CN111243681A - Method for predicting internal oxidation morphology of ceramic matrix composite in stress oxidation environment - Google Patents

Method for predicting internal oxidation morphology of ceramic matrix composite in stress oxidation environment Download PDF

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CN111243681A
CN111243681A CN202010041210.0A CN202010041210A CN111243681A CN 111243681 A CN111243681 A CN 111243681A CN 202010041210 A CN202010041210 A CN 202010041210A CN 111243681 A CN111243681 A CN 111243681A
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宋迎东
陈西辉
丁俊杰
牛序铭
孙志刚
靳彧
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a method for predicting the internal oxidation morphology of a unidirectional SiC/SiC composite material in a stress oxidation environment, which considers the morphology change of an oxidation gap on a C interface at the initial stage of a crack based on a mass transfer theory, uses a volume equivalence method to enable an arc oxidation gap to be equivalent to a rectangular gap after the oxidation gap reaches a SiC fiber, and adds oxygen consumed by oxidation of the SiC fiber into an established control equation, so that a model is closer to the actual situation, the oxidation of the inner crack wall of the ceramic matrix composite material after any time of stress oxidation, the time for the oxygen to start to oxidize the fiber, and the oxidation morphology of the fiber, the interface and a matrix after the oxygen enters the bottom of the crack can be accurately predicted, and theoretical support is provided for the subsequent calculation of the residual mechanical property problem of the ceramic matrix composite material in the stress oxidation environment.

Description

Method for predicting internal oxidation morphology of ceramic matrix composite in stress oxidation environment
Technical Field
The invention belongs to the technical field of composite materials, and particularly relates to a method for predicting the internal oxidation morphology of a ceramic matrix composite material in a stress oxidation environment.
Background
The silicon carbide fiber toughened silicon carbide ceramic matrix composite (SiC/SiC for short) has excellent performances of high temperature resistance, low density, high specific strength, high specific modulus and the like, and has wide application prospects in parts such as aircraft engine combustion chambers, tail nozzle adjusting sheets and the like.
Because carbon has good compatibility with silicon carbide fiber and a matrix, the carbon is widely applied to SiC/SiC materials as an interface phase. SiC/C/SiC materials are mainly applied to high-temperature (>900 ℃) stress oxidation environments at present. In the environment, the matrix can crack due to the existence of stress, and oxidizing gas in the environment can enter the interior of the material through the matrix crack to perform oxidation reaction with component materials such as a C interface, SiC fibers, the matrix and the like, so that the material is degraded. The method can accurately and effectively predict the change of the internal appearance of the SiC/SiC material in the stress oxidation environment, provide an important theoretical basis for later calculation of the degradation of the mechanical property of the SiC/SiC composite material in the stress oxidation environment, and provide a necessary technical support for the reliability design of the material.
The document 'microstructure evolution and failure mechanism of 3D C/SiC in an aviation engine hot end part simulation environment' uses a Transmission Electron Microscope (TEM) to observe the oxidation morphology of a C/SiC interface in an oxidation environment, but an oxidation kinetic model is not established, so that the change of the internal morphology of a SiC/C/SiC composite material in the oxidation environment at any time cannot be predicted.
According to the patent 201910198163.8 'a method for predicting residual tensile strength of a ceramic matrix composite material in a stress oxidation environment', 201910198773.8 'a method for predicting mass change of a ceramic matrix composite material in a stress oxidation environment', 201910198794.x 'a method for predicting residual stiffness of a ceramic matrix composite material in a stress oxidation environment', an oxidation dynamics model of the ceramic matrix composite material in a stress oxidation environment is established, and the residual mechanical property of the ceramic matrix composite material after oxidation is predicted.
Patent 201910520855.X "a method for predicting the internal oxidation morphology of a unidirectional ceramic matrix composite material in a stress water vapor environment" establishes a SiC/C/SiC water vapor oxidation model, and predicts the change of the oxidation morphology of the SiC/C/SiC composite material in the water vapor oxidation environment. However, the water vapor oxidation mechanism is different from the oxygen oxidation mechanism, and the model does not consider the change rule of the oxidation arc-shaped gap of the C interface, so that the oxidation process of the C interface is simplified into a rectangle, and the oxidation morphology of the inside of the 1D-SiC/C/SiC composite material at any moment cannot be accurately simulated.
The literature "Ludovic Filipuzzi, Roger Nasliin.Oxidation mechanics and kinetics of 1D-SiC/C/SiC Composite Materials: II, Modeling [ J]Journal of the American Ceramic Society,2005,77(2):459-466 ". based on simple axisymmetric fiber/interface/matrix bonding, a 1D-SiC/C/SiC model was established at 900-1300 ℃ and 10-<P<In the temperature and pressure range of 100KPa, the oxidation behavior of the 1D-SiC/C/SiC composite material and oxygen is researched, and the consumption of a C interface and SiO on the composite material matrix and fiber are predicted2The layer thickness changes over time. However, in the document, oxidation of the interface along the crack direction in the oxidation process of the composite material and oxygen is not considered, the oxidation time from the oxidation gap of the C interface to the SiC fiber is neglected, and oxidation of SiC matrixes at two ends of the crack is not considered, so that the oxidation morphology of the 1D-SiC/C/SiC composite material at any moment can not be accurately simulated.
