Ceramic matrix composite pore grading modeling and modulus prediction method

Abstract

The invention discloses a ceramic-based composite material pore grading modeling and modulus prediction method, relates to the technical field of material modulus prediction, and aims at solving the problems that in the prior art, in the modeling or prediction process of a ceramic-based composite material, pore modeling is slow, overall modeling of the material cannot be achieved, and the modeling efficiency is low. And errors are large when the modulus of the composite material is predicted. The ceramic-based composite material pore grading modeling method comprises the following steps: acquiring a microstructure of a ceramic-based composite material; extracting pores, and fitting the pores to obtain parameter values; establishing a unit cell model boundary and performing tetrahedron division; establishing a fiber bundle model in the unit cell model; single pores in the ceramic matrix composite are obtained, and first modeling is carried out according to the size from large to small; and determining a first critical volume of the pores, and carrying out second modeling. The technical scheme provided by the invention is used for providing the pore grading modeling and modulus prediction method for the ceramic-based composite material.

Description

Technical Field

[0001] The present invention relates to the technical field of material modulus prediction, and more specifically, to a method for pore classification modeling and modulus prediction of ceramic-based composite materials. Background Art

[0002] Ceramic matrix composites (CMC) have become the preferred material for thermal protection structures of supersonic vehicles due to their high temperature tolerance, corrosion resistance and thermal shock resistance. Their microstructure has a significant impact on their mechanical properties, so it is crucial to establish an accurate geometric model.

[0003] As an inevitable type of defect in composite materials, pores have different shapes, sizes, and position distributions, and their influence on the performance of materials cannot be ignored. Therefore, pore modeling is particularly important. In the process of modeling or predicting ceramic-based composite materials in the prior art, on the one hand, no modeling process of multiple pores in a unit cell or the entire component is given, no parameterized modeling of fiber bundles is performed, and the influence of the positional relationship between pores and pores and between pores and fiber bundles on the modeling results when fitting multiple pores is not considered. When establishing multiple pores in a unit cell, there is no standard for threshold division of pores, and it is impossible to make more in-depth use of pore information statistically obtained by CT, and it is impossible to achieve rapid modeling of pores without affecting the accuracy of modulus prediction; on the other hand, the actual pores are not taken into account in the establishment of the unit cell, and the actual overall modeling of the composite material (including matrix, fiber, pores) cannot be accurately modeled, nor can the modulus of the composite material be accurately predicted. It can be seen that in the process of modeling or predicting ceramic-based composite materials in the prior art, there are technical problems such as slow pore modeling, inability to achieve overall modeling of materials, and large errors in predicting the modulus of composite materials. Summary of the invention

[0004] The purpose of the present invention is to provide a method for pore hierarchical modeling and modulus prediction of ceramic matrix composite materials, which is used to solve the technical problems that the pore modeling is slow in the process of modeling or predicting ceramic matrix composite materials in the prior art, the overall modeling of the material cannot be achieved, and there is a large error in predicting the modulus of the composite material. In view of this, the present invention is implemented through the following scheme.

[0005] In a first aspect, the present invention provides a method for pore hierarchical modeling of a ceramic matrix composite material, comprising:

[0006] Obtain the microstructure of ceramic matrix composites;

[0007] reconstructing the ceramic matrix composite in three dimensions and identifying fiber bundles, matrix, and pores;

[0008] Extracting the pores, and fitting the pores to obtain parameter values;

[0009] Establish the unit cell model boundary and perform tetrahedron partitioning;

[0010] After determining the central axis and cross-sectional control equations of the fiber bundle, modeling the fiber bundle within the unit cell boundary;

[0011] Obtaining single pores in the ceramic-based composite material, arranging the single pores according to volume size, and performing a first modeling from large to small volume;

[0012] The first critical volume of the pores is determined, and a second modeling is performed. The second modeling process is as follows: single pores larger than the first critical volume are fixed to remain the same as the first modeling; and size parameters of single pores smaller than the first critical volume are randomly generated, and random modeling is performed.

[0013] Compared with the prior art, in the pore hierarchical modeling method of the ceramic-based composite material of the present invention, the parameter value of each pore can be obtained by three-dimensionally reconstructing the ceramic-based composite material, extracting the pores and fitting the pores; after establishing the boundary of the unit cell model and performing tetrahedral division, the central axis and cross-section control equation of the fiber bundle are determined, and the fiber bundle can be modeled within the boundary of the unit cell; after the fiber bundle modeling is completed, the pores are continued to be modeled, and the pore modeling process is: obtain a single pore in the ceramic-based composite material, arrange the single pores according to the volume size, and perform the first modeling from large to small according to the volume; further, determine the first critical volume of the pore, and perform the second modeling, and the second modeling process is: fix the single pore larger than the first critical volume and keep it the same as the first modeling; randomly generate size parameters for the single pore smaller than the first critical volume, and perform random modeling. According to the above technical solution, the present invention takes into account the geometric information and position information of the actual fibers and pores when establishing the unit cell model, and then accurately models the model through the extracted data of the microstructure of the actual ceramic-based composite material (the above parameter values); the present invention also proposes a method of modeling multiple pores when establishing the microstructure of the composite material to prevent the cross-overlap of the pores and the obstruction of the fiber bundles, which causes the modulus prediction error after modeling to be too large. Furthermore, the present invention proposes to classify the pores based on the volume of the pores, accurately model the large pores, and randomly model the small pores, so that the modulus can be predicted quickly on the basis of reducing the modeling time. The above technical solution of the present invention solves the technical problems that the existing technology has slow pore modeling in the process of modeling or predicting ceramic-based composite materials, and cannot achieve overall modeling of the material, as well as large errors in the subsequent prediction of the composite material modulus.

[0014] Furthermore, in the pore hierarchical modeling method of the ceramic matrix composite material of the present invention, in the process of fitting the pores to obtain parameter values, the parameter values ​​include the volume of the pores, the shape index, and the lengths of the pores in the x, y and z directions in the Cartesian coordinate system; and / or,

[0015] The parameter values ​​are obtained by fitting the following formula:

[0016] ;

[0017] V = k × a × b × c;

[0018] Among them, x, y and z are the coordinate values ​​in the Cartesian coordinate system, a, b, c are the lengths of the pore in the x, y and z axes respectively, (x0, y0, z0) represents the central coordinates of the pore, n is the shape index of the pore, V is the volume of the pore, k is a parameter related to the shape index n of the pore, and the value of k is determined by the shape index of the pore.

[0019] Furthermore, in the pore hierarchical modeling method of the ceramic-based composite material of the present invention, the ceramic-based composite material includes a 2D ceramic-based composite material and a 2.5D ceramic-based composite material, and the fiber bundle includes a warp fiber bundle and a weft fiber bundle; and / or,

[0020] For 2D ceramic matrix composites, the central axis of the warp fiber bundle is determined by the following formula:

[0021] ;

[0022] in, is the value of the ordinate on the central axis of the warp fiber bundle, is the circumference of a circle, is the position parameter, L is the period length of the fiber bundle axis, A is the fluctuation height of the fiber bundle, is the value of x in the coordinate system; and / or,

[0023] For 2D ceramic matrix composites, the central axis of the weft fiber bundle is determined by the following formula:

[0024] ;

[0025] in, is the value of the ordinate on the central axis of the weft fiber bundle, is the circumference of a circle, is the position parameter, L is the period length of the fiber bundle axis, A is the fluctuation height of the fiber bundle, is the value of y in the coordinate system;

[0026] and / or,

[0027] For 2D ceramic matrix composites, the cross-sectional control equation of the radial fiber bundle or the weft fiber bundle is:

[0028] ;

[0029] in, , and are the center coordinates of the fiber bundle cross section, is the x value of the point on the fiber bundle cross-section profile, is the y value of the point on the fiber bundle cross-section profile, is the z value of the point on the fiber bundle cross-section profile, is the major axis length of the fiber bundle, is the minor axis length of the fiber bundle, and n is the shape parameter of the cross section.

[0030] Further, in the pore hierarchical modeling method of the ceramic matrix composite material of the present invention, the warp fiber bundle of the 2.5D ceramic matrix composite material includes a first central axis and a second central axis, and the first central axis is determined by the following formula:

[0031] ;

[0032] in, is the value of the ordinate on the central axis of the fiber bundle, is the value of the ordinate of the initial position of the fiber bundle, is the amplitude of the fiber bundle, is the period of the fiber bundle, is the value of the ordinate on the central axis of the fiber bundle, is pi;

[0033] The second central axis is determined by the following formula:

[0034] ;

[0035] in, is the value of the ordinate on the central axis of the fiber bundle, is the value of the ordinate of the initial position of the fiber bundle, is the amplitude of the fiber bundle, is the period of the fiber bundle axis, is the value of the ordinate on the central axis of the fiber bundle, is the ratio of pi.

