An efficient solution method for the solid-thermal coupling probability model based on the correlation of input variables

Abstract

The present invention discloses an efficient solution method for a solid-thermal coupling probability model based on the correlation of input variables. First, a microscopic finite element model of a woven ceramic matrix composite material is established. According to the number and randomness of internal damage such as fiber pullout and matrix cracks that exist during its use, the probability distribution of the mechanical performance parameters of the microscopic model is established at different temperatures (normal temperature and high temperature conditions). The probability distribution of the internal damage (mechanical performance parameters) and temperature factors is considered to be independent of each other, and the correlation relationship between internal damage and random factors is established to study the probability distribution of variable correlation. The influence of internal damage on the mechanical and thermal performance parameters under the joint action of different damages is studied, and the probability distribution of the mechanical and thermal performance of CMCs due to the randomness of internal damage is fitted through parametric and non-parametric methods.

Description

Technical Field

[0001] The invention relates to the field of engine turbine blades, and in particular to an efficient solution method for a solid-thermal coupling probability model based on input variable correlation. Background Art

[0002] With the continuous development of propulsion technology, the industry has put forward higher requirements for the performance of engines used in aviation aircraft, requiring engines to have high propulsion efficiency, high thrust-to-weight ratio, good heat resistance and their own weight should be reduced as much as possible. As an extremely important part of turbine engine design, turbine blade design directly affects the performance of turbine engines. However, the high-temperature alloy blades commonly used in industry have always been close to the limits of the material itself in terms of strength and heat resistance, and the high-temperature alloy material itself has disadvantages such as high density and easy corrosion. If high-temperature alloy blades continue to be used, even if there are improvements in design, it will still be difficult to meet the growing industrial needs. Therefore, the development of new materials for engine turbine rotor blades has become a new demand in the industry. In order to meet this demand, ceramic matrix composites (Ceramic Matrix Composites, CMCs) came into being.

[0003] Due to the defects of the material itself and the inevitable loss during the processing and preparation process, there will inevitably be some damage inside the braided CMCs before they are put into use. As the CMCs are loaded and the mechanical properties limit is reached, damage will also occur. Therefore, studying CMCs damage has become an important part of CMCs research.

[0004] Since the actual working conditions of composite turbine blades are relatively complex, they will bear multiple types of loads during the working process, and the location of damage and the number of damaged units under different working conditions will also affect their performance parameters. At present, the research on engine turbine blades is more about studying each input variable independently, but the actual working conditions are that multiple input variables affect each other. Therefore, considering the impact of the correlation between external loads and other input variables (such as: solid-thermal coupling) on ​​performance parameters is an issue that technical personnel in this field urgently need to solve. Summary of the invention

[0005] In order to overcome the shortcomings of the prior art, the present invention proposes an efficient solution method for a composite material solid-thermal coupling probability model based on input variable correlation. By constructing a CMCs unit cell model, the failure forms of its fibers and matrix are considered. Under different loads, the internal damage position and quantity of the unit cell model are considered to make a probability distribution of mechanical and thermal performance parameters when factors such as damage and external loads act independently. At the same time, the correlation of many factors is considered through D-vine copula, and the probability distribution of mechanical and thermal performance parameters when the above factors influence each other is made and compared, so as to improve the accuracy of the change of mechanical and thermal performance parameters, thereby improving the accuracy of failure probability calculation, which can be closer to the mutual influence under real working conditions and increase the robustness and credibility of simulation results.

