A method for quantifying the uncertainties in the mechanical properties of composite materials and their sources

Abstract

The present invention discloses a method for quantifying the uncertainties of the mechanical properties of composite materials and their sources, including: quantifying the uncertainties of the anisotropic constitutive parameters of 3D printed continuous carbon fiber reinforced thermoplastic composites, and inferring the uncertainties of the microstructural parameters and constituent materials. First, a multi-scale micromechanical model based on the microstructure of 3D printed continuous carbon fiber reinforced thermoplastic composites is established, revealing the relationship between the constitutive parameters of constituent materials and microstructural parameters and the macroscopic anisotropic constitutive parameters, and deriving the joint probability distribution of the uncertainty parameters. Based on the Monte Carlo sampling method, the posterior probability distributions of the constitutive parameters and microstructural parameters are calculated, and the rationality of the multi-scale Bayesian method is verified through the posterior predictive distributions of the overall response, constitutive response, and noise response. The present invention quantifies the uncertainties of the anisotropic constitutive parameters of 3D printed continuous carbon fiber reinforced thermoplastic composites and their sources, which will promote the practical application of 3D printed composites.

Description

Technical Field

[0001] The present invention relates to the technical field of additive manufacturing, and particularly relates to a method for quantifying the uncertainty of the mechanical properties of composite materials and its sources. Background Art

[0002] Continuous fiber-reinforced composite materials have shown extensive application potential in the aerospace, automotive manufacturing, and shipbuilding industries due to their advantages of light weight, high strength, fatigue resistance, and corrosion resistance. Additive manufacturing technology, as a three-dimensional solid manufacturing technology that can directly and rapidly form, provides new possibilities for the integral manufacturing of complex components. Preparing continuous fiber composite materials using additive manufacturing technology can fully exert the performance advantages of composite materials and the forming advantages of additive manufacturing, meeting the development requirements of key composite components towards lightweight, precise shape and property control, short cycle, high performance, high precision, and integral manufacturing.

[0003] However, the in-situ forming technology of continuous fiber 3D printing has characteristics such as short impregnation time and low forming pressure, which are prone to microstructural and component material uncertainties such as insufficient impregnation, large inter-bundle porosity, fiber deflection, and fiber damage, resulting in significant dispersion of its macroscopic mechanical properties, severely restricting the application of such composite materials. To ensure the safety and reliability of composite material structures, traditional deterministic design methods often rely on a relatively high safety factor, but this conservative and inefficient design often leads to an increase in structural weight, thereby weakening the potential advantages of advanced composite materials in terms of lightweight. In previous studies, in order to simplify the analysis, researchers usually only quantitatively evaluate a single uncertainty parameter, ignoring that composite materials are a "structure" that couples material-process-performance, and their macroscopic mechanical properties depend on multi-scale component properties and microstructural parameters from multiple sources. Summary of the Invention

[0004] Aiming at the deficiencies existing in the prior art, the purpose of the present invention is to provide a method for quantifying the uncertainty of the mechanical properties of composite materials and its sources, and to evaluate the anisotropic elastic constants of composite materials under the uncertain effects of microstructural parameters and component materials; at the same time, combining Bayesian inference and Markov chain Monte Carlo methods, the posterior probability distribution of the uncertain parameters is calibrated, which has very important reference value for the preliminary selection of parameter design in engineering practice. To achieve the above object and other advantages according to the present invention, a method for quantifying the uncertainty of the mechanical properties of composite materials and its sources is provided, including:

[0005] 1) Construct a multi-scale micromechanical constitutive model, specifically including the following steps:

[0006] S1. Using the fast Fourier transform technology, for the microstructural uncertainty parameter fiber deflection angle Perform homogenization treatment and obtain the homogenized micromechanical properties of the matrix and continuous fibers at the microscale based on the Chamis model;

[0007] S2. Establish the generalized homogenization theory of a single tow of prepreg, introduce the uncertainty of the impregnation degree β, and calculate the homogenized mechanical properties of the prepreg at the mesoscale based on the idea of regional homogenization;

