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

Abstract

The invention discloses an image extraction-based carbon/carbon composite elastic property prediction method, so as to solve the technical problem that the existing carbon/carbon composite elastic property prediction method is poor in precision. According to the technical scheme, based on a carbon/carbon composite PLM (polarization image) image, an image calculation means is adopted to acquire information parameters for each microstructure, the microstructures serve as inclusion phases to be sequentially led to an analytical mechanics model, a theory of inclusion for mechanics of solid defects is used for solving the equivalent elastic property, and accurate and high-efficiency prediction on multi-group phase-separation carbon/carbon composite elastic property is realized. As the polarization image is adopted to acquire information of the microstructures such as fiber and a pore of the carbon/carbon composite, the built mechanics model is more accurate and closer to the actual condition. Important parameters such as the fiber bundle distribution, the fiber volume fraction, the pore volume fraction and the distribution influencing the equivalent elastic modulus of the carbon/carbon composite are acquired through calculation in no need of hypothesis.

Description

Carbon/carbon composite material elastic performance prediction method based on image extraction

Technical Field

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

Background

The carbon/carbon composite material is increasingly applied to the fields of aerospace and the like due to the advantages of high specific strength, high specific stiffness, good high-temperature mechanical property and the like, is considered to be a thermal structural material which can be used in an ultrahigh-temperature environment for a long time and has the greatest development prospect in the future, and therefore has important national defense strategic value. However, the material is often characterized by anisotropy, so that the mechanical property prediction is often complex. In conclusion, a method capable of quickly and accurately calculating the elastic parameters of the composite material has important significance. The test cost can be reduced to a certain extent, and the development period can be shortened.

The research on the equivalent performance of the continuous carbon fiber reinforced composite material mainly comprises an experimental method, an analytical method and a numerical simulation method, wherein the experimental method is to perform static test on the composite material according to relevant requirements in test standards such as ASTM (American society of testing materials) and the like, and required parameters are obtained from a test result curve. In this process, the sample is prepared according to certain standards, and the workload is usually large. In addition, for the composite material with more independent elastic parameters, the performance of the composite material is more difficult to study through an experimental method.

Finite element numerical simulations have proven to be an effective analytical tool. Document 1, the chinese patent application publication No. 104537259a, discloses the use of XCT technology to extract microstructure information of fiber reinforced composites and to build finite element models. However, in the case of carbon/carbon composite materials, due to the existence of pore microstructures, the model establishment and calculation are difficult, and the carbon/carbon composite materials are limited by computer capability and cannot be generally used.

In addition, document 2 "TSUKROVI, equivalent. mechanical advanced materials and structures,2005,12(1): 43-54" discloses a method of predicting the elastic properties of carbon/carbon composite materials by using the solid defect mechanical inclusion theory based on Eshelby tensor, but due to the particularity of CVI process, the microstructure of the material is generally complex, and in addition to a fiber phase and a matrix phase, a non-uniform pore structure is distributed in the matrix, and the fiber and pore structure has a large influence on the equivalent elastic modulus of the material. These factors are difficult to take into account based on the assumptions made in the above-mentioned documents about the microstructure of the material. Therefore, the analytical algorithms described in the literature deviate from the experimental values in the prediction of the elasticity parameters.

Disclosure of Invention

In order to overcome the defect that the existing method for predicting the elastic property of the carbon/carbon composite material is poor in precision, the invention provides a method for predicting the elastic property of the carbon/carbon composite material based on image extraction. The method is based on a PLM (polarized light image) image of the carbon/carbon composite material, information parameters of each microstructure are obtained by adopting an image calculation means, the microstructures are sequentially introduced into an analytic mechanical model as inclusion phases, the equivalent elastic performance of the microstructures is solved by using an inclusion theory of solid defect mechanics, and the accurate and efficient prediction of the elastic performance of the multi-component phase-separated carbon/carbon composite material is realized.

The technical scheme adopted by the invention for solving the technical problems is as follows: 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;

and step three, 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 adopting (i, j, k) (i belongs to (0, B-1), j belongs to (0, A-1) and k belongs to (0, N-1)) to represent the (k + 1) th image, the (j + 1) th row and the (i + 1) th column of pixels. 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);

and step four, identifying and extracting the carbon/carbon composite material fiber area according to the threshold value determined by the calculation result of the step two, and updating the Pixel gray level array Pixel { data }. And on the basis, the adaptive threshold algorithm of the second step is used again to determine the threshold of the pore structure, and the pore contour is identified and extracted. And updating the corresponding gray values of the different component areas in the step three again.

And 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 valuesAndand counting 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. An applied load P is applied at a location X on the outer surface of the model, and e is a unit of an external normal vector of the outer surface of the model. The stress and strain of the carbon/carbon composite material in the micromechanics model are expressed as follows

Defining the rigidity tensors of the matrix phase and the pore inclusion phase as N and N respectively^*. The flexibility tensors are respectively M ═ N^-1And M^*＝N^*-1. 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 that has 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_iiklAnd R_ijklWherein Q is_ijkl＝N_ijrs(I_rskl-S_rskl)，R_ijkl＝S_ijmnM_mnkl. 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) in which，a₁＝a₂＝a＝λa₃. The orientation distribution function of the pores is

Therein, Ψ_i(α)、Ψ_i(β)、Ψ_iAnd (phi) respectively represents the projection distribution angles of the ellipsoid under the local coordinates relative to three coordinate axes.

Expression of S from the Eshelby tensor occluded by ellipsoids_ijkl. 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 h₂According to different fibre orientation distributionsAn expression of Mori-Tanaka is obtained.

