Bending deformation and bending stress calculation method and reliability analysis method of flexible printed circuit board

Abstract

The invention belongs to the technical field of design and manufacturing of flexible printed circuit boards, and particularly relates to a bending deformation and bending stress calculation method and a reliability analysis method of a flexible printed circuit board. A flexible printed circuit board with a complex structure is reasonably simplified into a laminated plate structure model, and then a composite material stress calculation method and an ideal elastic compression bar deformation calculation method are applied to theoretical calculation of the flexible printed circuit board. The bending deformation and the bending stress of the flexible printed circuit board under the condition of large-deflection bending are theoretically solved, the workload of experiments or simulation is greatly reduced, and the reliability of the flexible printed circuit board can be quickly evaluated.

Description

TECHNICAL FIELD

[0001] The present application belongs to the technical field of design and manufacture of flexible printed circuit board, and particularly relates to a bending deformation and bending stress calculation method and a reliability analysis method for a flexible printed circuit board. BACKGROUND

[0002] Flexible electronic devices are applied to various key components of major national defense equipment and wearable electronic devices. As a carrier of electronic devices, a flexible printed circuit board is composed of a flexible substrate, a conductor layer and a cover layer, and is used for conformal mounting on a special-shaped surface and bearing various complex bending loads and facing various large-deflection bending. Under such large-deflection bending, not only a large in-plane stress is brought, but also a large out-of-plane stress is caused, thereby leading to damage such as fracture and delamination. Therefore, it is necessary to analyze the stress state and further study the reliability.

[0003] At present, the analysis workload of bending deformation and bending stress of a flexible printed circuit board is large through experiments or simulation, and therefore the deformation and stress calculation process needs to be optimized. SUMMARY

[0004] The present application provides a bending deformation and bending stress calculation method for a flexible printed circuit board, which can greatly reduce the workload of experiments or simulation and make the reliability analysis of the flexible printed circuit board faster.

[0005] The bending deformation of the flexible printed circuit board provided in the present application comprises:

[0006] S1: converting the structure of the flexible printed circuit board into a laminate structure model;

[0007] S2: converting the laminate model into a two-dimensional beam model, the length of the two-dimensional beam model being the same as the length of the laminate structure model and being set as L, the width being the same and being set as b, the total thickness being the same and being set as h, the moment of inertia of the cross section being the same and being set as I, and the minimum bending radius being the same and being set as p';

[0008] S3: calculating the bending deformation of the circuit board under the extrusion state of both ends, comprising:

[0009] S30: calculating the minimum curvature radius p' of the curve:

[0010]

[0011] wherein,

[0012] wherein, the value of the first intermediate variable p is obtained through formula (1.1);

[0013]

[0014] wherein K(p) is the first kind complete elliptic integral, and E(p) is the second kind complete elliptic integral;

[0015]

[0016] wherein the value of the second intermediate variable k is obtained by formula (1.3) and (1.4), The displacement constraint is applied to both ends of the length direction of the two-dimensional beam model, and the sum of the displacements of the two end points A1 and A2 is Y.

[0017] In an embodiment, S3 further comprises S31: calculating the displacement of any point between the midpoint O of the circuit board and the point P at L / 4 from one end;

[0018] S31: applying displacement constraint to both ends of the length direction of the two-dimensional beam model, and the sum of the displacements of the two end points A1 and A2 is Y, which is the known extrusion displacement, and x and y are the x coordinate and y coordinate of any point on the PO segment after deformation:

[0019]

[0020] In an embodiment, the length, width and thickness of each layer in the laminated plate structure model obtained by the transformation in S1 are the same as the maximum size of the outer contour of each layer structure of the flexible printed circuit board.

[0021] In an embodiment, the flexible printed circuit board is bent in the extrusion state at both ends, and the displacement of any point between the point P at L / 4 from one end Q and the midpoint O of the circuit board is 180 degree center symmetric with respect to the displacement of any point between the point P at L / 4 from one end and the midpoint O of the circuit board.

[0022] The bending stress calculation method provided in the application comprises: calculating the bending stress by using the small curvature radius p' described above.