[0006] The technical solution of the present invention is as follows:

[0007] Step 1, establish a unit cell model of woven CMCs at a microscopic perspective;

[0008] Step 2, analyze the mechanical properties parameters of the unit cell model established in step 1, establish a damaged fiber bundle model and a damaged matrix model at the microscale, study the constitutive relationship of the fiber bundle and the matrix under axial tension and compression, transverse tension and compression, and shear loads, and determine the most susceptible failure load form of the fiber bundle and the matrix, that is, under the action of transverse and shear loads, the matrix is ​​mainly damaged, while under the action of axial loads, the fiber-dominated damage is mainly caused;

[0009] Step 3, under the most prone to failure load form, different failure loads, randomness of damage positions and different damage rates are used as variables, and two situations are considered, namely, the independence of each variable and the correlation of each variable. The probability distribution law of the mechanical performance parameters and anisotropic thermal conductivity of the braided CMCs is fitted by parametric method and non-parametric method. When each variable is independent, each variable is used as an input variable; when each variable is correlated, a correlation formula between the input variables is established based on D-vine Copula to obtain new input variables when the correlation is considered;

[0010] Step 4: Compare the input variable related working conditions and independent working conditions to obtain the influence of variable correlation on mechanical and thermal parameters in actual working conditions.

[0011] Preferably, in step 1, the woven CMCs unit cell model is woven from fiber bundles and deposited in a SiC matrix, wherein the fiber bundles are a composite of SiC fiber filaments, a PyC interface layer and a SiC matrix material.

[0012] Preferably, in step 2, different strength criteria are set according to different components, and corresponding stiffness degradation criteria are given after the strength criteria are reached; the maximum principal stress criterion is used to judge the failure of SiC fiber, and the stiffness is reduced after the failure of SiC fiber, and the elastic modulus is reduced to 0.1% of the initial elastic modulus; the Mohr strength criterion is used to judge the failure of SiC matrix, and the stiffness is also reduced after the failure of SiC matrix, and the elastic modulus is reduced to 0.1% of the initial elastic modulus.

[0013] Preferably, in step 2, under different independent input variable conditions, a new failure criterion is established based on the Hashin criterion, the data of mechanical property parameters and thermal conductivity under different input variables are obtained, and the data are screened reasonably.

[0014] As a preferred method, the new failure criterion is: fiber tensile failure ( ): Fiber compression failure ( ): Matrix tensile failure ( ): Matrix compression failure ( ): In the formula are stress components in each principal direction; f and m represent fiber and matrix respectively; F is failure function; S represents strength; t, c, s represent tension, compression and shear; is the shear stress component in each direction; is the stiffness parameter of the fiber bundle in each direction. and 1, 2, 3, representing the main directions of the fiber bundle, namely the two directions perpendicular to the fiber and along the fiber direction.

[0015] Preferably, step 3 specifically includes:

[0016] Step 3.1, through the solution method of the anisotropic mechanical performance parameters and anisotropic thermal conductivity of the micro-model of woven CMCs, the mechanical performance parameters and anisotropic thermal conductivity of CMCs under undamaged conditions are solved; Step 3.2, based on the most prone to failure load form and the failure criterion given in step 2, under different independent input variable conditions, the failure form is studied, and the mechanical performance parameters and thermal conductivity of the unit cell model are obtained; Step 3.3, given the damage rate, the mechanical performance parameters and thermal conductivity of the CMCs micro-model in different directions under the damage rate are calculated, and the randomness is considered to determine the damage rate. The damage position is randomly and uniformly sampled several times to obtain the influence of the independent influence of the damage position on the anisotropic mechanical properties and anisotropic thermal conductivity of CMCs; Step 3.4, AD test is performed on the calculation results of Step 3.3, considering the independence of each variable and the correlation of each variable, and the parametric method and non-parametric method are used for fitting to obtain the probability distribution of mechanical and thermal performance parameters; Step 3.5, change the damage rate under high temperature conditions, repeat steps 3.3-3.4, and obtain the anisotropic mechanical properties and anisotropic thermal conductivity and the corresponding probability coefficient function under different damage rates.

[0017] As a preferred method, when considering the correlation of various variables, the correlation formula is established based on D-vine Copula to obtain new input variables when considering the correlation. D-vine Copula is a hierarchical correlation. The more variables there are, the more complex the correlation is. The complex relationship between the input variables is processed in a "hierarchical link" manner to obtain new input variables under the correlation, which can be expressed as: ,

[0018] is the marginal probability density function of the ith variable; is the conditional Copula function, which describes the dependency between the jth and j+ith variables under the condition of given i variables; Represents a conditional Copula function Parameters, control variables and the strength and type of dependencies between them; It is the conditional cumulative distribution function, which means the cumulative distribution function of the j+ith variable under the condition of given i variables.

