Method for acquiring constitutive curve of composite material by considering material dispersibility

Abstract

The invention belongs to the technical field of composite material mechanics, and provides a composite material constitutive curve obtaining method considering material dispersibility, and the method comprises the following steps: carrying out a static mechanical property test on a test piece, and obtaining a plurality of test stress-strain curves under given conditions; performing validity test on each test stress-strain curve, and removing invalid curves to obtain a test stress-strain curve set under the given condition; fitting and solving the constitutive model according to the test stress-strain curve set by adopting a gradient descent method to obtain characterization parameters; and adopting the characterization parameters, obtaining a composite material constitutive curve through a finite element method, and carrying out iterative correction on the composite material constitutive curve through the test stress-strain curve set until a final composite material constitutive curve is obtained. According to the method, the constitutive curve representing the composite material can be accurately obtained, and a foundation is laid for performance analysis of the composite material and high-fidelity simulation calculation of the composite material structure.

Description

Technical Field

[0001] This invention belongs to the field of composite material mechanics technology and relates to a method for obtaining constitutive curves of composite materials that takes into account material dispersion. Background Technology

[0002] The mechanical properties of composite materials exhibit a certain degree of dispersion due to variations in manufacturing processes, the randomness of component material properties, and the uncertainty of internal defects. Constitutive modeling is one of the most critical mechanical properties of composite materials, and this dispersion significantly limits performance analysis and simulation calculations of composite structures. The constitutive curve of a composite material is essential performance data for its engineering applications; its absence would hinder these applications. Therefore, it is crucial to determine a constitutive curve that accurately reflects the true strain-strain relationship while considering material dispersion. Consequently, a method for evaluating the constitutive curve of composite materials that considers material dispersion must be found.

[0003] Currently, two methods are commonly used in engineering. The first method involves selecting a representative stress-strain curve from multiple experimental curves based on experience as the constitutive curve for the composite material. This method heavily relies on individual cognitive abilities, and the results selected by different individuals vary, thus it lacks widespread acceptance. The second method involves averaging the stress at the same strain point from multiple experimental curves. This method is widely used in engineering and scientific research; however, it is only suitable for stress-strain curves without abrupt changes in stage. For most composite materials, after failure, they transition from the damage stage to the degradation stage, resulting in a sharp drop in the stress-strain curve. In such cases, averaging the stress at the same strain point from multiple experimental curves will not yield an accurate constitutive curve for the composite material. Summary of the Invention

[0004] To address the technical problem that existing methods cannot obtain accurate constitutive curves characterizing composite materials, this invention discloses a method for obtaining constitutive curves of composite materials considering material dispersion. The method includes the following steps: S1. Conduct static mechanical property tests on the test specimens and obtain multiple stress-strain curves under given conditions; S2. Perform validity checks on each of the aforementioned test stress-strain curves, and eliminate invalid curves to obtain the set of test stress-strain curves under the given conditions; S3. Using the gradient descent method, the constitutive model is fitted and solved according to the set of experimental stress-strain curves to obtain the characterization parameters. S4. Using the characterization parameters, obtain the constitutive curve of the composite material through the finite element method, and iteratively correct the constitutive curve of the composite material through the experimental stress-strain curve set until the final constitutive curve of the composite material is obtained.

[0005] Furthermore, in step S1, the set conditions include temperature and ambient atmosphere, and the static mechanical property test includes any one of tensile test, compression test and shear test.

[0006] Further, in step S2, the validity of each of the test stress-strain curves is checked, and invalid curves are removed to obtain the set of test stress-strain curves under the given conditions, including: S21. Obtain the mechanical property parameters of each of the test stress-strain curves, including the initial modulus, tensile strength, and maximum strain; S22. The validity of each mechanical performance parameter is tested according to the Z-score standardization method and aggregate classification analysis. The curves that fail the test are defined as invalid curves. After removing the invalid curves, the set of test stress-strain curves under the given conditions is obtained.

[0007] Further, in step S3, the gradient descent method is used to fit and solve the constitutive model based on the set of experimental stress-strain curves to obtain the characterization parameters, including: S31. For each test stress-strain curve in the set of test stress-strain curves, obtain the set of secant moduli under different stress levels by means of the secant method; S32. The characterization parameters of each of the experimental stress-strain curves are obtained by solving the constitutive model using the gradient descent method and each set of secant moduli.