[0008] S3. Based on image recognition technology, calibrate the pore defect ρ between prepregs, and combine the hole model and the classical lamination theory to calculate the homogenized mechanical properties of the unidirectional laminate at the macroscale;

[0009] 2) Construct a multi-scale Bayesian probability model, which specifically includes the following steps:

[0010] S4. Based on the multi-scale micromechanics constitutive model, combine the tensile test curves at 0°, ±45°, and 90° and the small deformation-linear elasticity hypothesis to determine the composite material noise model Ω and calculate the likelihood function;

[0011] S5. Construct an unknown parameter vector to be inferred that includes constituent materials and noise to determine the prior Gaussian field function;

[0012] S6. Based on the experimental data, likelihood function, and prior function obtained in steps S21-22, use Bayes' theorem to determine the posterior distribution function of the model parameters;

[0013] 3) Based on the Adaptive Metropolis algorithm sampling technique, combined with the Markov chain Monte Carlo method, perform inverse uncertainty quantification analysis to obtain the posterior distribution of the uncertain parameters;

[0014] 4) According to the multi-scale micromechanics model and the posterior distribution function of the uncertain parameters, perform Bayesian forward uncertainty quantification analysis to obtain the posterior probability distribution of the stress-strain curve.

[0015] Preferably, step S1 specifically includes the following steps:

[0016] S11. Use a scanning electron microscope to observe the surface of the composite material sample, obtain a pixel picture containing the spatial distribution information of the fiber deflection angle, and establish a pixel function f(x, y) of a single pixel point in the time domain;

[0017] S12. Convert the spatial information in the optical pixel image into a mathematical function F(u, v) in the frequency domain through a two-dimensional fast Fourier transform function, and output the frequency-domain pixel map, where the two-dimensional fast Fourier transform function is as follows:

[0018] ​

[0019] In the formula, (x, y) represents the pixel coordinates of the time-domain graph, and (u, v) are the pixel coordinates of the frequency-domain graph.

[0020] S13. Establish the circular projection boundary function of the frequency-domain pixel graph, project the frequency-domain image pixels from the center of the circle to the circular boundary, and output the sum of the frequency pixels along the radius direction and the angle of the projection radius to calculate the gray-scale distribution curve The formula for the circular projection boundary function of the frequency-domain pixel graph is as follows:

[0021] (u - u 0 ) 2 +(v - v 0 ) 2 =R 2 (20);

[0022] In the formula, (u 0 , v 0 ) are the coordinates of the center of the circle of the frequency-domain graph, and R is the radius of the projection boundary.

[0023] S14. Divide the gray-scale curve into different regions, and calculate the homogenized fiber deflection angle by Equation 3 As shown in the following formula:

[0024]

[0025] In the formula, are the sample points of the gray-scale distribution curve.

[0026] S15. Based on the fiber deflection angle, construct the composite material rotation axis matrix and calculate the average off-axis compliance matrix. The specific formulas for the composite material rotation axis matrix and the average off-axis compliance matrix are as follows:

[0027]

[0028]

[0029] In the formula, [S] micro represents the compliance matrix of the microstructure.

[0030] S16. Based on the average off-axis compliance matrix, the relationships between the five independent engineering elastic constants of the microstructure at the microscale and the average off-axis compliance coefficients can be obtained as follows:

[0031]

[0032] Preferably, the specific steps of step S2 are as follows:

[0033] S21. Use a milling machine to cut the composite 0° tensile specimen, and use sandpaper and polishing cloth with a particle size of P400 to P2500 to carefully polish the cross-section of the composite material to ensure that the observation surface is smooth and flawless, and use a scanning electron microscope to collect pore images;

[0034] S22. Adopt binary processing methods with different thresholds to obtain the boundary contours of the impregnated area, non-impregnated area, and pore area, and respectively count the effective pixels within their areas. The impregnation degree β can be obtained from the ratio of the pixels in the impregnated area to the total pixels in the effective area;

