CN114611782A - Rigidity prediction method for weaving C/C composite material in thermal oxidation environment - Google Patents

Rigidity prediction method for weaving C/C composite material in thermal oxidation environment Download PDF

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CN114611782A
CN114611782A CN202210219542.2A CN202210219542A CN114611782A CN 114611782 A CN114611782 A CN 114611782A CN 202210219542 A CN202210219542 A CN 202210219542A CN 114611782 A CN114611782 A CN 114611782A
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oxidation
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张宏建
刘帅
崔海涛
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a rigidity prediction method of a braided C/C composite material in a thermal oxidation environment, which comprises the following steps: s1: establishing an oxidation kinetic model of the braided C/C composite material with or without an anti-oxidation coating according to an Arrhenius equation and a diffusion theory by combining an oxidation rule of the C/C composite material; s2: calculating the oxidation amount of the fiber and the matrix according to an oxidation kinetic model and an oxidation mechanism, and integrating the influence of oxidation into the property change of the components; s3: establishing a calculation method for the elastic performance of the component fiber bundle considering temperature and oxidation; s4: analyzing the pore distribution rule in the C/C composite material, establishing a unit cell geometric model containing pores, discretizing the geometric model and applying periodic boundary conditions to obtain a unit cell finite element model. The rigidity of the braided C/C composite material in different oxidation time and different temperature ranges can be accurately predicted, a large amount of time and energy are not required to be consumed to test the rigidity of the braided C/C composite material through tests, and the test cost is saved.

Description

Rigidity prediction method for weaving C/C composite material in thermal oxidation environment
Technical Field
The invention belongs to the technical field of composite materials, relates to a calculation method of rigidity of a C/C composite material, and particularly relates to a rigidity prediction method of a woven C/C composite material in a thermal-oxygen environment.
Background
The C/C composite material is high in strength, can keep high strength in an ultrahigh-temperature environment, has good ablation performance, and is therefore important to be applied in the fields of aerospace, medical treatment, automobiles, ships and the like. The working temperature of the C/C composite material generally used in the high-temperature environment is 600 ℃ to 2500 ℃, the C/C composite material is influenced by factors such as temperature, oxidation and the like in the working process of the high-temperature environment, and the mechanical behavior is more complex than that of the C/C composite material at room temperature. Because the woven C/C composite material is a novel structural material, an efficient method for predicting the rigidity of the woven C/C composite material in a thermal oxidation environment is lacked at the present stage. And the manufacturing process is not completely mature and controllable, and a large amount of cost is consumed through an experimental mode. Therefore, how to accurately predict the rigidity of the braided C/C composite material in a hot oxygen environment is an urgent problem to be solved.
Disclosure of Invention
The purpose of the invention is as follows: in order to overcome the defects in the prior art, the rigidity prediction method for weaving the C/C composite material in the thermal-oxygen environment is provided, and the rigidity of the weaving C/C composite material in different oxidation time and different temperature intervals can be calculated on the premise of saving the experiment cost.
The technical scheme is as follows: in order to achieve the above object, the present invention provides a method for predicting the stiffness of a woven C/C composite material in a thermal oxygen environment, comprising the steps of:
s1, establishing a knitted C/C composite material oxidation kinetic model with or without an anti-oxidation coating according to an Arrhenius equation and a diffusion theory by combining the oxidation rule of the C/C composite material;
s2, calculating the oxidation amount of the fiber and the matrix according to the oxidation kinetic model and the oxidation mechanism, and integrating the influence of oxidation into the property change of the components;
s3, establishing a calculation method for the elastic performance of the fiber bundle considering temperature and oxidation;
s4, analyzing the pore distribution rule in the C/C composite material, establishing a unit cell geometric model containing pores, discretizing the geometric model and applying periodic boundary conditions to obtain a unit cell finite element model;
s5, endowing the elastic properties of the fiber bundle and the matrix to a unit cell finite element model, applying displacement load to the unit cell finite element model, and calculating the rigidity of the woven C/C composite material at different temperatures and different oxidation times by a finite element method.