[0008] Furthermore, in step S3, the expression for the constitutive model is: , where E and The initial modulus and strain, A and m, are obtained from the experimental stress-strain curves, respectively. f σ p ε0 and ε0 are both characterization parameters. For the natural constant e An exponential function with base 0. For stress.

[0009] Further, in step S4, the constitutive curve of the composite material is obtained using the aforementioned characterization parameters through the finite element method, including: S41. Mesh the established finite element model of the test piece and randomly select characterization parameters for each mesh using the roulette wheel method. S42. The effectiveness of the characterization parameters assigned to each grid is tested and corrected. The relationship between strain and stress is obtained by simulation test through the tested and corrected characterization parameters, and the constitutive curve of composite material characterization is obtained.

[0010] Furthermore, in step S42, the validity of the characterization parameters assigned to each grid is checked and corrected, including: S421. Select multiple cross sections at equal intervals on the finite element model of the test piece, and count the proportion of each characterization parameter assigned to the mesh in each cross section. S422. Calculate the ratio difference between the largest and smallest grids in each section. If the ratio difference is less than the threshold, the characterization parameter assigned to the grid is considered valid. If the ratio difference is greater than or equal to the threshold, the characterization parameter assigned to the grid is considered invalid. Correct the invalid characterization parameter.

[0011] Further, in step S4, the constitutive curve of the composite material is iteratively corrected using the set of experimental stress-strain curves until the final constitutive curve of the composite material is obtained, including: S43. The set of experimental stress-strain curves and the constitutive curves of the composite material are fitted and solved by the gradient descent method to obtain the first new characterization parameter. The first new characterization parameter is used to obtain the first new constitutive curve of the composite material by the finite element method. S44. The set of experimental stress-strain curves and the constitutive curve of the first new composite material are used to fit and solve the constitutive model using the gradient descent method to obtain the second new characterization parameters. The second new characterization parameters are then used to obtain the constitutive curve of the second new composite material through the finite element method. S45. Calculate the Euclidean distance R1 between the constitutive curve of the composite material and the constitutive curve of the first new composite material, and the Euclidean distance R2 between the constitutive curve of the first new composite material and the constitutive curve of the second new composite material, for the characterizing parameters. Then the constitutive curve of the second new composite material is taken as the final constitutive curve of the composite material.

[0012] The present invention provides a method for obtaining constitutive curves of composite materials that takes into account the dispersion of materials. This method fully considers the dispersion of composite materials and can obtain constitutive curves that characterize composite materials relatively accurately, laying the foundation for performance analysis of composite materials and high-fidelity simulation calculations of composite material structures. Attached Figure Description

[0013] To more clearly illustrate the technical solutions of the embodiments of this application, the drawings used in the embodiments will be briefly introduced below. Obviously, the drawings described below are only some embodiments of this application. For those skilled in the art, other drawings can be obtained based on these drawings without creative effort.

[0014] Figure 1 This is a flowchart of the method for obtaining constitutive curves of composite materials considering material dispersion according to the present invention; Figure 2 The experimental stress-strain curves of this invention and the constitutive curves obtained by conventional methods are used. Figure 3 A chart for evaluating the number of categories; Figure 4 This is a classification diagram of standardized parameters; Figure 5 This is the final constitutive curve of the composite material obtained by the method of the present invention. Detailed Implementation

[0015] The embodiments of this application will now be described in detail with reference to the accompanying drawings.

[0016] The following specific examples illustrate the implementation of this application. Those skilled in the art can easily understand other advantages and effects of this application from the content disclosed in this specification. Obviously, the described embodiments are only a part of the embodiments of this application, and not all of them. This application can also be implemented or applied through other different specific embodiments, and the details in this specification can also be modified or changed based on different viewpoints and applications without departing from the spirit of this application. It should be noted that, in the absence of conflict, the following embodiments and features of the embodiments can be combined with each other. Based on the embodiments in this application, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of this application.

[0017] This invention discloses a method for obtaining constitutive curves of composite materials considering material dispersion. See [link to relevant documentation]. Figure 1 As shown, the method includes the following steps: S1. Conduct static mechanical property tests on the test specimens and obtain multiple stress-strain curves under given conditions; S2. Perform validity checks on each of the aforementioned test stress-strain curves, and eliminate invalid curves to obtain the set of test stress-strain curves under the given conditions; S3. Using the gradient descent method, the constitutive model is fitted and solved according to the set of experimental stress-strain curves to obtain the characterization parameters. S4. Using the characterization parameters, obtain the constitutive curve of the composite material through the finite element method, and iteratively correct the constitutive curve of the composite material through the experimental stress-strain curve set until the final constitutive curve of the composite material is obtained.

