CN105930579A - Method for predicting residual stiffness of two-dimensional braided ceramic matrix composite material after oxidation - Google Patents

Abstract

The invention relates to a method for predicting residual stiffness of a two-dimensional braided ceramic matrix composite material after oxidation. The stiffness refers to elastic deformation resistance ability of the material under stress. By analyzing the stiffness of each component of the material, stress and strain distribution in the material can be determined. Therefore, the invention provides the method capable of accurately predicting the residual stiffness of the two-dimensional braided ceramic matrix composite material after oxidation. A kinetic model considering fiber oxidation is proposed, and based on this, a microscale model considering fiber oxidation and a mesoscale model of the two-dimensional braided ceramic matrix composite material are established. With the adoption of a finite element method, the residual stiffness of the material after oxidation is calculated by applying a periodic boundary condition. According to the method, the residual stiffness of the material in different oxidation temperature intervals at different oxidation time can be accurately predicted and does not need to be tested by a large amount of manpower and material resources through tests, so that a large amount of test costs are reduced.

Description

Residual Stiffness Forecasting Methodology after a kind of control of two-dimensional braided ceramic matric composite oxidation

Technical field

The present invention relates to Residual Stiffness Forecasting Methodology after a kind of control of two-dimensional braided ceramic matric composite oxidation.

Background technology

Control of two-dimensional braided ceramic matric composite have high than strong, Gao Bimo, the Optimality such as high temperature resistant, corrosion-resistant and low-density Can, at re-entry space vehicle high-temperature thermal protection system, there is demand widely.Material is during it uses, due to by high temperature The impact of environmental factors, can gradually produce oxidative damage, cause material mechanical performance to decline, and then have a strong impact on engineering structure The service life of part and safety.Rigidity refers to that the ability of elastic deformation resisted by material when stress, and study two-dimensional plain weave is made pottery After the oxidation of porcelain based composites, Residual Stiffness is applied to important in inhibiting.

Owing to unidirectional ceramic matric composite exists the shortcomings such as non-fiber direction mechanical property is weak, its range of application receives limit System.The appearance of control of two-dimensional braided structural ceramics based composites, the shortcoming overcoming unidirectional composite material, simultaneously in thickness side Upwards fibre bundle integration is higher, adds material interlaminar shear strength, decreases lamination, and improves composite wood Material shock resistance and fatigue property, be therefore greatly expanded the range of application of ceramic matric composite.

It is a kind of new structural material yet with control of two-dimensional braided ceramic matric composite, the most also there is no efficient method Predict the Residual Stiffness after its oxidation, the most not disclosed patent of invention.Yang Chengpeng (Yang Chengpeng, strong osmanthus fine jade, Wang Bo, etc. The oxidative damage of 2D-C/SiC composite and rigidity model [J]. composite journal, 2009,26 (3): 175-181.) use The method of experiment tests 2D C/SiC composite Residual Stiffness under 700 DEG C of environment, and change based on microscopical structure Changing and establish computing formula, value of calculation is the most identical with experiment value.But by the way of experiment, to consume substantial amounts of experiment money Gold, its computation model proposed also can only calculate the Residual Stiffness under discrete specified temp.

Currently, predict that the Residual Stiffness after the oxidation of control of two-dimensional braided ceramic matric composite is the art weight the most accurately Want and insoluble problem.

Summary of the invention

Goal of the invention: for above-mentioned prior art, proposes one and can effectively predict that control of two-dimensional braided ceramic matric composite aoxidizes Rear Residual Stiffness Forecasting Methodology.

