CN111241686B - Method for predicting stress-strain curve of ceramic matrix composite in high-temperature oxidation environment during random loading and unloading - Google Patents

Method for predicting stress-strain curve of ceramic matrix composite in high-temperature oxidation environment during random loading and unloading Download PDF

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CN111241686B
CN111241686B CN202010040082.8A CN202010040082A CN111241686B CN 111241686 B CN111241686 B CN 111241686B CN 202010040082 A CN202010040082 A CN 202010040082A CN 111241686 B CN111241686 B CN 111241686B
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oxidation
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CN111241686A (en
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宋迎东
陈西辉
刘炎
孙志刚
牛序铭
高希光
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Nanjing University of Aeronautics and Astronautics
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Abstract

The invention discloses a method for predicting a stress-strain curve of any loading and unloading of a ceramic matrix composite in a high-temperature oxidation environment, which can effectively simulate the stress-strain curve of any loading and unloading of a unidirectional SiC/SiC composite in the high-temperature oxidation environment, and takes the influences of the crack density and width of a matrix, the length consumed by interface oxidation and the tensile strength of fibers on the stress-strain curve of the composite during loading on the length and distribution of an interface sliding region into consideration; the method can provide a theoretical basis for the calculation of the fatigue life of the unidirectional SiC/SiC composite material under the spectral load in the high-temperature oxidation environment; the invention overcomes the defects of high test cost and large manpower and material resource consumption of the one-way ceramic matrix composite material random loading and unloading oxidation test, and can save a large amount of manpower and material resources.

Description

Method for predicting stress-strain curve of ceramic matrix composite in high-temperature oxidation environment during random loading and unloading
Technical Field
The invention belongs to the technical field of composite materials, and particularly relates to a method for predicting an arbitrary loading and unloading stress-strain curve of a ceramic matrix composite material in a high-temperature oxidation environment.
Background
The Silicon carbide fiber toughened Silicon carbide ceramic matrix composite (hereinafter referred to as SiC/SiC) is a novel high-temperature structural material of a hot end part of an aeroengine, has the characteristics of high specific strength, specific rigidity and the like, and can effectively realize weight reduction of the hot end part. In a service environment, the SiC/SiC composite material member is subjected to damage caused by a high-temperature oxidation environment on one hand, and on the other hand, the SiC/SiC composite material member is subjected to an external load, most of the external load is a variable load or a random load, and the inconstant load makes the change of components (matrix, interface and fiber) in the material more complicated than that under a constant amplitude load. The influence of the SiC/SiC composite material on the internal components of the composite material under the high-temperature oxidation environment and optional loading and unloading is considered, and the stress-strain relation of the SiC/SiC composite material is predicted, so that a solid foundation can be laid for analyzing the fatigue life of the material under the service environment.
In the prior art, a literature "matrix failure model of a ceramic matrix composite material" mainly studies the relationship between matrix cracking and external load of the ceramic matrix composite material, and a Monte Carlo method is adopted to simulate matrix cracking generation of the ceramic matrix composite material, so that the distance and the position of matrix cracks under different loading stresses are obtained, and an analysis basis is provided for matrix crack evolution of a unidirectional SiC/SiC composite material under any loading and unloading load. The relation between the crack width of the matrix and the applied stress and temperature is mainly studied in the literature "Modeling of large in elementary ceramic compositions and multi-scale experimental evaluation on third generation SiC/SiC principles", and the crack width of the SiC/SiC composite material under the normal temperature environment of 200MPa is measured to be 0.2 micron through experiments. The CN110096732A patent CN109992850A patent CN 18 prediction method CN 2, CN110096731A patent CN 3, provides a model of oxidation dynamics in high temperature oxidation environment, based on which the oxygen concentration, interface consumption length, and the change rule of SiC fiber surface oxidation layer thickness along with stress, temperature and time in different positions in the material at different time are calculated, the size of SiC fiber surface oxidation defect is determined and the SiC fiber characteristic intensity distribution expression is deduced, but the research is the oxidation morphology in creep single tensile stress oxidation environment, and the oxidation morphology under any loading and unloading load is not researched. The document 'fatigue failure mechanism and multi-scale simulation of complex preform ceramic matrix composite' mainly researches the fatigue failure of the ceramic matrix composite, obtains the distribution rule of the one-way SiC/SiC composite interface sliding region under any loading and unloading, but does not consider the influence of high-temperature oxidation environment on the internal components of the ceramic matrix composite. The document 'fatigue damage model and service life prediction of long fiber reinforced ceramic matrix composite' mainly researches fatigue failure of the ceramic matrix composite through a shear hysteresis model, gives a calculation formula of the shear hysteresis model, obtains the random failure percentage of fibers and the change rule of interface shear stress along with cycle number through calculation, but cannot be used for simulating the stress-strain curve of unidirectional SiC/SiC in a high-temperature oxidation environment. The document "Modeling the effect of oxidation on the hysteresis of carbon fiber-reinforced composites and static fatigue at an exposed temperature" mainly studies the influence of high-temperature oxidation on the normal fatigue hysteresis dissipation energy and the interface slip of the C/SiC composite, considers the influence of high-temperature oxidation on the interface consumption length of the C/SiC composite, does not consider the influence of fiber oxidation on the fiber strength, does not consider the influence of matrix crack oxidation on the oxygen channel width, and cannot be used for simulating the stress-strain curve of the unidirectional SiC/SiC composite under any loading and unloading.
In view of the foregoing, there is a need for a method for effectively predicting the stress-strain curve of a unidirectional SiC/SiC composite under any loading and unloading in a high-temperature oxidation environment.
Disclosure of Invention
The invention provides a method for predicting an arbitrary loading and unloading stress-strain curve of a ceramic matrix composite in a high-temperature oxidation environment, which aims to solve the problems in the prior art.