[0035] S23. Based on the impregnation degree β, establish a mesoscopic-scale generalized homogenization model, apply an axial external load to the representative volume element, and obtain the axial modulus and Poisson's ratio of the prepreg filament, where the expression of Poisson's ratio is as follows:

[0036]

[0037] In the formula, V i is the ideal impregnated volume fraction, which can be obtained by image recognition; the subscripts I and U represent the impregnated area and non-impregnated area respectively; the superscript meso represents the mesoscopic homogenization parameter;

[0038] S24. Based on the series-parallel model of the composite material, establish a mechanical model for the transverse loading process of the representative volume element, and output the transverse modulus as follows:

[0039]

[0040] In the formula, E m is the matrix elastic modulus;

[0041] S25. Apply a shear load to the representative volume element to obtain the analytical expressions of the shear modulus and of the prepreg filament, as follows:

[0042]

[0043] In the formula, G m is the matrix shear modulus.

[0044] Preferably, the specific steps of step S3 are as follows:

[0045] S31. Adopt the same steps as S21 and S22 to count the effective pixels in the pore area. The inter-bundle porosity ρ can be calculated from the ratio of the pixels in the pore area to the total pixels in the observation area;

[0046] S32. Based on the basic principles of elasticity, a macroscopic pore model is constructed by combining a concentric cylinder model with the porosity ρ, and an expression for the macroscopic homogenized elastic modulus of the continuous fiber 3D printed composite material is obtained as follows:

[0047]

[0048] where

[0049]

[0050] In the formula, C represents the stiffness matrix; the superscript macro represents the macroscopic homogenization parameter;

[0051] S33. For the macroscopic shear modulus it can be solved through Equation (12);

[0052]

[0053] where

[0054]

[0055] Preferably, the specific steps of Step S4 are as follows:

[0056] S41. According to the ASTM D3039 and ASTM D3518 standards, standard tensile tests are carried out on three groups of samples with different fiber orientations (0°, 90°, and ±45°), and each group of samples needs to be measured at least 5 times repeatedly;

[0057] S42. Under uniaxial stress conditions, the stress-strain response of small-deformation composite materials conforms to the linear elastic law. For unidirectional composite materials, its constitutive model with noise can be described as:

[0058]

[0059] In the formula, σ exp is the experimental measurement of stress; E pred is the predicted value of the elastic modulus, which can be calculated by the multi-scale micromechanics constitutive model of S1-S3, and is a function of the uncertain vector of the component materials and the uncertain vector of the microstructure parameters ; Ω is the random noise vector in the stress measurement values, and it is generally assumed to follow a Gaussian distribution N(Ω|0, ω 2 ); ω is the standard deviation of the noise distribution, is the uncertain vector of the noise to be inferred;

[0060] S43. The likelihood function is the joint probability distribution of all experimental data points, and its display expression can be described as follows:

[0061]

[0062] where M is the number of samples; N is the number of data points in each sample.

[0063] Preferably, the specific steps of step S5 are as follows:

[0064] S51. By analyzing the constitutive model and the noise model, the parameter vector to be inferred is:

[0065]

[0066] S52. A multivariate Gaussian distribution is used to describe the prior information of the parameter to be inferred, as shown in the following formula:

[0067]

[0068] In the formula, in the above formula, C is the covariance matrix, the diagonal elements of which are composed of the variances of random variables, and the off-diagonal elements are composed of covariances; μ represents the mean of the uncertain quantity.

