CN105825507A - Image extraction-based carbon/carbon composite elastic property prediction method - Google Patents

Abstract

The invention discloses a method for predicting elastic properties of carbon/carbon composite materials based on image extraction, which is used to solve the technical problem of poor accuracy of the existing methods for predicting elastic properties of carbon/carbon composite materials. The technical solution is based on the PLM (polarized light image) image of carbon/carbon composite material, and the information parameters of each microstructure are obtained by means of image calculation, and these microstructures are sequentially introduced into the analytical mechanical model as inclusion phases, and the inclusion theory of solid defect mechanics is used to solve the problem. Its equivalent elastic properties enable accurate and efficient prediction of the elastic properties of multi-component phase carbon/carbon composites. Due to the use of polarized light images to obtain information on the microstructure of carbon/carbon composite materials such as fibers and pores, the established mechanical model is more accurate and closer to the actual situation. Important parameters affecting the equivalent elastic modulus of carbon/carbon composites such as fiber bundle distribution, fiber volume fraction, pore volume fraction, and distribution are obtained by calculation without assumptions.

Description

Prediction Method of Elastic Properties of Carbon/Carbon Composite Materials Based on Image Extraction

technical field

The invention relates to a method for predicting elastic properties of carbon/carbon composite materials, in particular to a method for predicting elastic properties of carbon/carbon composite materials based on image extraction.

Background technique

Due to the advantages of high specific strength, high specific stiffness, and good high-temperature mechanical properties, carbon/carbon composite materials are more and more used in aerospace and other fields. Prospect of thermal structural materials, so it has important national defense strategic value. However, because the material often has anisotropic characteristics, the prediction of its mechanical properties is often complicated. In summary, a method that can quickly and accurately calculate the elastic parameters of the composite material will be of great significance. It can reduce the test cost and shorten the development cycle to a certain extent.

The research on the equivalent performance of continuous carbon fiber reinforced composite materials mainly includes experimental method, analytical method and numerical simulation method. Get the required parameters. In this process, samples need to be prepared according to certain standards, usually with a large workload. In addition, for composite materials with many independent elastic parameters, it is more difficult to study their properties through experimental methods.

Finite element numerical simulation has been proved to be an effective analysis method. Document 1 "Chinese Invention Patent Application Publication No. 104537259A" discloses a method of using XCT technology to extract the microstructure information of fiber-reinforced composite materials and establish a finite element model. However, for carbon/carbon composites, due to the existence of pore microstructure, it will bring great difficulty to model establishment and calculation, which is often limited by computer capabilities and cannot be widely used.

In addition, document 2 "TSUKROVI, etal. Mechanics of Advanced Materials and Structures, 2005, 12(1): 43-54" discloses a method using the inclusion theory of solid defect mechanics based on the Eshelby tensor to predict the carbon/carbon composite material However, due to the particularity of the CVI process, the microstructure of the material is usually complex. In addition to the fiber phase and the matrix phase, there are also uneven pore structures in the matrix. The fiber and pore structures have an impact on the equivalent elasticity of the material The modulus has a greater influence. It is difficult to take these factors into account based on the assumptions made in the above literature on the microstructure of the material. Therefore, the analytical algorithms described in the literature can deviate from the experimental values when predicting the elastic parameters.

Contents of the invention

In order to overcome the deficiency of poor accuracy of the existing methods for predicting elastic properties of carbon/carbon composite materials, the present invention provides a method for predicting elastic properties of carbon/carbon composite materials based on image extraction. This method is based on the PLM (polarized light image) image of carbon/carbon composite material, and the information parameters of each microstructure are obtained by means of image calculation. Equivalent elastic properties to achieve accurate and efficient prediction of elastic properties of multi-component phase carbon/carbon composites.