[0023] In an embodiment, the normal stress σ θ and the normal stress σ r in the direction of angle θ are ignored when calculating the bending stress.

[0024] In an embodiment, the normal stress σ θ in the direction of angle θ is the in-plane component of the bending stress of the flexible printed circuit board, and the calculation formula of σ θ is:

[0025]

[0026] And

[0027] wherein, a polar coordinate system is established with the neutral axis of the deformation section with bending curvature radius ρ, wherein, r represents the distance from the center of the circular arc corresponding to the centroid axis after deformation as the starting point; E represents the elastic modulus of the material of the flexible printed circuit board at r;

[0028] The origin of the local coordinate system z-axis is located on the neutral axis, then there is a relationship between z and z' as follows

[0029]

[0030] wherein, represents the distance between the centroid axis and the neutral axis.

[0031] In an embodiment, the normal stress σ r is the out-of-plane component of the bending stress of the flexible printed circuit board, σ r The calculation formula of σ

[0032]

[0033] r e represents the radius of curvature of the upper surface of the tensile layer, r int2 and r int1 respectively represent the radii of curvature of the upper and lower surfaces of the intermediate layer, r i represents the radius of curvature of the lower surface of the compression layer.

[0034] E t , E n , and E c respectively represent the elastic modulus of the corresponding material of the tensile layer, the intermediate layer, and the compression layer.

[0035] The reliability analysis method provided in the present application comprises: evaluating the reliability of the flexible printed circuit board according to the results of the bending deformation calculation method and the bending stress calculation method described above.

[0036] The computer readable storage medium provided in the present application is used to store program data, and the program data can realize the results of the bending deformation calculation method described above, or / and the bending stress calculation method described above when executed by a processor.

[0037] The application simplifies the complex flexible printed circuit board into a laminated structure model, and then applies the composite stress calculation method and the ideal elastic compression rod deformation calculation method to the theoretical calculation of the flexible printed circuit board, so as to theoretically solve the bending deformation and bending stress of the flexible printed circuit board under large deflection bending. The inventors verify the availability of the theoretical calculation method through finite element simulation, and the results of the finite element simulation show that the theoretical calculation method can accurately calculate the displacement and in-plane and out-of-plane stress of the flexible printed circuit board under large deflection deformation. The application greatly reduces the workload of experiments or simulations, and can quickly evaluate the reliability of the flexible printed circuit board. BRIEF DESCRIPTION OF DRAWINGS

[0038] Figure 1a ) is a complete flexible electronic system in embodiment 1 of the application;

[0039] Figure 1b ) is a single flexible printed circuit board in embodiment 1 of the application;

[0040] Figure 2a ) is a flexible printed circuit board original model in embodiment 1 of the application;

[0041] Figure 2b ) is Figure 2a ) is a schematic diagram of the layer structure of the flexible printed circuit board;

[0042] Figure 2c ) is a simplified model of the flexible printed circuit board original model in embodiment 1 of the application; Figure 2a

[0043] Figure 3a ) is a simplified two-dimensional beam structure of the flexible printed circuit board under extrusion bending in embodiment 1 of the application;

[0044] Figure 3b ) is a simplified model of the flexible printed circuit board in embodiment 1 of the application; Figure 3a ) is a schematic diagram of converting the B1C section into the PO section;

[0045] Figure 4 is a schematic diagram of the laminated structure of the flexible printed circuit board in embodiment 2 of the application;

[0046] Figure 5 is a finite element simulation model of the flexible printed circuit board with a three-layer structure in embodiment 2 of the application;

[0047] Figure 6 is a curve diagram of the deformation results of the flexible printed circuit board under different extrusion displacements in embodiment 2 of the application;

[0048] Figure 7 ​Fig. 2 is a graph of in-plane stress on the middle section of the flexible printed circuit board under different extrusion displacements in Embodiment 2 of the present application;

[0049] Figure 8 Fig. 3 is a graph of out-of-plane stress on the middle section of the flexible printed circuit board under different extrusion displacements in Embodiment 2 of the present application. DETAILED DESCRIPTION

[0050] The present application will be described in detail below with reference to the drawings and in conjunction with embodiments. The principles and characteristics of the present application are described below in conjunction with the drawings, and it should be noted that the embodiments in the present application and the features in the embodiments can be combined with each other without conflict. The examples are only used to explain the present application and are not used to limit the scope of the present application.