Therefore, a method capable of accurately predicting the internal oxidation morphology of the unidirectional SiC/C/SiC composite material in a stress oxidation environment is needed.
Disclosure of Invention
The invention provides a method for predicting the internal oxidation morphology of a ceramic matrix composite in a stress oxidation environment, which aims to solve the problem that the internal oxidation morphology of the ceramic matrix composite in the stress oxidation environment cannot be accurately predicted in the prior art.
In order to achieve the purpose, the invention adopts the technical scheme that:
a method for predicting the internal oxidation morphology of a ceramic matrix composite in a stress oxidation environment comprises the following steps:
step (1), determining the crack number of the ceramic matrix composite material substrate: considering the thermal residual stress, and calculating the change rule of the number of cracks in the unidirectional ceramic matrix composite material matrix along with the stress according to the stress borne by the matrix under the action of the tensile stress;
step (2), determining a crack width change rule: the change trend of the crack width along with the stress is predicted according to the original crack width of the matrix by considering the residual stress and the tensile stress born by the matrix;
step (3), determining a first-stage oxidation kinetic equation of the ceramic matrix composite material: the first stage is a carbon interface oxidation gap stage, and a carbon oxidation gap and SiO on the SiC substrate are constructed based on the oxidation mechanism of the carbon interface and the SiC substrate2The relation of the change of the layer thickness along with the time is based on the mass transfer theory, the oxidation kinetic equation of the first stage of the composite material is established, and the carbon interface oxidation gap and the SiC matrix SiO are obtained by calculation by combining the boundary conditions2Determining the change rule of the layer thickness at the crack so as to determine the internal oxidation morphology of the ceramic matrix composite material in the first stage and the time for the carbon interface oxidation notch to reach the SiC fiber;
step (4), determining a second-stage oxidation kinetic equation of the ceramic matrix composite material: the second stage is a SiC fiber oxidation stage, when the oxidation gap of the C interface reaches the SiC fiber, the arc-shaped oxidation gap of the C interface is equivalent to a rectangular gap by adopting an isovolumetric method, the initial oxidation length of the C interface is calculated, and then the SiO on the SiC fiber is constructed based on the oxidation mechanism of the SiC fiber2The relation of the change of the layer thickness along with time is based on the mass transfer theory, the oxidation kinetics equation of the second stage of the composite material is established by combining the carbon interface and the SiC matrix oxidation rule, the boundary condition is combined, the consumption length of the carbon interface and the oxide thickness change rule of the silicon carbide fiber and the matrix at the crack are calculated, the internal oxidation morphology of the second stage of the ceramic matrix composite material is determined, and the two stages of internal oxidation morphology are combinedAnd the internal oxidation morphology of the ceramic matrix composite at any time can be obtained.
Further, the specific steps of the step (1) are as follows:
assuming that the matrix failure of the ceramic matrix composite material obeys Poisson distribution under the action of tensile stress, the probability that the matrix fails due to at least one crack is as follows:
P(ξ＝σ,η＝Ls)＝1-exp{-M(A)}，N(A)≥1
wherein ：
Figure BDA0002367828930000031
wherein P (ξ) is a characteristic length LsThe probability of matrix failure when the stress is sigma, M (A) is a dimensionless Poisson parameter, N (A) is the number of cracks generated under the action of the stress, and sigmamcIs the initial cracking stress, σ, of the matrixthIs the residual thermal stress, σRIs the characteristic stress, m is the Weibull modulus;
simulating the number of cracks in the ceramic matrix composite material matrix under the action of stress in a programmable manner by adopting a Monte Carlo method;
to eliminate the influence of the total length of the substrate, the density rho is selectedcThe cracks of the matrix surface were characterized as a function of axial stress:
Figure BDA0002367828930000032
wherein ,ρcAnd n is the crack number of the matrix.
Further, in the step (2), the crack width of the matrix is expressed as:
Figure BDA0002367828930000033
wherein e represents a temperature T0Width of crack at stress σ, e0Denotes the initial crack width,. DELTA.T is the difference between the ambient temperature and the preparation temperature, αf、αmRespectively representing the coefficients of thermal expansion of the fiber and the matrix,Efdenotes the initial modulus of elasticity, V, of the fibermThe initial volume fraction of the matrix is expressed.
Further, in the step (3), under the condition that the oxygen supply is insufficient, the carbon interface reaction equation is as follows:
2C+O2＝2CO
the carbon interface depletion width is expressed as:
Figure BDA0002367828930000034
wherein ,lcIs the carbon interface oxidation width, KcIn order to be a constant of the reaction rate,
Figure BDA0002367828930000041
oxygen concentration, P, of reaction siteCIs the number of carbon reaction stages, McCarbon molar mass, gcThe amount of oxygen required to be consumed for 1mol C, ρcIs the carbon density; reaction rate constant KcThe calculation formula of (2) is as follows:
Kc＝kcexp(-Ec/RT)
wherein ,kcFor the constants characterizing the reaction rate, R is the ideal gas constant, R is 8.314J/(mol. K), EcT is the temperature for the activation energy of the reaction.