[0019] Preferably, the parametric method is to compare the simulation experimental data with the existing model to calculate the fit so as to compare the observational significance levels of different probability distribution models; the non-parametric method is to create a new fitting distribution for observation, combining non-parametric regression, non-parametric Bayesian method and Bootstrap method, without assuming that the data follows a specific function form, and making a priori assumptions about the data. Then, the Bootstrap method is used to expand the data, increase the sample size, and locally fit the relationship between variables to increase the data fit and accuracy.

[0020] As a preferred method, the nonparametric method is as follows: First, the original data set (X, Y) is subjected to regression analysis using local weighted regression to obtain a nonparametric regression estimate , and then use Bootstrap to extract multiple bootstrap samples (X b∗ ,Y b∗ ), where b=1,2,...,B, B is the number of samples drawn, and Gaussian process regression is used as the non-parametric Bayesian regression method. , where m(x) is the mean function and k(x,x′) is the covariance function; these models are then combined to estimate the original data regression function The posterior distribution of : and are the mean function and covariance function of the Gaussian process regression model of the b-th bootstrap sample, respectively.

[0021] Preferably, in step 4, the closest distribution type is selected according to the degree of fit and compared. Beneficial Effects

[0022] 1. The present invention proposes a solution to the problem of probability distribution of mechanical property parameters considering the correlation of input variables of composite materials. First, a CMCs unit cell model is established, and a new failure criterion is set. The failure criterion is set according to different components, and different components are subjected to different failure loads. Compared with directly applying loads, the upper and lower limits of the analysis are increased, which can improve the efficiency of simulation calculations.

[0023] 2. The present invention considers the independence and correlation of input variables and compares them. Considering the correlation of input variables can better simulate the actual working conditions, effectively reducing the uncertainty of the results when each variable is independently affected, and improving the robustness and credibility of the calculation results.

[0024] 3. The present invention improves the accuracy of the results by comparing the parameter estimation method and the non-parametric estimation method. Among them, the non-parametric method combines local weighted regression analysis, Bootstrap estimation method and non-parametric Bayesian estimation, which can make the results more accurate and applicable to a variety of working conditions. It can effectively solve the low accuracy of too few data samples and improve the fitting calculation efficiency when the data sample size is too large, thereby improving the robustness and credibility of the calculation results. BRIEF DESCRIPTION OF THE DRAWINGS

[0025] Figure 1 It is a schematic diagram of the process of the present invention;

[0026] Figure 2 This is a schematic diagram of the hierarchical correlation of the D-vine Copula of the present invention;

[0027] Figure 3 It is a flow chart of parameter estimation method of the present invention;

[0028] Figure 4 It is a flow chart of the non-parametric estimation method of the present invention;

[0029] Figure 5 This is the cloud diagram of the warp tensile stress of the present invention;

[0030] Figure 6 This is the latitudinal tensile stress cloud diagram of the present invention;

[0031] Figure 7 It is the CMCs mesoscopic model with 5% damage rate of the present invention;

[0032] Figure 8 The probability density function of thermal conductivity in the x direction is fitted for the parameters of the present invention (5% damage rate);

[0033] Fig. 9 The probability density function of thermal conductivity in the y direction is fitted by the parameters of the present invention (5% damage rate);

[0034] Fig.10 The probability density function of thermal conductivity in the z direction is fitted for the parameters of the present invention (5% damage rate);

[0035] Fig.11 The non-parametric fitting probability density function of thermal conductivity in the x direction of the present invention (5% damage rate);

[0036] Fig.12 The non-parametric fitting probability density function of thermal conductivity in the y direction of the present invention (5% damage rate);

