A microstructure reliability analysis method for braided composite materials

Abstract

The present invention discloses a method for analyzing the mesostructure reliability of a woven composite material, comprising the following steps: performing XCT scanning on the woven composite material structure to obtain a mesoscopic image of the interior of the woven composite material structure; grouping each yarn; measuring mesoscopic geometric parameters and recording the spatial coordinates of the measured parameters; establishing a mesoscopic geometric model based on the average values ​​of the mesoscopic geometric parameters; obtaining a probability density function of the cross-sectional area based on the real yarn; establishing a proxy model of the structure-function function using the response surface methodology; performing finite element meshing on the mesoscopic model; assigning material parameters to each region of the mesoscopic model; performing finite element calculations; and calculating the failure probability of each region under a given load using the verification point method. The present invention can simulate the differences in yarn mechanical properties caused by geometric factors without changing the mesoscopic geometric model; and based on the physical spatial distribution of structural characteristics, the material properties can characterize the presence of structural defects in specific regions.

Description

Technical Field

[0001] The invention belongs to the technical field of composite materials, and in particular relates to a method for analyzing the reliability of a microstructure of a braided composite material. Background Art

[0002] Spatial randomness in local properties is widespread in woven composites. Although the same fiber type is used in the preform preparation process, due to factors such as uneven structural thickness and internal extrusion deformation, it is difficult for the precursor to enter the preform during matrix densification. In some cases, this can lead to the loss of matrix within the fiber bundle and the reduction of matrix outside the fiber bundle. These spatially distributed fiber bundle deformations and uneven pore distribution lead to the dispersion of composite material properties after deposition, which is directly reflected in the random distribution of yarn cross-sectional area within the structure, which has a significant impact on the reliable use of woven composite structures in engineering applications.

[0003] Currently, performance predictions for complex woven composite structures are typically performed using macroscopic homogenization methods, with microscopic models used for supplementary analysis of simple local structures. For example, organizations such as NASA and IHI have fabricated composite turbine blades and established macroscopic models for performance analysis. However, the significant microscopic non-periodicity of woven composites in specific regions and mixed structures leads to a degree of randomness in the macroscopic properties of the material on a spatial scale. In such cases, the use of macroscopic homogenization methods is insufficient to meet the current demands of composite structural development.

[0004] When studying the impact of the dispersion of woven composite material properties on the mechanical response of structures, it is generally assumed that the material properties or geometric parameters follow a certain distribution, and the uncertainty of the mechanical response is studied by providing the distribution parameters. However, this parameter estimation method is highly dependent on the rationality of the preset parameters, lacks a basis for the selection of specific parameters, and cannot reflect the impact of the parameter distribution on the response in actual structures. Because some parameters in real-world engineering problems cannot be effectively measured, non-probabilistic methods such as interval, evidence, and fuzzy methods are used to address these cognitive uncertainties. However, the results obtained by this non-probabilistic method are too redundant and appear conservative when more precise results are required. Summary of the Invention

[0005] The technical problem to be solved by the present invention is to address the deficiencies of the above-mentioned prior art and provide a microstructure reliability analysis method for woven composite materials based on yarn performance equivalence and spatial distribution mapping. Compared with the existing woven composite material structure reliability analysis method, this patent adopts random performance analysis based on yarn performance equivalence, which can simulate the difference in yarn mechanical properties caused by geometric factors without changing the microscopic geometric model; the physical spatial distribution of material properties based on structural characteristics can characterize the existence of structural defects in specific areas; the statistical method based on kernel density estimation (KDE) can achieve accurate statistics of the microscopic geometric parameters of real yarns; the microstructure parameters based on X-ray computed tomography (XCT) are used for modeling, which can effectively simulate the interaction between yarns and realize the damage analysis of the woven structure at the microscale.