In the step (3), the reaction equation of the SiC matrix is as follows:
SiC+3/2O2＝SiO2+CO
formed SiO2Thickness of oxide layer with oxidation time t0Obey the parabolic criterion:
h2＝Bt0
wherein h represents the thickness of the oxide layer, B is a parabolic constant, and t0Is the oxidation time, expressed as:
Figure BDA0002367828930000042
wherein: k is a Henry constant and is,
Figure BDA0002367828930000045
for oxygen in SiO2Diffusion Rate in layer, gsTo produce 1mol SiO2The amount of oxygen species required;
in the step (3), in a binary diffusion system consisting of A and B, the actual effective diffusion coefficient D of the component AAThe calculation formula is as follows:
Figure BDA0002367828930000043
wherein ,DAIs the effective diffusion coefficient of component A, DABIs a free diffusion coefficient, DKAThe diffusion coefficient of the gas A in the pore channel; dABThe calculation formula of (2) is as follows:
Figure BDA0002367828930000044
wherein: p is the ambient pressure, MAAnd MBThe molar mass, Σ, of the respective component A, BvIs the diffusion volume of the molecule;
DKAthe calculation formula of (2) is as follows:
Figure BDA0002367828930000051
wherein: pi is the circumference ratio, and r is the radius of the material pore channel;
in the step (3), the oxidation kinetic equation established based on the mass conservation law is as follows:
Figure BDA0002367828930000052
wherein S is the cross-sectional area of gas flow,
Figure BDA0002367828930000053
is the flux of oxygen at that location,
Figure BDA0002367828930000054
is the amount of oxygen consumed at that location per unit length, and x is the gas channel length.
The first stage SiC matrix oxidation kinetics equation is then:
Figure BDA0002367828930000055
the first stage C interfacial oxidation kinetic equation is:
Figure BDA0002367828930000056
wherein y represents a coordinate value in the depth direction of the crack of the substrate, rtDenotes the distance, h, from the surface of the substrate to the center of the fiberm(y, t) is SiO at a certain time t and at a certain depth y of the crack in the substrate2The thickness of the layer projecting with respect to the wall surface, D being half the width of the crack, D1、D2Respectively, the effective diffusion coefficient of oxygen in the microcracks and at the interface, C0Initial oxygen concentration, α scaling factor, gmGenerating 1mol SiO for SiC substrates2The amount of oxygen required, psIs SiO2Density of (D), MsIs SiO2Pm is the matrix oxygen concentration index, hm(t) SiO generated on the substrate at time t2Thickness, BmParabolic constant, l, of the reaction of the substrate with oxygencThe width of the oxidation gap of the C interface is shown;
D1the calculation formula is as follows:
Figure BDA0002367828930000057
D2the calculation formula is as follows:
Figure BDA0002367828930000061
lcthe calculation formula is as follows:
Figure BDA0002367828930000062
C0the calculation formula is as follows:
Figure BDA0002367828930000063
wherein ,
Figure BDA0002367828930000064
the free diffusion speed of oxygen in CO;
the boundary conditions are expressed as:
(1) crack tip (y ═ 0), with:
Figure BDA0002367828930000065
(2) oxidation of C interface, O diffusion thereto2Is completely consumed by PyC interface and is O in unit time2Variation of (3) and O of interface consumption2Is equal, then there are:
Figure BDA0002367828930000066
wherein: z represents the coordinate along the axial direction of the fiber.
Further, in the step (4), after the gap of the interface layer reaches the fiber, setting the fiber radian gap function as y (z), and calculating the initial side interface consumption length l by using the same integral volumer0：
∫ydz＝lr0e0
Further, in the step (4), the second-stage side interface continuous consumption length is lrThe calculation formula is as follows:
Figure BDA0002367828930000067
in the step (4), the oxidation mechanism of the SiC fibers is the same as that of the SiC matrix, and an oxidation kinetic equation established based on mass conservation in combination with the oxidation mechanism of the C interface is as follows:
Figure BDA0002367828930000071
wherein z represents a coordinate value in the axial direction of the fiber, rm、rfRespectively representing the distance between the center of the fiber and the outer surface of the oxide layer on the surface of the matrix and the distance between the center of the fiber and the outer surface of the oxide layer on the surface of the fiber in the oxidation process, hf(t)、hm(t) SiO generated on the fiber and substrate at time t2Thickness, Bf、BmParabolic constants, g, for the reaction of the fiber and matrix with oxygenfGenerating 1mol SiO for SiC fibers2The amount of oxygen required, pf、pmRespectively, the concentration indexes of the fiber and the matrix reacting with oxygen;
(1) crack tip (y ═ 0), with:
Figure BDA0002367828930000072
(2) oxidation of C interface, O diffusion thereto2Is completely consumed by PyC interface and is O in unit time2Variation of (3) and O of interface consumption2Is equal, then there are:
Figure BDA0002367828930000073
(3) at the bottom of the crack, assuming there is no excess consumption of oxygen and no change in the amount of its species, there are:
Figure BDA0002367828930000074
wherein ,rf0Is the radius of the fiber, hf 1The thickness of the oxide layer at the fiber, hf(y, t) is SiO on the fiber at a certain time t and at a certain crack depth y2The thickness of the layer protrusion;
according toSolving the second order differential equation based on the classical fourth order Runge-Kutta method under the boundary conditions to obtain an oxygen concentration field at any moment, and further obtaining the oxidation gap of the carbon interface of the composite material, the interface consumption length and the oxidation of the fiber and the matrix at the crack to generate SiO2The thickness is changed regularly, so that the internal oxidation shape of the ceramic matrix composite at any time can be obtained.