The technical solution adopted by the present invention to solve its technical problems: a method for predicting elastic properties of carbon/carbon composite materials based on image extraction, which is characterized in that it includes the following steps:

Step 1. Take multiple PLM shots of the carbon/carbon composite material to be analyzed to obtain the pixel information of each image;

Step 2, performing denoising, contrast adjustment and smoothing filtering on the multiple groups of images taken, and using an adaptive threshold algorithm to determine the threshold of the image;

Step 3. Set the pixel size of each image to be A pixel long and B pixel wide, and the grayscale range of each pixel is 0-255, using (i, j, k) (i∈(0, B-1), j∈(0, A-1), k∈(0, N-1)) to represent the k+1th image, the j+1th row, and the i+1th column pixel. The pixels of the adjusted image in step 2 are used to establish the gray value array Pixel{data}, and the element poxel[A*B*k+A*j+i] in the array represents the gray value of the pixel (i, j, k);

Step 4: Identify and extract the carbon/carbon composite material fiber region according to the threshold determined by the calculation result of Step 2, and update the pixel grayscale array Pixel{data}. On this basis, the adaptive threshold algorithm in step 2 is used again to determine the threshold of the pore structure, and the pore outline will be identified and extracted. Update the corresponding gray value of different component regions in step 3 again.

Step 5. According to the calculation result of step 4, the gray values of the matrix phase, fiber phase and pore phase of the carbon/carbon composite material are respectively obtained as GVM, GVF and GVP. According to different gray values, the volume fractions of fiber phase and pore phase are calculated as and And count the aspect ratio range λ of the pore phase structure.

Step 6: Establishing a micromechanical model of the carbon/carbon composite material, wherein the pore phase Ω _i , the pyrolytic carbon matrix and the fiber phase D-Ω. An external load P acts on the X position on the outer surface τ of the model, and e is the unit external normal vector of the outer surface τ of the model. The stress and strain of the micromechanical model of carbon/carbon composites are expressed as follows

The stiffness tensors defining the matrix phase and pore inclusion phase are N and N ^* , respectively. Their flexibility tensors are respectively M=N ^-1 and M ^* =N ^*-1 . According to the theory of solid defect mechanics

$<span\; class="notranslate">\; <</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}}{<span\; class="notranslate">\; ></span>}_{\mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; V</span>}\mathrm{<span\; class="notranslate">\; E.</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; k</span>}\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; :</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; \&Delta;\&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}{<span\; class="notranslate">\; ></span>}_{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Among them, Δε _ij = C ^RVE : σ ^∞ , C ^RVE is the flexibility contribution tensor of the inclusion phase, since the pore inclusion phase is a homogeneous material, Δε _ij and σ ⁰ here are both symmetrical second-order tensors, so C ^RVE is a fourth-order tensor having the same symmetric properties as the stress-strain tensor. Therefore there is, So the contribution tensor here is

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; k</span>}\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; V</span>}\mathrm{<span\; class="notranslate">\; E.</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{cccccc}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1111</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1122</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1133</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1112</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1123</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1131</span>}}\\ {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2211</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2222</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2233</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2212</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2223</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2231</span>}}\\ {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3311</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3322</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3333</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3312</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3323</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3331</span>}}\\ {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1211</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1222</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1233</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1212</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1223</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1211</span>}}\\ {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2311</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2312</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2312</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2312</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2323</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2331</span>}}\\ {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3111</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3122</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3133</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3112</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3123</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3131</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

According to the definition about the fourth-order tensor Q _iikl and R _ijkl of the Eshelby tensor S _ijkl function, wherein, Q _ijkl =N _ijrs (I _rskl -S _rskl ), R _ijkl =S _ijmn M _mnkl . So the flexibility contribution tensor of the inclusion phase is

C ^RVE =v _i [(M ^* -M) ^-1 +Q] ^-1 (i∈[1,N])(5)

Step 7. The pore structure in the carbon/carbon composite material has different shapes, so it is approximated by using ellipsoids with different orientations and size ratios. The pore structure parameter is A _r (a _i , λ) where a ₁ =a ₂ =a=λa ₃ . The orientation distribution function of the pores is

Among them, Ψ _i (α), Ψ _i (β), and Ψ _i (Φ) represent the projection distribution angles of the ellipsoid about the three coordinate axes in local coordinates, respectively.