[0006] In order to achieve the above technical objectives, the technical solution adopted by the present invention is:

[0007] A method for analyzing the microstructure reliability of a braided composite material comprises the following steps:

[0008] Step 1: Perform XCT scanning on the woven composite material structure to obtain a microscopic image inside the woven composite material structure.

[0009] Step 2: Identify the yarns in the structure, number each yarn and group them according to yarn category,

[0010] Step 3: Measure the microscopic geometric parameters of each group of yarns and record the spatial coordinates of the measured parameters to obtain a large number of parameter samples.

[0011] Step 4: Establish a mesoscopic geometric model based on the average value of the mesoscopic geometric parameters.

[0012] Step 5: Partition the yarns according to the spatial coordinates of the statistical microscopic parameters, and use the KDE method to perform non-parametric estimation of the yarn cross-sectional area in each region to obtain the probability density function of the cross-sectional area based on the real yarn.

[0013] Step 6: Use response surface methodology to establish the structure function function of each region. Based on the Bucher sampling method and the 3σ principle, select sampling points at the mean cross-sectional area and the probability of 99.7%.

[0014] Step 7: Perform finite element meshing on the microscopic model and assign material parameters to each region of the microscopic model based on the yarn performance equivalent method according to the sampling points.

[0015] Step 8: Perform finite element calculations on each region to obtain the failure condition of the microscopic model under a given load.

[0016] Step 9: Based on the structural performance function, the failure probability of each area under a given load is calculated using the verification point method.

[0017] Step 10: By applying a load to the entire composite woven structure, the partial load borne by each area and its failure probability are calculated to complete the microstructure reliability analysis of the woven composite material.

[0018] To optimize the technical solution, the present invention further adopts the following measures:

[0019] In step 1, the parameters of the XCT scan include imaging resolution, radiation voltage, tube current, and integration time. The requirement for the XCT scan is that the scanned image can display both the yarn profile and the yarn cross-section sample.

[0020] In step 2, the yarn category includes yarn type, weaving process, weaving parameters and yarn brand, wherein the yarn type is warp or weft, the weaving process is two-dimensional weaving or three-dimensional weaving, and the weaving parameters include yarn strand number parameter and yarn density parameter.

[0021] In step 3, image processing software is used to measure the microscopic geometric parameters of each group of yarns, and the yarn cross-section and axial direction are parametrically defined according to the degree of compression of the yarns.

[0022] In step 5, the cross-sectional area probability density function based on the real yarn is obtained using the KDE method and is given by Obtain, among which, is the probability density function of the cross-sectional area, N is the number of samples of real yarn, h is the bandwidth selected for kernel density estimation, χ i is the cross-sectional area of ​​the real yarn sample, χ is an arbitrary cross-sectional area, K(·) represents the kernel function, and the bandwidth h is optimized by cross-validation or iteration method.

[0023] In step 6, the response surface method is used to establish the structural function of each region. The structural function of each region is g(x) = r(x) - S, where S is the load value in the corresponding direction and r(x) is the ultimate load that the region can withstand. The expression is: Among them, x i are the cross-sectional areas of various yarns as random variables, b0 and b i are polynomial coefficients, n is the number of yarn types, in order to obtain b0 and b in r(x) i The value of , select 2n+1 sample points X i , sample point X i The selection method is: the mean sample point X0 (x1, x2, ..., x i ,…,x n )=(μ1,μ2,…,μ i ,…,μn ), the remaining sample points X i (x1,x2,…,x i ,…,x n )=(μ1,μ2,…,μ i ±3σ i ,…,μ n ), μ i represents the mean cross-sectional area of ​​each type of yarn, σ i Represents the standard deviation of the cross-sectional area of ​​each type of yarn. According to the 3σ principle, μ i ±3σ i Corresponding to the samples with the probability of 0.3% and 99.7%, each sample point X i Substitute r(x) into the equation system and solve it to get b0 and b i The value of .