In order to achieve the purpose, the invention adopts the technical scheme that:
a method for predicting any stress-strain curve of loading and unloading of a ceramic matrix composite in a high-temperature oxidation environment comprises the following steps:
the method comprises the following steps: determining the crack density and the crack spacing of the unidirectional SiC/SiC ceramic matrix composite material matrix based on a Monte Carlo simulation method for the cracking of the unidirectional SiC/SiC ceramic matrix composite material matrix;
step two: determining the width of a diffusion channel of oxygen in the crack of the unidirectional SiC/SiC ceramic matrix composite;
step three: based on an oxidation dynamic model in a high-temperature oxidation environment, obtaining the thickness of an oxidation layer at each loading stress crack of the unidirectional SiC/SiC ceramic matrix composite substrate from a crack wall surface, the interface oxidation consumption length and the notch radius generated by the oxidation of the fiber; judging whether the thickness of the oxidation layer at the crack position of the matrix is larger than the width of the oxygen diffusion channel obtained in the step two or whether the notch radius generated by the oxidation of the fiber is larger than the thickness of the interface layer of the unidirectional SiC/SiC composite material, if so, determining that the oxygen cannot enter the composite material from the crack of the matrix in the subsequent loading, and the fiber and the interface of the unidirectional SiC/SiC composite material at the crack position cannot be oxidized any more;
step four: calculating and obtaining the interface slip region distribution under each stress point according to the interface friction slip model; then determining a stress-strain relation curve of the unidirectional SiC/SiC ceramic matrix composite based on a shear-lag model;
step five: simulating the degradation rule of the interface of the unidirectional SiC/SiC ceramic matrix composite material according to the improved interface shear stress degradation rule;
step six: judging whether the stress is loaded or not, if not, combining the results of the previous calculation, assuming that the strength distribution of the initial fiber of the unidirectional SiC/SiC composite material accords with the two-parameter Weibull distribution, calculating the fiber fracture failure percentage, reducing the fiber volume percentage, reducing the interface shear stress according to the fifth step, continuously loading the stress, and returning to the first step; and if the stress loading is finished, ending.
Further, the specific steps of the first step are as follows:
simulating matrix cracks of the unidirectional SiC/SiC composite material based on a Monte Carlo method, and determining the crack spacing of the matrix during initial loading, wherein the matrix failure probability is as follows:
Figure BDA0002367420550000031
wherein, P (xi ═ sigma, eta ═ Lc) Means that the total length of the composite material is LcThe probability of failure of the substrate, σ, when the applied stress is σthIs the residual thermal stress, sigma, generated in the manufacturing process of the composite materialRCharacteristic stress, sigma, for cracking of composite material matrix*Is the minimum initial cracking stress of the matrix, and m is the Weibull modulus; the Monte Carlo method is adopted to simulate and obtain the initial tensile stress sigma1Length L of the steel sheet under the action ofcK number of cracks generated in the composite material substrate1At (0, L)c) Between generate k1A random number of k1The distribution position of each crack; the continuous loading load increment is delta sigma, and the length LcThe composite material of (1) has an increment of the number of cracks generated on the substrate of Δ k, if Δ k<1, determining that the matrix can not generate new cracks, and if delta k is more than or equal to 1, calculating the total interface bonding area length of the composite material to be LbTotal length of (0, L)b) The bonding area generates evenly distributed delta k random numbers which are the positions of newly generated cracks, along with the increase of stress, when the interface has no bonding area, matrix cracks cannot be generated, the number of the matrix cracks reaches saturation, and unequal crack spacing L is generated along with the progress of loading.
Further, the second step comprises the following specific steps:
based on empirical formula, the crack width of the matrix is:
Figure BDA0002367420550000032
wherein: d is the crack width of the matrix under an applied stress of sigma at a temperature T, d0The crack width of the substrate is 200MPa at normal temperature, T0Is normal temperature,. DELTA.T is the difference between ambient temperature and normal temperature, EfIs the modulus of elasticity, V, of the fibermIs the volume fraction of the matrix, alpham,αfAre respectively a radicalCoefficient of thermal expansion of the body, fiber;
the width of oxygen in each load step zone in the diffusion channel of the composite material is equal to the load stress of
Figure BDA0002367420550000033
Crack width L of the substrateeWherein: sigmaiRepresenting the load value, σ, loaded at the ith load stepi-1The load value representing the load step loading of the i-1 st load step is as follows:
Figure BDA0002367420550000034
further, the third step comprises the following specific steps:
based on the high temperature oxidation kinetic model:
Figure BDA0002367420550000041
boundary conditions:
Figure BDA0002367420550000042
wherein: r istIs the distance from the surface of the matrix to the center of the fiber circle, y is the coordinate of the crack, z is the coordinate of the interface,
Figure BDA0002367420550000043
is SiO at y at time t2Thickness of layer projecting with respect to wall surface,/rFor the length of the interface consumption, hm、hfDenotes the thickness of the fiber oxide layer when y is 0 and z is 0, LeThe width of the oxygen channel at the crack of the matrix is obtained in the second step, gf,gmRespectively generating 1mol SiO for the oxidation reaction of the fiber and the substrate2Amount of oxygen required, MsIs SiO2Molar mass of (C)*Is the oxygen concentration of pure oxygen under the standard air pressure,
Figure BDA0002367420550000044
pm,pfparabolic constant for oxidation of SiC, D1Effective diffusion coefficient of oxygen in crack channels of the substrate, D2To be the effective diffusion coefficient of oxygen within the interface channel,
Figure BDA0002367420550000045
denotes oxygen molar solubility, C0Denotes the ambient oxygen solubility, psIs SiO2(ii) a density of (d); kcThe reaction rate constant of the interface carbon phase is shown, wherein rf, rm and rm0 are respectively a fiber, a matrix and an interface radius, and alpha is a scaling factor; obtaining the thickness of the oxidation delamination crack wall surface at the crack position of the matrix at the time t according to the formula and the boundary conditions
Figure BDA0002367420550000046
Length of interfacial oxidation consumption lr(t), let δd(t)＝hfObtaining the fiber defect radius deltad(t) law of change with oxidation time; the loading time of each loading step is the same as delta t, and the total number of the loading steps isnWhen it comes toiThickness of oxide delamination crack wall surface at crack position of matrix generated in each loading step
Figure BDA0002367420550000047
Length of consumption of interfacial oxidation
Figure BDA0002367420550000048
Radius of fiber defect
Figure BDA0002367420550000049
Wherein:
Figure BDA00023674205500000410
Δlr,Δδdrespectively representing the thickness of the oxidation delamination crack wall surface, the interface oxidation length and the increment of the fiber defect radius at the matrix crack after the time delta t;
judging the current load stepThickness of oxide delamination crack wall surface at each crack of matrix
Figure BDA0002367420550000051
Whether the width of the oxygen diffusion channel is more than half of the width of the oxygen diffusion channel obtained in the step two or the radius delta of the fiber defectdiWhether or not it is larger than the thickness r of the SiC/SiC interface layerm0-rfIf the value is larger than the above range, it is considered that oxygen does not enter the interior of the composite material from the crack during subsequent loading, and the fibers and the interface of the SiC/SiC composite material at the crack are not oxidized any more.