Express Sijkl in terms of _{Eshelby tensors entangled} in ellipsoids. Write out the flexibility contribution tensor for the pores Therefore, the expression of the flexibility tensor of the equivalent matrix with pores is

${\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}{\mathrm{<span\; class="notranslate">\; C</span>}}^{\mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; V</span>}\mathrm{<span\; class="notranslate">\; E.</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

in,

Step 8: Bring the fiber phase of the carbon/carbon composite material into the equivalent matrix obtained in step 7 as an inclusion phase, and the flexibility contribution tensor of the fiber phase is where _h1 and h2 are obtained according to the Mori _- Tanaka expression for different fiber orientation distributions.

Therefore, the overall flexibility contribution tensor is

M ^eff =M ^efM +C ^f (8)

Therefore, the elastic performance parameters of carbon/carbon composites are expressed according to the components of the overall flexibility matrix.

The beneficial effects of the present invention are: the method is based on the carbon/carbon composite material PLM (polarized light image) image, adopts image calculation means to obtain the information parameters of each microstructure, and introduces these microstructures as inclusion phases into the analytical mechanical model in sequence, using solid The inclusion theory of defect mechanics solves its equivalent elastic properties, and realizes accurate and efficient prediction of elastic properties of multi-component phase carbon/carbon composites. Due to the use of polarized light images to obtain information on the microstructure of carbon/carbon composite materials such as fibers and pores, the established mechanical model is more accurate and closer to the actual situation. Important parameters affecting the equivalent elastic modulus of carbon/carbon composites such as fiber bundle distribution, fiber volume fraction, pore volume fraction, and distribution are obtained by calculation without assumptions. To calculate the equivalent performance of carbon/carbon composite materials, only part of the structure of the material is needed, and the stiffness performance can be calculated by analyzing the polarized light images taken to obtain the corresponding microstructure parameters, which is simple and easy.

The present invention will be described in detail below in conjunction with the accompanying drawings and specific embodiments.

Description of drawings

Figure 1 is the polarized image of the carbon/carbon composite prepared by the CVI process;

Fig. 2 is the PLM image after preprocessing;

Fig. 3 is the image after the fiber structure is extracted according to the gray value;

Figure 4 is the image after extracting the pore structure according to the different gray levels;

Fig. 5 is the schematic diagram of the principle of the established micromechanics model;

Fig. 6 is a schematic diagram of the pore structure and distribution under local coordinates.

detailed description

Refer to Figure 1-6. The specific steps of the method for predicting the elastic properties of carbon/carbon composite materials based on image extraction in the present invention are as follows:

Step 1: Take multiple sets of PLM (polarized light microscopic image) shots of the analyzed carbon/carbon composite material sample (as shown in Figure 1), and obtain the pixel information of each image;

Figure 1 is a polarized image of a unidirectional preform reinforced carbon/carbon composite prepared by the CVI process. The reinforcing phase is T700 carbon fiber, and the matrix is pyrolytic carbon matrix. The elastic parameters of carbon fiber and matrix are as follows: E ₁₁ =230Gpa, E ₂₂ =E ₃₃ =15Gpa, G ₁₂ =G ₁₃ =9Gpa, G ₂₃ =9.5Gpa, μ ₁₂ =μ ₁₃ =0.2, μ ₂₃ =0.23. The elastic parameters of the matrix are: E=32.8Gpa, μ=0.159; and the transverse elastic modulus of the composite material is tested experimentally, and the result is 13.5Gpa.

Step 2: Remove noise, adjust contrast, and smooth filter processing (as shown in Figure 2) for the N groups of photographs taken; use an adaptive threshold algorithm to determine the threshold of the image;

Step 3: Set the pixel size of each image to be A pixel long and B pixel wide, and the gray scale range of each pixel is 0-255, using (i, j, k) (i∈(0, B-1), j∈(0, A-1), k∈(0, N-1)) to represent the k+1th image, the j+1th row, and the i+1th column pixel. The pixels of the adjusted image in step 2 are used to establish a gray value array Pixel{data}, and the element poxel[A*B*k+A*j+i] in the array represents the gray value of the pixel (i, j, k);

Step 4: According to the threshold determined by the calculation result in step 2, identify and extract the fiber region (as shown in Figure 3), and update the pixel grayscale array Pixel{data}. On this basis, the adaptive threshold algorithm in step 2 is used again to determine the threshold of the pore structure, and the pore outline will be identified and extracted (as shown in Figure 4). Update the corresponding gray value of different component regions in step 3 again.