[0051] Embodiment 1

[0052] As shown in Figs. 1 and 2, respectively, are a complete flexible electronic system and a separate flexible printed circuit board, the structure of which is shown in the figures, and the conductor layer is mainly bonded to the flexible substrate through an adhesive layer, and there are also cover layers on the upper and lower surfaces, which play the role of insulation and protection. Figure 1a ) and Figure 1b ) respectively. The flexible printed circuit board has a complex structure, some irregularly distributed small concave structures and irregular edges. Before theoretical calculation of large deflection bending displacement and stress, the structure is first reasonably simplified, the length, width and thickness of each layer are kept unchanged, and the layer structure shown in Fig. 3 is simplified to the regular laminate structure shown in Fig. 4.

[0053] The flexible printed circuit board original model shown in Fig. 3 is simplified to the regular laminate structure shown in Fig. 4. Through ABAQUS finite element software simulation, it can be obtained that compared with the original flexible printed circuit board, the simplified flexible printed circuit board has consistent stress distribution under the same bending load, and the displacement and the stress in each direction of the reference point are kept within a small error, so it is considered that this structure simplification is reasonable. Figure 2b Figure 2a First, the flexible printed circuit board shown in Fig. 3 is simplified to the regular laminate structure shown in Fig. 4. Figure 2c

[0054] First, the flexible printed circuit board shown in Fig. 3 is simplified to the regular laminate structure shown in Fig. 4. Figure 3a ​​)the flexible printed circuit board under the extrusion bending condition shown in the figure is calculated by displacement theory. In this stress condition, it can be regarded as a plane stress state, without considering edge effect, and simplified as a two-dimensional beam structure. The length of the circuit board is L, the width is b, the total thickness is h, the moment of inertia of the section is I, and the minimum bending radius is p'. The circuit board is bent under the extrusion condition at both ends, and there is an inflection point with zero bending moment at a distance of L / 4 from both ends, which are respectively denoted as B1 and B2. These two positions can be regarded as hinge connection points, and the B1B2 interval with a length of L / 2 can be regarded as a flexible rod with hinged ends. In the bending process, the bending of the circuit board is symmetrical, and the force analysis of the B1C segment can be carried out to simplify the calculation process. The B1C segment can be approximately regarded as an ideal elastic compression rod under large deformation condition, as shown in Figure 3a )and converted into the PO segment as shown in Figure 3b )and the coordinate system is created. Based on the ideal elastic compression rod under large deformation condition, the displacement of the flexible printed circuit board is theoretically derived.

[0055] The displacement constraint is applied to the flexible printed circuit board, and the sum of the displacements of the two end points A1 and A2 is Y. Given the extrusion displacement Y, the deformed curve and the curvature radius at each point on the curve can be obtained by the following formula. First, calculate the intermediate variable p

[0056]

[0057] Where K(p) is the first complete elliptic integral, and E(p) is the second complete elliptic integral.

[0058] The minimum curvature radius p' of the curve is calculated by the formula

[0059]

[0060] Where Thus, the minimum curvature radius control after deformation can be achieved by applying the extrusion displacement.

[0061]

[0062]

[0063] Where Thus, the intermediate variable k can be obtained.

[0064]

[0065] Where x and y represent the x coordinate and y coordinate of any point on the PO segment after deformation respectively. Thus, the shape of the entire curve can be solved to achieve deformation control.

[0066] In summary, the flexible printed circuit board bending deformation calculation method provided in the embodiment comprises the following steps.

[0067] S1: converting the structure of the flexible printed circuit board into a laminate structure model;

[0068] S2: converting the laminate model into a two-dimensional beam model, the length of the two-dimensional beam model being the same as the length of the laminate structure model and being set as L, the width being the same and being set as b, the total thickness being the same and being set as h, the moment of inertia of the cross section being the same and being set as I, and the minimum bending radius being the same and being set as p'; h

[0069] S3: calculating the bending deformation of the circuit board under the extrusion state of both ends, comprising the following steps.