[0036] Furthermore, in the pore hierarchical modeling method of the ceramic matrix composite material of the present invention, the process of first modeling the single pore is:

[0037] S1, randomly selected interlayer positions of the ceramic matrix composite as the pore center;

[0038] S2, establishing a distance equation, and selecting tetrahedrons from the matrix tetrahedron as the tetrahedrons of the pore, and determining whether the total volume of the tetrahedrons in the pore is equal to the original volume; the original volume is the volume obtained after fitting the pores after extracting the pores;

[0039] S3, if the total volume of the tetrahedrons in the pore is equal to the original volume, continue to judge whether the pore is a single pore, until all pores are judged, recorded and stored;

[0040] If the total volume of the tetrahedrons in the pore is smaller than the original volume, the pore size is proportionally enlarged, and steps S2 and S3 are repeated until the total volume of the tetrahedrons in the pore is equal to the original volume;

[0041] Wherein, judging whether the pore is a single pore includes:

[0042] S301, randomly select any tetrahedron in the pore;

[0043] S302, screening tetrahedrons in other pores adjacent to the tetrahedron until all are screened and marked;

[0044] S303, calculating whether the marked tetrahedron is equal to the pore volume, and judging whether the pore is separated by the fiber bundle. If the marked tetrahedron is equal to the pore volume, the pore is not separated by the fiber bundle, and the pore is a single pore; if the marked tetrahedron is smaller than the pore volume, the pore is separated by the fiber bundle, and it is necessary to regenerate the pore under the corresponding parameters by rotating or adjusting the pore center, and repeating this step until the volume of the generated pore is equal to the original volume, then it is confirmed that the generated pore is a single pore;

[0045] Wherein, the distance equation is determined by the following formula:

[0046] ;

[0047] Where a, b, c are the lengths of the pore in the x, y and z directions respectively, and n is the shape index of the pore. ( , , ) represents the coordinates of the pore center, Represents the distance function of the base tetrahedron vertices.

[0048] Furthermore, in the pore hierarchical modeling method of the ceramic matrix composite material of the present invention, after the single pore is modeled for the first time, it is necessary to determine whether there is overlap between the single pores and perform modeling, including:

[0049] S1, generating individual pores in descending order of volume;

[0050] S2, judging whether the pore overlaps with other pores; if so, returning to step S1 to generate a single pore with corresponding parameter values, and repeating steps S1 and S2 until the single pore with corresponding parameter values ​​obtained does not overlap with other pores;

[0051] S3, determining whether the volume of all pores satisfies the total volume under a given porosity, if not, continuing to repeat steps S1, S2 and S3 until the volume of all pores satisfies the total volume under a given porosity, thereby completing the modeling of multiple pores;

[0052] Wherein, judging whether the pore overlaps with other pores includes:

[0053] S201, screening the matrix tetrahedrons whose outer surface triangles are adjacent to the single pore tetrahedron generated in step S1, and marking them; it should be noted that the pore is composed of multiple tetrahedral units, and the tetrahedral unit has four triangular faces. If a unit is randomly selected from the tetrahedral units that constitute the pore, at least one face of the unit is adjacent to other tetrahedrons in the pore, and the triangular faces adjacent to other tetrahedrons are called "inner surface triangles", and the triangular faces that are not in contact with adjacent tetrahedrons are "outer surface triangles";

[0054] S202, when the marked tetrahedron overlaps with the tetrahedron of other pores, the pores under the corresponding parameter values ​​are regenerated, and steps S201 and S202 are repeated until the tetrahedron marked again has no intersection or overlap with other pores, and it is determined that the regenerated pores do not overlap with other pores.

[0055] Furthermore, in the pore hierarchical modeling method of the ceramic-based composite material of the present invention, after the second modeling, it also includes defining a second critical volume corresponding to the aspect ratio according to the first critical volume after the second modeling, and performing a third modeling on the pores, and the third modeling includes:

[0056] S1, determining the aspect ratio of the pores according to the parameter values ​​of the pores; for the 2.5D ceramic matrix composite material, the aspect ratio of the pores is determined by the following formula:

[0057] ;

[0058] in, is the aspect ratio of the pore, and is the parameter value of the pores, is the length of the pore in the x-axis direction, is the length of the pore in the y-axis direction, is the length of the pore in the z-axis direction; (•) means taking the maximum value, (•) means taking the minimum value;

[0059] For 2D ceramic matrix composites, the aspect ratio of the pores is determined by the following formula:

[0060] ;

[0061] in, is the aspect ratio of the pore, and is the parameter value of the pores, is the length of the pore in the x-axis direction, is the length of the pore in the y-axis direction, (•) means taking the maximum value, (•) means taking the minimum value;

[0062] S2, fixing the second critical volume of the pore and determining the values ​​of other parameters of the pore except the volume;

[0063] S3, statistically fit the aspect ratio of the actual pores to determine the value of the aspect ratio when modeling the pores. When the aspect ratio of the pores obtained in S2 is judged to meet the aspect ratio required for modeling according to the aspect ratio formula of the pores in step S1, the pores are modeled inside the unit cell according to the corresponding parameter values. When the aspect ratio of the pores does not meet the actual aspect ratio of the pores, continue to return to step S2 to redetermine the remaining parameter values ​​of the pores except the volume, and repeat steps S2 and S3 until the third modeling is completed.

[0064] In a second aspect, the present invention provides a modulus prediction method, using the above-mentioned ceramic matrix composite material pore classification modeling method, after the second modeling is completed, it also includes:

[0065] Structural discretization is performed on the modeled geometric region to obtain multiple units;

[0066] Establish the unit equation through the displacement function of any node in the unit and solve the unit stiffness matrix;

[0067] Assemble the units, add boundary conditions to the nodes, and obtain the node displacement and support reaction force;

[0068] Determine the unit strain stress according to the node displacement and the support reaction force, and obtain the stress vector and strain vector of the homogeneous equivalent body;

[0069] The elastic matrix of the homogeneous equivalent body is obtained according to the stress vector and the strain vector. The elastic matrix of the homogeneous equivalent body is the elastic matrix of the unit cell.

[0070] Compared with the prior art, the beneficial effects of the modulus prediction method of the present invention are the same as the beneficial effects of the pore classification modeling method of the ceramic matrix composite material described in the above technical solution, which will not be repeated here.

[0071] Furthermore, in the modulus prediction method of the present invention, after obtaining the elastic matrix of the homogeneous equivalent body, the method further includes:

[0072] Obtaining a first normalized value and a second normalized value of the elasticity matrix of the unit cell;

[0073] Obtaining the standard deviation of the first normalized value and the second normalized value respectively, and re-determining the value of the first critical volume or the second critical volume;

[0074] According to the re-determined value of the first critical volume or the second critical volume, the macropores are accurately fitted and modeled according to the actual morphology of the pores, and the small pores are modeled according to the statistical values ​​of the fitting parameters to obtain a unit cell model, and the macro boundary conditions are applied to the unit cell model to obtain the modulus of the macro material;

[0075] Wherein, the first normalized value is determined by the following formula:

[0076] ;

[0077] in, is the first normalized value, C n represents the stiffness matrix obtained after pore classification modeling, C0 represents the initial stiffness matrix, represents the two-norm of the matrix;

[0078] The second normalized value is determined by the following formula:

[0079] ;

[0080] in, is the second normalized value, C n represents the stiffness matrix obtained after pore classification modeling, C0 represents the initial stiffness matrix, Represents the infinity norm of a matrix.

[0081] Furthermore, in the modulus prediction method of the present invention, the re-determining the value of the first critical volume or the second critical volume includes:

[0082] The minimum value of the first normalized value and the second normalized value, and the minimum value of the standard deviation of the first normalized value and the standard deviation of the second normalized value are determined, and the critical volume corresponding to the elastic matrix of the unit cell is used as the new first critical volume or the second critical volume. BRIEF DESCRIPTION OF THE DRAWINGS

[0083] The drawings described herein are used to provide a further understanding of the present invention and constitute a part of the present invention. The exemplary embodiments of the present invention and their descriptions are used to explain the present invention and do not constitute an improper limitation of the present invention. In the drawings:

[0084] Figure 1 A schematic diagram of a warp section of a 2D C / SiC braided microstructure of the present invention;

[0085] Figure 2 are the design parameters of the 2.5D finite element model of the present invention, wherein: Figure 2 (a) is the cross-sectional view of the warp fiber. Figure 2 (b) cross-sectional view of the weft fiber;

[0086] Figure 3 It is a schematic diagram of the pore modeling process under the volume classification method of the present invention;

[0087] Figure 4 A schematic diagram of a process for determining whether overlap occurs between individual pores and performing modeling for the present invention;

[0088] Figure 5 It is a schematic diagram of the intersection of the pore unit tetrahedron and the pore model boundary in the present invention;

[0089] Figure 6 This is a schematic diagram of the cross-overlapping of pores in the present invention;

[0090] Figure 7 It is a schematic diagram of pore wrapping in the present invention;

[0091] Figure 8 A schematic diagram of the process of establishing the pore aspect ratio model in the present invention;

[0092] Fig. 9 This is a schematic diagram of the pore modeling results in the present invention;

[0093] Fig.10 is a curve diagram of the critical value of the pore volume of 2D C / SiC and its corresponding σ in the present invention;

[0094] Fig.11 It is a curve diagram of different pore aspect ratios and σ values ​​under different pore volume conditions of the 2D C / SiC composite material of the present invention;

[0095] Fig.12 This is a stress-strain schematic diagram obtained by performing a tensile test on a sample in the present invention;

[0096] Fig.13 It is a schematic diagram of the statistical results of the shape parameters and size parameters of the medium and small pores in the present invention. DETAILED DESCRIPTION

[0097] In order to make the technical problems, technical solutions and beneficial effects to be solved by the present invention more clearly understood, the present invention is further described in detail below in conjunction with the accompanying drawings and embodiments. It should be understood that the specific embodiments described herein are only used to explain the present invention and are not intended to limit the present invention.

[0098] It should be noted that when an element is referred to as being "fixed to" or "disposed on" another element, it can be directly on the other element or indirectly on the other element. When an element is referred to as being "connected to" another element, it can be directly connected to the other element or indirectly connected to the other element.

[0099] In addition, the terms "first" and "second" are used for descriptive purposes only and should not be understood as indicating or implying relative importance or implicitly indicating the number of the indicated technical features. Therefore, the features defined as "first" and "second" may explicitly or implicitly include one or more of the features. In the description of the present invention, the meaning of "multiple" is two or more, unless otherwise clearly and specifically defined. The meaning of "several" is one or more, unless otherwise clearly and specifically defined.