Technical scheme: Residual Stiffness Forecasting Methodology after a kind of control of two-dimensional braided ceramic matric composite oxidation, comprises the steps:

(1), based on mass loss rate theory and fiber degradation rule it is assumed that set up oxidation kinetics model；

(2), based on oxidation kinetics model, use finite element software, set up the single cell model of the micro-scale after oxidation；

(3) periodic boundary condition of the single cell model of micro-scale, is applied；

(4) elastic parameter in these 6 directions of single cell model, is calculated；

(5), use finite element software, set up control of two-dimensional braided ceramic matric composite single cell model；

(6), using basic as yarn of the elastic parameter in 6 directions of single cell model of micro-scale after calculated oxidation Attribute, brings control of two-dimensional braided ceramic matric composite single cell model into；

(7) periodic boundary condition of described control of two-dimensional braided ceramic matric composite single cell model, is applied；

(8) the residual elasticity modulus that control of two-dimensional braided ceramic matric composite is axial, it is calculated.

As the preferred version of the present invention, in described step (1), described mass loss rate theory is divided into two temperature ranges:

1) when temperature is when 400 DEG C～700 DEG C are interval, and formula is as follows:

${\mathrm{\λ}}_r=\frac{\mathrm{\Δ}W}{W}=\frac{K_0{\mathrm{\χ}}_{O_2}{\mathrm{PS}}_{eff}{M}_c}{RTW}\exp \left(\frac{-E_r}{RT}\right)t---\left(1\right)$

Wherein, λ_rBeing the mass loss rate of composite, W is the quality of composite, and Δ W is the mass change of material Amount, K₀It is the constant relevant to oxidation rate,Being the volume fraction of oxygen, P is atmospheric gas pressure, M_cIt is that carbon is fine The molal weight of dimension, R is gas constant, and T is ambient temperature, E_rBeing oxidation reaction activation energy, t is oxidization time, S_eff It it is the effective affecting acreage of carbon；Wherein, S_eff=μ W, μ are the valid reaction coefficient of carbon；

2) when temperature is when 700 DEG C～900 DEG C are interval, and formula is as follows:

${\mathrm{\λ}}_r=\frac{S_{eff}{N}_c{M}_c}{W}(\sqrt{\frac{4\mathrm{\λ}(T^{1/2}-T^{3/2}/T_c)}{N_c}\frac{P}{RT}ln\[1+{\mathrm{\χ}}_{o_2}\left(0\right)\]t}-L_c)---\left(2\right)$

Wherein, N_cBeing the molar density of carbon, λ is the constant relevant with original state, T_cIt is MATRIX CRACKING temperature, L_cIt is Coating layer thickness；

Described fiber degradation rule is assumed: assuming that fiber is at high temperature degenerated with circular rule, formula is as follows:

$\mathrm{\δ}={\left(\frac{{\mathrm{\λ}}_r{\mathrm{\ρ}}_{c}LH}{{\mathrm{\πn\ρ}}_f{N}_f}\right)}^{\frac{1}{2}}---\left(3\right)$

Wherein, δ is the oxidation length of fiber, ρ_fAnd ρ_cRepresenting fiber and the density of composite respectively, L is composite wood The length of material, H is the height of composite, and n is the amount of the material of carbon, N_fIt is the quantity of fiber in unit are；

By the mass loss rate λ of described composite_rBring the computing formula (3) of oxidation length δ of described fiber into, obtain:

1) when temperature is when 400 DEG C～700 DEG C are interval:

$\mathrm{\δ}={\[\frac{K_0{\mathrm{\χ}}_{O_2}{\mathrm{\μ\ρ}}_{c}LH\exp \left(\frac{-E_r}{RT}\right)t}{{\mathrm{\πnN}}_f}\]}^{\frac{1}{2}}---\left(4\right)$

2) when temperature is when 700 DEG C～900 DEG C are interval:

$\mathrm{\δ}={\[\frac{{\mathrm{\μN}}_c{M}_c{\mathrm{\ρ}}_{c}LH(\sqrt{\frac{4\mathrm{\λ}(T^{1/2}-T^{3/2}/T_c)}{N_c}\frac{P}{RT}ln\[1+{\mathrm{\χ}}_{o_2}\left(0\right)\]t}-L_c)}{{\mathrm{\πn\ρ}}_f{N}_f}\]}^{\frac{1}{2}}---\left(5\right)$