[0070] S30: calculating the minimum curvature radius p' of the curve:

[0071]

[0072] wherein,

[0073] wherein, the value of the first intermediate variable p is obtained by formula (0.1);

[0074]

[0075] wherein, K(p) is the first complete elliptic integral, and E(p) is the second complete elliptic integral;

[0076]

[0077] wherein, the value of the second intermediate variable k is obtained by formula (1.3) and (1.4), applying displacement constraints to both ends of the length direction of the two-dimensional beam model, and the sum of the displacements of the two end points A1 and A2 is Y.

[0078] S3 further comprises S31: calculating the displacement of any point between the P point at L / 4 from one end and the midpoint O of the circuit board.

[0079] S31: applying displacement constraints to both ends of the length direction of the two-dimensional beam model, and the sum Y of the displacements of the two end points A1 and A2 is the known extrusion displacement, and x and y are the x coordinate and y coordinate of any point on the PO segment after deformation:

[0080]

[0081] The length, width and thickness of each layer in the laminate structure model obtained by conversion in S1 are the same as the maximum size of the outer contour of each layer structure of the flexible printed circuit board.

[0082] ​A flexible printed circuit board bends under pressure at both ends. The displacement of any point between one end Q and point P, which is L / 4 away from Q, is symmetrical about 180 degrees with respect to the displacement of any point between point P, which is L / 4 away from Q, and point O, which is L / 4 away from Q, and the midpoint O of the circuit board.

[0083] Example 2

[0084] Based on the bending deformation results calculated in Example 1, an in-plane and out-of-plane stress analysis is performed on the flexible printed circuit board. First, a sufficiently small end is considered for study; it can be assumed that the bending curvature of the flexible circuit board remains constant within this small segment. Taking a three-layer flexible printed circuit board as an example, a global polar coordinate system and a local coordinate system are created, such as... Figure 4 As shown, the origin of the local coordinate system z′ lies on the geometric mid-surface of the laminated beam. In this global polar coordinate system, the stress components include σ. θ , σ r and τ rθ Simulation results show that during the bending process of the flexible printed circuit board, it mainly bears the normal stress σ along the angle θ direction. θ and the normal stress σ along the radius r direction r , τ rθ Compared to the other two stress components, which are very small and can be ignored in terms of damage, the stress analysis of printed circuit boards assumes that τ rθ It is zero.

[0085] When a beam is subjected to axial pressure and asymmetrical laminated structures, a neutral axis shift occurs, and the position of the beam's neutral axis no longer coincides with the centroidal axis. For example... Figure 4 As shown, the origin of the local coordinate system z-axis lies on the central axis. Therefore, the following relationship exists between z and z′.

[0086]

[0087] in, This represents the distance between the centroidal axis and the neutral axis.

[0088] Taking a three-layer laminated printed circuit board as an example, r e The radius of curvature of the upper surface of the stretched layer, r int2 and r int1 Let r represent the radii of curvature of the upper and lower surfaces of the intermediate layer, respectively. i This represents the radius of curvature of the lower surface of the compression layer.

[0089] Circumferential strain ε in the θ direction θ The local coordinates Z exhibit a linear relationship, which depends on the radius of curvature ρ of the neutral axis, and the relationship is as follows:

[0090]

[0091] According to the circumferential stress, the axial force and the bending moment on the cross section can be obtained

[0092] ∫ A σ θ dA=N(θ) (1.9)

[0093] ∫ A σ θ z‘dA=M(θ) (1.10)

[0094] Taking the three-layer structure as an example, it can be written as

[0095]

[0096] wherein b represents the width of the flexible printed circuit board, E t , E n , E c respectively represent the elastic modulus of the corresponding material of the tensile layer, the intermediate layer and the compression layer.