As a preferable scheme of the present invention, the oxidation kinetic model in the step S1 is divided into two parts due to different oxidation laws,
(1)400℃-700℃C-O2the chemical reaction controls the oxidation rate;
the oxidation rate is controlled by chemical reaction, the C/C composite material with or without the anti-oxidation coating is uniformly oxidized inside and outside, and an oxidation kinetic model of the C/C composite material is established according to the Arrhenius equation, namely
Figure BDA0003536506120000021
In the formula, kvIs the oxidation rate constant; k is a radical of0Is an integral constant obtained by fitting oxidation test data; erIs the activation energy of the reaction; t is the absolute temperature; r is a gas constant;
(2) the oxidation reaction rate is controlled by diffusion at the temperature of over 700 ℃;
the oxidation rate of the composite material in the temperature range is controlled by the diffusion of the oxidation gas through the defects of the oxidation resistant coating, cracks, pores and the like of the C/C composite material. The oxidation gradually extends from outside to inside, and the oxidation depth changes along with the oxidation time.
The C/C composite material is divided into an external oxidation part and an internal non-oxidation part, the oxidation depth becomes an important parameter in a prediction model, an oxidation amount and oxidation depth calculation model, namely an oxidation kinetic model, is deduced according to a mass transfer theory, and the calculation formula is as follows:
Figure BDA0003536506120000022
Figure BDA0003536506120000023
Figure BDA0003536506120000024
Figure BDA0003536506120000025
wherein N is the amount of a substance in which carbon participates in oxidation, i.e., the amount of oxidation,
Figure BDA0003536506120000026
coating of CO in region II for oxidation resistance2A is the surface area of the C/C composite material, t represents the oxidation time, L is the coating thickness, xfThe length of the oxidation-resistant coating region II,
Figure BDA0003536506120000027
is at the boundary of the coating layer O2The concentration of the amount of the substance,
Figure BDA0003536506120000028
is O2The effective diffusion coefficient of the light emitted from the light source,
Figure BDA0003536506120000029
is CO2H is the initial crack depth of the C/C composite material, l is the initial crack length, s is the initial crack thickness, AxThe area of the bottom of the cavity is quickly oxidized by the initial crack on the surface of the C/C composite material, C is the mass concentration of the ambient gas, H is the oxidation depth, H' is the size of the cavity, M is the volume concentration of the ambient gasCIs the molar mass of carbon, ρ is the density of the C/C composite, S0The area of exposed C/C per unit area of the coated sample is shown.
In a preferred embodiment of the present invention, in step S2, the carbon fibers and the carbon matrix are oxidized in equal volume, and the volume content of the fibers in the fiber bundle is decreased by the oxidation, and the size of the pores in the matrix and the pure matrix outside the fiber bundle are increased, so that the porosity is increased.
As a preferred embodiment of the present invention, the step S3 specifically includes: the mechanical property of the carbon matrix is referred to the performance of the graphite; calculating the elastic property of the oxidized fiber bundle based on an empirical formula of NASA (national aeronautics and telecommunications analysis), and the influence of pores in a matrix in the fiber bundle on the elastic property of components, performing equivalent treatment by using an Eshelby equivalent inclusion theory, introducing a heat treatment correction coefficient, a true density correction coefficient and a temperature correction coefficient into the empirical formula of NASA, and further establishing a fiber bundle elastic property calculation method considering temperature and oxidation.