Compared with the prior art, the invention has the following beneficial effects:
the invention provides a method for predicting the internal oxidation morphology of a unidirectional SiC/SiC composite material in a stress oxidation environment based on the mass transfer theory, which considers the morphology change of an oxidation gap on a C interface at the initial stage of a crack, uses a volume equivalence method to enable an arc oxidation gap to be equivalent to a rectangular gap after the oxidation gap reaches a SiC fiber, and adds oxygen consumed by oxidation of the SiC fiber into an established control equation, so that a model is closer to the actual situation, the oxidation of the internal crack wall of the ceramic matrix composite material after any time of stress oxidation, the time for the oxygen to start to oxidize the fiber, and the oxidation morphology of the fiber, the interface and a matrix after the oxygen enters the bottom of the crack can be accurately predicted, and theoretical support is provided for the subsequent calculation of the residual mechanical property problem of the ceramic matrix composite material in the stress oxidation environment.
Drawings
FIG. 1 is a graph of crack density as a function of applied load;
FIG. 2 is a graph of crack width as a function of temperature and stress;
FIG. 3 is a side view of a SiC/SiC composite model;
FIG. 4 is a side view of an oxidation model of a SiC/SiC composite;
FIG. 5 is a first stage SiC/SiC composite crack and interface geometry;
FIG. 6 shows the first stage SiC/SiC composite material with oxidized interface morphology under SEM observation;
FIG. 7 is a schematic diagram of a first-stage transition zone SiC/SiC composite material interface oxidation morphology model;
FIG. 8 is the geometry at the second stage of SiC/SiC composite cracks and interface channels;
FIG. 9 is a graph of the change in interface consumed length under 200MPa loading in an oxidizing environment at 900 deg.C;
FIG. 10 is a graph showing the thickness change of an oxide layer on a substrate after oxidation for 4 hours at 200MPa in an oxidation environment at 900 ℃;
FIG. 11 is a graph showing the thickness change of an oxide layer on a fiber after oxidation for 4 hours under 200MPa loading in an oxidizing environment at 900 ℃.
Detailed Description
The present invention will be further described with reference to the following examples.
In the embodiment, the internal oxidation morphology change of the unidirectional SiC/SiC composite material oxidized for 4 hours in the oxidation environment at 900 ℃ under the loading condition of 200MPa is predicted.
A method for predicting the internal oxidation morphology of a ceramic matrix composite in a stress oxidation environment specifically comprises the following steps:
step (1), determining the crack number of the ceramic matrix composite material substrate: considering the thermal residual stress, and calculating the change rule of the number of cracks in the unidirectional ceramic matrix composite material matrix along with the stress according to the stress borne by the matrix under the action of the tensile stress;
the step (1) specifically comprises the following steps:
the strength of the unidirectional SiC/SiC composite material matrix has certain dispersibility, and the cracking of the matrix under the action of stress is a random process. Assuming that the matrix failure of the ceramic matrix composite material obeys Poisson distribution under the action of tensile stress, the probability that the matrix fails due to at least one crack is as follows:
P(ξ＝σ,η＝Ls)＝1-exp{-M(A)}，N(A)≥1
wherein ：
Figure BDA0002367828930000081
wherein P (ξ) is a characteristic length LsThe probability of matrix failure when the stress is sigma, M (A) is a dimensionless Poisson parameter, N (A) is the number of cracks generated under the action of the stress, and sigmamcIs the initial cracking stress, σ, of the matrixthIs residual heatStress, σRIs the characteristic stress, m is the Weibull modulus;
the number of cracks in the composite material matrix under the action of stress can be simulated by computer programming by adopting a Monte Carlo method.
In order to eliminate the influence of the total length of the matrix, the crack density rho is selectedcThe cracks of the matrix surface were characterized as a function of axial stress:
Figure BDA0002367828930000091
wherein ,ρcAnd n is the crack number of the matrix.
FIG. 1 is a curve of crack density as a function of tensile stress obtained by simulation according to the method given in step (1). It can be seen that the crack density continues to increase with increasing stress, and the crack growth rate increases with increasing stress.