[0069] Preferably, in step S6, numerical solution is adopted. After ignoring the constant term normalization coefficient, the posterior distribution can be expressed as:

[0070]

[0071] Compared with the prior art, the beneficial effects of the present invention are as follows: The method for constructing the constitutive and probability models of composite materials considering multi-source uncertainties provided by the present invention can identify the elastic tensor of composite materials through at least three sets of tensile tests, and quantify the uncertainties of its microstructure and component materials. These quantified uncertain parameters can be used for numerical simulation or theoretical calculation to obtain statistical data of engineering interest, such as the strain and stress responses of the macroscopic structure, etc., and further provide a probability prediction framework for the lightweight design and manufacturing of composite materials. Description of the Drawings

[0072] Figure 1 It is a flow chart of the method for constructing the constitutive model and the probability model of continuous fiber 3D printed composite materials for quantifying the uncertainties of the mechanical properties of composite materials and their sources according to the present invention;

[0073] Figure 2 It is a multi-scale micromechanical constitutive model diagram established based on the three-step homogenization theory for the method of quantifying the uncertainties of the mechanical properties of composite materials and their sources according to the present invention;

[0074] Figure 3The construction and calculation flow chart of the multi-scale Bayesian probability model for the method of quantifying the uncertainty of the mechanical properties of composite materials and its sources according to the present invention;

[0075] Figure 4 The comparison diagram of the prediction results and experimental results of the multi-scale micromechanical constitutive model for the method of quantifying the uncertainty of the mechanical properties of composite materials and its sources according to the present invention;

[0076] Figure 5 The posterior predictive probability distribution diagram of the uncertain parameters of the microstructure and component materials for the method of quantifying the uncertainty of the mechanical properties of composite materials and its sources according to the present invention;

[0077] Figure 6 The posterior predictive probability distribution diagram of the stress-strain curve for the method of quantifying the uncertainty of the mechanical properties of composite materials and its sources according to the present invention;

[0078] Figure 7 The posterior predictive probability distribution diagram of the macroscopic modulus of the composite material for the method of quantifying the uncertainty of the mechanical properties of composite materials and its sources according to the present invention. Specific embodiments

[0079] The technical solutions in the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings in the embodiments of the present invention. Obviously, the described embodiments are only a part of the embodiments of the present invention, rather than all the embodiments. All other embodiments obtained by those of ordinary skill in the art based on the embodiments of the present invention without creative efforts shall fall within the protection scope of the present invention.

[0080] Embodiment

[0081] Refer to Figures 1-3 , a method for quantifying the uncertainty of the mechanical properties of composite materials and its sources, comprising the following steps:

[0082] S1. Using the fast Fourier transform technology, homogenize the microstructure uncertain parameter fiber deflection angle and obtain the homogenized micromechanical properties of the matrix and continuous fibers at the microscopic scale based on the Chamis model;

[0083] S2. Establish the generalized homogenization theory of a single tow of prepreg, introduce the uncertainty of the impregnation degree β, and calculate the homogenized mechanical properties of the prepreg at the mesoscopic scale based on the idea of regional homogenization;

[0084] S3. Based on the image recognition technology, calibrate the pore defect ρ between prepregs, and combine the pore model and the classical lamination theory to calculate the homogenized mechanical properties of the unidirectional laminate at the macroscopic scale;

[0085] S4. Based on the multi-scale micromechanical constitutive model constructed from S1 - S3, combined with the tensile test curves at 0°, ±45°, and 90° and the small deformation - linear elasticity hypothesis, determine the composite material noise model Ω and calculate the likelihood function;

[0086] S5. Construct a vector of parameters to be inferred that includes microstructural constituent materials and noise uncertainties, and determine the prior Gaussian field function;

[0087] S6. Based on the experimental data, likelihood function, and prior function obtained from S4 - S5, use Bayes' theorem to determine the posterior distribution function of the model parameters;

[0088] S7. Based on the Adaptive Metropolis algorithm sampling technique, combined with the Markov chain Monte Carlo method, perform inverse uncertainty quantification analysis to obtain the posterior distribution of the uncertain parameters;

[0089] S8. Based on the multi-scale micromechanical model and the posterior distribution function of the uncertain parameters, perform Bayesian forward uncertainty quantification analysis to obtain the posterior probability distribution of the stress - strain curve;

