Theoretical prediction and verification method for thermal expansion coefficient of composite 2D fabric

Abstract

The invention provides a theoretical prediction and verification method for a thermal expansion coefficient of a composite material 2D fabric, and the method comprises the steps: extracting a circulation structure in the composite material 2D fabric, and building an RVE model; predicting x-direction and y-direction thermal expansion coefficients of the RVE model, and predicting z-direction thermal expansion coefficients of the RVE model; establishing an RVE finite element numerical model based on the actual geometric dimension and the weaving structure of the composite material fabric, performing simulation analysis, and verifying an analytical solution; an RVE finite element model is established according to weaving structure parameters of the composite material fabric, a thermal expansion coefficient numerical solution is obtained through finite element simulation calculation, the prediction trend of the numerical solution and the prediction trend of an analytical solution are consistent, the error is within 2%, the prediction precision of an APTC method is verified, and the accuracy of the method is proved. The method can rapidly predict the thermal expansion coefficient of the composite material, reduces the cost, and improves the efficiency of scientific research and production.

Description

Technical Field

[0001] The present application belongs to the technical field of composite material design and curing deformation, and specifically relates to a theoretical prediction and verification method for the thermal expansion coefficient of a composite material 2D fabric. Background Art

[0002] As an advanced structural material, composite fabrics have been widely developed and applied in modern high-tech fields such as aerospace, automobiles, and sports. The main reason is that they have good dimensional stability and durability in special environments such as temperature fields. In particular, by selecting matrices and fibers with different properties and adjusting fiber weaving parameters, fiber volume content and other factors, a zero thermal expansion structure in a specific direction can be made, which shows unique advantages in high-precision engineering technologies such as precision instruments and aerospace.

[0003] The thermal expansion coefficient of a material is a very important performance parameter. It is generally believed that the thermal expansion coefficient of a composite material is related to factors such as the type of resin, fiber, curing agent, the volume fraction ratio of each component, and the interface condition.

[0004] In previous studies, the thermal expansion performance of composite laminates was studied using classical laminate theory and the law of mixtures, and the theoretical calculation results were compared with the experimental values, which preliminarily explained the influence of the ply conditions on the thermal expansion coefficient of the laminate. However, the use of classical laminate theory to predict the thermal expansion coefficient is inaccurate in the thickness direction.

[0005] Other scholars have used numerical methods and experiments to study the thermal expansion coefficient, and found that the thermal expansion behavior is interdependent with the fiber weaving pattern and fiber volume content. They have established a test system and numerical prediction model for the thermal expansion performance of composite specimens. The comparison between numerical solutions and experimental solutions has verified the feasibility and correctness of the numerical prediction method, but no theoretical prediction model has been given. The prediction of thermal expansion coefficient based on the self-consistent method of micromechanics is currently limited to single-layer plates, and there is a lack of theoretical prediction and verification methods for the thermal expansion coefficient of composite fabrics. Summary of the invention

[0006] Purpose of the invention: In order to solve the above-mentioned technical problems, the present invention takes composite material 2D fabric as the object, establishes a representative volume element (RVE) model, uses the mesomechanical self-consistent method to derive the theoretical formula of the thermal expansion coefficient, and verifies it through a finite element numerical model.

[0007] In a first aspect, the present application provides a method for theoretically predicting and verifying the thermal expansion coefficient of a composite material 2D fabric, the method comprising:

[0008] Extract the cyclic structure in the composite 2D fabric and establish the RVE model;

[0009] Predict the thermal expansion coefficients of the RVE model in the x-direction and y-direction, and predict the thermal expansion coefficient of the RVE model in the z-direction;

[0010] Based on the actual geometric dimensions and weaving structure of the composite fabric, a finite element numerical model of RVE is established, and simulation analysis is carried out to verify the analytical solution.

[0011] Preferably, extracting the cyclic structure in the composite material 2D fabric and establishing the RVE model comprises:

[0012] The composite 2D fabric is composed of warp yarn, weft yarn and resin matrix, and the RVE model is extracted in the loop structure.

[0013] Preferably, the predicting of the thermal expansion coefficients of the RVE model in the x-direction and the y-direction includes:

[0014] The thermal expansion coefficients α1 and α2 in the x- and y-directions in the plane are derived through the stress equilibrium equation and the deformation coordination equation.