Step (2), determining a crack width change rule: the change trend of the crack width along with the stress is predicted according to the original crack width of the matrix by considering the residual stress and the tensile stress born by the matrix;
in the step (2), the expression of the width of the crack under the action of stress is as follows:
Figure BDA0002367828930000092
wherein e represents a temperature T0Width of crack at stress σ, e0Expressing the initial crack width, Δ T is the difference between the ambient temperature and the composite preparation temperature, which is 1200 ℃; αf、αmRespectively representing the coefficients of thermal expansion of the fiber and the matrix, EfDenotes the initial modulus of elasticity, V, of the fibermThe initial volume fraction of the matrix is expressed. The values of the parameters used to determine the change in the crack width of the matrix are given in table 1.
TABLE 1 parameters for determining the crack width variation of a substrate
Figure BDA0002367828930000093
Figure BDA0002367828930000101
FIG. 2 is a graph showing the variation of crack width with applied stress and oxidation temperature calculated according to the above crack width expression. As can be seen from the figure, the width of the crack increases with the increase of the applied stress, and is in positive correlation with the magnitude of the applied stress; the lower the temperature, the larger the crack width under the same applied load.
And (3) determining a first-stage oxidation kinetic equation of the unidirectional SiC/SiC composite material.
Under conditions of insufficient oxygen supply, the carbon interface reaction equation is:
2C+O2＝2CO
the carbon interface depletion width is expressed as:
Figure BDA0002367828930000102
wherein ,lcIs the carbon interface oxidation width, KcAs a reaction rate constant, CO2Oxygen concentration, P, of reaction siteCIs the carbon reaction series, and the value is 0.3, McThe carbon molar mass is 12g/mol, gcThe amount of oxygen required to be consumed for 1mol C is 1, rhocThe carbon density is 1.8g/cm3. Reaction rate constant KcThe calculation formula is as follows:
Kc＝kcexp(-Ec/RT)
wherein ,kcIn order to characterize the reaction rate, R is the ideal gas constant (R ═ 8.314J/(mol · K)), EcThe activation energy for this reaction was 104433J/mol, and T is the temperature.
The reaction equation of the SiC matrix is as follows:
SiC(s)+3/2O2(g)＝SiO2(s)+CO(g)
formed SiO2Thickness of oxide layer with oxidation time t0Variations of (2)Obeying the parabolic criterion:
h2＝Bt0
wherein h represents the thickness of the oxide layer, B is a parabolic constant, and t0Is the oxidation time, expressed as:
Figure BDA0002367828930000103
wherein: k is a Henry constant and is,
Figure BDA0002367828930000104
for oxygen in SiO2Diffusion rate in the layer, R is the ideal gas constant, gsTo produce 1mol SiO2The amount of oxygen species required.
The diffusion of oxygen in the cracks is binary diffusion, and in a binary diffusion system consisting of A and B, the actual effective diffusion coefficient D of the component AAThe calculation formula is as follows:
Figure BDA0002367828930000111
wherein ,DAIs the effective diffusion coefficient of component A, DABIs a free diffusion coefficient, DKAThe diffusion coefficient of the gas A in the pore channel; dABThe calculation formula of (2) is as follows:
Figure BDA0002367828930000112
wherein: p is the ambient pressure, MAAnd MBThe molar mass of the respective component A, B being ∑vIs the diffusion volume of the molecule.
DKAThe calculation formula is as follows:
Figure BDA0002367828930000113
wherein: pi is the circumference ratio, and r is the radius of the material pore channel;
according to the formula, the oxidation kinetic equation established based on the mass conservation law is as follows:
Figure BDA0002367828930000114
wherein S is the cross-sectional area of gas flow,
Figure BDA0002367828930000115
is the flux of oxygen at that location,
Figure BDA0002367828930000116
is the amount of oxygen consumed at that location per unit length, and x is the gas channel length.
The first stage SiC matrix oxidation kinetics equation is then:
Figure BDA0002367828930000117
the first stage C interfacial oxidation kinetic equation is:
Figure BDA0002367828930000118
wherein y represents a coordinate value in the depth direction of the crack of the substrate, rtDenotes the distance, h, from the surface of the substrate to the center of the fiberm(y, t) is SiO at a certain time t and at a certain depth y of the crack in the substrate2The thickness of the layer projecting with respect to the wall surface, D being half the width of the crack, D1、D2Respectively, the effective diffusion coefficient of oxygen in the microcracks and at the interface, C0Initial oxygen concentration, α is a proportionality coefficient, and the value is 0.5 gmGenerating 1mol SiO for SiC substrates2The amount of oxygen required is as follows
Figure BDA0002367828930000121
ρsIs SiO2The density of (a) is 2.2g/cm3，，MsIs SiO2The molar mass of (b) is 60g/mol, Pm is the matrix oxygen concentration index and is 0.8, hm(t) is tFormation of SiO on the substrate2Thickness, BmParabolic constant, l, of the reaction of the substrate with oxygencThe oxidation kinetic model is shown in fig. 3 and 4 for the C interface oxidation gap width.
D1The calculation formula is as follows:
Figure BDA0002367828930000122
D2the calculation formula is as follows:
Figure BDA0002367828930000123
lcthe calculation formula is as follows:
Figure BDA0002367828930000124
C0the calculation formula is as follows:
Figure BDA0002367828930000125
wherein ,
Figure BDA0002367828930000126
the free diffusion rate of oxygen in CO is shown, where P is one standard atmosphere, i.e. 0.1MPa, R is the ideal gas constant (R ═ 8.314J/(mol · K)), and the temperature T is 900 ℃.