After thus can aoxidizing, the residue radius of fiber is:

1) when temperature is when 400 DEG C～700 DEG C are interval, and formula is as follows:

$rf={\mathrm{rf}}_0-{\[\frac{K_0{\mathrm{\χ}}_{O_2}{\mathrm{\μ\ρ}}_{c}LH\exp \left(\frac{-E_r}{RT}\right)t}{{\mathrm{\πnN}}_f}\]}^{\frac{1}{2}}---\left(6\right)$

2) when temperature is when 700 DEG C～900 DEG C are interval, and formula is as follows:

$rf={\mathrm{rf}}_0-{\[\frac{{\mathrm{\μN}}_c{M}_c{\mathrm{\ρ}}_{c}LH(\sqrt{\frac{4\mathrm{\λ}(T^{1/2}-T^{3/2}/T_c)}{N_c}\frac{P}{RT}ln\[1+{\mathrm{\χ}}_{o_2}\left(0\right)\]t}-L_c)}{{\mathrm{\πn\ρ}}_f{N}_f}\]}^{\frac{1}{2}}---\left(7\right)$

Wherein, rf is the residue radius after fiber oxidation, rf₀It it is fiber initial radium when not aoxidizing.

As the preferred version of the present invention, in described step (2), it is assumed that be oxidized to the oxidation of uniform penetration type, fiber after oxidation Radius is equal everywhere.

As the preferred version of the present invention, in described step (3), the boundary condition applied meet displacement seriality and The concordance of model contrary two plane stresses distribution.

As the preferred version of the present invention, in described step (4), the elastic parameter in described 6 directions includes x, y, z three The elastic modulus E in individual direction_x、E_y、E_z, the shear modulus G in tri-directions of xy, xz, yz_xy、G_xz、G_yz, Yi Jibo Pine compares v_xy、v_xz、v_yz。

As the preferred version of the present invention, in described step (7), applying periodic boundary condition is:

$u_i^{Z+}={\mathrm{\θ}}_i{x_i}^{Z+}+u_i^{*}---\left(8\right)$

$u_i^{Z-}={\mathrm{\θ}}_i{x_i}^{Z-}+u_i^{*}---\left(9\right)$

Wherein, Z+ and Z-represents two the contrary border surfaces being perpendicular to Z axis respectively,For at Z+ border table Displacement on face,For the displacement on Z-border surface, x_i ^Z+For the displacement of node, x on Z+ surface_i ^Z-For Z- The displacement of node on surface,For the periodic portions at border surface top offset, θ_iAveragely should for periodic structure Become tensor.

Beneficial effect: Residual Stiffness Forecasting Methodology after the control of two-dimensional braided ceramic matric composite oxidation that the present invention provides, based on Mass loss rate model and fiber degradation rule are it is assumed that propose the kinetic model considering fiber oxidation.Dynamic based on oxidation Mechanical model, uses FInite Element to establish micro-scale model and the control of two-dimensional braided ceramic base composite wood considering fiber oxidation Material list born of the same parents' Scale Model, it was predicted that the Residual Stiffness of material.The forecast model that the present invention proposes has taken into full account that fiber is with oxygen Change time, the deterioration law of temperature, therefore, it is possible to dope remaining after the oxidation of control of two-dimensional braided ceramic matric composite accurately Remaining rigidity and saved substantial amounts of experimental cost.

Accompanying drawing explanation

Fig. 1 is carbon fiber oxidative scan Electronic Speculum figure near crack tip；

Fig. 2 is ceramic matric composite two-dimensional model；

Fig. 3 is that unidirectional ceramic matric composite aoxidizes schematic diagram；

Fig. 4 is the micromodel after oxidation；

Fig. 5 is micromodel boundary condition schematic diagram after oxidation；

Fig. 6 is two dimension plain weave ceramic matric composite single cell model；

Fig. 7 is two dimension plain weave ceramic matric composite single cell model boundary condition schematic diagram；