[0100] As an inevitable type of defect in composite materials, pores have different shapes, sizes, and position distributions, and their influence on the performance of materials cannot be ignored. Therefore, pore modeling is particularly important. In the process of modeling or predicting ceramic-based composite materials in the prior art, on the one hand, no modeling process of multiple pores in a unit cell or the entire component is given, no parameterized modeling of fiber bundles is performed, and the influence of the positional relationship between pores and pores and between pores and fiber bundles on the modeling results when fitting multiple pores is not considered. When establishing multiple pores in a unit cell, there is no standard for threshold division of pores, and it is impossible to make more in-depth use of pore information statistically obtained by CT, and it is impossible to achieve rapid modeling of pores without affecting the accuracy of modulus prediction; on the other hand, pores are not taken into account in the establishment of unit cells, and it is impossible to achieve modeling of the composite material as a whole (including matrix, fiber, pores), and it is impossible to achieve accurate prediction of the modulus of the composite material. It can be seen that in the process of modeling or predicting ceramic-based composite materials in the prior art, there are technical problems such as slow pore modeling, inability to achieve overall modeling of materials, and large errors in predicting the modulus of composite materials.

[0101] In order to solve the above technical problems, in a first aspect, the present invention provides a pore classification modeling method for ceramic matrix composite materials, comprising:

[0102] Obtain the microstructure of ceramic matrix composites;

[0103] reconstructing the ceramic matrix composite in three dimensions and identifying fiber bundles, matrix, and pores;

[0104] Extracting the pores, and fitting the pores to obtain parameter values;

[0105] Establish the unit cell model boundary and perform tetrahedron partitioning;

[0106] After determining the central axis and cross-sectional control equations of the fiber bundle, modeling the fiber bundle within the unit cell boundary;

[0107] Obtaining single pores in the ceramic-based composite material, arranging the single pores according to volume size, and performing a first modeling from large to small volume;

[0108] The first critical volume of the pores is determined, and a second modeling is performed. The second modeling process is as follows: single pores larger than the first critical volume are fixed to remain the same as the first modeling; and size parameters of single pores smaller than the first critical volume are randomly generated, and random modeling is performed.

[0109] When the above technical scheme is adopted, in the pore hierarchical modeling method of the ceramic-based composite material of the present invention, the parameter value of each pore can be obtained by three-dimensionally reconstructing the ceramic-based composite material, extracting the pores and fitting the pores; after establishing the boundary of the unit cell model and performing tetrahedral division, the central axis and cross-sectional control equation of the fiber bundle are determined, and the fiber bundle can be modeled within the boundary of the unit cell; after the fiber bundle modeling is completed, the pores continue to be modeled, and the process of pore modeling is: obtain a single pore in the ceramic-based composite material, arrange the single pores according to the volume size, and perform the first modeling from large to small according to the volume; further, determine the first critical volume of the pore, and perform the second modeling, and the second modeling process is: fix the single pore larger than the first critical volume and keep it the same as the first modeling; randomly generate size parameters for the single pore smaller than the first critical volume, and perform random modeling. According to the above technical solution, the present invention takes into account the geometric information and position information of the actual fibers and pores when establishing the unit cell model, and then accurately models the model through the extracted data of the microstructure of the actual ceramic-based composite material (the above parameter values); the present invention also proposes a method of modeling multiple pores when establishing the microstructure of the composite material to prevent the cross-overlap of the pores and the obstruction of the fiber bundles, which causes the modulus prediction error after modeling to be too large. Furthermore, the present invention proposes to classify the pores based on the volume of the pores, accurately model the large pores, and randomly model the small pores, so that the modulus can be predicted quickly on the basis of reducing the modeling time. The above technical solution of the present invention solves the technical problems that the existing technology has slow pore modeling in the process of modeling or predicting ceramic-based composite materials, and cannot achieve overall modeling of the material, as well as large errors in the subsequent prediction of the composite material modulus.

[0110] In order to better understand the present invention, the content of the present invention is further explained below in conjunction with specific embodiments, but the content of the present invention is not limited to the following embodiments.

[0111] Unless otherwise specified, the raw materials used in the following examples are commercially available.

[0112] Example 1

[0113] This embodiment provides a method for pore classification modeling of a ceramic matrix composite material, comprising:

[0114] S100, obtaining the microstructure of ceramic matrix composites;

[0115] S200, three-dimensionally reconstructing the ceramic matrix composite material and determining the fiber bundles, matrix and pores;

[0116] S300, extracting the pores, and fitting the pores to obtain parameter values; the parameter values ​​include the volume of the pores, the shape index, and the lengths of the pores in the x, y, and z directions in a Cartesian coordinate system;

[0117] S400, establish the unit cell model boundary and perform tetrahedron division;

[0118] S500, after determining the central axis and cross-section control equation of the fiber bundle, modeling the fiber bundle within the unit cell boundary;

[0119] S600, obtaining a single pore in the ceramic-based composite material, arranging the single pore according to volume size, and performing a first modeling from large to small volume;

[0120] S700, determining the first critical volume of the pores, and performing a second modeling, wherein the second modeling process is as follows: fixing individual pores larger than the first critical volume, keeping them the same as the first modeling; and randomly generating size parameters for individual pores smaller than the first critical volume, and performing random modeling.

[0121] Example 2

[0122] S100, obtaining the microstructure of ceramic matrix composites;

[0123] S200, three-dimensionally reconstructing the ceramic matrix composite material and determining the fiber bundles, matrix and pores;

[0124] S300, extracting the pores, and fitting the pores to obtain parameter values;

[0125] The parameter values ​​include the volume of the pore, the shape index, and the length of the pore in the x, y and z directions in the Cartesian coordinate system, and the parameter values ​​are obtained by fitting the following formula:

[0126] ;

[0127] V = k × a × b × c;

[0128] Wherein, x, y and z are coordinate values ​​in the Cartesian coordinate system, a, b, c are the lengths of the pore in the x, y and z axis directions respectively, (x0, y0, z0) represents the central coordinates of the pore, n is the shape index of the pore, V is the volume of the pore, k is a parameter related to the shape index n of the pore, and the value of k is determined by the shape index of the pore;

[0129] S400, establish the unit cell model boundary and perform tetrahedron division;

[0130] S500, after determining the central axis and cross-section control equation of the fiber bundle, modeling the fiber bundle within the unit cell boundary;

[0131] Wherein, the ceramic-based composite material includes a 2D ceramic-based composite material and a 2.5D ceramic-based composite material, and the fiber bundle includes a warp fiber bundle and a weft fiber bundle; for the 2D ceramic-based composite material, the central axis of the warp fiber bundle is determined by the following formula:

[0132] ;

[0133] in, is the value of the ordinate on the central axis of the warp fiber bundle, is the circumference of a circle, is the position parameter, L is the period length of the fiber bundle axis, A is the fluctuation height of the fiber bundle, is the value of x in the coordinate system;

[0134] For 2D ceramic matrix composites, the central axis of the weft fiber bundle is determined by the following formula:

[0135] ;

[0136] in, is the value of the ordinate on the central axis of the weft fiber bundle, is the circumference of a circle, is the position parameter, L is the period length of the fiber bundle axis, A is the fluctuation height of the fiber bundle, is the value of y in the coordinate system;

[0137] For 2D ceramic matrix composites, the cross-sectional control equation of the radial fiber bundle or the weft fiber bundle is:

[0138] ;

[0139] in, , and are the center coordinates of the fiber bundle cross section, is the x value of the point on the fiber bundle cross-section profile, is the y value of the point on the fiber bundle cross-section profile, is the z value of the point on the fiber bundle cross-section profile, is the major axis length of the fiber bundle, is the minor axis length of the fiber bundle, and n is the shape parameter of the cross section;

[0140] The warp fiber bundle of the 2.5D ceramic matrix composite material includes a first central axis and a second central axis, and the first central axis is determined by the following formula:

[0141] ;

[0142] in, is the value of the ordinate on the central axis of the fiber bundle, is the value of the ordinate of the initial position of the fiber bundle, is the amplitude of the fiber bundle, is the period of the fiber bundle, is the value of the ordinate on the central axis of the fiber bundle, is pi;

[0143] The second central axis is determined by the following formula:

[0144] ;

[0145] in, is the value of the ordinate on the central axis of the fiber bundle, is the value of the ordinate of the initial position of the fiber bundle, is the amplitude of the fiber bundle, is the period of the fiber bundle axis, is the value of the ordinate on the central axis of the fiber bundle, is the ratio of pi;

[0146] S600, obtaining a single pore in the ceramic-based composite material, arranging the single pore according to volume size, and performing a first modeling according to volume from large to small; the first modeling specifically includes:

[0147] S601, randomly selecting the interlayer position of the ceramic matrix composite as the pore center;

[0148] S602, establishing a distance equation, and selecting tetrahedrons from the matrix tetrahedron as the tetrahedrons of the pore, and determining whether the total volume of the tetrahedrons in the pore is equal to the original volume; the original volume is the volume obtained after fitting the pores after extracting the pores;

[0149] S603, if the total volume of the tetrahedrons in the pore is equal to the original volume, continue to determine whether the pore is a single pore until all pores are determined, record and store; if the total volume of the tetrahedrons in the pore is smaller than the original volume, enlarge the pore size in proportion, and repeat steps S602 and S603 until the total volume of the tetrahedrons in the pore is equal to the original volume;

[0150] Wherein, judging whether the pore is a single pore includes:

[0151] S6031, randomly select any tetrahedron in the pore;

[0152] S6032, screening tetrahedrons of other pores adjacent to the tetrahedron until all are screened and marked;