[0090] The above step S1 is mainly based on the real microstructure of the material, statistically analyze the distribution function of the microstructure uncertainty fiber deflection angle and calculate the homogenized mechanical properties of the fiber and matrix at the microscale, preparing for the construction of the subsequent mesoscopic homogenization model. Therefore, the above step S1 is specifically as follows:

[0091] S11. Use a scanning electron microscope to observe the surface of the composite material sample, obtain a pixel image containing the spatial distribution information of the fiber deflection angle, and establish a pixel function f(x, y) of a single pixel point in the time domain;

[0092] S12. With the help of the two-dimensional fast Fourier transform function, convert the spatial information in the optical pixel image into a mathematical function F(u, v) in the frequency domain and output the frequency domain pixel map. The two-dimensional fast Fourier transform function is as follows;

[0093]

[0094] In the formula, (x, y) represents the pixel coordinates of the time domain map, and (u, v) are the pixel coordinates of the frequency domain map.

[0095] S13. Establish a circular projection boundary function for the frequency domain pixel map, project the frequency image pixels from the center of the circle to the circular boundary, and output the sum of the frequency pixels along the radius direction and the angle of the projection radius to calculate the gray level distribution curve The circular projection boundary function of the frequency-domain pixel map is as follows:

[0096] (u - u 0 ) 2 +(v - v 0 ) 2 =R 2 (38)

[0097] Where (u 0 , v 0 ) are the coordinates of the center of the frequency-domain map, and R is the radius of the projection boundary.

[0098] S14. Divide the gray curve into two intervals: Region I (45° to 135°) and Region II (135° to 225°). Since the fiber deflection angle is positive, Region I is selected as the target region, and the uniform fiber deflection angle is calculated by Equation 3 The results are shown in Table 1;

[0099]

[0100] Where are the sample points of the gray distribution curve.

[0101] Table 1 Statistical values of fiber deflection angles in different samples

[0102]

[0103] S15. Based on the fiber deflection angle, construct the composite material rotation axis matrix (Equation (4)), and combine the basic mechanical properties of carbon fiber T300B-1000 and matrix PLA-4032D in Table 2 to calculate the average off-axis compliance matrix (Equation (5));

[0104]

[0105] Table 2 Basic mechanical properties of component materials carbon fiber and matrix PLA

[0106]

[0107]

[0108] Where [S] micro represents the compliance matrix of the microstructure.

[0109] S16. Based on the average off-axis compliance matrix, five independent engineering elastic constants of the microstructure at the microscale can be obtained;

[0110]

[0111] Furthermore, the specific steps of S2 are as follows:

[0112] S21. Use a milling machine to cut the 0° tensile specimen of the composite material, and use sandpaper and polishing cloth with a particle size of P400 to P2500 to carefully polish the cross-section of the composite material to ensure that the observation surface is smooth and flawless, and collect pore images using a scanning electron microscope.

[0113] S22. Adopt binarization processing methods with different thresholds to obtain the boundary contours of the impregnated area, non-impregnated area, and pore area, and respectively count the effective pixels within their areas. The impregnation degree β can be obtained from the ratio of the pixels in the impregnated area to the total pixels in the effective area. The results are shown in Table 3.

[0114] Table 3 Statistical values of impregnation degree and inter-bundle porosity in different samples

[0115]

[0116] S23. Based on the impregnation degree β, establish a mesoscopic-scale generalized homogenization model, apply an axial external load to the representative volume element, and obtain the axial modulus and Poisson's ratio of the prepreg filament in the calculation formula (7);

[0117]

[0118] Note that other parameters in the model can be obtained by image recognition, and their statistical means are shown in Table 4.

[0119] Table 4 Statistical means of other parameters in the model

[0120]

[0121] S24. Based on the series-parallel model of the composite material, establish a mechanical model for the transverse loading process of the representative volume element and output the transverse modulus

[0122]

[0123] S25. Apply a shear load to the representative volume element to obtain the shear modulus and of the prepreg filament in the analytical expression (9);

[0124]

[0125] Furthermore, the specific steps of step S3 are as follows:

[0126] S31. Adopt the same steps as S21 and S22 to count the effective pixels in the pore area. The inter-bundle porosity ρ can be calculated from the ratio of the pixels in the pore area to the total pixels in the observation area. The results are shown in Table 3.

