[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=-4.4818993410×10 -6

[0173] a2=0.0003936159

[0174] a3=-0.0049760819

[0175] b1=-9.5843270320×10 -6

[0176] b2=0.0012440205

[0177] b3=-0.0015744634

[0178] Step 4: Substitute the predicted curvature coefficients into the calculation formula to obtain:

[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 × 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 × 10 12 z+100y 4 )x 2 +(−7,352 × 10 11 z − 7,464 × 10 8 )y 2 −2,234 × 10 10 z − 1,100 × 10 6

[0183] σ y =-40x 6 +(−4.905 × 10 11 z+300y 4 −2,362 × 10 8 )x 2 +(−2.099 × 10 12 z+0.2)y 2 −2,161 × 10 10 z − 1,713 × 10 6

[0184] τ xy =xy(−3.364×10 11 z-6,222 × 10 7 +1.119 × 10 11 x 4 +5.274 × 10 11 y 2 x 2 +1.738 × 10 10 x 2+2.148×10 11 y 4 +3.184×10 10 y 2 )

[0185] See also Figures 2 to 14 In the embodiment, Figure 2 The cross-section comparison diagram through the Y axis is shown. From this diagram, it can be observed that the deformation error obtained by the proposed method is significantly smaller than the deformation error obtained by the constant curvature method, which is a significant improvement. Figure 3 , Figure 4 , Figure 5 The layered diagrams of the stress component in the y direction distributed along the Y axis obtained by ANSYS simulation, the method proposed in this paper and the constant curvature method are shown respectively. The change trend of the stress in each layer along the Y axis obtained by the method proposed in this paper is the same as that of the ANSYS simulation, while the change trend of the stress obtained by the constant curvature method is very different from that of the ANSYS simulation. From the analytical formula of the stress in the y direction, it can be seen that there are coupling terms between y and z when the method proposed in this paper predicts, and the slope of each layer along the z direction is affected by y. Therefore, the stress distribution obtained by the method proposed in this paper is more in line with the actual situation. Figure 6 , Figure 7 , Figure 8 The layered diagrams of the y-direction strain components distributed along the Y-axis obtained by ANSYS simulation, the method in this paper, and the constant curvature method are shown respectively. The variation trend of the strain obtained by the method in this paper along the Y-axis on each layer is the same as that of the ANSYS simulation, while the variation trend of each layer of the constant curvature method is the same, which is not similar to the result of ANSYS simulation. From the y-direction strain analytical formula, when the method in this paper predicts, there are coupling terms between y and z, and the slope of each layer along the z direction is affected by y, so the stress distribution obtained by the method in this paper is more in line with the actual situation. Fig. 9 , Fig.10 , Fig.11 The layered diagrams of the stress components in the x-direction distributed along the x-axis obtained by ANSYS simulation, the method in this paper, and the constant curvature method are shown respectively. Similar to the stress components in the y-direction, the stress variation trend along the x-direction on each layer obtained by the method in this paper is the same as that in the ANSYS simulation, especially the stress values ​​of the top and bottom layers along the x-direction are obviously closer to the ANSYS simulation results compared with the constant curvature method. From the analytical formula of the stress in the x-direction, when the method in this paper predicts, there are coupling terms between x and z, and the slope of each layer along the z-direction is affected by x. Fig.12 , Fig.13 , Fig.14The layered diagrams of the x-direction strain components distributed along the X-axis obtained by ANSYS simulation, the method in this paper, and the constant curvature method are shown respectively. Similar to the y-direction strain components, 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 the variation trend of the ANSYS simulation, while the variation trend of each layer of the constant curvature method is the same, which is not similar to the result of the ANSYS simulation. From the x-direction strain analytical formula, when the method in this paper predicts, there are coupling terms between x and z, and the slope of each layer along the z direction is affected by x, while when the constant curvature method is used for prediction, the slope of each layer along the z direction is not affected by x, so the stress distribution obtained by the method in this paper is more in line with the actual situation. From the above x-direction stress and strain component diagrams, y-direction stress and strain component diagrams, and the displacement comparison diagram along the Y-axis, compared with the traditional constant curvature method for predicting the stress and strain of rectangular thin substrates, the results obtained by the variable curvature method in this paper are more in line with the actual situation, can reflect the real variation trend, and have significant progress.

[0186] The above-described embodiments only express several implementation methods of the present invention, and the description thereof is relatively specific and detailed, but it cannot be understood as limiting the scope of the invention application. It should be pointed out that, for a person of ordinary skill in the art, several modifications and improvements can be made without departing from the concept of the present invention, and these all belong to the protection scope of the present invention. Therefore, the protection scope of the present invention application shall be subject to the attached claims.