[0153] S6033, calculate whether the marked tetrahedron is equal to the pore volume, and determine whether the pore is separated by the fiber bundle. If the marked tetrahedron is equal to the pore volume, the pore is not separated by the fiber bundle, and the pore is a single pore; if the marked tetrahedron is smaller than the pore volume, the pore is separated by the fiber bundle, and it is necessary to regenerate the pore under the corresponding parameters by rotating or adjusting the pore center, and repeat this step until the volume of the generated pore is equal to the original volume, then it is confirmed that the generated pore is a single pore;

[0154] Wherein, the distance equation is determined by the following formula:

[0155] ;

[0156] Where a, b, c are the lengths of the pore in the x, y and z directions respectively, and n is the shape index of the pore. ( , , ) represents the coordinates of the pore center, represents the distance function of the vertices of the base tetrahedron;

[0157] Furthermore, after the first modeling is completed in step S600, it is necessary to determine whether there is overlap between the individual pores and perform modeling, including:

[0158] S604, generating individual pores in descending order of volume;

[0159] S605, determining whether the pore overlaps with other pores; if so, returning to step S604 to generate a single pore with corresponding parameter values, and repeating steps S604 and S605 until the single pore with corresponding parameter values ​​obtained does not overlap with other pores;

[0160] S606, determining whether the volume of all pores satisfies the total volume under a given porosity, if not, continuing to repeat steps S604, S605 and S606 until the volume of all pores satisfies the total volume under a given porosity, thereby completing the modeling of multiple pores;

[0161] Wherein, judging whether the pore overlaps with other pores includes:

[0162] S6051, screening the matrix tetrahedrons with adjacent outer surface triangles in the single pore tetrahedron generated in step S604, and marking them;

[0163] S6052, when the marked tetrahedron overlaps with the tetrahedron of other pores, regenerate the pores under the corresponding parameter value, and repeat steps S6051 and S6052 until the marked tetrahedron has no intersection or overlap with other pores, and it is determined that the regenerated pores have no overlap with other pores;

[0164] S700, determining a first critical volume of pores, and performing a second modeling, wherein the second modeling process is: fixing a single pore larger than the first critical volume to keep it the same as the first modeling; randomly generating size parameters for a single pore smaller than the first critical volume, and performing random modeling;

[0165] S800, defining a second critical volume corresponding to the aspect ratio according to the first critical volume after the second modeling, and performing a third modeling on the pores. In this process, only one pore needs to be established in a unit cell. The third modeling includes:

[0166] S801, determining the aspect ratio of the pores according to the parameter values ​​of the pores; for a 2.5D ceramic matrix composite material, the aspect ratio of the pores is determined by the following formula:

[0167] ;

[0168] in, is the aspect ratio of the pore, and is the parameter value of the pores, is the length of the pore in the x-axis direction, is the length of the pore in the y-axis direction, is the length of the pore in the z-axis direction; (•) means taking the maximum value, (•) means taking the minimum value;

[0169] For 2D ceramic matrix composites, the aspect ratio of the pores is determined by the following formula:

[0170] ;

[0171] in, is the aspect ratio of the pore, and is the parameter value of the pores, is the length of the pore in the x-axis direction, is the length of the pore in the y-axis direction, (•) means taking the maximum value, (•) means taking the minimum value;

[0172] S802, fixing the second critical volume of the pore, and determining other parameter values ​​of the pore except the volume;

[0173] S803, statistically fit the aspect ratio of the actual pores to determine the value of the aspect ratio when modeling the pores. When the aspect ratio of the pores obtained in S802 according to the aspect ratio formula of the pores in step S801 satisfies the aspect ratio required for modeling, the pair of pores are modeled inside the unit cell according to the corresponding parameter values. When the aspect ratio of the pores does not satisfy the actual aspect ratio of the pores, continue to return to step S802 to redetermine the remaining parameter values ​​of the pores except the volume, and repeat steps S802 and S803 until the third modeling is completed.

[0174] This embodiment further provides a modulus prediction method, which uses the pore classification modeling method of the ceramic matrix composite material in this embodiment, and after the second modeling is completed, further includes:

[0175] Step 1, structurally discretize the modeled geometric region to obtain multiple units;

[0176] Step 2, establish the unit equation through the displacement function of any node in the unit, and solve the unit stiffness matrix;

[0177] Step 3: Assemble the units, add boundary conditions to the nodes, and obtain the node displacement and support reaction force;

[0178] Step 4, determining the unit strain stress according to the node displacement and the support reaction force, and obtaining the stress vector and strain vector of the homogeneous equivalent body;

[0179] Step 5, obtaining an elastic matrix of a homogeneous equivalent body according to the stress vector and the strain vector, wherein the elastic matrix of the homogeneous equivalent body is the elastic matrix of a unit cell;

[0180] After obtaining the elastic matrix of the homogeneous equivalent body in step 5, the following steps are also included:

[0181] Step 501, obtaining a first normalized value and a second normalized value of the elasticity matrix of the unit cell;

[0182] Step 502, respectively obtaining the standard deviation of the first normalized value and the second normalized value, and re-determining the value of the first critical volume or the second critical volume;

[0183] Step 503, according to the re-determined value of the first critical volume or the second critical volume, accurately fit and model the macropores according to the actual morphology of the pores, and model the small pores according to the parameter statistics obtained by fitting, to obtain a unit cell model, and apply macro boundary conditions to the unit cell model to obtain the modulus of the macro material;

[0184] Wherein, the first normalized value is determined by the following formula:

[0185] ;

[0186] in, is the first normalized value, C n represents the stiffness matrix obtained after pore classification modeling, C0 represents the initial stiffness matrix, represents the two-norm of the matrix;

[0187] The second normalized value is determined by the following formula:

[0188] ;

[0189] in, is the second normalized value, C n represents the stiffness matrix obtained after pore classification modeling, C0 represents the initial stiffness matrix, Represents the infinite norm of a matrix;

[0190] In step 502, the value of the first critical volume or the second critical volume is re-determined, including:

[0191] Step 5021, determine the minimum value of the first normalized value and the second normalized value, and the minimum value of the standard deviation of the first normalized value and the standard deviation of the second normalized value. At this time, the critical volume corresponding to the elastic matrix of the unit cell is used as the new first critical volume or second critical volume.

[0192] Example 3

[0193] This embodiment provides a method for pore classification modeling and modulus prediction of a ceramic matrix composite material, wherein the method for pore classification modeling of a ceramic matrix composite material comprises:

[0194] S100, obtaining the microstructure of ceramic matrix composites;

[0195] S200, three-dimensionally reconstructing the ceramic matrix composite material and determining the fiber bundles, matrix and pores;

[0196] In this step, the ceramic matrix composite material to be modeled is subjected to CT scanning. Since the fiber bundles, matrix, and pores are composed of different materials, the three-dimensional reconstructed image presents different grayscale values;

[0197] S300, extracting the pores, and fitting the pores to obtain parameter values;

[0198] In this step, the pore defects are extracted and meshed by using the difference between the grayscale values ​​of the pores and the grayscale values ​​of the matrix and the preform, and discretization can be completed. It should be noted that discretization is to divide the continuum into a finite number of parts with imaginary lines or surfaces, and the parts are connected by a finite number of points. Each part is called a unit, and the connection point is called a node; the defects are meshed by finite element, discretized into multiple fine mesh tetrahedral units, and the unit number and node of each tetrahedron are recorded; the unit number, node number and node coordinates obtained by discretization are imported into the software to draw the meshed pores. The extracted pore tetrahedral unit information is actually the information of multiple defects in the selected area. Since these defects have different shapes and there is no regular distribution, it is necessary to extract and analyze each independent pore defect in order to count the data information of each defect. This embodiment uses a defect area segmentation algorithm based on "breadth first search". The main method is to randomly select a tetrahedral unit, then search for other tetrahedral units adjacent to it, mark them, enter the queue, and then find the adjacent tetrahedral units of the adjacent units and mark them until all tetrahedrons are screened.

[0199] For pore fitting and parameter value statistics, the principal axis distribution is first determined. The principal component analysis and least squares method are used to perform regression analysis on the central coordinates of each tetrahedral unit that constitutes the pore, and the eigenvectors and eigenvalues ​​are calculated. The dimensionality is reduced from the three-dimensional space to the surface, and then to the line. The data distribution law is found and the three principal axes are determined. These are used as the local coordinate axes of this pore (the three principal axes are perpendicular to each other). The local coordinates are rotated to coincide with the global coordinates. The coincidence of the local coordinates with the global coordinates is determined by the following formula: ;

[0200] in, is the total rotation matrix, is the rotation matrix of the x-axis in the coordinate system, is the rotation matrix of the y-axis in the coordinate system, is the rotation matrix of the z-axis in the coordinate system, is the angle between the local coordinate z-axis and the global coordinate z-axis, is the angle between the local coordinate y-axis and the global coordinate y-axis, is the angle between the local coordinate x-axis and the global coordinate x-axis;

[0201] The parameter values ​​include the volume of the pore, the shape index, and the length of the pore in the x, y and z directions in the Cartesian coordinate system, and the parameter values ​​are obtained by fitting the following formula:

[0202] ;

[0203] V = k × a × b × c;

[0204] Where x, y and z are coordinate values ​​in the Cartesian coordinate system, a, b, c are the lengths of the pore in the x, y and z directions respectively, (x0, y0, z0) represents the center coordinates of the pore, n is the shape index of the pore, V is the volume of the pore, and k is a parameter related to the shape index n of the pore;

[0205] The value of k is determined by the shape index of the pores. For example, the value of k is taken according to the following Table 1:

[0206] Table 1 Pore shape index and corresponding k value

[0207] S400, establish the unit cell model boundary and perform tetrahedron division;