The boundary conditions are expressed as:
(1) crack tip (y ═ 0), with:
Figure BDA0002367828930000127
(2) oxidation of C interface, O diffusion thereto2Is completely consumed by PyC interface and is O in unit time2Variation of (3) and O of interface consumption2Is equal, then there are:
Figure BDA0002367828930000131
wherein: z represents the coordinate along the axial direction of the fiber.
And (4) establishing a second stage oxidation kinetic equation to simulate the internal oxidation morphology of the material.
As shown in FIGS. 5 and 6, after the interface layer oxidation gap reaches the fiber, the interface consumption length after the interface layer gap reaches the fiber is calculated, the fiber radian gap function is set as y (z), and the initial interface consumption length l is calculated by using the same integral volumer0：
∫ydz＝lr0e0
The second stage continuous consumption length of one side interface is lrThe calculation formula is as follows:
Figure BDA0002367828930000132
the oxidation mechanism of the SiC fiber is the same as that of the SiC matrix, the oxidation mechanism of the C interface is combined, and an oxidation kinetic equation established based on mass conservation is as follows:
Figure BDA0002367828930000133
wherein z represents a coordinate value in the axial direction of the fiber, rm、rfRespectively representing the distance between the center of the fiber and the outer surface of the oxide layer on the surface of the matrix and the distance between the center of the fiber and the outer surface of the oxide layer on the surface of the fiber in the oxidation process, hf(t)、hm(t) SiO generated on the fiber and substrate at time t2Thickness, Bf、BmParabolic constants, g, for the reaction of the fiber and matrix with oxygenfGenerating 1mol SiO for SiC fibers2The amount of oxygen required is as follows
Figure BDA0002367828930000134
Bf、BmParabolic constants, g, for the reaction of the fiber and matrix with oxygenfGenerating 1mol SiO for SiC fibers2The amount of oxygen required, pf、pmThe concentration indexes of the fiber and the matrix reacting with oxygen are respectively 0.6 and 0.8. Table 2 shows the values of the parameters of the dynamic model of stress oxidation of the composite material.
TABLE 2
Figure BDA0002367828930000135
Figure BDA0002367828930000141
The boundary conditions are as follows:
(1) crack tip (y ═ 0), with:
Figure BDA0002367828930000142
(2) oxidation of C interface, O diffusion thereto2Is completely consumed by PyC interface and is O in unit time2Variation of (3) and O of interface consumption2Is equal, then there are:
Figure BDA0002367828930000143
(3) at the bottom of the crack, assuming there is no excess consumption of oxygen and no change in the amount of its species, there are:
Figure BDA0002367828930000144
wherein ,rf0Is the radius of the fiber, hf 1The thickness of the oxide layer at the fiber, hf(y, t) is SiO on the fiber at a certain time t and at a certain crack depth y2The thickness of the layer protrusion.
Solving the second-order differential equation based on the classical fourth-order Runge-Kutta method according to the boundary conditions to obtain an oxygen concentration field at any moment, and further solving the oxidation gap and the interface consumption of the carbon interface of the composite materialThe length and the fiber and the matrix are oxidized at the crack to generate SiO2The thickness is changed regularly, so that the internal oxidation morphology of the ceramic matrix composite at any time is obtained, as shown in FIGS. 5-8.
FIGS. 9-11 are graphs of the interface depletion length, fiber oxide thickness and matrix oxide thickness as a function of time.
In this embodiment, a process of interface layer consumption as shown in fig. 5 is added, and this stage is an oxidation C interface, and this process is omitted in the prior art, so the oxidation kinetics formula is added in this embodiment as follows:
Figure BDA0002367828930000145
Figure BDA0002367828930000146
Figure BDA0002367828930000147
therefore, in the present embodiment, the formula of the boundary condition is changed to:
Figure BDA0002367828930000151
due to the consideration of oxygen consumed by fiber oxidation, so as to increase
Figure BDA0002367828930000152
The part (a) of (b) of (a),
in the prior art, the arc-shaped notch structure of the interface layer is directly equivalent to a rectangular structure, and the arc-shaped notch is equivalent to a rectangular notch by using volume equivalence, so that the interface layer has an initial oxidation length.
The above description is only of the preferred embodiments of the present invention, and it should be noted that: it will be apparent to those skilled in the art that various modifications and adaptations can be made without departing from the principles of the invention and these are intended to be within the scope of the invention.