Step 5: According to the calculation results in step 4, the gray values of matrix phase, fiber phase and pore phase are respectively obtained as GVM, GVF and GVP. According to different gray values, the volume fractions of fiber phase and pore phase are calculated as and And the aspect ratio range λ∈(0.2, 7.5) of the pore structure in the statistics graph.

Step 6: Establish a micromechanical model of the material (as shown in FIG. 5 ), in which a pore phase (Ω _i ), a pyrolytic carbon matrix and a fiber phase (D-Ω) are established. An external load P acts on the X position on the outer surface τ of the model, and e is the unit external normal vector of the outer surface τ. So the stress and strain of the whole model are expressed as follows

The stiffness tensors defining the matrix phase and pore inclusion phase are N and N ^* , respectively. Their flexibility tensors are respectively M=N ^-1 and M ^* =N ^*-1 . According to the theory of solid defect mechanics

$<span\; class="notranslate">\; <</span>\stackrel{<span\; class="notranslate">\; \&OverBar;</span>}{{\mathrm{<span\; class="notranslate">\; \&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}}{<span\; class="notranslate">\; ></span>}_{\mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; V</span>}\mathrm{<span\; class="notranslate">\; E.</span>}}<span\; class="notranslate">\; =</span>{\mathrm{<span\; class="notranslate">\; m</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; k</span>}\mathrm{<span\; class="notranslate">\; l</span>}}<span\; class="notranslate">\; :</span>{\mathrm{<span\; class="notranslate">\; \&sigma;</span>}}_{\mathrm{<span\; class="notranslate">\; k</span>}\mathrm{<span\; class="notranslate">\; j</span>}}^{\mathrm{<span\; class="notranslate">\; 0</span>}}<span\; class="notranslate">\; +</span>\mathrm{<span\; class="notranslate">\; \&Sigma;</span>}<span\; class="notranslate">\; <</span>{\mathrm{<span\; class="notranslate">\; \&Delta;\&epsiv;</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}}{<span\; class="notranslate">\; ></span>}_{\mathrm{<span\; class="notranslate">\; \&Omega;</span>}<span\; class="notranslate">\; ,</span>\mathrm{<span\; class="notranslate">\; i</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 3</span>}<span\; class="notranslate">\; )</span>$

Among them, Δε _ij = C ^RVE : σ ^∞ , C ^RVE is the flexibility contribution tensor of the inclusion phase, since the pore inclusion phase is a homogeneous material, Δε _ij and σ ⁰ here are both symmetrical second-order tensors, so C ^RVE is a fourth-order tensor having the same symmetric properties as the stress-strain tensor. Therefore there is, So the contribution tensor here is .

${\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; i</span>}\mathrm{<span\; class="notranslate">\; j</span>}\mathrm{<span\; class="notranslate">\; k</span>}\mathrm{<span\; class="notranslate">\; l</span>}}^{\mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; V</span>}\mathrm{<span\; class="notranslate">\; E.</span>}}<span\; class="notranslate">\; =</span>\left[\begin{array}{cccccc}{\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1111</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1122</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1133</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1112</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1123</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1131</span>}}\\ {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2211</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2222</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2233</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2212</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2223</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2231</span>}}\\ {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3311</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3322</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3333</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3312</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3323</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3331</span>}}\\ {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1211</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1222</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1233</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1212</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1223</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 1211</span>}}\\ {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2311</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2312</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2312</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2312</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2323</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 2331</span>}}\\ {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3111</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3122</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3133</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3112</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3123</span>}}& {\mathrm{<span\; class="notranslate">\; C</span>}}_{\mathrm{<span\; class="notranslate">\; 3131</span>}}\end{array}\right]<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 4</span>}<span\; class="notranslate">\; )</span>$