As a preferred scheme of the invention, the tensile test results of different batches of C/C composite unidirectional plates are used for fitting the heat treatment correction coefficient of the manufacturing process influencing the modulus of the C/C composite
Figure BDA0003536506120000031
And true density correction factor
Figure BDA0003536506120000032
The temperature correction coefficient is obtained by judging the degree of the elastic property of each component of the C/C composite material changing with the temperature according to the change of the elastic property of the graphite changing with the temperature
Figure BDA0003536506120000033
The formula is calculated considering the temperature and the elastic properties of the oxidized fiber bundle,
Figure BDA0003536506120000034
Figure BDA0003536506120000035
Figure BDA0003536506120000036
Figure BDA0003536506120000037
νb12＝νb13＝Vbfν12+(1-Vbf)νm (10)
Figure BDA0003536506120000038
if i, j ∈ 1,2,3, then E in the formulaiIs the fiber elastic modulus, EbiIs the elastic modulus of the fiber bundle, VbfIs the volume fraction of the fibers of the oxidized fiber bundle, Em0Is equivalent elastic modulus, G, of a matrix equivalently treated by Eshelby equivalent inclusion theoryijIs the fiber shear modulus, GbijIs the shear modulus of the fiber bundle, GmIs the shear modulus of the matrix, vbijAs a fibre bundle, vijIs a fiber and vmIs the poisson's ratio of the matrix.
In a preferred embodiment of the present invention, in step S4, when the geometric model of the unit cell including pores is established, the fiber bundle is considered to be tightened, and the geometric model includes pores randomly distributed in a pure matrix.
As a preferred embodiment of the present invention, the step S5 specifically includes:
(1)400℃-700℃C-O2chemical reaction controls the oxidation rate, the mechanical properties of the fiber bundle and the matrix at corresponding temperature and oxidation time are endowed to a unit cell finite element model at the stage, displacement load is applied to the unit cell, and the finite element method is utilized to carry out C-O (carbon-oxygen) reaction2And (4) predicting the rigidity of the C/C composite material in the reaction rate control oxidation stage under the hot oxygen environment.
(2) The method comprises the steps of controlling the oxidation reaction rate by diffusion at the temperature of more than 700 ℃, respectively establishing a representative unit cell finite element model of an oxidized part and a non-oxidized part, endowing the two unit cell finite element models with the temperature and the elastic properties of an oxidized fiber bundle and a matrix considered, applying displacement load to a unit cell, respectively calculating the rigidity of the oxidized part and the non-oxidized part by using a finite element method, and then superposing the rigidity according to the oxidation depth and the volume ratio of the oxidized part and the non-oxidized part to further obtain the integral rigidity of the braided C/C composite material.
Has the advantages that: compared with the prior art, the invention has the following advantages:
1. the invention considers the uncontrollable property of the manufacturing process of the braided C/C composite material, and is suitable for different batches of braided C/C composite materials with different porosities and different true densities.
2. The influence of oxidation and temperature on the elastic property of the C/C composite material is quantitatively integrated into a rigidity prediction model, so that the designability of weaving the C/C composite material is greatly enhanced.
3. The rigidity prediction method for the braided C/C composite material in the thermal oxidation environment can accurately predict the rigidity of the braided C/C composite material in the thermal oxidation environment with different temperature ranges and different oxidation degrees, replaces a method for determining the rigidity of the material by a large number of experiments, and saves the experiment cost.
Drawings
FIG. 1 is a stiffness prediction flow chart;
FIG. 2 is a schematic view of the division of the oxidation resistant coating into regions;
FIG. 3 is a geometric model of a fiber bundle in a three-dimensional four-way braided C/C composite unit cell;
FIG. 4 is a geometric model of a three-dimensional four-way woven C/C composite unit cell including a pore matrix;
FIG. 5 is a geometric model of a three-dimensional four-way braided C/C composite unit cell.
Detailed Description
The present invention is further illustrated by the following figures and specific examples, which are to be understood as illustrative only and not as limiting the scope of the invention, which is to be given the full breadth of the appended claims and any and all equivalent modifications thereof which may occur to those skilled in the art upon reading the present specification.