Claims (5)

1. A method for predicting the internal oxidation morphology of a ceramic matrix composite in a stress oxidation environment is characterized by comprising the following steps:
(1) determining the crack number of the ceramic matrix composite material substrate: considering the thermal residual stress, and calculating the change rule of the number of cracks in the unidirectional ceramic matrix composite material matrix along with the stress according to the stress borne by the matrix under the action of the tensile stress;
(2) determining a crack width change rule: the change trend of the crack width along with the stress is predicted according to the original crack width of the matrix by considering the residual stress and the tensile stress born by the matrix;
(3) determining a first-stage oxidation kinetic equation of the ceramic matrix composite material: the first stage is a carbon interface oxidation gap stage, and a carbon oxidation gap and SiO on the SiC substrate are constructed based on the oxidation mechanism of the carbon interface and the SiC substrate2The relation of the change of the layer thickness along with the time is based on the mass transfer theory, the oxidation kinetic equation of the first stage of the composite material is established, and the carbon interface oxidation gap and the SiC matrix SiO are obtained by calculation by combining the boundary conditions2Determining the change rule of the layer thickness at the crack so as to determine the internal oxidation morphology of the ceramic matrix composite material in the first stage and the time for the carbon interface oxidation notch to reach the SiC fiber;
(4) determining a kinetic equation of the second-stage oxidation of the ceramic matrix composite material: the second stage is a SiC fiber oxidation stage, when the oxidation gap of the C interface reaches the SiC fiber, the arc-shaped oxidation gap of the C interface is equivalent to a rectangular gap by adopting an isovolumetric method, the initial oxidation length of the C interface is calculated, and then the SiO on the SiC fiber is constructed based on the oxidation mechanism of the SiC fiber2The relation of the change of the layer thickness along with the time is based on the mass transfer theory, the carbon interface and SiC matrix oxidation rule are combined, the oxidation kinetic equation of the composite material in the second stage is established, the boundary condition is combined, the consumption length of the carbon interface and the oxide thickness change rule of the silicon carbide fiber and the matrix at the crack are calculated, the internal oxidation shape of the ceramic matrix composite material in the second stage is determined, and the internal oxidation shape of the ceramic matrix composite material at any time can be obtained by combining the two stages。
2. The method for predicting the internal oxidation morphology of the ceramic matrix composite in the stress oxidation environment according to claim 1, wherein the method comprises the following steps: the specific steps of the step (1) are as follows:
if the matrix of the ceramic matrix composite fails under the action of tensile stress and follows Poisson distribution, the probability that the matrix fails due to at least one crack is as follows:
P(ξ＝σ,η＝Ls)＝1-exp{-M(A)}，N(A)≥1
wherein ：
Figure FDA0002367828920000011
wherein P (ξ) is a characteristic length LsThe probability of matrix failure when the stress is sigma, M (A) is a dimensionless Poisson parameter, N (A) is the number of cracks generated under the action of the stress, and sigmamcIs the initial cracking stress, σ, of the matrixthIs the residual thermal stress, σRIs the characteristic stress, m is the Weibull modulus;
simulating the number of cracks in the ceramic matrix composite material matrix under the action of stress in a programmable manner by adopting a Monte Carlo method;
to eliminate the influence of the total length of the substrate, the density rho is selectedcThe cracks of the matrix surface were characterized as a function of axial stress:
Figure FDA0002367828920000021
wherein ,ρcAnd n is the crack number of the matrix.
3. The method for predicting the internal oxidation morphology of the ceramic matrix composite in the stress oxidation environment according to claim 2, wherein the method comprises the following steps: in the step (2), the crack width of the matrix is expressed as:
Figure FDA0002367828920000022
wherein e represents a temperature T0Width of crack at stress σ, e0Denotes the initial crack width,. DELTA.T is the difference between the ambient temperature and the preparation temperature, αf、αmRespectively representing the coefficients of thermal expansion of the fiber and the matrix, EfDenotes the initial modulus of elasticity, V, of the fibermThe initial volume fraction of the matrix is expressed.
4. The method for predicting the internal oxidation morphology of the ceramic matrix composite in the stress oxidation environment according to claim 3, wherein the method comprises the following steps: in the step (3), under the condition of insufficient oxygen supply, the carbon interface reaction equation is as follows:
2C+O2＝2CO
the carbon interface depletion width is expressed as:
Figure FDA0002367828920000023
wherein ,lcIs the carbon interface oxidation width, KcIn order to be a constant of the reaction rate,
Figure FDA0002367828920000024
oxygen concentration, P, of reaction siteCIs the number of carbon reaction stages, McCarbon molar mass, gcThe amount of oxygen required to be consumed for 1mol C, ρcIs the carbon density; reaction rate constant KcThe calculation formula of (2) is as follows:
Kc＝kcexp(-Ec/RT)
wherein ,kcFor the constants characterizing the reaction rate, R is the ideal gas constant, R is 8.314J/(mol. K), EcT is the temperature for the activation energy of the reaction.