Further, the fourth step specifically comprises:
calculating the length of the debonding area according to the crack spacing calculated in the step one and the friction slip model
Figure BDA0002367420550000052
σmaxConsidering the maximum stress of the loaded load course, the distribution of the slippage area on each fiber is the same, and the length of the positive slippage area is equal when the fiber is loaded from 0 for the first time
Figure BDA0002367420550000053
When unloading, the length of the reverse slip zone is
Figure BDA0002367420550000054
The length of the forward slip region is l12＝l11-lR11There are at most two slip zones; upon reloading, the forward slip region has a length of
Figure BDA0002367420550000055
Reverse slip zone length of lR21＝lR11-l21The second forward slip zone has a length of l22＝l11-lR11-l21When at most three slip zones exist; the length of the reverse slip zone during further unloading is
Figure BDA0002367420550000056
The length of the forward slip zone is l31＝l11-lR31The second reverse slip zone has a length of lR32＝lR21-lR31-l31The second forward slip zone has a length of l32＝l11-lR31-lR32-l31At the moment, at most four slippage areas exist, and the distribution of the subsequent loading and unloading slippage areas is calculated according to the four slippage areas;
wherein: σ is the applied stress, Vf,VmVolume fractions of fiber and matrix, respectively, Em,Ef,EcRespectively the elastic modulus of the matrix, the fiber and the composite material, tau is the interface shear stress, rfIn order to be the radius of the fibers,
Figure BDA0002367420550000057
representing the 1 st peak and valley in the load history,
Figure BDA0002367420550000058
representing the 2 nd peak and valley in the load course; then
Figure BDA0002367420550000059
Representing the jth peak and valley in the load history,
determining the stress distribution of each unit cell fiber according to a shear lag model, and neglecting the fiber stress distribution on the crack opening section because the crack width is far smaller than the debonding length, and considering that the stress distribution situation on each fiber is the same; when loading, an oxidation area, a debonding area and a bonding area exist on the fiber, and the stress on any fiber is divided into the following conditions:
during initial loading, if the calculated result in the first step is that no crack exists, calculating the stress strain by using a mixing ratio formula:
Figure BDA0002367420550000061
if cracks exist on the composite material matrix, the cracks are randomly distributed on the composite material matrix, and the total length is LcEach unit cell length of Lic，LicThe index i in (a) indicates the ith loadStep (c) denotes a length LcThe composite material has the same stress distribution from the left to the right of the c single cell, the left and right sides of each single cell are the same, the left crack surface of each single cell is taken as the original point, the x axis is taken along the fiber direction, the single cell can be divided into an oxidation area, a forward sliding area and a bonding area, and the length of the oxidation area is lrThe length of the forward slip zone is l11The length of the bonding region is
Figure BDA0002367420550000062
ldLength of debonding region of interface,. alpha.at initial loadingd＝l11Then fiber stress σf(x) The distribution is as follows:
Figure BDA0002367420550000063
wherein: x is a coordinate position on the x-axis,
Figure BDA0002367420550000064
ρ is an intermediate quantity, with no practical meaning, simply to simplify the written length of the formula, R1The radius of the concentration for bearing the axial load for the matrix according to the formula
Figure BDA0002367420550000065
Calculating to obtain R1，GmShear modulus of the matrix;
when unloading, the matrix will not generate new cracks, and the interface area can be divided into oxidation area, reverse slip area, forward slip area and bonding area, the length of the oxidation area is lrThe reverse slip zone has a length of lR11The length of the forward slip zone is l12Length l of debonding aread＝lR11+l12Then fiber stress σf(x) The distribution is as follows:
Figure BDA0002367420550000066
wherein: sigmaf0For fibre-carrying of composite materials without damageAxial stress.
When loading, if the matrix does not generate new cracks, the interface can be divided into an oxidation area, a forward slip area, a reverse slip area, a forward slip area and a bonding area, wherein the length of the oxidation area is lrThe length of the first forward slip region is l21The reverse slip zone has a length of lR21The second forward slip zone has a length of l22Length l of debonding aread＝l21+lR21+l22The length of the bonding region is
Figure BDA0002367420550000071
The fiber stress σf(x) The distribution is as follows:
Figure BDA0002367420550000072
if the matrix generates new cracks, the forward slip region completely covers the reverse slip region generated during the previous unloading, the lengths of the interfaces consumed by oxidation are different due to different cracking times of the matrix cracks on the left side and the right side of the interface, and the length of the left side of the interface consumed by oxidation is lrlRight side interface consumption length is lrrThe left and right debonding regions have a length of ldAnd a forward slip region l21Equal, non-oxidized section having the coordinate of the center point at the interface of
Figure BDA0002367420550000073
I.e. the stress distribution of the debonding and bonding areas with respect to the coordinates
Figure BDA0002367420550000074
Symmetrically distributed, at which point the fibre stress σf(x) The distribution is as follows:
Figure BDA0002367420550000075
the strain of the composite material is equivalent to the strain of the fiber, then
Figure BDA0002367420550000076
Wherein: n is a radical of1The total length under the current load is LcC represents the length LcFrom left to right of the c-th unit cell, epsiloncIs strain of composite material, epsilonfIs the strain of the fiber.
Further, the concrete steps of the fifth step are as follows:
simulating the degradation failure rule of the interface according to the interface shear stress degradation criterion:
Figure BDA0002367420550000081
wherein: tau isiInterfacial shear stress at ith load peak, τ0Is the initial interfacial shear stress, τ, of the materialminShear stress, σ, at which the interface gradually approaches steady state with cyclic degradationAThe maximum applied load before the current load step, ω, λ are empirical parameters,
Figure BDA0002367420550000082
wherein: n is a radical of2Representing the number of peaks occurring before the current load step.