[0015] Preferably, the derivation of the thermal expansion coefficients α1 and a2 in the x-direction and y-direction in the plane through the stress balance equation and the deformation coordination equation includes:

[0016] On the cross section of the composite material 2D fabric RVE model in the x direction, the following equation is established based on the stress balance equation:

[0017] σ 1j S 1j +σ 1w S 1w +σ 1m S 1m =0 (1)

[0018] Among them, σ 1，j is the stress on the warp yarn in the cross section, σ 1w is the stress on the weft yarn in the cross section, σ 1m is the stress on the resin in the cross section, S 1j is the sum of the transverse cross-sectional areas of the warp yarns, S 1w is the sum of the longitudinal cross-sectional areas of the weft yarns, S 1m is the sum of the cross-sectional areas of the resin;

[0019] In the weaving structure of common composite 2D fabrics, the warp density and weft density are equal, that is, the length and width are equal, the number of warp yarns is n, the major axis length of the elliptical cross section of the yarn is l, the minor axis length is h, S 1j and S 1w It can be calculated as:

[0020]

[0021] In S1j , S 1w and S 1m From the deformation coordination equation, we can get:

[0022]

[0023] Where α1 is the thermal expansion coefficient of the composite 2D fabric in the x direction; the yarn is transversely isotropic, and α 1f is the yarn longitudinal thermal expansion coefficient, α 2f is the yarn transverse thermal expansion coefficient, E 1f is the longitudinal elastic modulus of the yarn, E 2f is the transverse elastic modulus of the yarn; the resin is isotropic, α m is the thermal expansion coefficient of the resin, E m is the elastic modulus of the resin;

[0024] Combine the three equations in equation (3):

[0025] α2·ΔT·(E 2f S 2j +E 2f S 2w +E m S 2m )=(α 1f E 1f S 1f +α 2f E 2f S 1w +α m E m S 1m )·ΔT+σ 1i S 1i +σ 1w S 1w +α 1m S 1m (4)

[0028] Combined with formula (1), the thermal expansion coefficient α1 of the composite 2D fabric in the x direction can be obtained:

[0029]

[0030] The yarn and resin are evenly distributed. In the composite 2D fabric RVE model, the cross-sectional area S of the warp, weft and resin can be i Approximately converted to volume fraction V i ;

[0031]

[0032] Where S is the cross-sectional area of ​​RVE, V 1j is the warp volume fraction, V1w is the weft volume fraction, V m is the resin volume fraction, V f is the fiber volume fraction.

[0033] Substituting equation (6) into equation (5), we can approximately obtain α1 as:

[0034]

[0035] Considering the weaving structure parameters, the yarn density ρ, in units of roots / cm; the yarn width l, in units of cm. The width b of the composite 2D fabric RVE model is related to the yarn density ρ:

[0036]

[0037] The bandwidth ratio k is introduced, which means the ratio of the total bandwidth nl of the warp yarn to the RVE width b in the cross section of the RVE model of the composite 2D fabric in the x direction, and is dimensionless.

[0038]

[0039] Substituting equations (8) and (9) into equation (7), we can obtain the simplified α1:

[0040]

[0041] Consider further simplifying the introduced k to obtain a formula that is easier to generalize and apply; consider from two aspects, first, from the perspective of RVE geometric relationship, k≤1; second, from the physical meaning of bandwidth ratio, k≤1; in general, it can be considered that k=1, then α1 can be further simplified:

[0042]

[0043] When the warp density is equal to the weft density, the composite 2D fabric is transversely isotropic in the xOy plane, and the thermal expansion coefficients in the x and y directions are considered to be equal;

[0044]

[0045] Preferably, the predicting of the thermal expansion coefficient of the RVE model in the z direction comprises:

[0046] The thermal expansion coefficient α3 in the z direction is derived from the Poisson effect.