[0018] Further, in step S1, the set conditions include temperature and ambient atmosphere, and the static mechanical property test includes any one of tensile test, compression test, and shear test. The shear test is achieved by constraining one side of a double-notched specimen while applying a tensile load to the other side, and the compression test is achieved by constraining one side while applying a compressive load to the other side.

[0019] When conducting static mechanical property tests, multiple identical test specimens are used to perform n≥5 parallel tests under given conditions to obtain at least 5 test stress-strain curves.

[0020] Further, in step S2, the validity of each of the test stress-strain curves is checked, and invalid curves are removed to obtain the set of test stress-strain curves under the given conditions, including: S21. Obtain the mechanical property parameters for each of the test stress-strain curves. The mechanical property parameters include the initial modulus, tensile strength, and maximum strain, wherein the initial modulus E corresponds to the slope of the test stress-strain curve; the tensile strength corresponds to the stress σ at which the test specimen breaks. bt The maximum strain corresponds to the stress σ. bt Response in time.

[0021] S22. The validity of each mechanical performance parameter is tested using the Z-score standardization method and aggregate classification analysis. Parameters that fail the test are defined as invalid curves. After removing the invalid curves, the set of test stress-strain curves under the given conditions is obtained. Specifically, this includes the following steps: S221. Calculate the average value and standard deviation of each mechanical property parameter in all test specimens: Analyze the stress-strain curves of the tests to obtain the value of a specific mechanical property parameter. X of n Group experimental data X i ( i = 1, 2,…, n This allows for the calculation of the mechanical performance parameters. X of n The average value of the group of experimental data with standard deviation : ; ; Among them, Z-score standardization is used to... X iThe specific method for converting to a distribution with a mean of 0 and a standard deviation of 1 is as follows: ;in: This represents the data before the i-th transformation of the mechanical performance parameter X. This is the standardized data of the i-th mechanical performance parameter among the X-th parameters.

[0022] S222. Cluster the standardized data and select the group with the most curves as the true data: (1) Determine the optimal number of classification groups. The method for determining the optimal number of classification groups is as follows: (11) Select the number of classification groups k ; (12) Randomly select a sample as the first classification center c 1; (13) Calculate the shortest distance between each sample and the current existing cluster center (i.e., the distance to the nearest cluster center), using... D ( x This indicates that the larger the value, the greater the probability of being selected as a cluster center; (14) Select the next classification center using the roulette wheel method; (15) Repeat steps (13) to (14) until selected. k One classification center; (16) For each sample in the dataset x i Calculate it to k The distance between each cluster center is used to assign the cluster to the cluster center with the smallest distance. (17) For each category M Recalculate its classification center ; (18) Repeat steps (16) to (17) until the classification center no longer changes; (19) Calculate the number of classification groups k The silhouette coefficient (SC) and the Davis-Bourdin index (DBI) under the following conditions. (110) Regarding the number of classification groups k =1~5, repeat steps 1~9 above, and select the value corresponding to the maximum silhouette coefficient and the minimum Davis-Bourdin exponent. k , as the optimal number of classification groups; The method for calculating the contour coefficient is as follows: a) For each sample point i Its contour coefficient is written as: ;in, a ( i (Refers to sample)i The average distance to other samples in the same dataset. b ( i (Refers to sample) i The minimum distance to other samples in the same dataset.

[0023] b) The silhouette coefficient of the entire dataset is the average of all sample points.

[0024] The Davis-Bourdin index is calculated as follows: ; N It is the number of categories. S i It is the first i Elements in class up to the first i The Euclidean distance between the centers of each class, || w i - w j || is the first i and the j The Euclidean distance between the centers of each class.

[0025] (2) If the number of optimal classification groups is greater than or equal to 2, select the group with the larger amount of data as the real data and remove the data from the other groups.

[0026] Further, in step S3, the gradient descent method is used to fit and solve the constitutive model based on the set of experimental stress-strain curves to obtain the characterization parameters, including: S31. For each test stress-strain curve in the set of test stress-strain curves, obtain the set of secant moduli under different stress levels by means of the secant method; S32. The characterization parameters of each of the experimental stress-strain curves are obtained by solving the constitutive model using the gradient descent method and each set of secant moduli.