[0037] Fig.13 The probability density function of the thermal conductivity in the z direction (5% damage rate) of the present invention is fitted by non-parametric method; DETAILED DESCRIPTION

[0038] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0039] like Figures 1 to 13 As shown, the present invention discloses an efficient solution method for the solid-thermal coupling probability model of composite materials. By constructing a CMCs unit cell model, the failure forms of its fibers and matrix are taken into consideration. Under different loads, the internal damage position and amount of the unit cell model are taken into consideration, and the probability distribution of mechanical and thermal performance parameters when factors such as damage and external loads act independently is made. At the same time, the correlation of many factors is considered through D-vine copula, and the probability distribution of mechanical and thermal performance parameters when the above factors influence each other is made, and a comparison is made, thereby improving the accuracy of the change of mechanical and thermal performance parameters, thereby affecting the improvement of the calculation accuracy of the failure probability, being able to be closer to the mutual influence under real working conditions, and increasing the robustness and credibility of the simulation results.

[0040] like Figure 1 As shown, an efficient solution method for the composite material solid-thermal coupling probability model includes the following steps:

[0041] Step 1: Construct a unit cell model of woven CMCs from a microscopic perspective using finite elements.

[0042] Step 2: Analyze the mechanical properties parameters of the unit cell model, establish a microscopic damage mechanical model of the fiber bundle and matrix, study the stress-strain curves of the fiber bundle and matrix under axial tension and compression, transverse tension and compression, and shear loads, and determine the most prone to failure load form of the fiber bundle and matrix.

[0043] The Hashin failure criterion is used to judge whether the fiber bundle has failed. The Hashin failure criterion believes that there are two main basic failure modes of fiber-reinforced composite materials: matrix-dominated failure mode and fiber-dominated failure mode (the failure modes are fiber damage and matrix damage, the main load form of fiber damage is axial load, and the main form of matrix damage is lateral or shear load). Among them, the matrix-dominated failure mode is manifested as in-plane shear failure in addition to the transverse tensile failure and transverse compression failure of the single layer. In-plane shear failure is a failure mode in which a single-layer composite material produces matrix parallel cracks between fibers under the action of in-plane shear stress. The Hashin failure criterion believes that the failure modes of composite materials include fiber tensile fracture, fiber compression buckling and fracture, matrix tensile cracking and matrix compression cracking. Therefore, the specific failure criterion formula established in this example is as follows:

[0044] Fiber tensile failure ( ):

[0045] ,

[0046] Fiber compression failure ( ):

[0047] ,

[0048] Matrix tensile failure ( ):

[0049] ,

[0050] Matrix compression failure ( ):

[0051] ,

[0052] In the formula are stress components in each principal direction; f and m represent fiber and matrix respectively; F is failure function; S represents strength; t, c, s represent tension, compression and shear; is the shear stress component in each direction; is the stiffness parameter of the fiber bundle in each direction. and 1, 2, 3, representing the main directions of the fiber bundle (two directions perpendicular to the fiber and along the fiber direction).

[0053] Step 3: Under the most vulnerable load form (i.e., matrix failure is the main cause under lateral and shear loads, and fiber-dominated failure is the main cause under axial loads), different failure loads, randomness of damage locations, and different damage rates are used as input variables, and two situations are considered: independence of each variable and correlation of each variable. When considering the correlation of each variable, the correlation formula is established based on D-vine Copula to obtain new input variables when considering the correlation, such as Figure 2 As shown, the probability distribution law of mechanical properties parameters and anisotropic thermal conductivity of woven CMCs is fitted by parametric and non-parametric methods, as shown in Figure 3 to Figure 4 Finally, the parameter estimation method and the non-parameter estimation method are used to compare the input variable related working conditions and independent working conditions, and the influence of variable correlation on mechanical and thermal parameters in actual working conditions is summarized.