[0047] Preferably, the z-direction thermal expansion coefficient α3 is derived from the Poisson effect, comprising:

[0048] For the composite material 2D fabric RVE model in the z direction, considering the Poisson effect, we can get:

[0049]

[0050] Among them, α zj represents the thermal expansion coefficient of the warp yarn in the z direction, αz w represents the thermal expansion coefficient of the weft yarn in the z direction, α zm Indicates the thermal expansion coefficient of the resin in the z direction, α 2f is the fiber transverse thermal expansion coefficient, α 1f is the longitudinal thermal expansion coefficient of the fiber, α m is the thermal expansion coefficient of the resin, v 1Ef and v 2Ef is the Poisson's ratio of the fiber, v m is the Poisson’s ratio of the resin;

[0051]

[0052] Among them, α 1z represents the influence of α1 on α3 in the z direction, α 2z represents the influence of α2 on α3 in the z direction;

[0053] α3=(α zj +α wz +α zm )-(α 1z +α 2z ) (15)

[0054] Substituting equation (13) and equation (14) into equation (15), we obtain α3:

[0055]

[0056] Preferably, the method of establishing a RVE finite element numerical model based on the actual geometric dimensions and weaving structure of the composite fabric, performing simulation analysis, and verifying the analytical solution includes:

[0057] S4.1. Observe the interlayer structure of the composite fabric after curing under a microscope, and measure the average thickness of a single layer of prepreg cured and the average thickness of a single yarn;

[0058] S4.2. Use Digimat software to establish the geometric model of yarn and fabric based on the extracted structural parameters;

[0059] S4.3. Import the established geometric model into the Abaqus finite element analysis software to establish a finite element analysis numerical model of the composite material plain fabric; divide the grids for the resin matrix, warp yarn, and weft yarn respectively; set the temperature range to increase the temperature, and assign the material parameter performance to the model;

[0060] S4.4. Calculate the numerical solution of thermal expansion coefficient through simulation results;

[0061] S4.5. Compare the numerical solution of the coefficient of thermal expansion with the analytical solution to verify the accuracy of the analytical solution.

[0062] Preferably, calculating the numerical solution of the coefficient of thermal expansion through simulation results comprises:

[0063] The initial length of each side of RVE is L i , finite element simulation calculation of the elongation ΔL of each side after heating ΔT t , α is calculated by the definition of thermal expansion coefficient i :

[0064]

[0065] Beneficial technical effects of this application:

[0066] The analytical prediction formula for the thermal expansion coefficient of composite fabrics established by the present invention fills the technical gap in the theoretical research field. This technical solution uses a micromechanical self-consistent method to quickly predict the thermal expansion coefficient of composite fabrics based on the performance parameters of the component materials, and can verify the accuracy of the analytical solution through a finite element simulation model.

[0067] In actual production applications, the technical solution established by the present invention can reduce the test of thermal expansion coefficient of composite materials, control project costs, shorten project cycles, improve the efficiency of scientific research and production, and obtain reliable thermal expansion coefficient of materials. In terms of simulation design, the present invention is conducive to the finite element analysis of composite material structure design stage, and can accurately provide the thermal expansion coefficient of composite fabric. At the same time, it is also helpful to study the problem of curing deformation caused by inconsistent thermal expansion coefficients of component materials, and provide theoretical support for the prediction and control of curing deformation. BRIEF DESCRIPTION OF THE DRAWINGS

[0068] Figure 1 is a flow chart of the present invention;

[0069] Figure 2 It is the composite material 2D fabric RVE model and its microstructure diagram in the technical solution of the present invention;

[0070] Figure 3 It is the RVE model of the composite material plain fabric in the example and its microstructure diagram;

[0071] Figure 4 is the interlayer metallographic micrograph of the AC531 / CF8611 plain weave fabric after curing in the example;

[0072] Figure 5 is a metallographic micrograph of the yarn thickness of AC531 / CF8611 plain weave fabric in the example;

[0073] Figure 6 It is a schematic diagram of the actual geometric model of AC531 / CF8611 in the example;

[0074] Figure 7 It is the RVE finite element model and boundary constraints in the example. DETAILED DESCRIPTION

[0075] See also Figure 1-Figure 7 Taking AC531 / CF8611 carbon fiber prepreg plain fabric as an example, the present invention first uses the established APTC method to predict the analytical solution of the thermal expansion coefficient, then establishes a geometric model according to the actual geometric dimensions and weaving structure parameters, and finally establishes a finite element numerical model through Abaqus simulation analysis software, and compares and verifies the obtained thermal expansion numerical solution with the analytical solution to prove the accuracy of the APTC method. The specific steps are as follows:

[0076] S1. The cyclic structure was extracted from the composite plain fabric AC531 / CF8611, the RVE model was established, and the calculation formula of the thermal expansion coefficient in the x direction of the RVE model was derived.