In this embodiment, the method of the present invention is applied to the stiffness prediction of a three-dimensional four-way woven C/C composite material in a thermal oxidation environment, and referring to fig. 1, two working conditions of 600 ℃ oxidation for 20min for a three-dimensional four-way woven C/C composite material without a coating and 900 ℃ oxidation for 30min for a three-dimensional four-way woven C/C composite material with a SiC coating are taken as examples. For convenience of explanation, the former is defined as operating condition 1, and the latter is defined as operating condition 2, and the stiffness of the former is predicted respectively, and the specific flow is as follows:
step 1: according to an Arrhenius equation and a diffusion theory, a braided C/C composite material oxidation kinetic model with or without a coating is established by combining the oxidation rule of the C/C composite material. The oxidation kinetic model is divided into two parts due to different oxidation laws:
(1) working conditions 1C and O2The reaction rate controls the oxidation rate of the C/C composite material, and the C/C composite material with or without the anti-oxidation coating is uniformly oxidized inside and outside. Establishing an oxidation kinetic model of the C/C composite material according to the Arrhenius equation, namely
Figure BDA0003536506120000041
In the formula, kvIs the oxidation rate constant; k is a radical of0Is an integration constant obtained by fitting oxidation test data, lgk0＝-0.633；ErIs 69 kJ/mol; t is the absolute temperature of 873K; r is 8.314 (J.K)-1·mol-1)。
And under the working condition 2, the oxidation reaction rate is controlled by diffusion of oxidation gas through defects such as cracks, pores and the like of the oxidation resistant coating and the C/C composite material. The oxidation gradually extends from outside to inside, and the oxidation depth changes along with the oxidation time. The C/C composite material is divided into an external oxidation part and an internal non-oxidation part, the oxidation depth becomes an important parameter in a prediction model, an oxidation amount and oxidation depth calculation model is deduced according to a mass transfer theory, and the calculation formula is as follows:
Figure BDA0003536506120000051
Figure BDA0003536506120000052
Figure BDA0003536506120000053
Figure BDA0003536506120000054
wherein N is the amount of carbon participating in oxidation,
Figure BDA0003536506120000055
is CO in region II of FIG. 22A is the surface area of the C/C composite; t represents oxidation time, 30 min; l is the thickness of the coating, 0.35 mm; x is the number offThe length of region II of FIG. 2;
Figure BDA0003536506120000056
is at the boundary of the coating layer O2The quantity concentration of the substance, c is the quantity concentration of the substance of the ambient gas, and the ratio of the quantity concentration of the substance to the concentration of the substance of the ambient gas is 0.21;
Figure BDA0003536506120000057
is O2The effective diffusion coefficient of the light emitted from the light source,
Figure BDA0003536506120000058
is CO2The effective diffusion coefficient of (2) is obtained by a diffusion coefficient calculation method; h is the initial crack depth of the C/C composite material, l is the initial crack length, s is the initial crack thickness, and a specific numerical value is obtained by observing a sample; a. thexThe area of the bottom of the cavity is quickly oxidized from the initial crack on the surface of the C/C composite material; h' is the size of a cavity, and the maximum value of h, l and s is taken; h is the oxidation depth; m is a group ofCIs the molar mass of carbon, 12 g/mol; ρ is the density of the C/C composite material, 2.03g/cm3；S0The area of exposed C/C per unit area of the sample is shown.
Step 2: and calculating the oxidation amount of the fiber and the matrix according to an oxidation kinetic model and an oxidation mechanism, and integrating the influence of oxidation into the property change of the components. The equal volume of the carbon fiber and the carbon matrix is oxidized, the volume content of the fiber bundle is reduced by the oxidization, the sizes of the pores of the matrix in the fiber bundle and the pure matrix outside the fiber bundle are increased, and the porosity is increased.