The overall compliance contribution tensor is thus

M^eff＝M^efM+C^f(8)

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

The invention has the beneficial effects that: the method is based on a PLM (polarized light image) image of the carbon/carbon composite material, information parameters of each microstructure are obtained by adopting an image calculation means, the microstructures are sequentially introduced into an analytic mechanical model as inclusion phases, the equivalent elastic performance of the microstructures is solved by using an inclusion theory of solid defect mechanics, and the accurate and efficient prediction of the elastic performance of the multi-component phase-separated carbon/carbon composite material is realized. Due to the fact that the information of microstructures such as fibers, pores and the like of the carbon/carbon composite material is obtained through the polarized light image, the established mechanical model is more accurate and closer to the actual situation. The fiber bundle distribution, the fiber volume fraction, the pore volume fraction, the distribution and other important parameters influencing the equivalent elastic modulus of the carbon/carbon composite material are obtained by calculation without assumption. The equivalent performance of the carbon/carbon composite material is calculated only by partial structure of the material, and the rigidity performance of the material can be calculated by analyzing the photographed polarized light image to obtain corresponding microstructure parameters, so that the method is simple and easy to implement.

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

Drawings

FIG. 1 is a polarization image of a carbon/carbon composite prepared by the CVI process;

FIG. 2 is a pre-processed PLM image;

FIG. 3 is an image after extraction of the fiber structure according to gray scale values;

FIG. 4 is an image of extracted pore structure according to the number of gray scales;

FIG. 5 is a schematic view of the established micromechanical model;

fig. 6 is a schematic diagram of pore structure and distribution in local coordinates.

Detailed Description

Reference is made to fig. 1-6. The method for predicting the elastic property of the carbon/carbon composite material based on image extraction comprises the following specific steps:

step 1: taking multiple sets of PLM (polarization microscopic image) photographs (shown in figure 1) of the analyzed carbon/carbon composite material sample, and obtaining pixel information of each image;

fig. 1 is a polarization image of a unidirectional preform reinforced carbon/carbon composite prepared using a CVI process. The reinforcing phase is T700 carbon fiber, the matrix is pyrolytic carbon matrix, and the elasticity parameters of the carbon fiber and the matrix are as follows: e₁₁＝230Gpa,E₂₂＝E₃₃＝15Gpa，G₁₂＝G₁₃＝9Gpa，G₂₃＝9.5Gpa，μ₁₂＝μ₁₃＝0.2，μ₂₃0.23. The elastic parameters of the matrix are: e ═ 32.8Gpa, μ ═ 0.159; the transverse elastic modulus of the composite material is tested experimentally, and the result is 13.5 Gpa.

Step 2: respectively carrying out noise point removal, contrast adjustment and smooth filtering processing on the N groups of shot pictures (as shown in figure 2); determining a threshold value of the image by adopting an adaptive threshold value algorithm;

and step 3: the pixel size of each image is set as a long A pixel and a wide B pixel, the gray scale range of each pixel is 0-255, and (i, j, k) (i belongs to (0, B-1), j belongs to (0, A-1), k belongs to (0, N-1)) is adopted to represent the (k + 1) th image, the (j + 1) th row and the (i + 1) th column. Establishing a gray value array Pixel { data } of the pixels of the image adjusted in the step 2, 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);

and 4, step 4: and (3) identifying and extracting the fiber area according to the threshold determined by the calculation result in the step (2) (as shown in figure 3), and updating the Pixel gray level array Pixel data. On the basis of the above, the adaptive threshold algorithm of step 2 is used again to determine the threshold value of the pore structure, and the pore contour is subjected to identification extraction (as shown in fig. 4). And updating the corresponding gray values of the different component areas in the step 3 again.

And 5: according to the calculation result in the step 4, the gray values of the matrix phase, the fiber phase and the pore phase are GVM, GVF and GVP respectively. Respectively calculating the volume fractions of the fiber phase and the pore phase according to different gray valuesAndand the aspect ratio range lambda ∈ (0.2, 7.5) of the pore structure in the statistical chart.

Step 6: a micromechanical model of the material was created (as shown in FIG. 5), in which the pore phase (Ω)_i) A pyrolytic carbon matrix and a fibrous phase (D- Ω). An applied load P is applied at a location X on the outer surface τ of the model, e being the unit outer normal vector of the outer surface τ. The stress and strain of the entire model are expressed as follows

Defining the rigidity tensors of the matrix phase and the pore inclusion phase as N and N respectively^*. The flexibility tensors are respectively M ═ N^-1And M^*＝N^*-1. 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 that has the same symmetric properties as the stress strain tensor. Therefore, the method has the advantages that,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. So that the compliance contribution tensor of the inclusion phase is

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

And 7: since the pore structure in carbon/carbon composites tends to have different shapes, it is approximated here using ellipsoids of different orientation and size ratio, the structural parameter of the pores being a_r(a_iλ), wherein a₁＝a₂＝a＝λa₃. The orientation distribution function of the pores is as follows.

Therein Ψ_i(α)、Ψ_i(β)、Ψ_i(Φ) respectively represent the distribution angles of the projections of the ellipsoid in the local coordinates with respect to the three coordinate axes (as shown in fig. 6).

Expression of S from the Eshelby tensor occluded by ellipsoids_ijkl. 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,

and 8: taking the fiber phase as an inclusion phase into the equivalent matrix obtained in the step 7, wherein the tensor of the flexibility contribution of the fiber phase isWherein h is₁And h₂Then according to the expression of Mori-Tanaka for different fiber orientation distributions.

The overall compliance contribution tensor is thus

M^eff＝M^efM+c^f(8)

The elastic performance parameters of the material are expressed according to the components of the overall compliance matrix. So that it has a transverse modulus of elasticity ofThe difference of the test result and the tested result is 13.5Gpa, and the result is better in coincidence.

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.