[0054] It should be noted that the steps for variable correlation and variable independence are the same. The difference between the two is that the data processing process of the input variables is different. The correlated variables have an additional step of correlation investigation before the independent variable input (substitute into the subroutine code formula to automatically output a set of related new input variables). The other steps are the same and will not be repeated. Independent variables refer to damage location, damage rate, load form, temperature environment, etc., and variable correlation refers to temperature, damage rate, damage location, etc.

[0055] Specifically,

[0056] Step 3.1, through the solution method of the anisotropic mechanical properties parameters and anisotropic thermal conductivity of the microscopic model of woven CMCs, the mechanical properties parameters (Young's modulus and ultimate strength, etc.) and anisotropic thermal conductivity of CMCs under undamaged conditions are solved, including the warp axial Direction, weft axial Direction and perpendicular to the warp and weft yarn directions The thermal conductivity in three directions and the mechanical properties parameters in the warp and weft directions.

[0057] Step 3.2, based on the most vulnerable load form (mainly the failure load that the damaged fiber bundle model or damaged matrix model can withstand, failure under a certain load (may be warp load, weft load, etc.)), according to the failure criterion given in step 2 (new failure criterion based on Hashin criterion), under different independent input variable conditions, study the failure form. For example, the matrix is ​​destroyed first, and then the main stress-bearing part is the fiber, so the fiber is mainly studied; for example, under the action of weft tensile load, the matrix between the warp and weft fiber bundles will have stress concentration, and the matrix unit will be damaged, so the main analysis is the constitutive relationship of the fiber bundle. And the mechanical performance parameters of the unit cell model can be obtained through its constitutive relationship, and the thermal conductivity coefficient is the same.

[0058] Considering the independence and correlation of various variables, parametric and non-parametric methods are used to fit and obtain the probability distribution of mechanical and thermal performance parameters.

[0059] In this embodiment, in the CMCs microscopic model, when the fiber bundle is subjected to axial tension and axial compression loads, it exhibits a fiber-dominated failure mode, while when the fiber bundle is subjected to transverse tension, transverse compression and shear loads, it exhibits a matrix-dominated failure mode. Figure 5 and Figure 6 It is the cloud diagram of longitudinal and latitudinal tensile stress.

[0060] Step 3.3, given the damage rate, calculate the mechanical properties parameters and thermal conductivity of the CMCs microscopic model in different directions under this damage rate, and consider the randomness, perform several random uniform samplings on the damage position to obtain the influence of the damage position (independent influence) on the anisotropic mechanical properties parameters and anisotropic thermal conductivity of CMCs.

[0061] In this embodiment, under the action of different loads, the position and amount of internal damage in the unit cell model are considered, and the probability distribution of mechanical and thermal performance parameters when factors such as damage and external load act independently is made. At the same time, the correlation of many factors is considered through D-vine copula, and the probability distribution of mechanical and thermal performance parameters under the mutual influence of the above factors is made, and a comparison is formed between related variables and independent variables, so as to improve the accuracy of changes in mechanical and thermal performance parameters, and further improve the accuracy of failure probability calculation.

[0062] This example takes thermal conductivity as an example. The steps for mechanical property parameters (such as strength limit, Young's modulus, etc.) are the same. You can directly follow the following steps to reproduce the operation, and no further details will be given.

[0063] According to Fourier's law, the formula for solving the thermal conductivity is:

[0064] ,

[0065] The research object is a 2.5D woven CMCs microscopic model. When performing steady-state thermal analysis, the temperature change rate is Is a constant value.

[0066] In the CMCs microscopic model, the axial direction of the warp is the x direction, the axial direction of the weft is the y direction, and the z direction is perpendicular to the x and y directions. Then in the x direction, the thermal conductivity is

[0067] ,

[0068] In the formula is the area of ​​the heat flow through the i-th unit in the plane perpendicular to the x-axis; m is the total number of all units in the plane perpendicular to the x-axis; The heat flux per unit area is called heat flux density, and its unit is W / m 2 When the 2.5D woven CMCs micro-model is established and the meshing is completed, Can be considered as a constant , then

[0069] ,

[0070] Similarly, in the y and z directions, the thermal conductivity is

[0071] , .