[0027] Furthermore, in step S3, the expression for the constitutive model is: , where E and The initial modulus and strain, A and m, are obtained from the experimental stress-strain curves, respectively. f σ p ε0 and ε0 are both characterization parameters. For the natural constant e An exponential function with base 0. Let be the stress, where σ p It can also be called the proportional limit, which is obtained by translating the initial linear segment of the test stress-strain curve in the positive direction of the strain axis to obtain a new line segment, and then obtaining the ordinate of the intersection point of the extension line of the new line segment and the test stress-strain curve.

[0028] Further, in step S4, the constitutive curve of the composite material is obtained using the aforementioned characterization parameters through the finite element method, including: S41. Mesh the established finite element model of the test piece and randomly select characterization parameters for each mesh using the roulette wheel method. S42. The effectiveness of the characterization parameters assigned to each grid is tested and corrected. The relationship between strain and stress is obtained by simulation test through the tested and corrected characterization parameters, and the constitutive curve of composite material characterization is obtained.

[0029] Furthermore, in step S42, the validity of the characterization parameters assigned to each grid is checked and corrected, including: S421. Select multiple cross sections at equal intervals on the finite element model of the test piece, and count the proportion of each characterization parameter assigned to the mesh in each cross section. S422. Calculate the ratio difference between the largest and smallest grids in each section. If the ratio difference is less than the threshold, the characterization parameter assigned to the grid is considered valid. If the ratio difference is greater than or equal to the threshold, the characterization parameter assigned to the grid is considered invalid. Correct the invalid characterization parameter.

[0030] Further, in step S4, the constitutive curve of the composite material is iteratively corrected using the set of experimental stress-strain curves until the final constitutive curve of the composite material is obtained, including: S43. The set of experimental stress-strain curves and the constitutive curves of the composite material are fitted and solved by the gradient descent method to obtain the first new characterization parameter. The first new characterization parameter is used to obtain the first new constitutive curve of the composite material by the finite element method. S44. The set of experimental stress-strain curves and the constitutive curve of the first new composite material are used to fit and solve the constitutive model using the gradient descent method to obtain the second new characterization parameters. The second new characterization parameters are then used to obtain the constitutive curve of the second new composite material through the finite element method. S45. Calculate the Euclidean distance R1 between the constitutive curve of the composite material and the constitutive curve of the first new composite material, and the Euclidean distance R2 between the constitutive curve of the first new composite material and the constitutive curve of the second new composite material, for the characterizing parameters. Then the constitutive curve of the second new composite material is taken as the final constitutive curve of the composite material.

[0031] The present invention provides a method for obtaining constitutive curves of composite materials that takes into full account the dispersion of composite materials. This invention can obtain constitutive curves characterizing composite materials with relatively high accuracy, laying the foundation for performance analysis of composite materials and high-fidelity simulation calculations of composite material structures.

[0032] The present invention illustrates the method for obtaining constitutive curves of composite materials considering material dispersion through the following examples: Step 1: Perform quasi-static tensile tests on 5 identical SiC / SiC composite specimens to obtain the following results. Figure 2 The five test stress-strain curves are shown in Table 1. The mechanical property parameters of the test stress-strain curves are shown in Table 2 after standardization.

[0033] Table 1: Mechanical property parameters of SiC / SiC composite specimens

[0034] Table 2: Standardized mechanical properties of SiC / SiC composite specimens

[0035] The above five sets of data were classified, and the optimal number of classifications was evaluated as follows: Figure 3 As shown, the optimal number of categories is 3, and the classification results at this point are as follows. Figure 4 As shown, Figure 4 As shown in the figure, green represents valid data, corresponding to group 2, group 4, and group 5 in Table 1.

[0036] For the remaining three sets of data, the constitutive model was fitted respectively, and the results are shown in Table 3 below: Table 3: Parameter values ​​for each curve fitting

[0037] The above curve fitting parameters were arbitrarily extracted and applied to the constitutive curves of all meshes for the established tensile analysis model. One side of the tensile analysis model was fixed with a constraint plate, and a tensile load was applied to the other side for simulation experiments. The final constitutive curves were obtained as follows: Figure 5 As shown.

[0038] Obviously, those skilled in the art should understand that the above description is merely a preferred embodiment of the present invention and is not intended to limit the present invention. Various modifications and variations of the embodiments of the present invention are possible for those skilled in the art. Any modifications, equivalent substitutions, improvements, etc., made within the spirit and principles of the present invention should be included within the protection scope of the present invention.