Further, the sixth step comprises the following specific steps:
in the fatigue loading process, the fiber can have a fracture failure behavior, the fractured fiber cannot bear load, assuming that the strength distribution of the initial fiber conforms to the two-parameter Weibull distribution, the maximum stress borne by the fiber is calculated in the loading process, the fiber with the fiber strength smaller than the stress is considered to be fractured, based on a global sharing model, the residual fiber is considered to share all the stress, and the fracture probability P (i) of the fiber is as follows:
Figure BDA0002367420550000083
wherein: m isfIs the strength of the fibreDistributed Weibull modulus, σ0Representing the characteristic strength, σ, of the fibrefiThe maximum stress borne by the loaded fiber in the ith step is shown, the fiber strength is influenced in the oxidation process of the fiber, and according to the fracture mechanics, when the defect size delta of the fiber isd<a is considered to be a fiber strength which is not changed by oxidation, and a fiber defect size δ is considered to be a fiber defect sizedAnd when the fiber is more than or equal to a, the reference strength of the fiber is as follows:
Figure BDA0002367420550000084
wherein: sigma0(z) is the reference fiber length l0Zeta is the distance of the oxidation defect from the location at which the size of the oxidation defect is the critical defect size a from the crack length, reference strength of the unoxidized fiber
Figure BDA0002367420550000091
Is σ00And a is the critical crack size of the fiber,
Figure BDA0002367420550000092
KICis the fracture toughness of the fiber, and Y is the defect shape parameter; reference strength of the fiber after oxidation is
Figure BDA0002367420550000093
Make Vf(i)＝Vf0(1-p (i)), the composite interfacial shear stress is reduced by step seven, wherein: vf(i) Is the volume percent of the fiber at the loading of the ith load, Vf0Is the initial volume percentage of the fiber and then returns to the step one.
Compared with the prior art, the invention has the following beneficial effects:
the invention provides a method capable of effectively simulating the stress-strain curve of any loading and unloading of a unidirectional SiC/SiC composite material in a high-temperature oxidation environment, and the influence of the density and width of matrix cracks, the length consumed by interface oxidation and the fiber tensile strength on the stress-strain curve of the composite material due to the length and distribution of an interface sliding region during loading in the high-temperature oxidation environment are considered;
the method can provide a theoretical basis for the calculation of the fatigue life of the unidirectional SiC/SiC composite material under the spectral load in the high-temperature oxidation environment;
the invention overcomes the defects of high test cost and large manpower and material resource consumption of the one-way ceramic matrix composite material random loading and unloading oxidation test, and can save a large amount of manpower and material resources.
Drawings
FIG. 1 is a flow chart;
FIG. 2 is a Monte Carlo simulation flow;
FIG. 3 is a graph of Monte Carlo modeling non-uniform matrix cracking;
FIG. 4 is a composite matrix cracking signature element;
FIG. 5 is a schematic view of SiC/SiC internal oxidation;
FIG. 6 shows the geometry of the SiC/SiC composite at the crack;
FIG. 7 is a composite interface diffusion channel geometry;
FIG. 8 is a graph of interfacial oxidation depletion length versus oxidation time;
FIG. 9 is a load history;
FIG. 10 is a plot of arbitrary loading and unloading stress strain.
Detailed Description
The present invention will be further described with reference to the following examples.
Some of the parameters in this example are shown in Table 1
TABLE 1
Figure BDA0002367420550000101
A method for predicting any stress-strain curve of loading and unloading of a ceramic matrix composite in a high-temperature oxidation environment comprises the following steps:
the method comprises the following steps: determining the crack density and the crack spacing of the unidirectional SiC/SiC ceramic matrix composite material matrix based on a Monte Carlo simulation method for the cracking of the unidirectional SiC/SiC ceramic matrix composite material matrix;
the specific steps of the first step are as follows:
matrix cracks of the unidirectional SiC/SiC composite material are simulated based on a Monte Carlo method, the loading process is shown in figure 9, the crack distance of the matrix during initial loading is determined, and the matrix failure probability is as follows:
Figure BDA0002367420550000102
wherein, P (xi ═ sigma, eta ═ Lc) Means that the total length of the composite material is LcThe probability of failure of the substrate, σ, when the applied stress is σthIs the residual thermal stress, sigma, generated in the manufacturing process of the composite materialRCharacteristic stress, sigma, for cracking of composite material matrix*Is the minimum initial cracking stress of the matrix, and m is the Weibull modulus; the Monte Carlo method is adopted to simulate and obtain the initial tensile stress sigma1Length L of the steel sheet under the action ofcK number of cracks generated in the composite material substrate1At (0, L)c) Between generate k1A random number of k1The distribution position of each crack; the continuous loading load increment is delta sigma, and the length LcThe composite material of (1) has an increment of the number of cracks generated on the substrate of Δ k, if Δ k<1, determining that the matrix can not generate new cracks, and if delta k is more than or equal to 1, calculating the total interface bonding area length of the composite material to be LbTotal length of (0, L)b) The bonding area generates evenly distributed delta k random numbers which are the positions of newly generated cracks, along with the increase of stress, when the interface has no bonding area, the matrix cracks cannot be generated, at the moment, the number of the matrix cracks reaches saturation, and along with the loading, unequal crack distances L are generated, and the Monte Carlo simulation idea is shown in figure 1.
Step two: determining the width of a diffusion channel of oxygen in the crack of the unidirectional SiC/SiC ceramic matrix composite;
the second step comprises the following specific steps:
based on empirical formula, the crack width of the matrix is:
Figure BDA0002367420550000111
wherein: d is the crack width of the matrix under an applied stress of sigma at a temperature T, d0The crack width of the substrate is 200MPa at normal temperature, T0Is normal temperature,. DELTA.T is the difference between ambient temperature and normal temperature, EfIs the modulus of elasticity, V, of the fibermIs the volume fraction of the matrix, alpham,αfThe thermal expansion coefficients of the matrix and the fiber are respectively;
the width of oxygen in each load step zone in the diffusion channel of the composite material is equal to the load stress of
Figure BDA0002367420550000112
Crack width L of the substrateeWherein: sigmaiRepresenting the load value, σ, loaded at the ith load stepi-1The load value representing the load step loading of the i-1 st load step is as follows:
Figure BDA0002367420550000113
step three: based on an oxidation dynamic model in a high-temperature oxidation environment, obtaining the thickness of an oxidation layer at each loading stress crack of the unidirectional SiC/SiC ceramic matrix composite substrate from a crack wall surface, the interface oxidation consumption length and the notch radius generated by the oxidation of the fiber; judging whether the thickness of the oxidation layer at the crack position of the matrix is larger than the width of the oxygen diffusion channel obtained in the step two or whether the notch radius generated by the oxidation of the fiber is larger than the thickness of the interface layer of the unidirectional SiC/SiC composite material, if so, determining that the oxygen cannot enter the composite material from the crack of the matrix in the subsequent loading, and the fiber and the interface of the unidirectional SiC/SiC composite material at the crack position cannot be oxidized any more;