And step 3: a calculation method of the elastic property of the component considering temperature and oxidation is established. The mechanical property of the carbon matrix is referred to the performance of the graphite; calculating the elastic property of the oxidized fiber bundle based on an empirical formula of NASA (national advanced chemical analysis A), performing equivalent treatment by using Eshelby equivalent inclusion theory, and introducing a heat treatment correction coefficient into the empirical formula of NASA
Figure BDA0003536506120000059
True density correction factor
Figure BDA00035365061200000510
And temperature correction coefficient
Figure BDA00035365061200000511
The tensile test results of the unidirectional plates of the C/C composite materials of different batches are utilized to fit the heat treatment correction coefficient and the true density correction coefficient which are influenced by the manufacturing process to the modulus of the C/C composite materials,
Figure BDA00035365061200000512
and
Figure BDA00035365061200000513
0.75 and 1.20, respectively; the degree of the elastic property of each component of the C/C composite material changing along with the temperature is judged by utilizing the elastic property of the graphite changing along with the temperature to obtain the temperature correction coefficient, and the working conditions 1 and 2
Figure BDA00035365061200000514
Take 1.18 and 1.27, respectively. The equation for the elastic properties of the fiber bundle considering temperature and oxidation is:
Figure BDA0003536506120000061
Figure BDA0003536506120000062
Figure BDA0003536506120000063
Figure BDA0003536506120000064
νb12＝νb13＝Vbfν12+(1-Vbf)νm (10)
Figure BDA0003536506120000065
international general mechanical expression, E1, E2, E3 represent the moduli of the fiber bundle in three different directions, i, j ∈ 1,2,3, where EiIs the modulus of elasticity of the fiber, EbiIs the elastic modulus of the fiber bundle, VbfIs the volume fraction of the fibers of the oxidized fiber bundle, Em0Is equivalent elastic modulus, G, of a matrix equivalently treated by Eshelby equivalent inclusion theoryijIs the fiber shear modulus, GbijIs the shear modulus of the fiber bundle, GmIs the shear modulus of the matrix, vbij、νijV and vmThe poisson ratios of the fiber bundle, the fibers and the matrix, respectively. The mechanical properties of the carbon matrix and the carbon fiber at room temperature are shown in table 1.
TABLE 1 mechanical Properties of carbon matrix and carbon fiber Table
Components E1/Em(GPa) E2(GPa) G12(GPa) G23(GPa) ν12/νm
Carbon fiber 202 40 17 14.3 0.3
Carbon substrate 8.8 — — — 0.23
And 4, step 4: and establishing a unit cell model. The fiber bundle adopts a tightened hexagonal shape, pores are simulated to be randomly distributed in the material by using a random sequence adsorption method, the established fiber bundle, a geometric model containing a pore matrix and a unit cell are shown in figures 3-5, and a unit cell finite element model is obtained by discretizing and applying periodic boundary conditions.
And 5: because the working condition 1 and the working condition 2 are in different temperature intervals and the oxidation mechanism is different, the working condition 1 and the working condition 2 are divided for analysis.
(1) The three-dimensional four-way woven C/C composite material is uniformly oxidized inside and outside under the working condition 1. Of fibre bundles and matrices at corresponding temperatures and oxidation timesMechanical properties are given to a unit cell finite element model, displacement load is applied to the unit cell, and the finite element method is utilized to carry out C-O2And (4) predicting the rigidity of the C/C composite material in the reaction rate control oxidation stage under the hot oxygen environment.
(2) Under the working condition 2, the three-dimensional four-way braided C/C composite material is oxidized and gradually extends from outside to inside, and the C/C composite material is divided into an external oxidized part and an internal unoxidized part. Therefore, it is necessary to establish a representative unit cell finite element model of the oxidized part and the unoxidized part respectively, endow the two unit cell finite element models with consideration of temperature and elastic properties of the oxidized fiber bundle and the matrix, apply displacement load to the unit cell, calculate the rigidity of the oxidized part and the unoxidized part respectively by using a finite element method, and then superimpose the rigidity according to the oxidation depth and the volume ratio of the oxidized part and the unoxidized part, thereby obtaining the overall rigidity of the woven C/C composite material.
The rigidity prediction value and the test value of the three-dimensional four-way woven C/C composite material under two working conditions are shown in the table 2 by using the rigidity prediction method for weaving the C/C composite material under the thermal-oxygen environment. Compared with the prior art, the method provided by the invention opens up a convenient channel for predicting the elastic property of the woven C/C composite material on the premise of ensuring the precision.
TABLE 2 Table of predicted values and test values of stiffness of three-dimensional four-way braided C/C composite material
Working conditions Test values (GPa) Predicted value (GPa) Error (%)
1 58.25 61.70 5.92
2 64.43 66.13 2.64
The complex influence of temperature and oxidation on the elastic property of the C/C composite material is considered, and based on the test, the rigidity of the woven C/C composite material in different oxidation time and different temperature intervals can be accurately predicted by the prediction method provided by the invention, the rigidity of the woven C/C composite material can be tested through the test without consuming a large amount of time and energy, and the test cost is saved.