[0024] In step 7, the 1st direction of the microscopic model for finite element mesh division is along the axis direction of the yarn, and the 2nd and 3rd directions are perpendicular to the 1st direction and perpendicular to each other. The specific method of assigning material parameters to each region of the microscopic model based on the method of equivalent yarn performance is as follows: Assume that the ratio of the actual cross-sectional area of ​​the yarn in a certain region of the microscopic model to the average cross-sectional area is m, multiply the corresponding correction coefficient f(m) by the yarn material property, and assign the material parameter of the region to the result. The distribution of material properties is used to characterize the random distribution of the yarn cross-sectional area, where the actual cross-sectional area is calculated according to the probability density function Random sampling is performed, and the average cross-sectional area is obtained by averaging the sample points in each region. The material properties include Young's modulus in 1 direction, stress-strain curve fitting coefficient in 1 direction, shear modulus in 12 planes, shear modulus in 13 planes, maximum tensile strain in 1 direction, maximum shear strain in 12 planes, and maximum shear strain in 13 planes. Among them, Young's modulus in 1 direction f(m)=m, stress-strain curve fitting coefficient in 1 direction f(m)=m, shear modulus in 12 planes f(m)=m 2 ,13 plane shear modulus f(m)=m 2 , the maximum tensile strain in the 1st direction The maximum shear strain in the 12th plane is f(m)=1 / m, and the maximum shear strain in the 13th plane is f(m)=1 / m.

[0025] In step 9, according to the JC method, the kernel density estimation The obtained probability density function is transformed into an equivalent normal distribution, and then the failure probability of each area under a given load is calculated using the verification point method based on the structural performance function.

[0026] In step 9, according to the structural function g(x) = r(x) - S, the verification point method calculates the reliability index β through successive iterations. Assume that the initial verification point x0* =(μ1,μ2,…,μ i ,…,μ n ), by calculating its reliability index and direction cosine α i , update the verification point x * =(x1 * ,x2 * ,…,x n * ), when the convergence index is satisfied is the latest verification point, The verification point calculated in the previous iteration is terminated when ε reaches the minimum value, and the failure probability P corresponding to the regional reliability index β under the current load is found. f , and obtain the failure probability of each region.

[0027] The calculation formula is as follows:

[0028]

[0029]

[0030]

[0031] Where, is the mean value of the linear limit state equation obtained based on the current verification point, is the standard deviation of the linear limit state equation obtained based on the current verification point, is the mean of the i-th random variable, is the value of the i-th random variable in the current verification point, is the standard deviation of the ith random variable.

[0032] Compared with the prior art, the present invention has the following beneficial effects:

[0033] 1. A structural reliability analysis method for woven composite materials based on yarn performance equivalence and spatial distribution mapping can simulate geometrically influenced differences in yarn mechanical properties without changing the microscopic geometric model. This method only requires a single model build, significantly reducing the time required for microscopic modeling.

[0034] 2. Material property distribution, based on the physical spatial distribution of structural features, can characterize the presence of structural defects in specific areas and predict structural failure areas. The size of the partitions can be selected independently, balancing prediction accuracy and computational efficiency.

[0035] 3. Compared with the parametric estimation method (such as Gaussian distribution, Weibull distribution, etc.), the kernel density estimation method based on non-parametric estimation does not rely on the preset distribution model parameters. Its distribution is formed by the superposition of each real sample, which can achieve accurate statistics of real yarn parameters.