Claims

1. A method for obtaining constitutive curves of composite materials considering material dispersion, characterized in that, include: Static mechanical property tests were conducted on the test specimens to obtain multiple stress-strain curves under given conditions; The validity of each of the aforementioned test stress-strain curves is verified, and invalid curves are eliminated to obtain the set of test stress-strain curves under the given conditions; The gradient descent method is used to fit and solve the constitutive model based on the set of experimental stress-strain curves to obtain the characterization parameters. Using the aforementioned characterization parameters, the constitutive curve of the composite material is obtained through the finite element method. The constitutive curve of the composite material is then iteratively corrected using the set of experimental stress-strain curves until the final constitutive curve of the composite material is obtained.

2. The method for obtaining constitutive curves of composite materials considering material dispersion according to claim 1, characterized in that, The set conditions include temperature and ambient atmosphere, and the static mechanical property test includes any one of tensile test, compression test and shear test.

3. The method for obtaining constitutive curves of composite materials considering material dispersion according to claim 1, characterized in that, The validity of each of the aforementioned test stress-strain curves is verified, and invalid curves are removed to obtain the set of test stress-strain curves under the given conditions, including: Obtain the mechanical property parameters for each of the test stress-strain curves, including initial modulus, tensile strength, and maximum strain; The validity of each mechanical performance parameter is tested using the Z-score standardization method and aggregate classification analysis. Curves that fail the test are defined as invalid curves. After removing the invalid curves, the set of test stress-strain curves under the given conditions is obtained.

4. The method for obtaining constitutive curves of composite materials considering material dispersion according to claim 1, characterized in that, The gradient descent method is used to fit the constitutive model to obtain the characterization parameters, including: For each test stress-strain curve in the set of test stress-strain curves, the secant modulus set under different stress levels is obtained by the secant method; The characterization parameters of each of the experimental stress-strain curves are obtained by solving the constitutive model using the gradient descent method and each set of secant moduli.

5. The method for obtaining constitutive curves of composite materials considering material dispersion according to claim 1 or 3, characterized in that, The expression for the constitutive model is: ,in, E and The initial modulus and strain, A and m, are obtained from the experimental stress-strain curves, respectively. f σ p ε0 and ε0 are both characterization parameters. For the natural constant e An exponential function with base 0. For stress.

6. The method for obtaining constitutive curves of composite materials considering material dispersion according to claim 1, characterized in that, Using the aforementioned characterization parameters, the constitutive curve of the composite material is obtained through the finite element method, including: The established finite element model of the test piece was meshed, and the characterization parameters were randomly selected and assigned to each mesh using the roulette wheel method. The effectiveness of the characterization parameters assigned to each grid is tested and corrected. The relationship between strain and stress is obtained through simulation experiments using the tested and corrected characterization parameters, and the constitutive curve of the composite material is obtained.

7. The method for obtaining constitutive curves of composite materials considering material dispersion according to claim 6, characterized in that, The validity of the characterization parameters assigned to each grid is checked and corrected, including: Multiple cross sections are selected at equal intervals on the finite element model of the test piece, and the proportion of each characterization parameter assigned to the mesh in each cross section is statistically analyzed. Calculate the ratio difference between the largest and smallest grids in each cross section. If the ratio difference is less than a threshold, the characterization parameters assigned to the grid are considered valid. If the ratio difference is greater than or equal to the threshold, the characterization parameters assigned to the grid are considered invalid. Correct the invalid characterization parameters.

8. The method for obtaining constitutive curves of composite materials considering material dispersion according to claim 1, characterized in that, The constitutive curve of the composite material is iteratively corrected by the set of experimental stress-strain curves until the final constitutive curve of the composite material is obtained, including: The set of experimental stress-strain curves and the constitutive curves of the composite material are used to fit and solve the constitutive model using the gradient descent method to obtain the first new characterization parameters. Using the first new characterization parameters, the first new constitutive curves of the composite material are obtained through the finite element method. The set of experimental stress-strain curves and the constitutive curve of the first new composite material are used to fit and solve the constitutive model using the gradient descent method to obtain the second new characterization parameters. The second new characterization parameters are then used to obtain the constitutive curve of the second new composite material through the finite element method. Calculate the Euclidean distance R1 between the constitutive curve of the composite material and the constitutive curve of the first new composite material, and the Euclidean distance R2 between the constitutive curve of the first new composite material and the constitutive curve of the second new composite material, for the characteristic parameters. Then the constitutive curve of the second new composite material is taken as the final constitutive curve of the composite material.

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