[0072] In order to obtain the anisotropic thermal conductivity of CMCs under steady-state thermal analysis, it is necessary to assign temperatures to the opposite surfaces of CMCs when the components of the CMCs micro-model are known, and the temperatures on the opposite surfaces have differences. In this example, the temperatures set for the opposite surfaces are room temperature 25°C and the working environment temperature of the turbine blade 1000°C, that is, 298.15K and 1273.15K. The thermal conductivity of each component of the CMCs micro-model is shown in Table 1.

[0073] Table 1

[0074]

[0075] Substituting the data in Table 1 into the damaged fiber bundle model, the thermal conductivity of the damaged fiber bundle is calculated to be 0.001 .

[0076] The thermal conductivity of the 5% damaged CMCs micro-model in different directions is calculated. The results are as follows:

[0077] Table 2 Thermal conductivity of each component in the CMCs microscopic model

[0078] .

[0079] At a damage rate of 5%, considering the randomness of the damage position, random uniform sampling was performed at 30 positions to study the effect of the damage position on the anisotropic thermal conductivity of CMCs. The probability density function of the thermal conductivity in the x and y directions of the parameter fitting at a damage rate of 5% is shown in Figures 8 to 9 As shown, the probability density function of thermal conductivity in the x, y, and z directions under nonparametric fitting at 5% damage rate is as follows: Figures 10 to 13 shown.

[0080] Step 3.4, AD test is performed on the calculation results of step 3.3, and the parameter fitting method of AD test is used to calculate the OSL value of the probability distribution model, and the probability distribution law of the anisotropic mechanical performance parameters and the anisotropic thermal conductivity is obtained by fitting with the local weighted analysis, Bootstrap and non-parametric Bayesian estimation method. Among them, the AD test in the parameter estimation method believes that the thermal conductivity in the three directions obeys the normal distribution with respect to the damage position; the calculation results are then non-parametrically estimated, and the non-parametric estimation is combined with the local weighted analysis, Bootstrap and non-parametric Bayesian estimation method. There are thirty groups of simulation result data.

[0081] It should be noted that parametric method and non-parametric estimation method are two methods, such as Figure 3As shown in the figure, the parameter method is: based on the existing model (normal distribution, Weibull distribution, etc.), the significance observation level (OSL) of the output variable mechanical and thermal performance parameters is calculated, the degree of fit is compared, and the probability distribution of the mechanical and thermal performance parameters is obtained. The smaller the OSL, the better the fit.

[0082] Nonparametric estimation methods such as Figure 4 As shown, the curve is directly fitted according to the given data, which is similar to the exact value. The approximate and rough estimate of the parameter method is more accurate. Specifically, the original data set (X, Y) (30 groups of original sample data) is regressed using local weighted regression to obtain a non-parametric regression estimate , and then use Bootstrap to extract multiple bootstrap samples (X b∗ ,Y b∗ ), (this is equal to enlarging the sample size to 100 groups) where b = 1, 2, ..., B. Then Gaussian process regression is used as the non-parametric Bayesian regression method.

[0083] ,

[0084] Among them, m(x) is the mean function and k(x,x′) is the covariance function.

[0085] Then combine these models to estimate the original data regression function The posterior distribution of .

[0086] ,

[0087] and are the mean function and covariance function of the Gaussian process regression model of the b-th bootstrap sample, respectively.

[0088] Considering the random distribution of damage locations, this example selects a 5% damage rate. Figure 7 As shown, random uniform sampling is performed at 30 positions to study the effect of damage position on the thermal conductivity (thermal performance parameter) of CMCs. This example only studies the thermal conductivity, and the other examples can be studied based on this example.

[0089] The AD test was performed on the 30 groups of calculation results, and the OSL values ​​corresponding to each probability distribution were obtained as shown in Table 3.

[0090] Table 3 OSL values ​​of probability distribution model of thermal conductivity in all directions (5% damage rate)

[0091] .