[0036] 4. The microscopic structural parameters based on X-ray computed tomography are used for modeling, which can effectively simulate the interaction between yarns. Compared with the macroscopic model, it can realize the damage analysis and failure prediction of the woven structure at the microscopic scale. BRIEF DESCRIPTION OF THE DRAWINGS

[0037] Figure 1 Schematic diagram of the mesoscopic model of woven composite materials containing different yarn types;

[0038] Figure 2 Marking of yarn microscopic features in XCT images;

[0039] Figure 3 It is a schematic diagram of the structural partition of the braided composite material;

[0040] Figure 4 Obtain the probability density function based on kernel density estimation;

[0041] Figure 5 This is a reliability analysis flow chart. DETAILED DESCRIPTION

[0042] In order to make the purpose, technical solutions and advantages of this application more clearly understood, the present application is described and illustrated below in conjunction with the accompanying drawings and examples. It should be understood that the specific embodiments described herein are merely used to explain this application and are not intended to limit this application. Based on the embodiments provided in this application, all other embodiments obtained by those of ordinary skill in the art without making any creative efforts are within the scope of protection of this application.

[0043] Obviously, the drawings described below are merely examples or embodiments of the present application. Those skilled in the art can, without inventive effort, apply the present application to other similar scenarios based on these drawings. Furthermore, it is also understood that, although the effort involved in such a development process may be complex and lengthy, for those skilled in the art related to the content disclosed in this application, changes in design, manufacturing, or production based on the technical content disclosed in this application are merely conventional technical means and should not be construed as an insufficiency of the content disclosed in this application.

[0044] References to "embodiments" in this application mean that a particular feature, structure, or characteristic described in connection with the embodiment may be included in at least one embodiment of the application. The appearance of this phrase in various places in the specification does not necessarily refer to the same embodiment, nor does it refer to independent or alternative embodiments that are mutually exclusive of other embodiments. It is understood, both explicitly and implicitly, by those skilled in the art that the embodiments described in this application may be combined with other embodiments unless there is a conflict.

[0045] This example uses the woven composite material microstructure reliability analysis method based on yarn performance equivalence and spatial distribution mapping described in the invention to perform reliability analysis on the woven composite material blade crown structure.

[0046] Step 1: Perform an XCT scan of the blade crown structure to obtain a microscopic image of its interior. The resolution is set to 10 microns, the X-ray voltage is 80 kilovolts, the tube current is 80 microamperes, and the integration time is 2000 milliseconds. This ensures that the image not only displays basic information such as yarn profiles but also includes a large number of yarn cross-sectional samples. During reconstruction, the image coordinate axes should be aligned with the principal axes of the structure to ensure that the microstructure is not distorted.

[0047] Step 2: Identify and mark the yarns in the structure, number each yarn and group them according to yarn categories such as yarn type, weaving process, weaving parameters, yarn brand, etc. The weaving processes of the structure in this example use two-dimensional plain weaving and three-dimensional orthogonal weaving, and the yarn types of the leaf crown structure are divided into five categories: two-dimensional plain warp yarn, two-dimensional plain weft yarn, three-dimensional orthogonal warp yarn, three-dimensional orthogonal weft yarn, and three-dimensional orthogonal binding yarn. Figure 1 shown.

[0048] Step 3: Measure the microscopic geometric parameters of each group of yarns and record the spatial coordinates of the measured parameters. The yarn cross section and axis direction can be parametrically defined according to the degree of compression of the yarn. For example, the yarn cross section can be defined as an ellipse, a quadrilateral, a racetrack, etc., and the axis direction can be defined as a spline curve, a trigonometric function curve, or a curve defined according to the yarn cross section profile to obtain a large number of parameter samples. Figure 2 shown.

[0049] Step 4: Define the warp yarn cross section as a racetrack shape and the weft yarn cross section as an ellipse. Build a meso-geometric model based on the average values ​​of the meso-geometric parameters.

[0050] Step 5: Divide the area according to the spatial coordinates of the statistical microscopic parameters. The size of the partition depends on the reliability calculation accuracy and the number of samples. It should be ensured that the sample can meet the parameter distribution characteristics of the area when the partition is small. Figure 3The KDE method is used to perform non-parametric estimation of the yarn cross-sectional area and obtain the probability density function of the cross-sectional area based on the real yarn. The probability distribution function obtained by the KDE method is given by Definition, where is the probability density function of the cross-sectional area, N is the number of samples of real yarn, h is the bandwidth selected for kernel density estimation, χ i is the cross-sectional area of ​​the real yarn sample, χ is an arbitrary cross-sectional area, K(·) represents the kernel function (Gaussian function is used in this example), and the bandwidth h is optimized by cross-validation or iteration. The obtained probability density function is as follows: Figure 4 shown.