[0208] S500, after determining the central axis and cross-section control equation of the fiber bundle, modeling the fiber bundle within the unit cell boundary;

[0209] In this step, the fiber bundle parameters in the unit cell are measured according to the CT scanning results, and the size and shape of the microstructure model are determined according to the fiber bundle parameters, that is, the cross-sectional curve of the fiber bundle is described by using the Lame curve, and the path direction of the fiber bundle of the plain woven composite material is described by using the sine function;

[0210] Wherein, the ceramic matrix composite material includes 2D ceramic matrix composite material and 2.5D ceramic matrix composite material, and the fiber bundle includes warp fiber bundle and weft fiber bundle; for 2D ceramic matrix composite material, please refer to Figure 1 The 2D C / SiC braided microstructure warp cross-section is shown, and the central axis of the warp fiber bundle is determined by the following formula:

[0211] ;

[0212] in, is the value of the ordinate on the central axis of the warp fiber bundle, is the circumference of a circle, is the position parameter, L is the period length of the fiber bundle axis, A is the fluctuation height of the fiber bundle, is the value of x in the coordinate system;

[0213] For 2D ceramic matrix composites, the central axis of the weft fiber bundle is determined by the following formula:

[0214] ;

[0215] in, is the value of the ordinate on the central axis of the weft fiber bundle, is the circumference of a circle, is the position parameter, L is the period length of the fiber bundle axis, A is the fluctuation height of the fiber bundle, is the value of y in the coordinate system;

[0216] Furthermore, for the period length of the fiber bundle axis, the fluctuation height of the fiber bundle and the length of the model along the z-axis, we have:

[0217] ;

[0218] ;

[0219] ;

[0220] in, is the period length of the fiber bundle axis, , and are the lengths of the model along the x, y and z axes respectively, is the fluctuation height of the fiber bundle, is the major axis length of the fiber bundle, is the length of the minor axis of the fiber bundle, c is the distance from the vertex on the long axis of the latitudinal fiber in the radial cross-section to the boundary of the finite element model, and d is the distance from the vertex below the long axis of the latitudinal fiber in the radial cross-section to the midpoint of the boundary of the finite element model;

[0221] For 2D ceramic matrix composites, the cross-sectional control equation of the radial fiber bundle or the weft fiber bundle is:

[0222] ;

[0223] in, , and are the center coordinates of the fiber bundle cross section, is the x value of the point on the fiber bundle cross-section profile, is the y value of the point on the fiber bundle cross-section profile, is the z value of the point on the fiber bundle cross-section profile, is the major axis length of the fiber bundle, is the minor axis length of the fiber bundle, and n is the shape parameter of the cross section;

[0224] For 2.5D CMC, Figure 2 The warp and weft cross-sections of the microstructure of the 2.5DC / SiC single cell braid are shown, where: Figure 2 There are two states of fiber bundles in (a), which are represented by solid lines and dotted lines respectively. The central axis of the warp fiber bundle of the solid line is recorded as the first central axis, and the central axis of the warp fiber bundle of the dotted line is recorded as the second central axis. That is, the warp fiber bundle of the 2.5D ceramic-based composite material includes a first central axis and a second central axis. The first central axis is determined by the following formula:

[0225] ;

[0226] in, is the value of the ordinate on the central axis of the fiber bundle, is the value of the ordinate of the initial position of the fiber bundle, is the amplitude of the fiber bundle, is the period of the fiber bundle, is the value of the ordinate on the central axis of the fiber bundle, is pi;

[0227] The second central axis is determined by the following formula:

[0228] ;

[0229] in, is the value of the ordinate on the central axis of the fiber bundle, is the value of the ordinate of the initial position of the fiber bundle, is the amplitude of the fiber bundle, is the period of the fiber bundle axis, is the value of the ordinate on the central axis of the fiber bundle, is pi;

[0230] Furthermore, for the length of the finite element model in the x and z directions, and the amplitude of the fiber bundle, we have:

[0231] ;

[0232] ;

[0233] ;

[0234] Among them, L x , L y , L z Respectively represent the length of the finite element model in the x, y, and z directions, A and B represent the major and minor axes of the cross section of the warp fiber bundle, and H represents the amplitude of the warp fiber bundle. , represents the position function, determined by the fiber cross-section, is the minor axis length of the weft fiber bundle;

[0235] Furthermore, after determining the fiber bundle cross section and axis, the fiber bundle boundary is established in the unit cell, that is, the ceramic matrix composite (CMC) microstructure is automatically divided using the level set function. The steps are as follows:

[0236] S501, dividing a unit cell model of a given size into three-dimensional tetrahedral basic grid units, and the number of grid units is determined according to the complexity of the model contour;

[0237] S502, using the fiber axial equation and the cross-sectional equation to establish a level set function Φ(x, y, z)=0 to represent the target boundary to be modeled, and using the distance function f(x, y, z) to represent the distance from a tetrahedral unit to the corresponding level set function center or central axis, then:

[0238] ;

[0239] in, ;

[0240] S503, using the level set function to filter out the intersecting units, when the level set function is equal to 1, the maximum value of the distance function is less than 0, indicating that the tetrahedral unit is located in the area of ​​the model to be built; when it is equal to -1, the minimum value of the distance function is greater than 0, indicating that the tetrahedral unit is located outside the area of ​​the model to be built; when it is equal to 0, it means that the tetrahedral unit intersects with the boundary of the model to be built; it needs to be filtered out and re-meshed;

[0241] S504, using the bisection method to calculate the point where the level set function intersects with the edge of the intersecting tetrahedral unit, recording the coordinates of the node, updating to the original node coordinate set, using the node to re-divide a smaller tetrahedral mesh, and updating the tetrahedral unit number;

[0242] S505, repeating steps S503 and S504 until the four nodes of each newly generated tetrahedral unit are all on the same side of the boundary of the model to be built, and then the modeling of the fiber bundle is terminated;

[0243] S600, Porosity Modeling with Volume Fractionation, see Figure 3 , Figure 3 The specific steps of pore volume classification are as follows: the pores scanned by CT are statistically analyzed to obtain the shape parameters of the pores, and then the volumes are arranged according to the sizes, and the pore volumes are modeled in descending order; for example, a single pore in the ceramic matrix composite material is obtained, and the single pore is arranged according to the volume size, and the first modeling is performed according to the volume from large to small; please refer to Figure 3 , the first modeling specifically includes:

[0244] S601, randomly selecting the interlayer position of the ceramic matrix composite as the pore center;

[0245] In this step, according to the position of the pore in the CT image, a point is randomly selected at the position as the center of the pore. For 2.5D CMC, a tetrahedron is randomly selected in the area around the intersection of the warp fibers and the weft fibers as the pore center tetrahedron. For 2D CMC, a tetrahedron is randomly selected between the layers as the pore center tetrahedron. The coordinates of the center c are determined by the following formula:

[0246] ;

[0247] Among them, x i ,y i ,z i are the coordinates of the four vertices of the randomly selected pore center tetrahedron, Indicates the coordinates of the center point;

[0248] S602, establishing a distance equation, and selecting tetrahedrons from the matrix tetrahedron as the tetrahedrons of the pore, and determining whether the total volume of the tetrahedrons in the pore is equal to the original volume; the original volume is the volume obtained after fitting the pores after extracting the pores;

[0249] Furthermore, consistent with the fiber bundle modeling, the distance equation is used to perform parameterized modeling based on the pore parameters obtained by fitting, that is, the control function is transformed into the level set function used in the automatic modeling method, and the grid units that satisfy the pore control equation are selected from the matrix for marking. If the value of the level set function is equal to 0, it means that the node is just located on the outer contour line of the pore. If the level set function values ​​of the four nodes of the grid unit are all greater than 0, it means that the unit is not in the distance equation, that is, it does not belong to the pore; if the level set function values ​​of the four nodes are all less than 0, it means that the unit is in the distance equation of the pore, that is, the unit belongs to the unit in the pore model, and is marked as 1; if the level set function values ​​of the four nodes in the grid unit have both positive and negative values, it means that the tetrahedral unit has nodes outside the pore model to be built and nodes inside the pore model to be built, which means that the unit intersects with the level set function of the pore, and such intersecting units are screened out, their numbers are saved, and marked as 0;

[0250] Furthermore, the distance equation is determined by the following formula:

[0251] ;

[0252] ;

[0253] Where a, b, c are the lengths of the pore in the x, y and z directions respectively, and n is the shape index of the pore. ( , , ) represents the coordinates of the pore center, represents the distance function of the vertices of the base tetrahedron;

[0254] Furthermore, the mesh is subdivided. Specifically, the tetrahedral units marked as 0 are meshed; because there are more than one unit intersecting with the pore model boundary, each unit is located at a different position and has different types of intersections with the model boundary; Figure 5 The four types of intersections shown in the figure indicate that the tetrahedral element intersects with the boundary to be modeled by one edge, two edges, three edges, and four edges respectively; see Figure 5 For case 1, the tetrahedral unit has an intersection with the boundary of the model to be built. If the product of the level set function values ​​of the two nodes in the unit is less than 0, it means that the intersection is on the edge of the line connecting the two nodes. The level set function values ​​of these two points and the bisection method can be used to find the intersection of the outer contour boundary of the pore model and the intersection edge of this type of tetrahedral unit. As shown in the right figure of case 1, the intersection points are connected to obtain two mesh tetrahedrons. At this time, it is necessary to ensure that the newly generated units are on the same side of the model to be built, replace the original mesh unit with the unit of one of the tetrahedrons, create a new number for the other tetrahedral unit, and mark and save the mesh unit belonging to the pore model, thereby completing the mesh division. This is a simpler mesh division step. For case 3, there are two intersecting edges, such as Figure 5 As shown in case 3, two intersection points P5 and P6 are connected with P4P5 and P3P5, and two new tetrahedral meshes P4P5P3P1 and P4P5P3P2 are generated. P4P5P3P2 is given a new unit number, and there is an edge with an intersection point P6 in the tetrahedral unit P4P5P3P1, so it is necessary to divide the mesh again, connect P6P5 and P3P6, and get two new mesh units P6P5P3P1 and P4P5P3P6, one of which replaces the original mesh unit, and the other establishes a new unit number, thus completing the mesh division; the other two types of intersection methods are similar to the above two types, using the binary method to find the intersection points, and meshing is performed one by one. Compared with case 1 and case 3, case 2 and case 4 require more steps to complete the mesh subdivision, and the new units generated are also much smaller. Note that the new tetrahedral units obtained after the final subdivision must be on the same side of the pore model to be built;