Claims

1. A method for predicting the curvature of a rectangular thin substrate after deformation and stress state, comprising the following steps: Establishing 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 of the rectangular thin substrate respectively, and the Z-axis is perpendicular to the plane where the X-axis and the Y-axis are located; The X-axis strain ε of the rectangular thin substrate at the coordinate (x, y, z) is obtained by the following strain model: x , Y-axis strain ε y , shear strain γ xy : In the formula, and are the X-axis strain, Y-axis strain and shear strain of the middle surface respectively, and ω is the deflection of the rectangular thin substrate; The characteristic is that x , ε y , γ xy Optimize and establish a deflection model in which the curvature of the thin substrate changes with the position coordinates. The optimized ε x , ε y , γ xy The strain models are: ε x =a1+a2x 2 +a3y 2 -z(12ax 2 +2cy 2 +2d) ε y =b1+b2y 2 +b3x 2 -z(12by 2 +2cx 2 +2e) 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 intermediate surface.

2. The method for predicting the curvature of deformation and stress state of a rectangular thin substrate after deformation according to claim 1, characterized in that: The method of strain model optimization includes the following steps: First, ω is designed as: ω=ax 4 +by 4 +cx 2 y 2 +dx 2 +ey 2 At this point, a, b, c, d, e, a1, a2, a3, b1, b2, and b3 are all unknowns; Secondly, the minimum energy method is used to predict a, b, c, d, e, a1, a2, a3, b1, b2, and b3.

3. The method for predicting curvature of deformation and stress state of a rectangular thin substrate after deformation according to claim 2, characterized in that: The prediction method for predicting a, b, c, d, e, a1, a2, a3, b1, b2, and b3 using the minimum energy method includes the following steps: First, the strain energy density V of the rectangular thin substrate without the damaged layer is obtained. d1 : In the formula, Q 11 , Q 12 , Q 13 , Q 66 is the element in the elastic stiffness matrix; Secondly, the strain energy density V of the damaged layer of the rectangular thin substrate is obtained. d2 : V d2 =σ0ε x +σ0ε y Where σ0 is the residual stress in the damaged layer; Next, the strain energy density V in the Z-axis direction is obtained by integrating in the Z-axis direction. dz : Where h is the thickness of the thin plate and t is the thickness of the damaged layer; Then, continue to integrate 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, 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 calculated to be zero, which is the solution to the minimum energy state of the rectangular thin substrate:

4. The method for predicting curvature of deformation and stress state of a rectangular thin substrate after deformation according to claim 3, characterized in that: Q 11 , Q 12 , Q 13 , Q 66 They are:

5. The method for predicting curvature of deformation and stress state of a rectangular thin substrate after deformation according to claim 3, characterized in that: Features a1, a2, a3, b1, b2, b3 are:

6. The method for predicting curvature of deformation and stress state of a rectangular thin substrate after deformation according to claim 1, characterized in that: The deformation and stress state variable curvature prediction method also includes: The stress state σ in the X-axis direction of the rectangular thin substrate at the coordinate (x, y, z) is calculated by the following stress state model: x , stress state in the Y-axis direction σ y , shear stress state τ xy : Wherein, E is the elastic modulus of the rectangular thin substrate, and μ is the Poisson's ratio of the rectangular thin substrate.

7. A device for predicting the curvature variation of the deformation and stress state of a rectangular thin substrate after deformation, which adopts the method for predicting the curvature variation of the deformation and stress state of a rectangular thin substrate after deformation according to any one of claims 1 to 6, characterized in that: The deformation and stress state variable curvature prediction device comprises: A three-dimensional coordinate system establishment module, which is used to 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 of the rectangular thin substrate respectively, and the Z axis is perpendicular to the plane where the X axis and the Y axis are located; the rectangular thin substrate includes a base and a film laid on the base; The strain stress calculation module is used to obtain the X-axis strain ε of the rectangular thin substrate at the coordinate (x, y, z) through the following strain model x , Y-axis strain ε y , shear strain γ xy : In the formula, and are the X-axis strain, Y-axis strain and shear strain of the middle surface respectively, and ω is the deflection of the rectangular thin substrate; The strain stress calculation module also calculates ε x , ε y , γ xy Optimize and establish a deflection model in which the curvature of the thin substrate changes with the position coordinates. The optimized ε x , ε y , γ xy The strain models are: ε x =a1+a2x 2 +a3y 2 -z(12ax 2 +2cy 2 +2d) ε y =b1+b2y 2 +b3x 2 -z(12by 2 +2cx 2 +2e) The strain-stress module also adds x , σ y , τ xy The calculations were performed using the following stress state model: In the formula, σ x , σ y , τ xy They are the stress state in the X-axis direction, the stress state in the Y-axis direction, and the shear force state at the corresponding coordinates; Among them, a, b, c, d, e are the curvature coefficients of the rectangular thin substrate respectively, a1, a2, a3, b1, b2, b3 are the 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 instrument for predicting curvature of deformation and stress state of a rectangular thin substrate after deformation, characterized in that: The deformation and stress state variable curvature prediction instrument comprises: A processor, which is used to predict ε according to the method for predicting the curvature of a rectangular thin substrate after deformation and stress state according to any one of claims 1 to 6. x , ε y , γ xy , σ x , σ y , τ xy ; A display 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 .

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

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

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