According to the definition about the fourth-order tensors Q _ijkl and R _ijkl of the Eshelby tensor S _ijkl function, wherein, Q _ijkl =N _ijrs (I _rskl -S _rskl ), R _ijkl =S _ijmn M _mnkl . So the flexibility contribution tensor of the inclusion phase is

C ^RVE =v _i [(M ^* -M) ^-1 +Q] ^-1 (i∈[1,N])(5)

Step 7: Because the pore structure in carbon/carbon composites often has different shapes, it is approximated here using ellipsoids with different orientations and size ratios, and the structure parameters of the pores are A _r (a _i , λ), where a ₁ =a ₂ =a=λa ₃ . The orientation distribution function of the pores is .

Among them, Ψ _i (α), Ψ _i (β), and Ψ _i (Φ) respectively represent the projection distribution angles of the ellipsoid about the three coordinate axes in local coordinates (as shown in Figure 6).

Express Sijkl in terms of _{Eshelby tensors entangled} in ellipsoids. Write out the flexibility contribution tensor for the pores Therefore, the expression of the flexibility tensor of the equivalent matrix with pores is

${\mathrm{<span\; class="notranslate">\; m</span>}}^{\mathrm{<span\; class="notranslate">\; e</span>}\mathrm{<span\; class="notranslate">\; f</span>}\mathrm{<span\; class="notranslate">\; m</span>}}<span\; class="notranslate">\; =</span>\mathrm{<span\; class="notranslate">\; m</span>}<span\; class="notranslate">\; +</span>\underset{\mathrm{<span\; class="notranslate">\; i</span>}}{<span\; class="notranslate">\; \&Sigma;</span>}{\mathrm{<span\; class="notranslate">\; C</span>}}^{\mathrm{<span\; class="notranslate">\; R</span>}\mathrm{<span\; class="notranslate">\; V</span>}\mathrm{<span\; class="notranslate">\; E.</span>}}<span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; -</span><span\; class="notranslate">\; (</span>\mathrm{<span\; class="notranslate">\; 7</span>}<span\; class="notranslate">\; )</span>$

in,

Step 8: Bring the fiber phase as an inclusion phase into the equivalent matrix obtained in step 7, and the flexibility contribution tensor of the fiber phase is Among them, h ₁ and h ₂ are derived from the Mori-Tanaka expression of different fiber orientation distributions.

Therefore, the overall flexibility contribution tensor is

M ^eff =M ^efM +c ^f (8)

The elastic performance parameters of the material are expressed according to the components of the overall flexibility matrix. So its transverse modulus of elasticity is It is 6% different from the tested result of 13.5Gpa, and the result is in good agreement.

Claims (1)

1. A carbon/carbon composite material elastic performance prediction method based on image extraction is characterized by comprising the following steps:

step one, carrying out multiple groups of PLM shooting on the carbon/carbon composite material to be analyzed to obtain pixel information of each image;

secondly, respectively carrying out noise point removal, adjustment and comparison and smooth filtering processing on the multiple groups of shot images, and determining the threshold value of the images by adopting a self-adaptive threshold value algorithm;

setting the pixel size of each image as a long A pixel and a wide B pixel, wherein the gray scale range of each pixel is 0-255, and expressing the (k + 1) th image, the (j + 1) th row and the (i + 1) th column of pixels by adopting (i, j, k) (i belongs to (0, B-1), j belongs to (0, A-1) and k belongs to (0, N-1)); establishing a gray value array Pixel { data } of the pixels of the image adjusted in the step two, wherein the elements of the Pixel [ A × B × k + A × j + i ] in the array represent the gray value of the Pixel (i, j, k);

step four, according to the threshold value determined by the calculation result of the step two, identifying and extracting the carbon/carbon composite material fiber area, and updating the Pixel gray level array Pixel { data }; determining the threshold of the pore structure by using the self-adaptive threshold algorithm of the second step again on the basis, and identifying and extracting the pore contour; updating the corresponding gray values of the different component areas in the step three again;

step five, respectively obtaining the gray values of the matrix phase, the fiber phase and the pore phase of the carbon/carbon composite material, namely GVM, GVF and GVP according to the calculation result of the step four; respectively calculating the volume fractions of the fiber phase and the pore phase according to different gray valuesAndcounting the length-diameter ratio range lambda of the pore phase structure;

step six, establishing a micro-mechanical model of the carbon/carbon composite material, wherein a pore phase omega is formed_iA pyrolytic carbon matrix and a fibrous phase D-omega; applying an external load P at the position X on the outer surface tau of the model, wherein e is a unit external normal vector of the outer surface tau of the model; the stress and strain of the carbon/carbon composite material in the micromechanics model are expressed as follows