the third step comprises the following specific steps:
based on the high temperature oxidation kinetic model:
Figure BDA0002367420550000121
boundary conditions:
Figure BDA0002367420550000122
wherein: r istIs the distance from the surface of the matrix to the center of the fiber circle, y is the coordinate of the crack, z is the coordinate of the interface,
Figure BDA0002367420550000123
is SiO at y at time t2Thickness of layer projecting with respect to wall surface,/rFor the length of the interface consumption, hm、hfDenotes the thickness of the fiber oxide layer when y is 0 and z is 0, LeThe width of the oxygen channel at the crack of the matrix is obtained in the second step, gf,gmRespectively generating 1mol SiO for the oxidation reaction of the fiber and the substrate2Amount of oxygen required, MsIs SiO2Molar mass of (C)*Is the oxygen concentration of pure oxygen under the standard air pressure,
Figure BDA0002367420550000124
pm,pfparabolic constants for oxidation of SiC, as shown in Table 2, D1Effective diffusion coefficient of oxygen in crack channels of the substrate, D2To be the effective diffusion coefficient of oxygen within the interface channel,
Figure BDA0002367420550000125
denotes oxygen molar solubility, C0Denotes the ambient oxygen solubility, psIs SiO2(ii) a density of (d); kcIs an interfacial carbon phase reaction rate constant, rf,rm,rm0Respectively, the fiber, the matrix and the interface radius, and alpha is a scale conversion factor; obtaining the thickness of the oxidation delamination crack wall surface at the crack position of the matrix at the time t according to the formula and the boundary conditions
Figure BDA0002367420550000126
Length of interfacial oxidation consumption lr(t), let δd(t)＝hfObtaining the fiber defect radius deltad(t) law of change with oxidation time; the loading time of each loading step is the same as delta t, and the total number of the loading steps isnWhen it comes toiThickness of oxide delamination crack wall surface at crack position of matrix generated in each loading step
Figure BDA0002367420550000127
Length of consumption of interfacial oxidation
Figure BDA0002367420550000128
Radius of fiber defect
Figure BDA0002367420550000129
Wherein:
Figure BDA00023674205500001210
Δlr,Δδdrespectively representing the thickness of the oxidation delamination crack wall surface, the interface oxidation length and the increment of the fiber defect radius at the matrix crack after the time delta t;
judging the thickness of the oxidation delamination crack wall surface at each crack of the matrix in the current load step
Figure BDA0002367420550000131
Whether the width of the oxygen diffusion channel is more than half of the width of the oxygen diffusion channel obtained in the step two or the radius delta of the fiber defectdiWhether or not it is larger than the thickness r of the SiC/SiC interface layerm0-rfIf the oxygen content is larger than the preset value, oxygen cannot enter the composite material from the crack in subsequent loading, and the fiber and the interface of the SiC/SiC composite material at the crack cannot be oxidized any more;
TABLE 2 Nicalon fibers and SiC matrix high temperature Oxidation parameters
Figure BDA0002367420550000132
Step four: calculating and obtaining the interface slip region distribution under each stress point according to the interface friction slip model; then determining a stress-strain relation curve of the unidirectional SiC/SiC ceramic matrix composite based on a shear-lag model;
the fourth step comprises the following specific steps:
calculating the length of the debonding area according to the crack spacing calculated in the step one and the friction slip model
Figure BDA0002367420550000133
σmaxConsidering the maximum stress of the loaded load course, the distribution of the slippage area on each fiber is the same, and the length of the positive slippage area is equal when the fiber is loaded from 0 for the first time
Figure BDA0002367420550000134
When unloading, the length of the reverse slip zone is
Figure BDA0002367420550000135
The length of the forward slip region is l12＝l11-lR11There are at most two slip zones; upon reloading, the forward slip region has a length of
Figure BDA0002367420550000136
Reverse slip zone length of lR21＝lR11-l21The second forward slip zone has a length of l22＝l11-lR11-l21When at most three slip zones exist; the length of the reverse slip zone during further unloading is
Figure BDA0002367420550000137
The length of the forward slip zone is l31＝l11-lR31The second reverse slip zone has a length of lR32＝lR21-lR31-l31The second forward slip zone has a length of l32＝l11-lR31-lR32-l31At the moment, at most four slippage areas exist, and the distribution of the subsequent loading and unloading slippage areas is calculated according to the four slippage areas;
wherein: σ is the applied stress, Vf,VmVolume fractions of fiber and matrix, respectively, Em,Ef,EcRespectively the elastic modulus of the matrix, the fiber and the composite material, tau is the interface shear stress, rfIn order to be the radius of the fibers,
Figure BDA0002367420550000141
representing the 1 st peak and valley in the load history,
Figure BDA0002367420550000142
representing the 2 nd peak and valley in the load course; then
Figure BDA0002367420550000143
Representing the jth peak and valley in the load history,
determining the stress distribution of each unit cell fiber according to a shear lag model, and neglecting the fiber stress distribution on the crack opening section because the crack width is far smaller than the debonding length, and considering that the stress distribution situation on each fiber is the same; when loading, an oxidation area, a debonding area and a bonding area exist on the fiber, and the stress on any fiber is divided into the following conditions:
during initial loading, if the calculated result in the first step is that no crack exists, calculating the stress strain by using a mixing ratio formula:
Figure BDA0002367420550000144
if cracks exist on the composite material matrix, the cracks are randomly distributed on the composite material matrix, and the total length is LcEach unit cell length of Lic，LicThe index i in (1) indicates the ith load step and the index c indicates the length LcThe composite material has the same stress distribution from the left to the right of the c single cell, the left and right sides of each single cell are the same, the left crack surface of each single cell is taken as the original point, the x axis is taken along the fiber direction, the single cell can be divided into an oxidation area, a forward sliding area and a bonding area, and the length of the oxidation area is lrThe length of the forward slip zone is l11The length of the bonding region is
Figure BDA0002367420550000145
ldLength of debonding region of interface,. alpha.at initial loadingd＝l11Then fiber stress σf(x) The distribution is as follows:
Figure BDA0002367420550000146
wherein: x is a coordinate position on the x-axis,
Figure BDA0002367420550000147
ρ is an intermediate quantity, with no practical meaning, simply to simplify the written length of the formula, R1The radius of the concentration for bearing the axial load for the matrix according to the formula
Figure BDA0002367420550000148
Calculating to obtain R1，GmShear modulus of the matrix;
when unloading, the matrix will not generate new cracks, and the interface area can be divided into oxidation area, reverse slip area, forward slip area and bonding area, the length of the oxidation area is lrThe reverse slip zone has a length of lR11The length of the forward slip zone is l12Length l of debonding aread＝lR11+l12Then fiber stress σf(x) The distribution is as follows:
Figure BDA0002367420550000151
wherein: sigmaf0The axial stress borne by the fibers when the composite material is intact.