[0255] The pore model volume is the sum of the volumes of the marked tetrahedral units. The following formula is used to calculate whether the pore meets the original extracted pore volume. If not, the pore size needs to be enlarged in proportion (enlarge the values ​​of the parameters a, b, and c) to meet the pore shape as much as possible. If it meets the original pore volume, proceed to the following steps;

[0256] ;

[0257] in, is the volume of the pores, each x i ,y i ,z i The values ​​(i=1, 2, 3, 4) are the x, y, z coordinates of the vertices of the tetrahedron contained in the pore;

[0258] S603, if the total volume of the tetrahedrons in the pore is equal to the original volume, continue to determine whether the pore is a single pore until all pores are determined, record and store; if the total volume of the tetrahedrons in the pore is smaller than the original volume, enlarge the pore size in proportion, and repeat steps S602 and S603 until the total volume of the tetrahedrons in the pore is equal to the original volume;

[0259] Wherein, judging whether the pore is a single pore includes:

[0260] S6031, randomly select any tetrahedron in the pore;

[0261] This step may be specifically as follows: randomly selecting a tetrahedral unit from the units constituting the pore model, marking it as 1, and selecting tetrahedral units adjacent to the pore unit and marking them (marking them as 1);

[0262] S6032, screening tetrahedrons of other pores adjacent to the tetrahedron until all are screened and marked;

[0263] This step may be specifically as follows: taking the adjacent tetrahedral units that have been screened as target units, searching for tetrahedral units adjacent to the target units, and repeating step S6031 until there are no more adjacent tetrahedral units to be selected. At this time, the screening of a pore model is completed. In this process, if there are still pore tetrahedral units remaining after all adjacent tetrahedral units have been screened, it means that the pores are separated by fibers, then a tetrahedral mesh is randomly selected from the remaining tetrahedral units, and steps S6031 and S6032 are repeated until all tetrahedral units constituting the pore model have been screened.

[0264] S6033, calculate whether the marked tetrahedron is equal to the pore volume, and determine whether the pore is separated by the fiber bundle. If the marked tetrahedron is equal to the pore volume, the pore is not separated by the fiber bundle, and the pore is a single pore; if the marked tetrahedron is smaller than the pore volume, the pore is separated by the fiber bundle, and it is necessary to regenerate the pore under the corresponding parameters by rotating or adjusting the pore center, and repeat this step until the volume of the generated pore is equal to the original volume, then it is confirmed that the generated pore is a single pore;

[0265] For further information, see Figure 4After the first modeling is completed in step S600, it is still necessary to determine whether there is overlap between the individual pores and perform modeling, including:

[0266] S604, generating individual pores in descending order of volume;

[0267] S605, determining whether the pore overlaps with other pores; if so, returning to step S604 to generate a single pore with corresponding parameter values, and repeating steps S604 and S605 until the single pore with corresponding parameter values ​​obtained does not overlap with other pores;

[0268] S606, determining whether the volume of all pores satisfies the total volume under a given porosity, if not, continuing to repeat steps S604, S605 and S606 until the volume of all pores satisfies the total volume under a given porosity, thereby completing the modeling of multiple pores;

[0269] Wherein, judging whether the pore overlaps with other pores includes:

[0270] S6051, screening the matrix tetrahedrons with adjacent outer surface triangles in the single pore tetrahedron generated in step S604, and marking them;

[0271] S6052, when the marked tetrahedron overlaps with the tetrahedron of other pores, regenerate the pores under the corresponding parameter value, and repeat steps S6051 and S6052 until the marked tetrahedron has no intersection or overlap with other pores, and it is determined that the regenerated pores have no overlap with other pores;

[0272] For example, after all the single pores are established, it can be determined whether the fitted volume is equal to the pore volume at a given porosity. If not, the following may occur: Figure 6The pores shown overlap, and the pore "wrapping" method is needed to make a judgment. The specific judgment process is as follows: In order to prevent the pores from contacting each other, the outer surface of the pore needs to be "wrapped"; the pore is composed of multiple tetrahedral units, and the tetrahedral unit has four triangular faces; if a unit is randomly selected from the tetrahedral units that make up the pore, at least one face of the unit is adjacent to other tetrahedrons in the pore, and the triangular faces adjacent to other tetrahedrons are called "inner surface triangles", and the triangular faces that are not in contact with adjacent tetrahedrons are "outer surface triangles"; if the four triangular faces of the unit All of them are adjacent to other tetrahedral units in the pore, that is, the tetrahedral unit has four faces that are "inner surface triangles", then this tetrahedral unit is inside the pore and it does not belong to the outer surface unit of the pore; if the tetrahedral unit has less than four faces that are "inner surface triangles", it means that at least one face of the unit is located on the outer surface of the pore, and the unit is called an outer surface unit; after finding all the outer surface units of the pore, it is necessary to screen all tetrahedral meshes belonging to the matrix; find all matrix units adjacent to the pore outer surface units; that is, find the mesh units that have common faces with the pore outer surface units; such as Figure 7 As shown in the yellow part, it is like wrapping the pore with a shell. If this "shell" repeats the tetrahedron contained in other pores, it means that the pores overlap and need to be regenerated according to the pore parameters.

[0273] According to the above steps, the pores are modeled in order from large to small in volume to ensure the isolated state of the pores. After reaching the established porosity, the elastic modulus is calculated by the finite element calculation method, and this modulus is used as the initial elastic modulus C0. At the same time, the center point of each pore, as well as the rotation angle and size parameters, etc. need to be recorded.

[0274] S700, determining a first critical volume of pores, and performing a second modeling, wherein the second modeling process is: fixing a single pore larger than the first critical volume to keep it the same as the first modeling; randomly generating size parameters for a single pore smaller than the first critical volume, and performing random modeling;

[0275] For example, in the second pore modeling, the pores with a single pore volume larger than a certain volume (the first critical volume) are fixed, and the pores with a volume smaller than a certain volume (the first critical volume) are randomly generated with the help of the rand random function. The size parameters are random, and the position is random; until the initial porosity is met; in multiple modeling, the pores larger than a certain volume (the first critical volume) are always fixed, and the pores smaller than the volume (the first critical volume) are changed; its purpose is to explore the impact of random modeling of pores smaller than the volume on the performance;

[0276] S800, defining a second critical volume corresponding to the aspect ratio according to the first critical volume after the second modeling, and performing a third modeling on the pores (modeling of the pores when the aspect ratio is used as a standard), wherein the third modeling includes:

[0277] S801, determining the aspect ratio of the pores according to the parameter values ​​of the pores; for a 2.5D ceramic matrix composite material, the aspect ratio of the pores is determined by the following formula:

[0278] ;

[0279] in, is the aspect ratio of the pore, and is the parameter value of the pores, is the length of the pore in the x-axis direction, is the length of the pore in the y-axis direction, is the length of the pore in the z-axis direction; (•) means taking the maximum value, (•) means taking the minimum value;

[0280] For 2D ceramic matrix composites, the aspect ratio of the pores is determined by the following formula:

[0281] ;

[0282] in, is the aspect ratio of the pore, and is the parameter value of the pores, is the length of the pore in the x-axis direction, is the length of the pore in the y-axis direction, (•) means taking the maximum value, (•) means taking the minimum value;

[0283] S802, fixing the second critical volume of the pore, and determining other parameter values ​​of the pore except the volume;

[0284] S803, statistically fit the aspect ratio of the actual pores to determine the value of the aspect ratio when modeling the pores. When the aspect ratio of the pores obtained in S802 according to the aspect ratio formula of the pores in step S801 satisfies the aspect ratio required for modeling, the pair of pores are modeled inside the unit cell according to the corresponding parameter values. When the aspect ratio of the pores does not satisfy the actual aspect ratio of the pores, continue to return to step S802 to redetermine the remaining parameter values ​​of the pores except the volume, and repeat steps S802 and S803 until the third modeling is completed.

[0285] Figure 8For the pore modeling process when the aspect ratio is used as the standard, for example, the modeling process can also be: fix the volume of the pore, randomly select two pore parameters, use the pore volume formula to obtain another size parameter, substitute the three parameters into the above aspect ratio formula, and judge whether the specified aspect ratio value is met. If it is met, substitute it into the pore control equation, screen the pore units, and record it. If not, randomly select two pore parameters again and repeat the above process until the specified aspect ratio value is met, substitute it into the pore control equation, screen the pore units, and record it. After completing the fiber modeling, when establishing a model for the aspect ratio study, it is only necessary to establish a single pore model in the unit cell. There is no need to establish multiple pore models to meet the established porosity, which saves a lot of time. The volume of the pore is divided according to the critical volume data assumption, and the pore modeling process is the same as the modeling process of a single pore. When modeling the pore, find the correct position, the rotation angle of the pore is random, and for 2.5D CMC uses a random function to randomly generate a, b, c, and n values, but the aspect ratio and volume must meet the requirements. For 2D CMC, a, b, and n are generated using a random function, but the aspect ratio must be guaranteed. The c parameter is calculated from the volume and a, b, and n parameters.