Claims (7)

1. A rigidity prediction method of a braided C/C composite material in a thermal oxygen environment is characterized by comprising the following steps:
s1, establishing a knitted C/C composite material oxidation kinetic model with or without an anti-oxidation coating according to an Arrhenius equation and a diffusion theory by combining the oxidation rule of the C/C composite material;
s2, calculating the oxidation quantity of the fiber and the matrix according to the oxidation kinetic model and the oxidation mechanism, and blending the influence of oxidation into the performance change of the components;
s3, establishing a calculation method for the elastic performance of the fiber bundle considering temperature and oxidation;
s4, analyzing the pore distribution rule in the C/C composite material, establishing a unit cell geometric model containing pores, discretizing the geometric model and applying periodic boundary conditions to obtain a unit cell finite element model;
s5, endowing the elastic properties of the fiber bundle and the matrix to a unit cell finite element model, applying displacement load to the unit cell finite element model, and calculating the rigidity of the woven C/C composite material at different temperatures and different oxidation times by a finite element method.
2. The method for predicting the rigidity of the braided C/C composite material in the thermo-oxidative environment according to claim 1, wherein: the oxidation kinetic model in step S1 is divided into two parts due to different oxidation laws,
(1)400℃-700℃C-O2the chemical reaction controls the oxidation rate;
the oxidation rate is controlled by chemical reaction, the C/C composite material with or without the anti-oxidation coating is uniformly oxidized inside and outside, and an oxidation kinetic model of the C/C composite material is established according to the Arrhenius equation, namely
Figure FDA0003536506110000011
In the formula, kvIs the oxidation rate constant; k is a radical of0Is an integral constant obtained by fitting oxidation test data; erIs the activation energy of the reaction; t is the absolute temperature; r is a gas constant;
(2) the oxidation reaction rate is controlled by diffusion at the temperature of over 700 ℃;
the C/C composite material is divided into an external oxidation part and an internal non-oxidation part, the oxidation depth becomes an important parameter in a prediction model, an oxidation amount and oxidation depth calculation model, namely an oxidation kinetic model, is deduced according to a mass transfer theory, and the calculation formula is as follows:
Figure FDA0003536506110000012
Figure FDA0003536506110000013
Figure FDA0003536506110000014
Figure FDA0003536506110000015
wherein N is the amount of a substance in which carbon participates in oxidation, i.e., the amount of oxidation,
Figure FDA0003536506110000016
by oxidation of CO in zone II2A is the surface area of the C/C composite material, t represents the oxidation time, L is the coating thickness, xfThe length of the oxidation-resistant coating region II,
Figure FDA0003536506110000021
is at the boundary of the coating layer O2The concentration of the amount of the substance,
Figure FDA0003536506110000022
is O2The effective diffusion coefficient of the light emitted from the light source,
Figure FDA0003536506110000023
is CO2H is the initial crack depth of the C/C composite material, l is the initial crack length, s is the initial crack thickness, AxThe area of the bottom of the cavity is quickly oxidized by the initial crack on the surface of the C/C composite material, C is the mass concentration of the ambient gas, H is the oxidation depth, H' is the size of the cavity, M is the volume concentration of the ambient gasCIs the molar mass of carbon, ρ is the density of the C/C composite, S0The area of exposed C/C per unit area of the coated sample is shown.
3. The method for predicting the rigidity of the woven C/C composite material under the thermal oxygen environment according to claim 1, wherein the carbon fibers and the carbon matrix are oxidized in the same volume in the step S2, the volume content of the fibers in the fiber bundle is reduced due to the oxidation, the sizes of the pores of the matrix in the fiber bundle and the pure matrix outside the fiber bundle are increased, and the porosity is increased.