Fig. 8 is the particular flow sheet of this forecast model；

The residual elasticity Modulus Prediction that when Fig. 9 is lower 700 DEG C of air ambient, two dimension Characteristics of Plain-Woven C/SiC ceramic matrix composite material is axial Value and the correlation curve of experiment value；

The residual elasticity Modulus Prediction that when Figure 10 is lower 800 DEG C of air ambient, two dimension Characteristics of Plain-Woven C/SiC ceramic matrix composite material is axial Value and the correlation curve of experiment value；

The residual elasticity Modulus Prediction that when Figure 11 is lower 850 DEG C of air ambient, two dimension Characteristics of Plain-Woven C/SiC ceramic matrix composite material is axial Value and the correlation curve of experiment value；

The residual elasticity Modulus Prediction that when Figure 12 is lower 900 DEG C of air ambient, two dimension Characteristics of Plain-Woven C/SiC ceramic matrix composite material is axial Value and the correlation curve of experiment value.

Detailed description of the invention

Below in conjunction with the accompanying drawings the present invention is done and further explain.

The present embodiment is as a example by two dimension Characteristics of Plain-Woven C/SiC ceramic matrix composite material, to material oxygen in 700 DEG C～900 DEG C of interval ranges Residual Stiffness after change is predicted, and wherein material property parameter is as shown in table 1.

Table 1

As shown in Figure 8, this method specifically comprises the following steps that

(1), based on mass loss rate theory and fiber degradation rule it is assumed that set up oxidation kinetics model.Wherein, quality Loss rate theory is divided into two temperature ranges:

1) when temperature is when 400 DEG C～700 DEG C are interval, and the mass loss rate formula of composite is as follows:

${\mathrm{\λ}}_r=\frac{\mathrm{\Δ}W}{W}=\frac{K_0{\mathrm{\χ}}_{O_2}{\mathrm{PS}}_{eff}{M}_c}{RTW}\exp \left(\frac{-E_r}{RT}\right)t---\left(1\right)$

Wherein, λ_rIt it is the mass loss rate of composite；W is the quality of composite；Δ W is the quality of composite The mass change amount of loss rate；K₀It is the constant relevant to oxidation rate；It is the volume fraction of oxygen, here takes 20.95%；P is atmospheric gas pressure, here takes 101.325KPa；M_cIt is the molal weight of carbon fiber, here takes 12×10³kg/mol；R is gas constant, here takes 8.3145J/ (mol K)；T is ambient temperature；E_rIt is oxygen Change reaction activity；T is oxidization time；S_effIt is the effective affecting acreage of carbon, S_effRelevant with the quality of sample, represent For S_eff=μ W, μ are the valid reaction coefficient of carbon, μ depend on the micro-crack area of sample and hole cross-sectional area and Sample density, can be recorded by experiment.

2) when temperature is when 700 DEG C～900 DEG C are interval, and the mass loss rate formula of composite is as follows:

${\mathrm{\λ}}_r=\frac{S_{eff}{N}_c{M}_c}{W}(\sqrt{\frac{4\mathrm{\λ}(T^{1/2}-T^{3/2}/T_c)}{N_c}\frac{P}{RT}ln\[1+{\mathrm{\χ}}_{o_2}\left(0\right)\]t}-L_c)---\left(2\right)$

Wherein, N_cIt it is the molar density of carbon；λ is the constant relevant with original state；T_cIt is MATRIX CRACKING temperature, at this In take 1030 DEG C；L_cIt it is coating layer thickness.