When loading, if the matrix does not generate new cracks, the interface can be divided into an oxidation area, a forward slip area, a reverse slip area, a forward slip area and a bonding area, wherein the length of the oxidation area is lrThe length of the first forward slip region is l21The reverse slip zone has a length of lR21The second forward slip zone has a length of l22Length l of debonding aread＝l21+lR21+l22The length of the bonding region is
Figure BDA0002367420550000152
The fiber stress σf(x) The distribution is as follows:
Figure BDA0002367420550000153
if the matrix generates new cracks, the forward slip region completely covers the reverse slip region generated during the previous unloading, the lengths of the interfaces consumed by oxidation are different due to different cracking times of the matrix cracks on the left side and the right side of the interface, and the length of the left side of the interface consumed by oxidation is lrlRight side interface consumption length is lrrThe left and right debonding regions have a length of ldAnd a forward slip region l21Equal, non-oxidized section having the coordinate of the center point at the interface of
Figure BDA0002367420550000154
I.e. the stress distribution of the debonding and bonding areas with respect to the coordinates
Figure BDA0002367420550000155
Symmetrically distributed, at which point the fibre stress σf(x) The distribution is as follows:
Figure BDA0002367420550000161
the strain of the composite material is equivalent to the strain of the fiber, then
Figure BDA0002367420550000162
Wherein: n is a radical of1The total length under the current load is LcC represents the length LcFrom left to right of the c-th unit cell, epsiloncIs strain of composite material, epsilonfIs the strain of the fiber.
Step five: simulating the degradation rule of the interface of the unidirectional SiC/SiC ceramic matrix composite material according to the improved interface shear stress degradation rule;
the concrete steps of the fifth step are as follows:
simulating the degradation failure rule of the interface according to the interface shear stress degradation criterion:
Figure BDA0002367420550000163
wherein: tau isiInterfacial shear stress at ith load peak, τ0Is the initial interfacial shear stress, τ, of the materialminShear stress, σ, at which the interface gradually approaches steady state with cyclic degradationAThe maximum applied load before the current load step, ω, λ are empirical parameters,
Figure BDA0002367420550000164
wherein: n is a radical of2Representing the number of peaks occurring before the current load step.
Step six: judging whether the stress is loaded or not, if not, combining the results of the previous calculation, assuming that the strength distribution of the initial fiber of the unidirectional SiC/SiC composite material accords with the two-parameter Weibull distribution, calculating the fiber fracture failure percentage, reducing the fiber volume percentage, reducing the interface shear stress according to the fifth step, continuously loading the stress, and returning to the first step; and if the stress loading is finished, ending.
The sixth step comprises the following specific steps:
in the fatigue loading process, the fiber can have a fracture failure behavior, the fractured fiber cannot bear load, assuming that the strength distribution of the initial fiber conforms to the two-parameter Weibull distribution, the maximum stress borne by the fiber is calculated in the loading process, the fiber with the fiber strength smaller than the stress is considered to be fractured, based on a global sharing model, the residual fiber is considered to share all the stress, and the fracture probability P (i) of the fiber is as follows:
Figure BDA0002367420550000171
wherein: m isfWeibull modulus, σ, for fiber strength distribution0Representing the characteristic strength, σ, of the fibrefiThe maximum stress borne by the loaded fiber in the ith step is shown, the fiber strength is influenced in the oxidation process of the fiber, and according to the fracture mechanics, when the defect size delta of the fiber isd<a is considered to be a fiber strength which is not changed by oxidation, and a fiber defect size δ is considered to be a fiber defect sizedAnd when the fiber is more than or equal to a, the reference strength of the fiber is as follows:
Figure BDA0002367420550000172
wherein: sigma0(z) is the reference fiber length l0Zeta is the distance of the oxidation defect from the location at which the size of the oxidation defect is the critical defect size a from the crack length, reference strength of the unoxidized fiber
Figure BDA0002367420550000173
Is σ00And a is the critical crack size of the fiber,
Figure BDA0002367420550000174
KICis the fracture toughness of the fiber, and Y is the defect shape parameter; reference strength of the fiber after oxidation is
Figure BDA0002367420550000175
Make Vf(i)＝Vf0(1-p (i)), the composite interfacial shear stress is reduced by step seven, wherein: vf(i) Is the volume percent of the fiber at the loading of the ith load, Vf0Is the initial volume percentage of the fiber and then returns to the step one.
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 (4)

1. A method for predicting any stress-strain curve of loading and unloading of a ceramic matrix composite in a high-temperature oxidation environment is characterized by comprising the following steps of:
the method comprises the following steps: determining the crack density and the crack spacing of the unidirectional SiC/SiC ceramic matrix composite material matrix based on a Monte Carlo simulation method for the cracking of the unidirectional SiC/SiC ceramic matrix composite material matrix;
step two: determining the width of a diffusion channel of oxygen in the crack of the unidirectional SiC/SiC ceramic matrix composite;
step three: based on an oxidation dynamic model in a high-temperature oxidation environment, obtaining the thickness of an oxidation layer at each loading stress crack of the unidirectional SiC/SiC ceramic matrix composite substrate from a crack wall surface, the interface oxidation consumption length and the notch radius generated by the oxidation of the fiber; judging whether the thickness of the oxidation layer at the crack position of the matrix is larger than the width of the oxygen diffusion channel obtained in the step two or whether the notch radius generated by the oxidation of the fiber is larger than the thickness of the interface layer of the unidirectional SiC/SiC composite material, if so, determining that the oxygen cannot enter the composite material from the crack of the matrix in the subsequent loading, and the fiber and the interface of the unidirectional SiC/SiC composite material at the crack position cannot be oxidized any more;
step four: calculating and obtaining the interface slip region distribution under each stress point according to the interface friction slip model; then determining a stress-strain relation curve of the unidirectional SiC/SiC ceramic matrix composite based on a shear-lag model;
the fourth step comprises the following specific steps: calculating the length of the debonding area according to the crack spacing calculated in the step one and the friction slip model
Figure FDA0003223676530000011
σmaxConsidering the maximum stress of the loaded load course, the distribution of the slippage area on each fiber is the same, and the length of the positive slippage area is equal when the fiber is loaded from 0 for the first time
Figure FDA0003223676530000012
When unloading, the length of the reverse slip zone is
Figure FDA0003223676530000013
The length of the forward slip region is l12＝l11-lR11There are at most two slip zones;
upon reloading, the forward slip region has a length of
Figure FDA0003223676530000014
Reverse slip zone length of lR21＝lR11-l21The second forward slip zone has a length of l22＝l11-lR11-l21When at most three slip zones exist; the length of the reverse slip zone during further unloading is
Figure FDA0003223676530000015
The length of the forward slip zone is l31＝l11-lR31The second reverse slip zone has a length of lR32＝lR21-lR31-l31The second forward slip zone has a length of l32＝l11-lR31-lR32-l31At the moment, at most four slippage areas exist, and the distribution of the subsequent loading and unloading slippage areas is calculated according to the four slippage areas;