4. The method for predicting the rigidity of the braided C/C composite material in the thermo-oxidative environment according to claim 1, wherein the step S3 is specifically as follows: the mechanical property of the carbon matrix is referred to the performance of the graphite; calculating the elastic property of the oxidized fiber bundle based on an empirical formula of NASA (national aeronautics and telecommunications analysis), and the influence of pores in a matrix in the fiber bundle on the elastic property of components, performing equivalent treatment by using an Eshelby equivalent inclusion theory, introducing a heat treatment correction coefficient, a true density correction coefficient and a temperature correction coefficient into the empirical formula of NASA, and further establishing a fiber bundle elastic property calculation method considering temperature and oxidation.
5. The method for predicting the rigidity of the braided C/C composite material in the thermo-oxidative environment according to claim 4, wherein: heat treatment correction coefficient for fitting manufacturing process to influence C/C composite material modulus by utilizing tensile test results of different batches of C/C composite material unidirectional plates
Figure FDA0003536506110000024
And true density correction factor
Figure FDA0003536506110000025
The degree of the elastic property of each component of the C/C composite material changing with the temperature is judged by utilizing the change of the elastic property of the graphite changing with the temperature to obtain the temperature correction coefficient
Figure FDA0003536506110000026
The formula is calculated considering the temperature and the elastic properties of the oxidized fiber bundle,
Figure FDA0003536506110000027
Figure FDA0003536506110000028
Figure FDA0003536506110000029
Figure FDA00035365061100000210
νb12＝νb13＝Vbfν12+(1-Vbf)νm (10)
Figure FDA00035365061100000211
if i, j ∈ 1,2,3, then E in the formulaiIs the modulus of elasticity of the fiber, EbiIs the elastic modulus of the fiber bundle, VbfIs the volume fraction of the fibers of the oxidized fiber bundle, Em0Is equivalent elastic modulus, G, of a matrix equivalently treated by Eshelby equivalent inclusion theoryijIs the fiber shear modulus, GbijIs the shear modulus of the fiber bundle, GmIs matrix shear modulus, vbijAs a fibre bundle, vijAs fibres and vmIs the poisson's ratio of the matrix.
6. The method for predicting the stiffness of the woven C/C composite material under the thermal-oxygen environment according to claim 1, wherein in the step S4, when a unit cell geometric model containing pores is established, the fiber bundle is considered to be tightened, and the geometric model contains pores randomly distributed in a pure matrix.
7. The method for predicting the rigidity of the braided C/C composite material in the thermo-oxidative environment according to claim 1, wherein the step S5 is specifically as follows:
(1)400℃-700℃C-O2chemical reaction controls the oxidation rate, the mechanical properties of the fiber bundle and the matrix at corresponding temperature and oxidation time are endowed to a unit cell finite element model at the stage, displacement load is applied to the unit cell, and the finite element method is utilized to carry out C-O (carbon-oxygen) reaction2And (4) predicting the rigidity of the C/C composite material in the reaction rate control oxidation stage under the hot oxygen environment.
(2) The method comprises the steps of controlling the oxidation reaction rate by diffusion at the temperature of over 700 ℃, respectively establishing representative unit cell finite element models of oxidized and unoxidized parts, endowing the two unit cell finite element models with temperature and the elastic properties of oxidized fiber bundles and matrixes considered, applying displacement load to unit cells, respectively calculating the rigidity of the oxidized and unoxidized parts by using a finite element method, and then superposing the rigidity according to the oxidation depth and the volume ratio of the oxidized and unoxidized parts to obtain the integral rigidity of the woven C/C composite material.
CN202210219542.2A 2022-03-08 2022-03-08 Rigidity prediction method for weaving C/C composite material in thermal oxidation environment Pending CN114611782A (en)

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CN115938494A (en) * 2022-11-24 2023-04-07 中国科学院大气物理研究所 DCU accelerated calculation method, equipment and storage medium of gas-phase chemical module
CN115938494B (en) * 2022-11-24 2024-01-09 中国科学院大气物理研究所 DCU acceleration calculation method, equipment and storage medium of gas phase chemical module
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