Fiber degradation rule is assumed: according to the stereoscan photograph shown in Fig. 1 and the ceramic matric composite shown in Fig. 2 Two-dimensional model, it is assumed that fiber is at high temperature degenerated, as it is shown on figure 3, the oxidation of fiber is long with circular rule Degree is the length of BD section in figure；r₀The distance of i.e. OD, refers to the center of circle O of oxide regions of matching to fiber not The distance on surface during oxidation；R' is the distance of OC, refers to the radius of the oxide regions of matching；α is r₀With r' it Between angle.Fiber degradation rule formula is as follows:

$\mathrm{\δ}={\left(\frac{{\mathrm{\λ}}_r{\mathrm{\ρ}}_{c}LH}{{\mathrm{\πn\ρ}}_f{N}_f}\right)}^{\frac{1}{2}}---\left(3\right)$

Wherein, δ is the oxidation length of fiber；ρ_fAnd ρ_cRepresent fiber and the density of composite respectively；L is composite wood The length of material, H is the height of composite, as shown in Figure 2；N is the amount of the material of carbon；N_fIn being unit are The quantity of fiber.

By the mass loss rate λ of composite_rBring the computing formula (3) of oxidation length δ of fiber into, obtain:

1) when temperature is when 400 DEG C～700 DEG C are interval:

$\mathrm{\δ}={\[\frac{K_0{\mathrm{\χ}}_{O_2}{\mathrm{\μ\ρ}}_{c}LH\exp \left(\frac{-E_r}{RT}\right)t}{{\mathrm{\πnN}}_f}\]}^{\frac{1}{2}}---\left(4\right)$

2) when temperature is when 700 DEG C～900 DEG C are interval:

$\mathrm{\δ}={\[\frac{{\mathrm{\μN}}_c{M}_c{\mathrm{\ρ}}_{c}LH(\sqrt{\frac{4\mathrm{\λ}(T^{1/2}-T^{3/2}/T_c)}{N_c}\frac{P}{RT}ln\[1+{\mathrm{\χ}}_{o_2}\left(0\right)\]t}-L_c)}{{\mathrm{\πn\ρ}}_f{N}_f}\]}^{\frac{1}{2}}---\left(5\right)$

If initial radium when fiber does not aoxidizes is rf₀, the residue radius after fiber oxidation is rf, according to relation Rf=rf₀After-δ can aoxidize, the residue radius of fiber is:

1) when temperature is when 400 DEG C～700 DEG C are interval, and formula is as follows:

$rf={\mathrm{rf}}_0-{\[\frac{K_0{\mathrm{\χ}}_{O_2}{\mathrm{\μ\ρ}}_{c}LH\exp \left(\frac{-E_r}{RT}\right)t}{{\mathrm{\πnN}}_f}\]}^{\frac{1}{2}}---\left(6\right)$

2) when temperature is when 700 DEG C～900 DEG C are interval, and formula is as follows:

$rf={\mathrm{rf}}_0-{\[\frac{{\mathrm{\μN}}_c{M}_c{\mathrm{\ρ}}_{c}LH(\sqrt{\frac{4\mathrm{\λ}(T^{1/2}-T^{3/2}/T_c)}{N_c}\frac{P}{RT}ln\[1+{\mathrm{\χ}}_{o_2}\left(0\right)\]t}-L_c)}{{\mathrm{\πn\ρ}}_f{N}_f}\]}^{\frac{1}{2}}---\left(7\right)$

(2), based on the oxidation kinetics model i.e. formula (6) in above-mentioned steps (1) and (7), ANSYS software is used, Set up the single cell model of the micro-scale after oxidation, as shown in Figure 4.Wherein assume to be oxidized to the oxidation of uniform penetration type, oxygen After change, fiber radius everywhere is equal.

(3) periodic boundary condition of the single cell model of micro-scale, is applied: the boundary condition applied meets the company of displacement Continuous property and the concordance of single cell model contrary two plane stresses distribution at micro-scale, as shown in Figure 5；Applied Periodic boundary condition is as shown in table 2.