[0051] Step 6: Response surface methodology was used to establish the structure performance function, and sampling points were selected at the mean cross-sectional area and 99.7% probability based on the Bucher sampling method and the 3σ principle.

[0052] The response surface function used in the response surface method is a quadratic polynomial, and its expression is: Among them, r(x) is the ultimate load that the area can withstand, x i are the cross-sectional areas of various yarns as random variables, b0 and b i The polynomial is the coefficient, and n is the number of yarn types. In order to obtain b0 and b in r(x) i The value of , select 2n+1 sample points X i Construct a set of equations to solve, sample point X i The selection method is: the mean sample point X0 (x1, x2, ..., x i ,…,x n )=(μ1,μ2,…,μ i ,…,μ n ), the remaining sample points X i (x1,x2,…,x i ,…,x n )=(μ1,μ2,…,μ i ±3σ i ,…,μ n ), μ i represents the mean cross-sectional area of ​​each type of yarn, σ i Represents the standard deviation of the cross-sectional area of ​​each type of yarn. According to the 3σ principle, μ i ±3σ i These correspond to samples with generation probabilities of 0.3% and 99.7% respectively.

[0053] In this example, n = 5, then

[0054]

[0055] Each area takes 2×5+1=11 sampling points, which are:

[0056] X0=(μ1,μ2,μ3,μ4,μ5)

[0057] X1=(μ1+3σ1,μ2,μ3,μ4,μ5) X6=(μ1-3σ1,μ2,μ3,μ4,μ5)

[0058] X2=(μ1,μ2+3σ2,μ3,μ4,μ5) X7=(μ1,μ2-3σ2,μ3,μ4,μ5)

[0059] X3=(μ1,μ2,μ3+3σ3,μ4,μ5) X8=(μ1,μ2,μ3-3σ3,μ4,μ5)

[0060] X4=(μ1,μ2,μ3,μ4+3σ4,μ5) X9=(μ1,μ2,μ3,μ4-3σ4,μ5)

[0061] X5=(μ1,μ2,μ3,μ4,μ5+3σ5) X 10 =(μ1,μ2,μ3,μ4,μ5-3σ5)

[0062] μ i represents the mean cross-sectional area of ​​each type of yarn, σ i Represents the mean cross-sectional area of ​​each type of yarn. Solve the limit load value r corresponding to each sample point separately i (x), substitute the 11 sample points into r(x) to form a system of equations, and solve them to obtain b0 and b i The value of .

[0063] Step 7: Perform finite element meshing on the microscopic model. The material direction 1 of the divided finite element mesh model should be along the axis of the yarn, and the directions 2 and 3 are perpendicular to the direction 1 and perpendicular to each other. Assuming that the ratio of the actual cross-sectional area of ​​the yarn to the average cross-sectional area is m, multiply the corresponding correction coefficient f(m) by the yarn material properties according to Table 1, and use the distribution of material properties to characterize the random distribution of the yarn cross-sectional area. The actual cross-sectional area is calculated according to the probability density function in step 5. Random sampling is performed, and the average cross-sectional area is obtained by averaging the sample points in each region.

[0064] Table 1 Material performance correction factors

[0065]

[0066] Step 8: Use the progressive damage method to perform finite element calculations on the blade crown structure to obtain the failure condition of the microscopic model under a given load.