[0077] S1.1. Composite material plain fabric AC531 / CF8611 is composed of warp yarn, weft yarn and resin matrix. The RVE model is extracted in the loop structure, such as Figure 3 .

[0078] S1.2. On the cross section of the RVE model of the composite material plain fabric in the x direction, the following equation is established based on the stress equilibrium equation:

[0079] σ 1f S 1j +σ 1w S 1w +σ 1m S 1m =0 (1)

[0080] Among them, σ 1j is the stress on the warp yarn in the cross section, σ 1w is the stress on the weft yarn in the cross section, σ 1m is the stress on the resin in the cross section, S 1j is the sum of the transverse cross-sectional areas of the warp yarns, S 1w is the sum of the longitudinal cross-sectional areas of the weft yarns, S 1m It is the sum of the cross-sectional areas of the resin.

[0081] S1.3. In the weaving structure of composite plain fabric, the warp density and weft density are equal, that is, the length and width are equal. The number of warp yarns is 2, and the length of the major axis of the elliptical cross section of the yarn is l, and the length of the minor axis is h. 1j and S 1w It can be calculated as:

[0082]

[0083] S1.4. In S 1j , S 1w and S 1m From the deformation coordination equation, we can get:

[0084]

[0085] Where α1 is the thermal expansion coefficient of the composite plain fabric in the x direction; the yarn is transversely isotropic, α 1j is the yarn longitudinal thermal expansion coefficient, α 2f is the yarn transverse thermal expansion coefficient, E 1f is the longitudinal elastic modulus of the yarn, E 2f is the transverse elastic modulus of the yarn; the resin is isotropic, α m is the thermal expansion coefficient of the resin, E m is the elastic modulus of the resin.

[0086] S1.5. Combine the three equations in equation (3):

[0087] α1·ΔT·(E 1f S 1j +E 2f S 1w +E m S 1m )=(α 1f E 1f S 1j +α 2f E 2f S 1w +α m E m Sσ 1w S 1w +σ 1m S 1m (4)

[0088] Combined with formula (1), the thermal expansion coefficient α1 of the composite material plain fabric in the x direction can be obtained:

[0089]

[0090] S1.6. The yarn and resin are evenly distributed. In the RVE model of composite plain fabric, the cross-sectional area S of the warp, weft and resin can be i Approximately converted to volume fraction V i .

[0091]

[0092] Where S is the cross-sectional area of ​​RVE, V 1j is the warp volume fraction, V 1w is the weft volume fraction, V m is the resin volume fraction, V f is the fiber volume fraction.

[0093] Substituting equation (6) into equation (5), we can approximately obtain α1 as:

[0094]

[0095] S1.7. Considering the weaving structure parameters, the yarn density ρ, the unit is the number of roots / cmm ; Yarn width l, unit is c m The width b of the RVE model of the composite plain fabric is related to the yarn density ρ:

[0096]

[0097] The bandwidth ratio k is introduced, and its meaning is expressed in the cross section of the composite 2D fabric RVE model in the x direction, as follows: Figure 1 , the ratio of the total bandwidth of the warp yarn 2l to the RVE width b, dimensionless.

[0098]

[0099] Substituting equations (8) and (9) into equation (7), we can obtain the simplified α1:

[0100]

[0101] S1.8. Consider further simplifying the introduced k to obtain a formula that is easier to generalize and apply. Consider from two aspects: first, from the perspective of RVE geometric relationship, k≤1; second, from the physical meaning of bandwidth ratio, k≤1 can also be obtained. In general, it can be considered that k=1, and α1 can be further simplified:

[0102]

[0103] When the warp yarn density is equal to the weft yarn density, the composite plain fabric has transverse isotropy in the xOy plane, and the thermal expansion coefficients in the x direction and the y direction are considered to be equal.