Defining a matrix phase andthe stiffness tensors of the pore inclusion phases are N and N, respectively^*(ii) a The flexibility tensors are respectively M ═ N^-1And M^*＝N^*-1(ii) a According to the theory of solid defect mechanics

$<\stackrel{\&OverBar;}{{\mathrm{\&epsiv;}}_{ij}}{>}_{RVE}=M_{ijkl}:{\mathrm{\&sigma;}}_{kj}^0+\mathrm{\&Sigma;}<{\mathrm{\&Delta;\&epsiv;}}_{ij}{>}_{\mathrm{\&Omega;},i}---\left(3\right)$

Wherein, Delta_ij＝C^RVE:σ^∞，C^RVETensor contribution to the compliance of the inclusion phase, where Δ is due to the fact that the pore inclusion phase is a homogeneous material_ijAnd σ⁰Are all symmetric second-order tensors, so C^RVEIs a fourth order tensor having the same symmetric properties as the stress strain tensor; therefore, the method has the advantages that,so the contribution tensor here is

$C_{ijkl}^{RVE}=\left[\begin{array}{cccccc}{C}_{1111}& C_{1122}& C_{1133}& C_{1112}& C_{1123}& C_{1131}\\ C_{2211}& C_{2222}& C_{2233}& C_{2212}& C_{2223}& C_{2231}\\ C_{3311}& C_{3322}& C_{3333}& C_{3312}& C_{3323}& C_{3331}\\ C_{1211}& C_{1222}& C_{1233}& C_{1212}& C_{1223}& C_{1211}\\ C_{2311}& C_{2312}& C_{2312}& C_{2312}& C_{2323}& C_{2331}\\ C_{3111}& C_{3122}& C_{3133}& C_{3112}& C_{3123}& C_{3131}\end{array}\right]---\left(4\right)$

By definition with respect to the Eshelby tensor S_ijklFourth order tensor Q of function_ijklAnd R_ijklWherein Q is_ijkl＝N_ijrs(I_rskl-S_rskl)，R_ijkl＝S_ijmnM_mnkl(ii) a So that the compliance contribution tensor of the inclusion phase is

C^RVE＝v_i[(M^*-M)^-1+Q]^-1(i∈[1，N])(5)

Seventhly, the pore structures in the carbon/carbon composite material have different shapes, so ellipsoids with different orientations and size ratios are used for approximating the pore structures, and the structural parameter of the pores is A_r(a_iλ), wherein a₁＝a₂＝a＝λa₃(ii) a The orientation distribution function of the pores is

Wherein psi_i(α)ψ_i(β)、ψ_i(Φ) indicates the relationship of the ellipsoid at the local coordinatesThe projection distribution angles of the three coordinate axes;

expression of S from the Eshelby tensor occluded by ellipsoids_ijkl(ii) a Writing the compliance contribution tensor of the apertureThe expression of the flexibility tensor of the equivalent matrix containing the holes is

$M^{efM}=M+\underset{i}{\&Sigma;}{C}^{RVE}---\left(7\right)$

Wherein,

step eight, taking the fiber phase of the carbon/carbon composite material as an inclusion phase to be brought into the equivalent matrix obtained in the step seven, wherein the flexibility contribution tensor of the fiber phase isWherein h is₁And h₂Obtaining the fiber according to an expression of Mori-Tanaka of different fiber orientation distribution;

the overall compliance contribution tensor is thus

M^eff＝M^efM+C^f(8)

Therefore, each elastic performance parameter of the carbon/carbon composite material is expressed according to the component of the whole flexibility matrix.