[0067] Step 9: According to the JC method, first use the kernel density estimation The obtained probability density function is converted into an equivalent normal distribution. According to the structural performance function, the verification point method is used to calculate the failure probability of each area under a given load. The structural performance function g(x) = r(x) - S, where S is the load value in the corresponding direction. The verification point method calculates the reliability index β through successive iterations. Assume that the initial verification point x0 * =(μ1,μ2,…,μ i ,…,μ n ). By calculating its reliability index and direction cosine α i , update the verification point x * =(x1 * ,x2 * ,…,x n * ). When the convergence index is satisfied is the latest verification point, The verification point calculated in the previous iteration is terminated when ε reaches the minimum value, and the failure probability P corresponding to the regional reliability index β under the current load is found. f , the failure probability of each area can be obtained.

[0068] Step 10: By applying load to the entire blade crown structure, calculate the load borne by each area and its failure probability. Figure 5 shown.

[0069] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions based on the principles of the present invention are within the scope of protection of the present invention. It should be noted that for those skilled in the art, various improvements and modifications that do not depart from the principles of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A method for analyzing the reliability of a microstructure of a braided composite material, characterized in that: The following steps are involved: Step 1: Perform XCT scanning on the woven composite material structure to obtain a microscopic image inside the woven composite material structure. Step 2: Identify the yarns in the structure, number each yarn and group them according to yarn category, Step 3: Measure the microscopic geometric parameters of each group of yarns and record the spatial coordinates of the measured parameters to obtain a large number of parameter samples. Step 4: Establish a mesoscopic geometric model based on the average value of the mesoscopic geometric parameters. Step 5: Partition the yarns according to the spatial coordinates of the statistical microscopic parameters, and use the KDE method to perform non-parametric estimation of the yarn cross-sectional area in each region to obtain the probability density function of the cross-sectional area based on the real yarn. Step 6: Use response surface methodology to establish the structure function function of each region. Based on the Bucher sampling method and the 3σ principle, select sampling points at the mean cross-sectional area and the probability of 99.7%. Step 7: Perform finite element meshing on the microscopic model and assign material parameters to each region of the microscopic model based on the yarn performance equivalent method according to the sampling points. Step 8: Perform finite element calculations on each region to obtain the failure condition of the microscopic model under a given load. Step 9: Based on the structural performance function, the failure probability of each area under a given load is calculated using the verification point method. Step 10: By applying a load to the entire composite woven structure, the partial load borne by each area and its failure probability are calculated to complete the microstructure reliability analysis of the woven composite material.

2. A method for analyzing the microstructure reliability of a braided composite material according to claim 1, characterized in that: In step 1, the parameters of the XCT scan include imaging resolution, radiation voltage, tube current, and integration time. The requirement for the XCT scan is that the scanned image can display both the yarn profile and the yarn cross-section sample.

3. A method for analyzing the microstructure reliability of a braided composite material according to claim 2, characterized in that: In step 2, the yarn category includes yarn type, weaving process, weaving parameters and yarn brand, wherein the yarn type is warp or weft, the weaving process is two-dimensional weaving or three-dimensional weaving, and the weaving parameters include yarn strand number parameter and yarn density parameter.

4. A method for analyzing the microstructure reliability of a braided composite material according to claim 3, characterized in that: In step 3, image processing software is used to measure the microscopic geometric parameters of each group of yarns, and the yarn cross-section and axial direction are parametrically defined according to the degree of compression of the yarns.

5. A method for analyzing the microstructure reliability of a braided composite material according to claim 4, characterized in that: In step 5, the cross-sectional area probability density function based on the real yarn is obtained using the KDE method and is given by Obtain, among which, is the probability density function of the cross-sectional area, N is the number of samples of real yarn, h is the bandwidth selected for kernel density estimation, χ i is the cross-sectional area of ​​the real yarn sample, χ is an arbitrary cross-sectional area, K(·) represents the kernel function, and the bandwidth h is optimized by cross-validation or iteration method.