[0104]

[0105] S2. Derive the formula for calculating the thermal expansion coefficient in the z direction of the RVE model.

[0106] S2.1. For the RVE model of composite plain fabric in the z direction, considering the Poisson effect, we can get:

[0107]

[0108] Among them, α zj represents the thermal expansion coefficient of the warp yarn in the z direction, α zw represents the thermal expansion coefficient of the weft yarn in the z direction, α zm represents the thermal expansion coefficient of the resin in the z direction, x 2f is the fiber transverse thermal expansion coefficient, α 1f is the longitudinal thermal expansion coefficient of the fiber, α m is the thermal expansion coefficient of the resin, v 13f and v 23f is the Poisson's ratio of the fiber, v m is the Poisson's ratio of the resin.

[0109]

[0110] Among them, α 1z represents the influence of α1 on α3 in the z direction, α 2z Represents the influence of α2 on α3 in the z direction.

[0111] a3=(α zf +α wz +α zm )-(α 1z +α 2z ) (15)

[0112] S2.2. Substitute equation (13) and equation (14) into equation (15) to obtain α3:

[0113] α3=(α 2f +v 1Efα1f +v 2Ef α 2f )V f +α m (1+2v m )(1-V f )-(α1+α2)[(v m (1-V f )] (16)

[0114] S3. Based on the actual geometric dimensions and weaving structure of the composite fabric, a RVE finite element numerical model is established for simulation analysis.

[0115] S3.1. Through observation and measurement, there are 44 yarns in a width of 10 cm, so the yarn density of CF8611 plain fabric is: ρ = 4.4 yarns / cm, and the width of RVE is: b = 4.5464 mm. Observe the interlayer structure of the composite fabric after curing under a microscope, such as Figure 4 , Figure 5The measured results are shown in Table 1 and Table 2. The average thickness of the cured single-layer prepreg is 0.223 mm, and the average thickness of a single yarn is 0.110 mm.

[0116] Table 1 Single layer thickness of AC531 / CF8611 plain weave fabric

[0117]

[0118] Table 2 Thickness of single-layer yarn of CF8611 fabric

[0119] Single yarn thickness L1 0.117mm L2 0.104mm L3 0.113mm L4 0.101mm average value 0.110mm

[0120] S3.2. The geometric model of yarn and fabric is established based on the extracted structural parameters. Digimat software is used to establish the geometric model of yarn and fabric. The major axis length of the yarn cross-section ellipse is 2 mm, the minor axis length is 0.110 mm, and the RVE geometric size is 4.5454 mm*4.5454 mm*0.2230 mm. Figure 6 shown.

[0121] S3.3. Import the established geometric model into Abaqus finite element analysis software to establish a numerical model for finite element analysis of composite plain fabric. Divide the grids for the resin matrix, warp yarn, and weft yarn respectively. Set the temperature range and assign the material parameter properties to the model, such as Figure 7 shown.

[0122] S3.4. Calculate the numerical solution of the thermal expansion coefficient based on the simulation results.

[0123] The initial length of each side of RVE is L i , finite element simulation calculation of the elongation ΔL of each side after heating ΔT i , α is calculated by the definition of thermal expansion coefficient i :

[0124]

[0125] S3.5. Compare the numerical solution of the coefficient of thermal expansion with the analytical solution to verify the accuracy of the analytical solution.

[0126] The performance parameters of the component materials were input into the theoretical analytical formula and the finite element numerical model respectively, and the calculation results are shown in Table 3.

[0127] Table 3 Calculation results of numerical and analytical solutions for thermal expansion coefficient of AC531 / CF8611 plain fabric

[0128]

[0129] Note: Analytical solution 1 is the result of calculation of formula (7), and analytical solution 2 is the result of calculation of formula (11).

[0130] The prediction trends of the analytical solution and the numerical solution are consistent. The α1 and α3 of the numerical solution are very close and can be considered equal, which is consistent with the analytical formula prediction that the composite fabric has transverse isotropy in the xOy plane, and α3 is much larger than α1 and α2. The error between the numerical solution and the analytical solution is within 2%, which verifies the accuracy of the analytical formula. Among them, analytical solution 1 is the calculation result corresponding to formula (7), and analytical solution 2 is the calculation result corresponding to the simplified formula (11). The error of analytical solution 2 in predicting α1 and α2 is lower than that of analytical solution 1, with errors of -0.15% and -0.19% respectively; the error of analytical solution 1 in predicting α3 is lower than that of analytical solution 2, with an error of -0.67%.