In the step (3), the reaction equation of the SiC matrix is as follows:
SiC+3/2O2＝SiO2+CO
formed SiO2Thickness of oxide layer with oxidation time t0Obey the parabolic criterion:
h2＝Bt0
wherein h represents the thickness of the oxide layer, B is a parabolic constant, and t0Is the oxidation time, expressed as:
Figure FDA0002367828920000031
wherein: k is a Henry constant and is,
Figure FDA0002367828920000032
for oxygen in SiO2Diffusion Rate in layer, gsTo produce 1mol SiO2The amount of oxygen species required;
in the step (3), in a binary diffusion system consisting of A and B, the actual effective diffusion coefficient D of the component AAThe calculation formula is as follows:
Figure FDA0002367828920000033
wherein ,DAIs the effective diffusion coefficient of component A, DABIs a free diffusion coefficient, DKAThe diffusion coefficient of the gas A in the pore channel; dABThe calculation formula of (2) is as follows:
Figure FDA0002367828920000034
wherein: p is the ambient pressure, MAAnd MBThe molar mass, Σ, of the respective component A, BvIs the diffusion volume of the molecule;
DKAthe calculation formula of (2) is as follows:
Figure FDA0002367828920000035
wherein: pi is the circumference ratio, and r is the radius of the material pore channel;
in the step (3), the oxidation kinetic equation established based on the mass conservation law is as follows:
Figure FDA0002367828920000036
wherein S is the cross-sectional area of gas flow,
Figure FDA0002367828920000037
is the flux of oxygen at that location,
Figure FDA0002367828920000038
is the amount of oxygen consumed at that location per unit length, and x is the gas channel length.
The first stage SiC matrix oxidation kinetics equation is then:
Figure FDA0002367828920000041
the first stage C interfacial oxidation kinetic equation is:
Figure FDA0002367828920000042
wherein y represents a coordinate value in the depth direction of the crack of the substrate, rtDenotes the distance, h, from the surface of the substrate to the center of the fiberm(y, t) is SiO at a certain time t and at a certain depth y of the crack in the substrate2The thickness of the layer projecting with respect to the wall surface, D being half the width of the crack, D1、D2Respectively, the effective diffusion coefficient of oxygen in the microcracks and at the interface, C0Initial oxygen concentration, α scaling factor, gmGenerating 1mol SiO for SiC substrates2The amount of oxygen required, psIs SiO2Density of (D), MsIs SiO2Pm is the matrix oxygen concentration index, hm(t) SiO generated on the substrate at time t2Thickness, BmParabolic constant, l, of the reaction of the substrate with oxygencThe width of the oxidation gap of the C interface is shown;
D1the calculation formula is as follows:
Figure FDA0002367828920000043
D2the calculation formula is as follows:
Figure FDA0002367828920000044
lcthe calculation formula is as follows:
Figure FDA0002367828920000045
C0the calculation formula is as follows:
Figure FDA0002367828920000046
wherein ,
Figure FDA0002367828920000047
the free diffusion speed of oxygen in CO;
the boundary conditions are expressed as:
(1) crack tip y is 0, with:
Figure FDA0002367828920000051
(2) oxidation of C interface, O diffusion thereto2Is completely consumed by PyC interface and is O in unit time2Variation of (3) and O of interface consumption2Is equal, then there are:
Figure FDA0002367828920000052
wherein: z represents the coordinate along the axial direction of the fiber.
5. The ceramic matrix composite under stress oxidizing environment of claim 4The partial oxidation morphology prediction method is characterized by comprising the following steps: in the step (4), after the gap of the interface layer reaches the fiber, setting the radian gap function of the fiber as y (z), and calculating the interface consumption length l at the initial side by using the same integral volumer0：
∫ydz＝lr0e0
In the step (4), the continuous consumption length of the second-stage side interface is lrThe calculation formula is as follows:
Figure FDA0002367828920000053
in the step (4), the oxidation mechanism of the SiC fibers is the same as that of the SiC matrix, and an oxidation kinetic equation established based on mass conservation in combination with the oxidation mechanism of the C interface is as follows:
Figure FDA0002367828920000054
wherein z represents a coordinate value in the axial direction of the fiber, rm、rfRespectively representing the distance between the center of the fiber and the outer surface of the oxide layer on the surface of the matrix and the distance between the center of the fiber and the outer surface of the oxide layer on the surface of the fiber in the oxidation process, hf(t)、hm(t) SiO generated on the fiber and substrate at time t2Thickness, Bf、BmParabolic constants, g, for the reaction of the fiber and matrix with oxygenfGenerating 1mol SiO for SiC fibers2The amount of oxygen required, pf、pmRespectively, the concentration indexes of the fiber and the matrix reacting with oxygen;
(1) crack tip y is 0, with:
Figure FDA0002367828920000055
(2) oxidation of C interface, O diffusion thereto2Is completely consumed by PyC interface and is O in unit time2Variation of (3) and O of interface consumption2Is equal, then there are:
Figure FDA0002367828920000061
(3) at the bottom of the crack, assuming there is no excess consumption of oxygen and no change in the amount of its species, there are:
Figure FDA0002367828920000062
wherein ,rf0Is the radius of the fiber, hf 1The thickness of the oxide layer at the fiber, hf(y, t) is SiO on the fiber at a certain time t and at a certain crack depth y2The thickness of the layer protrusion;
according to the boundary conditions, based on a classical fourth-order Runge-Kutta method, solving the second-order differential equation to obtain an oxygen concentration field at any moment, and further solving the problem that the carbon interface oxidation gap of the composite material, the fiber and the matrix are oxidized at the crack to generate SiO2The thickness is changed regularly, so that the internal oxidation shape of the ceramic matrix composite at any time can be obtained.
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