[0286] This comparative example also provides a modulus prediction method, using the ceramic matrix composite material pore classification modeling method of this embodiment, after the second modeling is completed, it also includes:

[0287] Step 1, structurally discretize the modeled geometric region to obtain multiple units;

[0288] Step 2, establish the unit equation through the displacement function of any node in the unit, and solve the unit stiffness matrix;

[0289] Step 3: Assemble the units, add boundary conditions to the nodes, and obtain the node displacement and support reaction force;

[0290] Step 4, determining the unit strain stress according to the node displacement and the support reaction force, and obtaining the stress vector and strain vector of the homogeneous equivalent body;

[0291] Step 5, obtaining an elastic matrix of a homogeneous equivalent body according to the stress vector and the strain vector, wherein the elastic matrix of the homogeneous equivalent body is the elastic matrix of a unit cell;

[0292] Step 6, based on the re-determined value of the first critical volume or the second critical volume, the large pores are accurately fitted and modeled according to the actual morphology of the pores, and the small pores are modeled according to the statistical values ​​of the parameters obtained by fitting to obtain a unit cell model, and macroscopic boundary conditions are applied to the unit cell model to obtain the modulus of the macroscopic material.

[0293] Furthermore, in the above modulus prediction method, the finite element model established by the pore classification modeling method of the ceramic matrix composite material in this embodiment is used to calculate the modulus of the unit cell; the finite element method for processing elastic body problems needs to satisfy the three major mechanical equations and corresponding boundary conditions; the indicator forms of the equilibrium equation, geometric deformation equation, and material physics equation are respectively:

[0294] ;

[0295] ;

[0296] ;

[0297] where σ ij is the second-order stress tensor, σ ij,j It means to find the partial derivative in the j direction; is the body force component in the i direction; u j，i It means the partial derivative of the displacement in the j direction with respect to the i direction, Denotes the partial derivative of the displacement in the i direction with respect to the j direction; D ijkl represents the elastic coefficient matrix, is the second-order strain tensor;

[0298] The boundary conditions of force and displacement must also be met, where the boundary conditions of displacement and force are given as follows:

[0299] ;

[0300] ;

[0301] l j Direction cosines of the normal outside the boundary, u i is the displacement component in the i direction, is the displacement value specified in the i direction or the known displacement on the boundary, is the component of the external force acting on the boundary in the direction i, is the second-order stress tensor.

[0302] Furthermore, for carbon fiber toughened silicon carbide composite materials, the specific solution is as follows: first determine the material properties, the basic modulus of carbon fiber, the modulus of silicon carbide matrix, and the modulus of pores, and the modulus of pores is set to 10 - 10 GPa, Poisson's ratio is 0, then:

[0303] (1) Geometric region discretization:

[0304] ;

[0305] in For the whole area, For sub-region

[0306] (2) Unit study, obtain the node displacement vector array q e and the nodal force vector array P e :

[0307] q e =[u1 u2u3u4] T ;

[0308] P e =[P1 P2 P3 P4] T ;

[0309] Among them, q e is the node displacement vector array, u1, u2, u3, u4 are the node displacement components, P e is the nodal force vector array, P1 P2 P3P4 are the components of the nodal force respectively, [] T is the transpose of the matrix;

[0310] Furthermore, the fields of the three major types of variables are described by node displacements, which are the displacement field functions: , strain field function And the stress field function , then:

[0311] ;

[0312] ;

[0313] ;

[0314] in, represents the shift field function, and are displacement-related parameters, is the shape function, B is the strain matrix, q e is the node displacement vector array, represents the strain field function, is the shape function, represents the stress field function, is the material elastic matrix, is the displacement value in any direction;

[0315] For the element stiffness matrix, we have:

[0316] ;

[0317] in, is the element stiffness matrix, is the transpose of the shape function B matrix, D is the material elasticity matrix, Represents the overall area;

[0318] For strain energy and external work, we have:

[0319] ;

[0320] ;

[0321] in, is the strain energy, is stress, For strain, Represents the overall area, is the node force vector matrix q e The transpose of q e is the node displacement vector array, is the external force work, P i Nodal force matrix, u i is the node displacement moment, is the element stiffness matrix, q e is the node displacement vector array, p1, p2, p3, p4 are the force matrix components, u1, u2, u3, u4 are the displacement matrix components;

[0322] For the system potential energy, we have:

[0323] ;

[0324] in, is the system potential energy, is strain energy, W is external force work, is the node force vector matrix q e The transpose of q e is the node displacement vector array, is the element stiffness matrix, P e is the nodal force vector array, P e The transpose of

[0325] According to the principle of minimum potential energy, find the partial derivative of the system potential energy and take the extreme value: ,in, is the system potential energy, q e is the node displacement vector array;

[0326] The unit stiffness equation is obtained:

[0327] ;

[0328] in, is the element stiffness matrix, q eis the node force vector matrix, is the matrix P e The transpose of e is the nodal force vector array;

[0329] (3) Unit assembly:

[0330] The unit stiffness equation is assembled and integrated to obtain the overall stiffness equation, which is:

[0331] ;

[0332] , , ;

[0333] in, is the element stiffness matrix, q e is the node force vector matrix, is the matrix P e The transpose of e is the nodal force vector array, The overall force vector array, is the overall displacement vector array, is the overall stiffness matrix;

[0334] (4) Processing of boundary conditions and calculation of node displacements

[0335] ;

[0336] Among them, q u is the unknown node displacement; q k is the known node displacement; is a known external force; P R is the unknown support reaction; k1, k2, k3, k4 are the local stiffness matrices;

[0337] Furthermore, the unknown node displacements can be calculated from the known node displacements and the known external forces, and we have:

[0338] ;

[0339] Among them, q u is the unknown node displacement, q k is the known node displacement; is a known external force, is the k1 inverse matrix, is the local stiffness matrix;

[0340] Furthermore, after obtaining the unknown node displacement and adding the node boundary conditions, all node displacements can be obtained, and then the support reaction force can be directly calculated from the equation, which is:

[0341] ;

[0342] in, is the support reaction force, k1, k2, k3, k4 are the local stiffness matrices, q k are known node displacements, is a known external force, is the k1 inverse matrix;

[0343] (5) Calculation of other mechanical quantities:

[0344] After obtaining the overall node displacement, the stress and strain of each unit can be obtained. The strain is calculated by the geometric equation, and the stress is calculated by the physical equation:

[0345] ;

[0346] ;

[0347] in, is the unit strain, B is the strain matrix, is the elasticity matrix, is the node displacement vector array, for stress;

[0348] Furthermore, by applying mandatory boundary conditions to the model and using the homogenization formula to obtain the stress vector and strain vector of the homogeneous equivalent body, we have:

[0349] ;

[0350] ;

[0351] ;

[0352] in, represents the displacement field function, is the boundary condition matrix, is the stress of the homogeneous equivalent body, is the homogeneous equivalent volume, is the equivalent volume area, is the unit stress, is the strain of the homogeneous body, is the unit strain, is the displacement value in any direction;

[0353] Furthermore, after obtaining the stress vector and strain vector of the homogeneous equivalent body, the elastic matrix C of the unit cell is obtained through the stress-strain relationship. For the elastic matrix C of the unit cell, further, we have: =C ,in, is the stress of the homogeneous equivalent body, is the strain of the homogeneous body.

[0354] Furthermore, when the critical value is divided by volume, the unit cell elastic matrix C0 is calculated for the first modeling. For the second and subsequent modeling, the large pores larger than the critical volume are fixed and the small pores are randomly modeled according to the assumed critical volume. The unit cell elastic matrix obtained is C n For the partitioning criterion based on aspect ratio, C0 is the elastic matrix of the unit cell containing the pores with aspect ratio of 1 in the corresponding volume, and C n is the elastic matrix of the unit cell containing the pore with the corresponding volume and aspect ratio.

[0355] Furthermore, the elasticity matrix is ​​normalized by the following formula, and the standard deviations of the normalized δ1 (first normalized value) and δ2 (second normalized value) are calculated and recorded as σ1 and σ2 respectively; compared with the size and fluctuation degree of δ1 and δ2 values ​​under different critical volumes, if δ1, δ2 and σ1, σ2 are very small, it can be considered as the critical volume; specifically, the minimum value of the first normalized value and the second normalized value, as well as the minimum value of the standard deviation of the first normalized value and the standard deviation of the second normalized value are determined, and the critical volume corresponding to the elasticity matrix of the unit cell is taken as the new first critical volume or second critical volume.

[0356] The first normalized value is determined by the following formula:

[0357] ;

[0358] Among them, among them, is the first normalized value, C n represents the stiffness matrix obtained after pore classification modeling, C0 represents the initial stiffness matrix, Represents the two-norm of the matrix, which is the maximum value of the eigenvalue of the matrix;

[0359] The second normalized value is determined by the following formula:

[0360] ;

[0361] Among them, among them, is the second normalized value, C n represents the stiffness matrix obtained after pore classification modeling, C0 represents the initial stiffness matrix, Represents the infinite norm of a matrix. The infinite norm of a matrix is ​​the element with the largest absolute value in the matrix.

[0362] σ 1= ;

[0363] Where σ1 is the standard deviation of the first normalized value, When modeling for the i-th time The value of For multiple modeling The average value of The number of modeling times for multiple modeling under a certain critical volume;

[0364] σ 2= ;

[0365] Where σ2 is the standard deviation of the first normalized value, When modeling for the i-th time The value of For multiple modeling The average value of The number of modeling for multiple modeling under a certain critical volume.