[0131] Combined with the above examples, the analytical solution prediction method for the thermal expansion coefficient of composite fabrics is accurate and effective, and its simplified formula is easier to promote and apply.

[0132] The present invention relates to the field of composite material design and curing deformation, and establishes an analytical prediction method for the thermal expansion coefficient of composite 2D fabric. Using the self-consistent method of composite micromechanics, the stress balance equation and the deformation coordination equation are applied on the x-direction section of the RVE model to derive the in-plane thermal expansion coefficients α1 and α2, and the thermal expansion coefficient α3 is derived from the Poisson effect on the z-direction section. An analytical prediction method (APTC) for the thermal expansion coefficient of composite 2D fabric is established to obtain an analytical solution. An RVE finite element model is established according to the weaving structure parameters of the composite fabric, and a numerical solution of the thermal expansion coefficient is obtained by finite element simulation calculation. The numerical solution is consistent with the prediction trend of the analytical solution, and the error is within 2%, which verifies the prediction accuracy of the APTC method and proves the accuracy of the method. The present invention can quickly predict the thermal expansion coefficient of composite materials, reduce costs, and improve the efficiency of scientific research and production.

Claims

1. A theoretical prediction and verification method for thermal expansion coefficient of composite 2D fabric, characterized in that: The method comprises: Extract the cyclic structure in the composite 2D fabric and establish the RVE model; Predict the thermal expansion coefficients of the RVE model in the x-direction and y-direction, and predict the thermal expansion coefficient of the RVE model in the z-direction; Based on the actual geometric dimensions and weaving structure of the composite fabric, a finite element numerical model of RVE is established, and simulation analysis is carried out to verify the analytical solution.

2. The method according to claim 1, characterized in that The method of extracting the cyclic structure in the composite material 2D fabric and establishing the RVE model comprises: The composite 2D fabric is composed of warp yarn, weft yarn and resin matrix, and the RVE model is extracted in the loop structure.

3. The method according to claim 2, characterized in that The predicted RVE model thermal expansion coefficients in the x-direction and the y-direction include: The thermal expansion coefficients α1 and α2 in the x- and y-directions in the plane are derived through the stress equilibrium equation and the deformation coordination equation.