[0092] In step 3.5, considering different damage rates under high temperature conditions (i.e. changing the damage rate, in this case the temperature and the damage rate act together), repeat the ABAQUS finite element simulation of steps 3.3-3.4 at different damage rates to obtain the anisotropic mechanical properties parameters and anisotropic thermal conductivity and probability distribution.

[0093] Step 4: Compare the input variable related working conditions and independent working conditions to obtain the influence of variable correlation on mechanical and thermal parameters in actual working conditions.

[0094] This embodiment performs finite element simulation at different damage rates, and the calculated anisotropic thermal conductivity and the calculated decrease rate are listed in Table 4. The purpose of selecting damage with different change rates is to illustrate that the less material damage, the better, which is more intuitive than other related variables.

[0095] Table 4 Longitudinal tensile mechanical properties and reduction rates at different damage rates

[0096] .

[0097] According to the different damage rate results, the conclusion is: the higher the damage rate, the smaller the thermal conductivity in each direction. The thermal conductivity decreases less in the x and z directions, and the decrease in the y direction is greater.

[0098] The above is only a preferred embodiment of the present invention. It should be pointed out that for ordinary technicians in this technical field, several improvements and modifications can be made without departing from the principle of the present invention. These improvements and modifications should also be regarded as the scope of protection of the present invention.

Claims

1. An efficient solution method for the solid-thermal coupling probability model based on the correlation of input variables, characterized in that: The following steps are involved: Step 1, establish a unit cell model of woven CMCs at a microscopic perspective; Step 2: Analyze the mechanical performance parameters of the unit cell model established in step 1, establish a damaged fiber bundle model and a damaged matrix model at the microscale, study the constitutive relationship between the fiber bundle and the matrix under axial tension and compression, transverse tension and compression, and shear loads, and determine the most prone to failure load form of the fiber bundle and the matrix. Specifically, under different independent input variable conditions, a new failure criterion is established based on the Hashin criterion, and the data of mechanical performance parameters and thermal conductivity under different input variables are obtained, and data screening is performed reasonably. The new failure criteria are: Fiber tensile failure, σ1 ≥ 0: Fiber compression failure, σ1≤0: Matrix tensile failure, σ2+σ3≥0: Matrix compression failure, σ2+σ3<0: Where σ i are stress components in each principal direction; f and m represent fiber and matrix respectively; F is failure function; S represents strength; t, c, s represent tension, compression and shear; τ ij is the shear stress component in each direction; Step 3, under the most prone to failure load form, different failure loads, randomness of damage positions and different damage rates are used as variables, and two situations where the variables are independent of each other and the variables are correlated are considered respectively, and the probability distribution law of the mechanical performance parameters and anisotropic thermal conductivity of the braided CMCs is fitted by parametric method and non-parametric method, wherein when the variables are independent, each variable is used as an input variable; When there is correlation among the variables, the correlation formula between the input variables is established based on D-vine Copula to obtain new input variables when the correlation is considered; Step 4: Compare the input variable related working conditions and independent working conditions to obtain the influence of variable correlation on mechanical and thermal parameters in actual working conditions.

2. The efficient solution method of the solid-thermal coupling probability model based on input variable correlation according to claim 1 is characterized in that: In step 1, the woven CMCs unit cell model is woven from a fiber bundle and deposited in a SiC matrix, wherein the fiber bundle is a composite of SiC fiber filaments, a PyC interface layer, and a SiC matrix material.

3. The efficient solution method of the solid-thermal coupling probability model based on input variable correlation according to claim 1 is characterized in that: In step 2, different strength criteria are set according to different components, and corresponding stiffness degradation criteria are given after the strength criteria are reached; the maximum principal stress criterion is used to judge the failure of SiC fiber, and the stiffness is reduced after the failure of SiC fiber, and the elastic modulus is reduced to 0.1% of the initial elastic modulus; The failure of the SiC matrix is ​​judged by the Mohr strength criterion. The stiffness reduction is also performed after the failure of the SiC matrix, and the elastic modulus is reduced to 0.1% of the initial elastic modulus.