wherein: σ is the applied stress, Vf,VmVolume fractions of fiber and matrix, respectively, Em,Ef,EcRespectively the elastic modulus of the matrix, the fiber and the composite material, tau is the interface shear stress, rfIn order to be the radius of the fibers,
Figure FDA0003223676530000021
representing the 1 st peak and valley in the load history,
Figure FDA0003223676530000022
representing the 2 nd peak and valley in the load course; then
Figure FDA0003223676530000023
Representing the jth peak and valley in the load history,
determining the stress distribution of each unit cell fiber according to a shear lag model, and neglecting the fiber stress distribution on the crack opening section because the crack width is far smaller than the debonding length, and considering that the stress distribution situation on each fiber is the same; when loading, an oxidation area, a debonding area and a bonding area exist on the fiber, and the stress on any fiber is divided into the following conditions:
during initial loading, if the calculated result in the first step is that no crack exists, calculating the stress strain by using a mixing ratio formula:
Figure FDA0003223676530000024
wherein: epsiloncStrain for composite material:
if cracks exist on the composite material matrix, the cracks are randomly distributed on the composite material matrix, and the total length is LcEach unit cell length of Lic，LicThe index i in (1) indicates the ith load step and the index c indicates the length LcThe composite material has the stress distribution of the left side and the right side of each unit cell from the left to the right c, the unit cell is divided into an oxidation area, a forward slip area and a bonding area by taking a crack surface at the left side of the unit cell as an original point and an x axis along the fiber direction, and the length of the oxidation area is lrThe length of the forward slip zone is l11The length of the bonding region is
Figure FDA0003223676530000025
ldLength of debonding region of interface,. alpha.at initial loadingd＝l11Then fiber stress σf(x) The distribution is as follows:
Figure FDA0003223676530000026
wherein: x is a coordinate position on the x-axis,
Figure FDA0003223676530000027
R1the radius of the concentration for bearing the axial load for the matrix according to the formula
Figure FDA0003223676530000028
Calculating to obtain R1，GmShear modulus of the matrix;
when unloading, the substrate will not generate new cracks, and the interface area is divided into an oxidation area, a reverse slip area, a forward slip area and a bonding area, wherein the length of the oxidation area is lrThe reverse slip zone has a length of lR11The length of the forward slip zone is l12Length l of debonding aread＝lR11+l12Then fiber stress σf(x) The distribution is as follows:
Figure FDA0003223676530000031
wherein: sigmaf0Axial stress borne by the fibers when the composite material is not damaged;
when loading, if the matrix does not generate new cracks, the interface is divided into an oxidation area, a forward slip area, a reverse slip area, a forward slip area and a bonding area, wherein the length of the oxidation area is lrThe length of the first forward slip region is l21The reverse slip zone has a length of lR21The second forward slip zone has a length of l22Length l of debonding aread＝l21+lR21+l22The length of the bonding region is
Figure FDA0003223676530000032
The fiber stress σf(x) The distribution is as follows:
Figure FDA0003223676530000033
if the matrix generates new cracks, the forward slip regionThe reverse slip region generated during the previous unloading is completely covered, the lengths of the interfaces consumed by oxidation are different due to different cracking times of matrix cracks on the left side and the right side of the interface, and the length consumed by oxidation on the left side of the interface is lrlRight side interface consumption length is lrrThe left and right debonding regions have a length of ldAnd a forward slip region l21Equal, non-oxidized section having the coordinate of the center point at the interface of
Figure FDA0003223676530000034
I.e. the stress distribution of the debonding and bonding areas with respect to the coordinates
Figure FDA0003223676530000035
Symmetrically distributed, at which point the fibre stress σf(x) The distribution is as follows:
Figure FDA0003223676530000041
the strain of the composite material is equivalent to the strain of the fiber, then
Figure FDA0003223676530000042
Wherein: n is a radical of1The total length under the current load is LcC represents the length LcFrom left to right of the c-th unit cell, epsiloncIs strain of composite material, epsilonfIs the strain of the fibre, EfIs the modulus of elasticity of the fiber;
step five: simulating the degradation rule of the interface of the unidirectional SiC/SiC ceramic matrix composite material according to the improved interface shear stress degradation rule;
the concrete steps of the fifth step are as follows: simulating the degradation failure rule of the interface according to the interface shear stress degradation criterion:
τi-τ0＝[1-exp(-ω((∫|dσ|)/σA)λ](τmin-τ0)
wherein: tau isiThe interfacial shear stress at the ith loading peak,τ0is the initial interfacial shear stress, τ, of the materialminShear stress, σ, at which the interface gradually approaches steady state with cyclic degradationAThe maximum applied load before the current load step, ω, λ are empirical parameters,
Figure FDA0003223676530000043
wherein: n is a radical of2Indicating the number of peaks, σ, occurring before the current load stepj-1 minRepresents the j-1 th valley value in the load course;
step six: judging whether the stress is loaded or not, if not, combining the results of the previous calculation, assuming that the strength distribution of the initial fiber of the unidirectional SiC/SiC composite material accords with the two-parameter Weibull distribution, calculating the fiber fracture failure percentage, reducing the fiber volume percentage, reducing the interface shear stress according to the fifth step, continuously loading the stress, and returning to the first step; if the stress loading is finished, ending;
the sixth step comprises the following specific steps: in the fatigue loading process, the fiber can have a fracture failure behavior, the fractured fiber cannot bear load, assuming that the strength distribution of the initial fiber conforms to the two-parameter Weibull distribution, the maximum stress borne by the fiber is calculated in the loading process, the fiber with the fiber strength smaller than the stress is considered to be fractured, based on a global sharing model, the residual fiber is considered to share all the stress, and the fracture probability P (i) of the fiber is as follows:
Figure FDA0003223676530000051
wherein: m isfWeibull modulus, σ, for fiber strength distribution0Representing the characteristic strength, σ, of the fibrefiThe maximum stress borne by the loaded fiber in the ith step is shown, the fiber strength is influenced in the oxidation process of the fiber, and according to the fracture mechanics, when the defect size delta of the fiber isdWhen < a, it is considered that the fiber strength does not change by oxidation, and when the fiber is usedDimension defect size deltadAnd when the fiber is more than or equal to a, the reference strength of the fiber is as follows:
Figure FDA0003223676530000052
wherein: sigma0(z) is the reference fiber length l0Zeta is the distance of the oxidation defect from the location at which the size of the oxidation defect is the critical defect size a from the crack length, reference strength of the unoxidized fiber
Figure FDA0003223676530000053
Is σ00Z is the interface coordinate, a is the critical crack size of the fiber,
Figure FDA0003223676530000054
KICis the fracture toughness of the fiber, and Y is the defect shape parameter; reference strength of the fiber after oxidation is
Figure FDA0003223676530000055
Make Vf(i)＝Vf0(1-p (i)), the composite interfacial shear stress is reduced by step six, wherein: vf(i) Is the volume percent of the fiber at the loading of the ith load, Vf0Is the initial volume percentage of the fiber and then returns to the step one.