6. A method for analyzing the microstructure reliability of a braided composite material according to claim 5, characterized in that: In step 6, the response surface method is used to establish the structural function of each region. The structural function of each region is g(x) = r(x) - S, where S is the load value in the corresponding direction and r(x) is the ultimate load that the region can withstand. The expression is: Among them, x i are the cross-sectional areas of various yarns as random variables, b0 and b i are polynomial coefficients, n is the number of yarn types, in order to obtain b0 and b in r(x) i The value of , select 2n+1 sample points X i , sample point X i The selection method is: the mean sample point X0 (x1, x2, ..., x i ,…,x n )=(μ1,μ2,…,μ i ,…,μ n ), the remaining sample points X i (x1,x2,…,x i ,…,x n )=(μ1,μ2,…,μ i ±3σ i ,…,μ n ), μ i represents the mean cross-sectional area of ​​each type of yarn, σ i Represents the standard deviation of the cross-sectional area of ​​each type of yarn. According to the 3σ principle, μ i ±3σ i Corresponding to the samples with the probability of 0.3% and 99.7%, each sample point X i Substitute r(x) into the equation system and solve it to get b0 and b i The value of .

7. A method for analyzing the reliability of a braided composite material microstructure according to claim 6, characterized in that: In step 7, the 1st direction of the microscopic model for finite element mesh division is along the axis direction of the yarn, and the 2nd and 3rd directions are perpendicular to the 1st direction and perpendicular to each other. The specific method of assigning material parameters to each region of the microscopic model based on the method of equivalent yarn performance is as follows: Assume that the ratio of the actual cross-sectional area of ​​the yarn in a certain region of the microscopic model to the average cross-sectional area is m, multiply the corresponding correction coefficient f(m) by the yarn material property, and assign the material parameter of the region to the result. The distribution of material properties is used to characterize the random distribution of the yarn cross-sectional area, where the actual cross-sectional area is calculated according to the probability density function Random sampling is performed, and the average cross-sectional area is obtained by averaging the sample points in each region. The material properties include Young's modulus in 1 direction, stress-strain curve fitting coefficient in 1 direction, shear modulus in 12 planes, shear modulus in 13 planes, maximum tensile strain in 1 direction, maximum shear strain in 12 planes, and maximum shear strain in 13 planes. Among them, Young's modulus in 1 direction f(m)=m, stress-strain curve fitting coefficient in 1 direction f(m)=m, shear modulus in 12 planes f(m)=m 2 ,13 plane shear modulus f(m)=m 2 , the maximum tensile strain in the 1st direction The maximum shear strain in the 12th plane is f(m)=1 / m, and the maximum shear strain in the 13th plane is f(m)=1 / m.

8. A method for analyzing the microstructure reliability of a braided composite material according to claim 7, characterized in that: In step 9, according to the JC method, the kernel density estimation The obtained probability density function is transformed into an equivalent normal distribution, and then the failure probability of each area under a given load is calculated using the verification point method based on the structural performance function.

9. A method for analyzing the microstructure reliability of a braided composite material according to claim 8, characterized in that: In step 9, according to the structural function g(x) = r(x) - S, the verification point method calculates the reliability index β through successive iterations. Assume that the initial verification point x0 * =(μ1,μ2,…,μ i ,…,μ n ), by calculating its reliability index β x * and direction cosine α i , update the verification point x * =(x1 * ,x2 * ,…,x n * ), when the convergence index is satisfied is the latest verification point, The verification point calculated in the previous iteration is terminated when ε reaches the minimum value, and the failure probability P corresponding to the regional reliability index β under the current load is found. f , and obtain the failure probability of each region.

10. A method for analyzing the reliability of a braided composite material microstructure according to claim 9, characterized in that: The calculation formula is as follows: Where, is the mean value of the linear limit state equation obtained based on the current verification point, is the standard deviation of the linear limit state equation obtained based on the current verification point, is the mean of the i-th random variable, is the value of the i-th random variable in the current verification point, is the standard deviation of the ith random variable.

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