Table 2

No

S(x-,y,z)

S(x+,y,z)

S(x,y-,z)

S(x,y+,z)

S(x,y,z-)

S(x,y,z+)

1

ux=0

ux=0.1

uy=0

uy=const

uz=0

uz=const

2

ux=0

ux=const

uy=0

uy=0.1

uz=0

uz=const

3

ux=0

ux=const

uy=0

uy=const

uz=0

uz=0.1

4

ux=0

ux=const

uz=0

uz=0

uy=0

uy=0.1

5

uz=0

uz=0

uy=0

uy=const

ux=0

ux=0.1

6

uy=0

uy=0

ux=0

ux=0.1

uz=0

uz=const

In table: S (x^-,y,z)、S(x⁺, y, z) it is respectively two planes of x direction coordinate minimum and maximum, S (x, y^-,z)、 S(x,y⁺, z) it is respectively two planes of y direction coordinate minimum and maximum, S (x, y, z^-)、S(x,y,z⁺) it is respectively z direction seat Two planes of mark minimum and maximum.u_x、u_y、u_zBeing respectively the displacement constraint in x, y, z direction, const represents flat All modal displacements coupling in face.

(4), calculating the elastic parameter in these 6 directions of single cell model, the elastic parameter in 6 directions includes x, y, z three The elastic modulus E in direction_x、E_y、E_z, the shear modulus G in tri-directions of xy, xz, yz_xy、G_xz、G_yz, and Poisson Compare v_xy、v_xz、v_yz。

(5), use ANSYS software, set up control of two-dimensional braided ceramic matric composite single cell model, as shown in Figure 6；Mould The dimensional parameters of type is as shown in table 3.

Table 3

hf	a	hb	b
				0.056	0.4	0.02	0.2

Wherein, a is yarn width, and b is spacing between yarn, h in the same direction_fFor yarn thickness, h_bFor matrix ligament thickness.

(6), using basic as yarn of the elastic parameter in 6 directions of single cell model of micro-scale after calculated oxidation Attribute, brings control of two-dimensional braided ceramic matric composite single cell model into；

(7), the periodic boundary condition of control of two-dimensional braided ceramic matric composite single cell model is applied, as it is shown in fig. 7, its table Reaching formula is:

$u_i^{Z+}={\mathrm{\θ}}_i{x_i}^{Z+}+u_i^{*}---\left(8\right)$

$u_i^{Z-}={\mathrm{\θ}}_i{x_i}^{Z-}+u_i^{*}---\left(9\right)$

Wherein, Z+ and Z-represents two the contrary border surfaces being perpendicular to Z axis respectively,For at Z+ border table Displacement on face,For the displacement on Z-border surface, x_i ^Z+For the displacement of node, x on Z+ surface_i ^Z-For Z- The displacement of node on surface,For the periodic portions at border surface top offset, θ_iAveragely should for periodic structure Become tensor.

Relative shift between two boundary faces of Z+ and Z-is expressed as:

$u_i^{Z+}-u_i^{Z-}={\mathrm{\θ}}_i(x_i^{Z+}-x_i^{Z-})={\mathrm{\θ}}_i{\mathrm{\Δx}}_i^Z$

Wherein,Represent the displacement knots modification of node in two boundary faces of Z+ and Z-.

(8), according to formulaE_LFor the axial modulus of elasticity of material, σ_mFor the axial mean stress of unit, ε_m For the axial mean strain of unit, the residual elasticity modulus that two dimension Characteristics of Plain-Woven C/SiC ceramic matrix composite material is axial can be calculated.

It is pre-that Fig. 9 gives the residual elasticity modulus that under 700 DEG C of ambient temperatures, two dimension Characteristics of Plain-Woven C/SiC ceramic matrix composite material is axial Measured value and the correlation curve of experiment value.Figure 10 gives two dimension Characteristics of Plain-Woven C/SiC composite wood under 800 DEG C of ambient temperatures Expect axial residual elasticity Modulus Prediction value and the correlation curve of experiment value.Figure 11 gives under 850 DEG C of ambient temperatures two The dimension axial residual elasticity Modulus Prediction value of Characteristics of Plain-Woven C/SiC ceramic matrix composite material and the correlation curve of experiment value.Figure 12 Give under 900 DEG C of ambient temperatures the axial residual elasticity Modulus Prediction value of two dimension Characteristics of Plain-Woven C/SiC ceramic matrix composite material and The correlation curve of experiment value.Visible by contrast, the method for the present invention can effectively predict control of two-dimensional braided ceramic base composite wood Residual Stiffness after material oxidation.