[0097] According to the mechanical equilibrium equation, it can be known that

[0098] N(θ)y α +M(θ)=0 (1.13)

[0099] By combining equations (1.11), (1.12) and (1.13), the offset amount of the intermediate axis about the centroid axis can be determined and ρ.

[0100] The calculation formula of the stress component σ θ in the θ direction is

[0101]

[0102] wherein r represents the distance from the center of the circular arc corresponding to the centroid axis after deformation, and r=z′+ρ′.

[0103] After obtaining the in-plane stress, the out-of-plane stress σ r can be solved according to the stress function in the polar coordinate system, and the stress function in the polar coordinate system is

[0104]

[0105] In strict sense, the stress function is a function of angle θ, and a small segment of the laminate is studied, the curvature radius of the segment does not change with θ, so the in-plane stress is independent of θ, so the stress function can be assumed to be independent of θ, and the stress function is simplified.

[0106] Taking the radial stress of the tensile layer as an example, the derivation process is

[0107]

[0108] Continuing the integration of the above equation

[0109]

[0110] Substituting equation (1.14) into equation (1.20) gives

[0111]

[0112] Substituting equation (1.14) into the above equation gives

[0113]

[0114] Since the curvature radius is assumed to be constant with respect to angle, σ θ , σ r is independent of θ, the stress function is also independent of θ, then Therefore

[0115]

[0116] Substituting equation (1.24) into the above equation gives

[0117]

[0118] Similarly, the out-of-plane stresses of the intermediate and compression layers can be obtained

[0119]

[0120] According to the boundary conditions, when located at the top and bottom surfaces of the laminate, i.e. r = r e , r = r i , σ r = 0, substituting it into equations (1.26) and (1.28) gives

[0121] f 1t = 0 (1.29)

[0122] f 1c = 0 (1.30)

[0123] Therefore, the following equations can be obtained

[0124]

[0125]

[0126] According to the continuity condition of the out-of-plane stress σ r , σ r is continuous between layers, so when r = r int2 , σ rt = σrn When r = r int1 At that time, σ rn =σ rc When one of the stress continuity conditions is satisfied, the other continuity condition is automatically satisfied. Let r = r int2 Substituting into equations (1.26) and (1.27), we can obtain

[0127]

[0128] Taking a three-layer flexible printed circuit board as an example, the thicknesses of each layer from top to bottom are 0.1mm, 0.6mm, and 0.1mm, respectively. Its model is as follows: Figure 5 As shown in Table 1, the top and bottom layers are made of epoxy resin, and the middle layer is made of PI, all assumed to be isotropic materials. The material parameters are shown in Table 1. Hypermesh software was used to mesh the material and assign material properties, and the mesh in the middle section was refined. Simulation was performed using ABAQUS software.

[0129] Table 1 Flexible Plate Material Parameters

[0130]

[0131] Verification process:

[0132] A boundary condition of horizontal compression from both sides was applied, and a quarter of the model on the left side was used for simulation calculations to verify the theoretical calculation results. Figure 6 The figure shows the deformation calculation results of a quarter-sized flexible printed circuit board under different extrusion displacements. The error between the theoretical calculation results and the simulation results remains within 1%. A cross-section of the circuit board is taken, and the in-plane stress on the cross-section is verified. Figure 7 The figure shows the variation of in-plane stress along the thickness direction on the cross-section. The error between the theoretical calculation results and the simulation results remains within 4%. Similarly, the out-of-plane stress on the middle cross-section of the circuit board is verified. Figure 8 The figure shows the variation of out-of-plane stress along the thickness direction on the cross-section. The error between the theoretical calculation results and the simulation results remains within 7%. These results demonstrate that this theoretical calculation method can accurately calculate the displacement and in-plane and out-of-plane stresses of flexible printed circuit boards under large deflection deformation.

[0133] In summary, the bending stress calculation method for flexible printed circuit boards provided in this embodiment calculates the bending stress using the small radius of curvature ρ′ described in Embodiment 1.

[0134] In this method, the normal stress σ along the angle θ direction is ignored when calculating the bending stress. θ and the normal stress σ along the radius r direction r External forces.