2. The method for predicting the stress-strain curve of any load and unload stress of the ceramic matrix composite in the high-temperature oxidation environment according to claim 1, wherein the specific step of the first step is as follows:
simulating matrix cracks of the unidirectional SiC/SiC composite material based on a Monte Carlo method, and determining the crack spacing of the matrix during initial loading, wherein the matrix failure probability is as follows:
Figure FDA0003223676530000056
wherein, P (xi ═ sigma, eta ═ Lc) Means that the total length of the composite material is LcProbability of failure of the substrate, σ, when the applied stress is σthIs the residual thermal stress, sigma, generated in the manufacturing process of the composite materialRCharacteristic stress, sigma, for cracking of composite material matrix*Is the minimum initial cracking stress of the matrix, and m is the Weibull modulus; the Monte Carlo method is adopted to simulate and obtain the initial tensile stress sigma1Length L of the steel sheet under the action ofcK number of cracks generated in the composite material substrate1At (0, L)c) Between generate k1A random number of k1The distribution position of each crack; the continuous loading load increment is delta sigma, and the length LcThe increment of the number of cracks generated on the matrix of the composite material is delta k, if delta k is less than 1, the matrix is considered not to generate new cracks, and if delta k is more than or equal to 1, the total interface bonding area length of the composite material is calculated to be LbTotal length of (0, L)b) The bonding area generates evenly distributed delta k random numbers which are the positions of newly generated cracks, along with the increase of stress, when the interface has no bonding area, matrix cracks cannot be generated, the number of the matrix cracks reaches saturation, and unequal crack spacing L is generated along with the progress of loading.
3. The method for predicting the stress-strain curve of any loading and unloading of the ceramic matrix composite in the high-temperature oxidation environment according to claim 2, wherein the specific steps in the second step are as follows:
based on empirical formula, the crack width of the matrix is:
Figure FDA0003223676530000061
wherein: d is the crack width of the matrix under an applied stress of sigma at a temperature T, d0The crack width of the substrate is 200MPa at normal temperature, T0Is normal temperature,. DELTA.T is the difference between ambient temperature and normal temperature, EfIs the modulus of elasticity, V, of the fibermIs the volume fraction of the matrix, alpham,αfRespectively being a substrate and a fiberThe coefficient of thermal expansion of the dimension;
the width of oxygen in each load step zone in the diffusion channel of the composite material is equal to the load stress of
Figure FDA0003223676530000062
Crack width L of the substrateeWherein: sigmaiRepresenting the load value, σ, loaded at the ith load stepi-1The load value representing the load step loading of the i-1 st load step is as follows:
Figure FDA0003223676530000063
4. the method for predicting the stress-strain curve of any loading and unloading of the ceramic matrix composite in the high-temperature oxidation environment according to claim 3, wherein the concrete steps in the third step are as follows:
based on the high temperature oxidation kinetic model:
Figure FDA0003223676530000064
boundary conditions:
Figure FDA0003223676530000071
wherein: r istIs the distance from the surface of the matrix to the center of the fiber circle, y is the coordinate of the crack, z is the coordinate of the interface,
Figure FDA00032236765300000710
is SiO at y at time t2Thickness of layer projecting with respect to wall surface,/rIs the length of the oxidation zone, hm、hfDenotes the thickness of the fiber oxide layer when y is 0 and z is 0, LeThe width of the oxygen channel at the crack of the matrix is obtained in the second step, gf,gmRespectively generating 1mol SiO for the oxidation reaction of the fiber and the substrate2Amount of oxygen required, MsIs SiO2Molar mass of (C)*Is the oxygen concentration of pure oxygen under the standard air pressure,
Figure FDA0003223676530000072
pm,pfparabolic constant for oxidation of SiC, D1Effective diffusion coefficient of oxygen in crack channels of the substrate, D2To be the effective diffusion coefficient of oxygen within the interface channel,
Figure FDA0003223676530000073
denotes oxygen molar solubility, C0Denotes the ambient oxygen solubility, psIs SiO2(ii) a density of (d); kcIs an interfacial carbon phase reaction rate constant, rf,rm,rm0Respectively, the fiber, the matrix and the interface radius, and alpha is a scale conversion factor; obtaining the thickness of the oxidation delamination crack wall surface at the crack position of the matrix at the time t according to the formula and the boundary conditions
Figure FDA0003223676530000074
Length of interfacial oxidation consumption lr(t), let δd(t)＝hfObtaining the fiber defect radius deltad(t) law of change with oxidation time; the loading time of each loading step is the same as delta t, and when the total number of the loading steps is n, the thickness of the oxidation delamination crack wall surface at the position of the matrix crack generated in the ith loading step is
Figure FDA0003223676530000075
Length of consumption of interfacial oxidation
Figure FDA0003223676530000076
Radius of fiber defect
Figure FDA0003223676530000077
Wherein:
Figure FDA0003223676530000078
Δlr,Δδdrespectively representing the thickness of the oxidation delamination crack wall surface, the interface oxidation length and the increment of the fiber defect radius at the matrix crack after the time delta t;
judging the thickness of the oxidation delamination crack wall surface at each crack of the matrix in the current load step
Figure FDA0003223676530000079
Whether the width of the oxygen diffusion channel is more than half of the width of the oxygen diffusion channel obtained in the step two or the radius delta of the fiber defectdiWhether or not it is larger than the thickness r of the SiC/SiC interface layerm0-rfIf the value is larger than the above range, it is considered that oxygen does not enter the interior of the composite material from the crack during subsequent loading, and the fibers and the interface of the SiC/SiC composite material at the crack are not oxidized any more.
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