The above is only the preferred embodiment of the present invention, it is noted that for those skilled in the art For, under the premise without departing from the principles of the invention, it is also possible to make some improvements and modifications, these improvements and modifications are also Should be regarded as protection scope of the present invention.

Claims (6)

1. Residual Stiffness Forecasting Methodology after a control of two-dimensional braided ceramic matric composite oxidation, it is characterised in that include as follows Step:

(1), based on mass loss rate theory and fiber degradation rule it is assumed that set up oxidation kinetics model；

(2), based on oxidation kinetics model, use finite element software, set up the single cell model of the micro-scale after oxidation；

(3) periodic boundary condition of the single cell model of micro-scale, is applied；

(4) elastic parameter in these 6 directions of single cell model, is calculated；

(5), use finite element software, set up control of two-dimensional braided ceramic matric composite single cell model；

(6), using basic as yarn of the elastic parameter in 6 directions of single cell model of micro-scale after calculated oxidation Attribute, brings control of two-dimensional braided ceramic matric composite single cell model into；

(7) periodic boundary condition of described control of two-dimensional braided ceramic matric composite single cell model, is applied；

(8) the residual elasticity modulus that control of two-dimensional braided ceramic matric composite is axial, it is calculated.

Residual Stiffness Forecasting Methodology after control of two-dimensional braided ceramic matric composite the most according to claim 1 oxidation, it is special Levying and be: in described step (1), described mass loss rate theory is divided into two temperature ranges:

1) when temperature is when 400 DEG C～700 DEG C are interval, and formula is as follows:

${\mathrm{\λ}}_r=\frac{\mathrm{\Δ}W}{W}=\frac{K_0{\mathrm{\χ}}_{O_2}{\mathrm{PS}}_{eff}{M}_c}{RTW}\exp \left(\frac{-E_r}{RT}\right)t---\left(1\right)$

Wherein, λ_rBeing the mass loss rate of composite, W is the quality of composite, and Δ W is the mass change of material Amount, K₀It is the constant relevant to oxidation rate,Being the volume fraction of oxygen, P is atmospheric gas pressure, M_cIt is that carbon is fine The molal weight of dimension, R is gas constant, and T is ambient temperature, E_rBeing oxidation reaction activation energy, t is oxidization time, S_eff It it is the effective affecting acreage of carbon；Wherein, S_eff=μ W, μ are the valid reaction coefficient of carbon；

2) when temperature is when 700 DEG C～900 DEG C are interval, and formula is as follows:

${\mathrm{\λ}}_r=\frac{S_{eff}{N}_c{M}_c}{W}(\sqrt{\frac{4\mathrm{\λ}(T^{1/2}-T^{3/2}/T_c)}{N_c}\frac{P}{RT}ln\[1+{\mathrm{\χ}}_{o_2}\left(0\right)\]t}-L_c)---\left(2\right)$

Wherein, N_cBeing the molar density of carbon, λ is the constant relevant with original state, T_cIt is MATRIX CRACKING temperature, L_cIt is Coating layer thickness；

Described fiber degradation rule is assumed: assuming that fiber is at high temperature degenerated with circular rule, formula is as follows:

$\mathrm{\δ}={\left(\frac{{\mathrm{\λ}}_r{\mathrm{\ρ}}_{c}LH}{{\mathrm{\πn\ρ}}_f{N}_f}\right)}^{\frac{1}{2}}---\left(3\right)$

Wherein, δ is the oxidation length of fiber, ρ_fAnd ρ_cRepresenting fiber and the density of composite respectively, L is composite wood The length of material, H is the height of composite, and n is the amount of the material of carbon, N_fIt is the quantity of fiber in unit are；

By the mass loss rate λ of described composite_rBring the computing formula (3) of oxidation length δ of described fiber into, obtain:

1) when temperature is when 400 DEG C～700 DEG C are interval:

$\mathrm{\δ}={\[\frac{K_0{\mathrm{\χ}}_{O_2}{\mathrm{\μ\ρ}}_{c}LH\exp \left(\frac{-E_r}{RT}\right)t}{{\mathrm{\πnN}}_f}\]}^{\frac{1}{2}}---\left(4\right)$

2) when temperature is when 700 DEG C～900 DEG C are interval:

$\mathrm{\δ}={\[\frac{{\mathrm{\μN}}_c{M}_c{\mathrm{\ρ}}_{c}LH(\sqrt{\frac{4\mathrm{\λ}(T^{1/2}-T^{3/2}/T_c)}{N_c}\frac{P}{RT}ln\[1+{\mathrm{\χ}}_{o_2}\left(0\right)\]t}-L_c)}{{\mathrm{\πn\ρ}}_f{N}_f}\]}^{\frac{1}{2}}---\left(5\right)$

After thus can aoxidizing, the residue radius of fiber is:

1) when temperature is when 400 DEG C～700 DEG C are interval, and formula is as follows:

$rf={\mathrm{rf}}_0-{\[\frac{K_0{\mathrm{\χ}}_{O_2}{\mathrm{\μ\ρ}}_{c}LH\exp \left(\frac{-E_r}{RT}\right)t}{{\mathrm{\πnN}}_f}\]}^{\frac{1}{2}}---\left(6\right)$

2) when temperature is when 700 DEG C～900 DEG C are interval, and formula is as follows:

$rf={\mathrm{rf}}_0-{\[\frac{{\mathrm{\μN}}_c{M}_c{\mathrm{\ρ}}_{c}LH(\sqrt{\frac{4\mathrm{\λ}(T^{1/2}-T^{3/2}/T_c)}{N_c}\frac{P}{RT}ln\[1+{\mathrm{\χ}}_{o_2}\left(0\right)\]t}-L_c)}{{\mathrm{\πn\ρ}}_f{N}_f}\]}^{\frac{1}{2}}---\left(7\right)$

Wherein, rf is the residue radius after fiber oxidation, rf₀It it is fiber initial radium when not aoxidizing.

Residual Stiffness Forecasting Methodology after control of two-dimensional braided ceramic matric composite the most according to claim 1 oxidation, it is special Levy and be: in described step (2), it is assumed that being oxidized to the oxidation of uniform penetration type, after oxidation, fiber radius everywhere is equal.

Residual Stiffness Forecasting Methodology after control of two-dimensional braided ceramic matric composite the most according to claim 1 oxidation, it is special Levying and be: in described step (3), the boundary condition applied meets the seriality of displacement and answers in contrary two planes of model The concordance of power distribution.

Residual Stiffness Forecasting Methodology after control of two-dimensional braided ceramic matric composite the most according to claim 1 oxidation, it is special Levying and be: in described step (4), the elastic parameter in described 6 directions includes the elastic modelling quantity in three directions of x, y, z E_x、E_y、E_z, the shear modulus G in tri-directions of xy, xz, yz_xy、G_xz、G_yz, and Poisson's ratio v_xy、v_xz、v_yz。

Residual Stiffness Forecasting Methodology after control of two-dimensional braided ceramic matric composite the most according to claim 1 oxidation, it is special Levying and be: in described step (7), applying periodic boundary condition is:

$u_i^{Z+}={\mathrm{\θ}}_i{x_i}^{Z+}+u_i^{*}---\left(8\right)$

$u_i^{Z-}={\mathrm{\θ}}_i{x_i}^{Z-}+u_i^{*}---\left(9\right)$

Wherein, Z+ and Z-represents two the contrary border surfaces being perpendicular to Z axis respectively,For at Z+ border table Displacement on face,For the displacement on Z-border surface, x_i ^Z+For the displacement of node, x on Z+ surface_i ^Z-For Z- The displacement of node on surface,For the periodic portions at border surface top offset,Averagely should for periodic structure Become tensor.