[0135] Specifically, the normal stress σ along the direction of angle θ is θ is the in-plane component of the bending stress of the flexible printed circuit board, σ θ The calculation formula of σ is:

[0136]

[0137] And

[0138] wherein, the neutral axis of the deformation section with bending curvature radius ρ is established as a polar coordinate system, wherein, r represents the distance from the center of the circular arc corresponding to the centroid axis after deformation as the starting point; E represents the elastic modulus of the material of the flexible printed circuit board at r;

[0139] The origin of the local coordinate system z axis is located on the neutral axis, then there is a relationship between z and z' as follows

[0140]

[0141] wherein, represents the distance between the centroid axis and the neutral axis.

[0142] Specifically, the normal stress σ along the direction of radius r is r is the out-of-plane component of the bending stress of the flexible printed circuit board, σ r The calculation formula of σ includes:

[0143]

[0144] r e represents the curvature radius of the upper surface of the tensile layer, r int2 and r int1 respectively represent the curvature radius of the upper and lower surfaces of the intermediate layer, r i represents the curvature radius of the lower surface of the compression layer;

[0145] E t , E n , E c respectively represent the elastic modulus of the corresponding material of the tensile layer, the intermediate layer and the compression layer.

[0146] Embodiment 3

[0147] The embodiment provides a reliability analysis method of a flexible printed circuit board, which evaluates the reliability of the flexible printed circuit board according to the results of the bending deformation calculation method in embodiment 1 and the results of the bending stress calculation method in embodiment 2.

[0148] Embodiment 4

[0149] The embodiment provides a computer readable storage medium for storing program data, which, when executed by a processor, can realize the result of the bending deformation calculation method in the embodiment 1, or / and the bending stress calculation method in the embodiment 2.

[0150] In the description of the present application, it needs to be understood that the terms "upper", "lower", "front", "back", "left", "right", "vertical", "horizontal", "top", "bottom", "inner", "outer", "circumferential" and the like indicate the orientation or positional relationship based on the orientation or positional relationship shown in the drawings, and are only for the convenience of describing the present application and simplifying the description, and do not indicate or imply that the device or element referred to must have a particular orientation, be constructed and operated in a particular orientation, and therefore cannot be understood as a limitation on the present application.

[0151] In the present application, unless otherwise explicitly specified and limited, the terms "mounting", "connection", "connecting", "fixing" and the like should be understood in a broad sense, for example, can be fixed connection, can also be detachable connection, or integral; can be mechanical connection, can also be electrical connection; can be directly connected, can also be indirectly connected through an intermediate medium, can be the internal communication of two elements or the interaction relationship of two elements, unless otherwise explicitly limited. For those skilled in the art, the specific meaning of the above terms in the present application can be understood according to the specific circumstances.

[0152] In the present application, unless otherwise explicitly specified and limited, the first feature "on" or "under" the second feature can be that the first and second features are in direct contact, or the first and second features are in indirect contact through an intermediate medium. Moreover, the first feature "above", "over" and "on" the second feature can be that the first feature is directly above or obliquely above the second feature, or only indicates that the horizontal height of the first feature is higher than that of the second feature. The first feature "below", "under" and "under" the second feature can be that the first feature is directly below or obliquely below the second feature, or only indicates that the horizontal height of the first feature is less than that of the second feature.

[0153] In the description of the present application, the description of the terms "one embodiment", "some embodiments", "example", "specific example", or "some examples" and the like means that the specific features, structures, materials or characteristics described in connection with the embodiment or example are included in at least one embodiment or example of the present application. In the present application, the illustrative description of the above terms does not necessarily refer to the same embodiment or example. Moreover, the specific features, structures, materials or characteristics described can be combined in any one or more embodiments or examples in a suitable manner. In addition, those skilled in the art can combine and combine the different embodiments or examples described in the present application and the features of the different embodiments or examples without contradiction.

[0154] Although the embodiments of the present application have been shown and described above, it is understood that the above-described embodiments are exemplary and are not to be construed as limiting the present application, and that variations, modifications, substitutions and changes can be made by those skilled in the art without departing from the scope of the present application.