4. The method according to claim 3, characterized in that The thermal expansion coefficients α1 and α2 in the x-direction and y-direction in the plane are derived by the stress balance equation and the deformation coordination equation, including: On the cross section of the composite material 2D fabric RVE model in the x direction, the following equation is established based on the stress balance equation: s 1j S 1j +s 2w S 2w +s 1m S 1m =0 (1) Among them, σ 1j is the stress on the warp yarn in the cross section, σ 1w is the stress on the weft yarn in the cross section, σ 1m is the stress on the resin in the cross section, S 1j is the sum of the transverse cross-sectional areas of the warp yarns, S 1w is the sum of the longitudinal cross-sectional areas of the weft yarns, S 1m is the sum of the cross-sectional areas of the resin; In the weaving structure of common composite 2D fabrics, the warp density and weft density are equal, that is, the length and width are equal, the number of warp yarns is n, the major axis length of the elliptical cross section of the yarn is l, the minor axis length is h, S 1j and S 1w It can be calculated as: In S 1j , S 1w and S 1m The deformation coordination equations can be obtained as follows: Where α1 is the thermal expansion coefficient of the composite 2D fabric in the x direction; the yarn is transversely isotropic, and α 1f is the yarn longitudinal thermal expansion coefficient, α 2f is the yarn transverse thermal expansion coefficient, E 2f is the longitudinal elastic modulus of the yarn, E 2f is the transverse elastic modulus of the yarn; the resin is isotropic, α m is the thermal expansion coefficient of the resin, E m is the elastic modulus of the resin; Combine the three equations in equation (3): α1·ΔT·(E 1f S 1j +E 2f S 1w +E m S 1m )=(a 1f E 1f S 1j +a 2f E 2f S 1w +a m E m S 1m )·ΔT+σ 1j S 1j +s 1w S 1w +s 1m S 1m (4) Combined with formula (1), the thermal expansion coefficient α1 of the composite 2D fabric in the x direction can be obtained: The yarn and resin are evenly distributed. In the composite 2D fabric RVE model, the cross-sectional area S of the warp, weft and resin can be i Approximately converted to volume fraction V i ; Where S is the cross-sectional area of ​​RVE, V 1j is the warp volume fraction, V 1w is the weft volume fraction, V m is the resin volume fraction, V f is the fiber volume fraction. Substituting equation (6) into equation (5), we can approximately obtain α, which is: Considering the weaving structure parameters, the yarn density ρ, in units of roots / cm; the yarn width l, in units of cm. The width b of the composite 2D fabric RVE model is related to the yarn density ρ: The bandwidth ratio k is introduced, which means the ratio of the total bandwidth nl of the warp yarn to the RVE width b in the cross section of the RVE model of the composite 2D fabric in the x direction, and is dimensionless. Substituting equations (8) and (9) into equation (7), we can obtain the simplified α1: Consider further simplifying the introduced k to obtain a formula that is easier to generalize and apply; consider from two aspects, first, from the perspective of RVE geometric relationship, k≤1; second, from the physical meaning of bandwidth ratio, k≤1; in general, it can be considered that k=1, then α1 can be further simplified: When the warp density is equal to the weft density, the composite 2D fabric is transversely isotropic in the xOy plane, and the thermal expansion coefficients in the x and y directions are considered to be equal; 5. The method according to claim 4, characterized in that The predicted RVE model z-direction thermal expansion coefficient includes: The thermal expansion coefficient α3 in the z direction is derived from the Poisson effect.

6. The method according to claim 5, characterized in that The thermal expansion coefficient α3 in the z direction derived from the Poisson effect includes: For the composite material 2D fabric RVE model in the z direction, considering the Poisson effect, we can get: Among them, α zj represents the thermal expansion coefficient of the warp yarn in the z direction, α zw represents the thermal expansion coefficient of the weft yarn in the z direction, α zm Indicates the thermal expansion coefficient of the resin in the z direction, α 2f is the fiber transverse thermal expansion coefficient, α 1f is the longitudinal thermal expansion coefficient of the fiber, α m is the thermal expansion coefficient of the resin, V 1sf and V 2sf is the Poisson's ratio of the fiber, V r1 is the Poisson’s ratio of the resin; Among them, α 1z represents the influence of α1 on α3 in the z direction, α 2z represents the influence of α2 on α3 in the z direction; α s ＝(α zj +α wz +α zm )-(α 1z +α 2z ) (15) Substituting equation (13) and equation (14) into equation (15), we obtain α3: a s =(a 2f +v 1sf a 1f +v 2sf a 2f )V f +a m (1+2v m )(1-V f )-(α1+α2)[(v 1sf +v m (1-V f )] (16).

7. The method according to claim 6, characterized in that Based on the actual geometric dimensions and weaving structure of the composite fabric, the RVE finite element numerical model is established, simulation analysis is performed, and the analytical solution is verified, including: S4.

1. Observe the interlayer structure of the composite fabric after curing under a microscope, and measure the average thickness of a single layer of prepreg cured and the average thickness of a single yarn; S4.

2. Use Digimat software to establish the geometric model of yarn and fabric based on the extracted structural parameters; S4.

3. Import the established geometric model into the Abaqus finite element analysis software to establish a finite element analysis numerical model of the composite material plain fabric; divide the grids for the resin matrix, warp yarn, and weft yarn respectively; set the temperature range to increase the temperature, and assign the material parameter performance to the model; S4.

4. Calculate the numerical solution of thermal expansion coefficient through simulation results; S4.

5. Compare the numerical solution of the coefficient of thermal expansion with the analytical solution to verify the accuracy of the analytical solution.

8. The method according to claim 7, characterized in that The method of calculating the numerical solution of the coefficient of thermal expansion through simulation results comprises: The initial length of each side of RVE is L i , finite element simulation calculation of the elongation ΔL of each side after heating ΔT t , α is calculated by the definition of thermal expansion coefficient i :

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