4. The efficient solution method of the solid-thermal coupling probability model based on input variable correlation according to claim 1 is characterized in that: Step 3 specifically includes: Step 3.1, by using the solution method of the anisotropic mechanical properties parameters and anisotropic thermal conductivity coefficient of the mesoscopic model of woven CMCs, the mechanical properties parameters and anisotropic thermal conductivity coefficient of CMCs under undamaged conditions are solved; Step 3.2, based on the most prone failure load form and the failure criterion given in step 2, study the failure form under different independent input variable conditions, and obtain the mechanical performance parameters and thermal conductivity of the unit cell model; Step 3.3, given the damage rate, calculate the mechanical properties and thermal conductivity of the CMCs mesoscopic model in different directions under the damage rate, and consider the randomness, perform random uniform sampling of the damage position several times, and obtain the influence of the independent influence of the damage position on the anisotropic mechanical properties and anisotropic thermal conductivity of CMCs; Step 3.4, perform AD test on the calculation results of step 3.3, consider the independence of each variable and the correlation of each variable, use parametric method and non-parametric method to fit, and obtain the probability distribution of mechanical and thermal performance parameters; Step 3.5, change the damage rate under high temperature conditions, repeat steps 3.3-3.4, and obtain the anisotropic mechanical performance parameters and anisotropic thermal conductivity and corresponding probability coefficient functions under different damage rates.

5. The efficient solution method of the solid-thermal coupling probability model based on input variable correlation according to claim 1 is characterized in that: When considering the correlation between variables, the correlation formula is established based on D-vine Copula to obtain new input variables when considering the correlation. D-vine Copula is a hierarchical correlation. The more variables there are, the more complex the correlation is. The complex relationship between the input variables is processed in a "hierarchical link" manner to obtain new input variables under the correlation, which can be expressed as: f i (x i ) is the marginal probability density function of the ith variable; c j,j+i|(j+1):(j+i-1) is the conditional Copula function, which describes the dependency between the jth and j+ith variables under the condition of given i variables; θ j,j+i Represents the conditional Copula function c j,j+i Parameters, control variables x i With x j+i The strength and type of dependence between j+i |x j+1 ,...,x j+i-1 ) is the conditional cumulative distribution function, which represents the cumulative distribution function of the j+ith variable under the condition of given i variables.

6. The efficient solution method of the solid-thermal coupling probability model based on input variable correlation according to claim 1 is characterized in that: The parametric method is to compare the simulation experimental data with the existing model to calculate the fit so as to compare the observational significance levels of different probability distribution models; the non-parametric method is to create a new fitting distribution for observation, combining non-parametric regression, non-parametric Bayesian method and Bootstrap method, without assuming that the data follows a specific function form, and making a priori assumptions about the data. Then, the Bootstrap method is used to expand the data, increase the sample size, and locally fit the relationship between variables to increase the data fit and accuracy.

7. The efficient solution method of the solid-thermal coupling probability model based on input variable correlation according to claim 1 is characterized in that: The non-parametric method is specifically: First, we use local weighted regression to perform regression analysis on the original data set (X, Y) to obtain nonparametric regression estimates. Then use Bootstrap to extract multiple bootstrap samples (X, Y) from the original data set (X, Y) with replacement. b* ,Y b* ), where b = 1, 2, ..., B, B is the number of samples drawn, and Gaussian process regression is used as a non-parametric Bayesian regression method. Among them, m(x) is the mean function, k(x,x′) is the covariance function; Then combine these models to estimate the original data regression function The posterior distribution of : m b (x) and k b (x,x') are the mean function and covariance function of the Gaussian process regression model of the b-th bootstrap sample.

8. The efficient solution method of the solid-thermal coupling probability model based on input variable correlation according to claim 1 is characterized in that: In step 4, the closest distribution type is selected based on the degree of fit and compared.

Images