Claims

1. A method for calculating the bending deformation of flexible printed circuit boards, characterized in that, include: S1: Transform the structure of the flexible printed circuit board into a laminate structure model; S2: Convert the laminated plate model into a two-dimensional beam model. The length of the two-dimensional beam model is the same as the length of the laminated plate structure model and is set as L, the width is the same and is set as b, the total thickness is the same and is set as h, the moment of inertia of the cross section is the same and is set as I, and the minimum bending radius is the same and is set as ρ′. S3: Calculate the bending deformation of the circuit board under pressure at both ends, including: S30: Calculate the minimum radius of curvature ρ′ of the curve. in, The value of the first intermediate variable p is obtained through equation (1.1); Where K(p) is the complete elliptic integral of the first kind, and E(p) is the complete elliptic integral of the second kind; The value of the second intermediate variable k is obtained through equations (1.3) and (1.4). Displacement constraints are applied to both ends of the two-dimensional beam model along its length, and the sum of the displacements of the two end points A1 and A2 is Y.

2. The bending deformation calculation method according to claim 1, characterized in that, S3 also includes S31: Calculate the displacement of any point between point P, which is located at a distance of L / 4 from one end, and the midpoint O of the circuit board; S31: Apply displacement constraints to both ends of the two-dimensional beam model along its length. The sum of the displacements Y at the two end points A1 and A2 is the known compressive displacement, and x and y are the x and y coordinates of any point on segment PO after deformation.

3. The bending deformation calculation method according to claim 1 or 2, characterized in that, The length, width, and thickness of each layer in the laminate structure model obtained in S1 are the same as the maximum outer contour dimensions of each layer of the flexible printed circuit board.

4. The bending deformation calculation method according to claim 1, characterized in that, A flexible printed circuit board bends under pressure at both ends. The displacement of any point between one end Q and point P, which is L / 4 away from Q, is symmetrical about 180 degrees with respect to the displacement of any point between point P, which is L / 4 away from Q, and point O, which is L / 4 away from Q, and the midpoint O of the circuit board.

5. A method for calculating the bending stress of a flexible printed circuit board, characterized in that, The bending stress is calculated using the small radius of curvature ρ′ as described in any one of claims 1 to 4.

6. The bending stress calculation method according to claim 5, characterized in that, When calculating the bending stress, the normal stress σ along the angle θ direction is ignored. θ and the normal stress σ along the radius r direction r External forces.

7. The bending stress calculation method according to claim 5, characterized in that, Normal stress σ along angle θ θ σ is the in-plane component of the bending stress of the flexible printed circuit board. θ The formula for calculation is: and A polar coordinate system is established with the neutral axis of the deformed segment having a curvature radius of ρ, where r represents the distance from the center of the arc corresponding to the centroidal axis after deformation; E represents the elastic modulus of the material of the flexible printed circuit board at point r. If the origin of the local coordinate system's z-axis lies on the neutral axis, then the following relationship exists between z and z′. in, This represents the distance between the centroidal axis and the neutral axis.

8. The bending stress calculation method according to claim 7, characterized in that, Normal stress σ along the radius r r σ is the out-of-plane component of the bending stress of the flexible printed circuit board. r The calculation formulas include: r e The radius of curvature of the upper surface of the stretched layer, r int2 and r int1 Let r represent the radii of curvature of the upper and lower surfaces of the intermediate layer, respectively. i Represents the radius of curvature of the lower surface of the compression layer; E t E n E c These represent the elastic modulus of the materials corresponding to the stretch layer, intermediate layer, and compression layer, respectively.

9. A reliability analysis method for flexible printed circuit boards, characterized in that, The reliability of the flexible printed circuit board is evaluated based on the results of the bending deformation calculation method according to any one of claims 1 to 4 and the results of the bending stress calculation method according to any one of claims 5 to 8.

10. A computer-readable storage medium, characterized in that, The computer-readable storage medium is used to store program data, which, when executed by a processor, can realize the result of the bending deformation calculation method according to any one of claims 1 to 4, or / and the bending stress calculation method according to any one of claims 5 to 8.

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