[0127] S32. Based on the basic principles of elasticity, a macroscopic pore model is constructed by combining the concentric cylinder model with the porosity ρ, and the expression (10) of the macroscopic homogenized elastic modulus of the continuous fiber 3D printed composite material is obtained. The results are shown in Table 5;

[0128]

[0129] Among them

[0130]

[0131] In the formula, C represents the stiffness matrix; the superscript macro represents the macroscopic homogenization parameter. S33. For the macroscopic shear modulus It can be solved by formula (12);

[0132]

[0133] Among them

[0134]

[0135] Table 5 Predicted values of the macroscopic modulus of the composite material under small samples

[0136]

[0137]

[0138] Furthermore, the specific content of step S4 is as follows:

[0139] S41. According to the ASTM D3039 and ASTM D3518 standards, standard tensile tests are carried out on three groups of samples with different fiber orientations (0°, 90° and ±45°), and each group of samples needs to be measured at least 5 times repeatedly;

[0140] S42. Under the uniaxial stress state, the stress-strain response of the small-deformation composite material conforms to the linear elastic law. For the unidirectional composite material, its constitutive model with noise can be described as:

[0141]

[0142] In the formula, σ exp is the experimental measurement of stress; E pred is the predicted value of the elastic modulus, which can be calculated by the multi-scale micromechanics constitutive model of S1-S3, and is a function of the uncertain vector of the component materials and the uncertain vector of the microstructure parameters. Ω is the random noise vector in the stress measurement values, and it is generally assumed to follow a Gaussian distribution with a mean of 0, N(Ω|0,ω2 );ω is the standard deviation of the noise distribution, is the noise uncertainty vector to be inferred.

[0143] S43. The likelihood function is the joint probability distribution of all experimental data points, and its display expression can be described as:

[0144]

[0145] where M is the number of samples; N is the number of data points in each sample.

[0146] Furthermore, the specific step S5 is as follows:

[0147] S51. By analyzing the constitutive model and the noise model, the parameter vector to be inferred can be determined as:

[0148]

[0149] S52. A multivariate Gaussian distribution is used to describe the prior information of the parameter to be inferred (Equation 17);

[0150]

[0151] In the formula, in the above formula, C is the covariance matrix, the diagonal elements of which are composed of the variances of random variables, and the non-diagonal elements are composed of covariances; μ represents the mean of the uncertainty.

[0152] Furthermore, the specific step S6 is as follows:

[0153] S61. Using numerical solution, after ignoring the constant term normalization coefficient, the posterior distribution can be expressed as:

[0154]

[0155] The stress-strain curve results predicted by the multi-scale micromechanics constitutive model in the present invention under uniaxial tension at 0°, ±45° and 90° are as Figure 4 (a-c) shown. The theoretical prediction and the experimental results show good consistency. As the strain value increases, both the mean and standard deviation of the stress show an approximately linear increasing trend. For the 0° tensile test, the predicted mean is almost completely consistent with the experimental mean.

[0156] The prediction results of the multi-scale Bayesian method in the present invention are as Figure 5 shown. Among them, Figure 5 is the posterior predictive probability distribution of the uncertain parameters of the microstructure and component materials. Due to the conjugate relationship between the prior and the posterior, after large-sample sampling, the posterior distribution of the uncertain parameters is approximately Gaussian distribution; Figure 6The posterior predictive probability distribution of the stress-strain curve is given, and the 95% and 99% confidence intervals are marked in the figure. The predicted values are in very good agreement with the experimental values, and almost all the data are within the 99% confidence interval, which demonstrates the effectiveness of this method; Figure 7 It is the posterior predictive probability distribution of the macroscopic modulus of the composite material, and most of the experimental measurement values are within the 95% confidence interval.

[0157] The number of devices and the processing scale described here are used to simplify the description of the present invention. Applications, modifications, and variations of the present invention will be obvious to those skilled in the art.

[0158] Although the embodiments of the present invention have been disclosed above, it is not limited to the applications listed in the specification and the embodiments. It can be fully applied to various fields suitable for the present invention. For those familiar with the art, additional modifications can be easily achieved. Therefore, without departing from the general concept defined by the claims and their equivalents, the present invention is not limited to the specific details and the illustrated and described examples here.

Claims

1. A method for quantifying the uncertainty of mechanical properties of composite materials and its sources, characterized in that: The following steps are involved: 1) Construct a multi-scale micromechanical constitutive model, which specifically includes the following steps: S1. Using fast Fourier transform technology, the microstructural parameter fiber deflection angle The homogenization treatment is carried out, and the homogenized mechanical properties of the matrix and continuous fibers at the microscopic scale are obtained based on the Chamis model; S2. Establish a generalized homogenization theory of a single bundle of prepreg yarns, introduce the uncertainty of the impregnation degree β, and calculate the homogenized mechanical properties of the prepreg yarns at a mesoscopic scale based on the idea of ​​regional homogenization; the specific steps of step S2 are: S21. Use a milling machine to cut the 0° tensile specimen of the composite material, use sandpaper and polishing cloth with a grit of P400 to P2500 to carefully polish the cross section of the composite material to ensure that the observation surface is smooth and flawless, and use a scanning electron microscope to collect pore images; S22, using a binarization method with different thresholds to obtain the boundary contours of the impregnated area, the non-impregnated area and the pore area, and counting the effective pixels in each area, and the impregnation degree β is obtained by the ratio of the pixels in the impregnated area to the total pixels in the effective area; S23. Based on the impregnation degree β, a generalized homogenization model at the mesoscopic scale is established, and an axial external load is applied to the characteristic volume element to obtain the axial modulus of the prepreg and Poisson's ratio The expression of Poisson's ratio The expression is as follows: （7）； Where V i is the Poisson's ratio of the ideal impregnated body, obtained by image recognition; the subscripts I and U represent the impregnated area and the unimpregnated area, respectively; the superscript meso represents the mesoscopic homogenization parameter; S24. Based on the composite material series-parallel model, establish the mechanical model of the characteristic element transverse loading process and output the transverse modulus As follows: （8）； In the formula, E m is the matrix elastic modulus; S25. Apply shear load to the characteristic element to obtain the shear modulus of the prepreg , and The analytical expression of is as follows: （9）； In the formula, G m is the matrix shear modulus; , is the shear modulus of the impregnation zone in the 12 and 23 directions; S3. Based on image recognition technology, the pore defects ρ between prepreg wires are calibrated, and the homogenized mechanical properties of unidirectional laminates at the macroscopic scale are calculated by combining the pore model and classical lamination theory. 2) Construct a multi-scale Bayesian probability model, which specifically includes the following steps: S4. Based on the multi-scale micromechanical constitutive model, combined with the 0°, ±45° and 90° tensile test curves and the small deformation linear elasticity hypothesis, the noise model Ω of the composite material is determined and the likelihood function is calculated; S5. Constructing a microstructure containing uncertainties , component material uncertainty and noise uncertainty The parameter vector to be inferred , determine the a priori Gaussian field function; S6. Based on the experimental data, likelihood function and prior function obtained in steps S21-S22, using Bayes' theorem, determine the posterior distribution of the model parameters; 3) Based on the sampling technology of Adaptive Metropolis algorithm and combined with Markov chain Monte Carlo method, inverse uncertainty quantification analysis is performed to obtain the posterior distribution of uncertain parameters; 4) Based on the multi-scale micromechanical model and the posterior distribution function of the uncertain parameters, a Bayesian forward uncertainty quantification analysis is performed to obtain the posterior probability distribution of the stress-strain curve.

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