[0366] It should be noted that after obtaining the above-mentioned new first critical volume or second critical volume (the actual volume obtained is recorded as the new critical volume), modeling is performed again according to the new critical volume; specifically, the basis for determining the pore division is found according to the influence of the pore volume and the aspect ratio on the mechanical properties, and the new critical volume is selected as the critical volume of large and small pores. For large pores, their morphology has a more significant effect on the modulus, so accurate fitting and modeling must be performed based on the actual morphology of the pores. In the finite element model of the unit cell, once the volume ratio of large pores reaches the established pore volume standard, parametric modeling of small pores is continued. At this time, the aspect ratio of the pores has little effect on the performance, and the size parameters of the small pore system are statistically analyzed; for example, according to a statistical result of this embodiment, 2D C f 72% of the small pores in / SiC have a shape parameter of 2, indicating that there are many ellipsoidal small pores in the matrix, and among the size parameters, only the length a of the pore in the x-axis direction satisfies the gamma distribution, and the distribution of other size parameters has no obvious regularity and requires random modeling. Therefore, the size parameter a is obtained by gamma distribution, while b, c and spatial angle are generated by random functions. When generating data, ensure that the parameters are in the specified interval, see Fig.13 , and combined with the following formula, use the following formula to keep the data within the specified range:

[0367] ;

[0368] in, is any value of the pore parameters a, b, c, n, x0 and x max They represent the minimum and maximum values ​​of the pore parameters, respectively, and P represents the probability density;

[0369] It should be noted that x0 and x max Both and P can be obtained by statistics, see Fig.13 , Fig.13 Figure 1 is a schematic diagram of the statistical results of the distribution of small pore shape parameters and size parameters. Shape parameters and size parameters are collectively referred to as pore parameters. Specifically, Fig.13 (a) is the statistical result of the pore parameter n, Fig.13 (b) is the statistical result of pore parameter b, Fig.13 (c) is the statistical result of the pore parameter a, Fig.13 (d) is the statistical result of the pore parameter c. For example, x0, x max Both P and Fig.13 The above process continues until the sum of the volumes of all pores reaches the specified porosity. If the volume of the last pore and the sum of the volumes of all previous pores exceed the established target volume, the size parameters of the last pore should be kept consistent (a=b=c). The size parameters recorded in the present invention are equivalent to the recorded parameter values. After accurate modeling, macroscopic boundary conditions are applied to the model to obtain the mechanical parameters of the component.

[0370] Calculation example 1;

[0371] 2D C / SiC assumes that the critical pore volume values ​​are 0.055mm³, 0.04mm³, 0.025mm³, and 0.015mm³, and the modeling is as follows Fig. 9 , grouped by pore volume, each group was randomly modeled 50 times, the modulus was calculated by finite element method, and the normalized δ1 and δ2 values ​​were recorded (see Table 2 and Table 3). Every 10 random modelings were divided into a small group, i represents the i-th 10 random modelings, and its value is the average of the 10 modelings. Fig.10 It reflects the relationship between σ1, σ2 and their corresponding critical values, where Fig.10 (a) and Fig.10 (b) It can be seen that as the critical value decreases, the standard deviation of δ1 and δ2 also decreases, indicating that the pore volume of random modeling decreases, the amplitude of the change in elastic modulus caused by the pores decreases, and the impact decreases. When the critical value is less than 0.04mm³, the curve converges and the standard deviation fluctuates slightly around a certain value, so 0.04mm³ can be used as the correct critical value. Pores greater than this value are refined modeled, and those less than this value are randomly modeled. At this time, the random changes of small pores have little effect on the modulus.

[0372] Table 2 2D C / SiC pore volume critical value and corresponding δ1 value

[0373] Table 3 2D C / SiC pore volume critical value and corresponding δ2 value

[0374] Furthermore, the aspect ratio of the pore size of the two-dimensional plain woven material after fitting is mostly between 1 and 5, so the aspect ratio h is set to 1, 2, 3, 4, and 5. According to the analysis of the critical volume, it can be obtained that the critical volume is approximately 0.01 mm 3 of the order of magnitude, so the pore volume was established at 0.01 3 mm 3 、0.018mm 3 、0.021mm 3 、0.028mm 3 、0.035mm 3 、0.052mm 3 、0.070mm 3 The finite element model at the time of , each column in Table 4 and Table 5 shows the standard deviation of δ1 and δ2 corresponding to the same pore volume and different aspect ratios, and each row shows the standard deviation of δ1 and δ2 with different volumes and the same aspect ratio, which are denoted as σ1 and σ2 respectively. Fig.11 (a) and Fig.11 (b) shows the curve of different pore aspect ratios and σ values ​​under different pore volume conditions. It can be seen that when the volume is less than 0.021m 3 When , the curve tends to converge, and the influence of size and shape on performance can be ignored during modeling.

[0375] Table 4 2D C f σ1 corresponding to different volume pore aspect ratios of SiC composites

[0376] Table 5 2D C f σ2 corresponding to different volume pore aspect ratios of SiC composites

[0377] Furthermore, in order to verify the accuracy of the model constructed by the present invention, a tensile test was performed on the sample, and the following results were obtained: Fig.12 The stress-strain diagram is shown. The porosity of the tensile specimen is 9%, the volume fraction of the fiber bundle is about 60%, and the calculated tensile modulus is about 110 GPa. After the pore division is completed, the effective elastic modulus of the entire model including the pores is calculated by the macro-modulus finite element method to be 113 GPa, with an error of 2.7%, which is close to the experimental data. The error may be caused by interface factors. The interface affects the bonding strength between the fiber and the matrix, and its composition and structure greatly affect the mechanical properties of the material.

[0378] In the description of the above embodiments, specific features, structures, materials or characteristics may be combined in a suitable manner in any one or more embodiments or examples.

[0379] The above is only a specific embodiment of the present invention, but the protection scope of the present invention is not limited thereto. Any person skilled in the art can easily think of changes or substitutions within the technical scope disclosed by the present invention, which should be included in the protection scope of the present invention. Therefore, the protection scope of the present invention should be based on the protection scope of the claims.

Claims

1. A method for pore classification modeling of ceramic matrix composite materials, characterized in that: include: Obtain the microstructure of ceramic matrix composites; reconstructing the ceramic matrix composite in three dimensions and identifying fiber bundles, matrix, and pores; Extracting the pores, and fitting the pores to obtain parameter values; Establish the unit cell model boundary and perform tetrahedron partitioning; After determining the central axis and cross-sectional control equations of the fiber bundle, modeling the fiber bundle within the unit cell boundary; Obtaining single pores in the ceramic-based composite material, arranging the single pores according to volume size, and performing a first modeling from large to small volume; The first critical volume of the pores is determined, and a second modeling is performed. The second modeling process is as follows: single pores larger than the first critical volume are fixed to remain the same as the first modeling; and size parameters of single pores smaller than the first critical volume are randomly generated, and random modeling is performed.

2. The method for pore classification modeling of ceramic matrix composite materials according to claim 1, characterized in that: In the process of fitting the pores to obtain parameter values, the parameter values ​​include the volume of the pores, the shape index, and the lengths of the pores in the x, y and z directions in a Cartesian coordinate system; and / or, The parameter values ​​are obtained by fitting the following formula: ； V = k × a × b × c; Among them, x, y and z are the coordinate values ​​in the Cartesian coordinate system, a, b, c are the lengths of the pore in the x, y and z axes respectively, (x0, y0, z0) represents the central coordinates of the pore, n is the shape index of the pore, V is the volume of the pore, k is a parameter related to the shape index n of the pore, and the value of k is determined by the shape index of the pore.

3. The method for pore classification modeling of ceramic matrix composite materials according to claim 2, characterized in that: The ceramic-based composite material includes a 2D ceramic-based composite material and a 2.5D ceramic-based composite material, and the fiber bundle includes a warp fiber bundle and a weft fiber bundle; and / or, For 2D ceramic matrix composites, the central axis of the warp fiber bundle is determined by the following formula: ； in, is the value of the ordinate on the central axis of the warp fiber bundle, is the circumference of a circle, is the position parameter, L is the period length of the fiber bundle axis, A is the fluctuation height of the fiber bundle, is the value of x in the coordinate system; and / or, For 2D ceramic matrix composites, the central axis of the weft fiber bundle is determined by the following formula: ； in, is the value of the ordinate on the central axis of the weft fiber bundle, is the circumference of a circle, is the position parameter, L is the period length of the fiber bundle axis, A is the fluctuation height of the fiber bundle, is the value of y in the coordinate system; and / or, For 2D ceramic matrix composites, the cross-sectional control equation of the radial fiber bundle or the weft fiber bundle is: ； in, , and are the center coordinates of the fiber bundle cross section, is the x value of the point on the fiber bundle cross-section profile, is the y value of the point on the fiber bundle cross-section profile, is the z value of the point on the fiber bundle cross-section profile, is the major axis length of the fiber bundle, is the minor axis length of the fiber bundle, and n is the shape parameter of the cross section.

4. The method for pore classification modeling of ceramic matrix composite materials according to claim 3, characterized in that: The warp fiber bundle of the 2.5D ceramic matrix composite material includes a first central axis and a second central axis, and the first central axis is determined by the following formula: ； in, is the value of the ordinate on the central axis of the fiber bundle, is the value of the ordinate of the initial position of the fiber bundle, is the amplitude of the fiber bundle, is the period of the fiber bundle, is the value of the ordinate on the central axis of the fiber bundle, is the ratio of pi; The second central axis is determined by the following formula: ； in, is the value of the ordinate on the central axis of the fiber bundle, is the value of the ordinate of the initial position of the fiber bundle, is the amplitude of the fiber bundle, is the period of the fiber bundle axis, is the value of the ordinate on the central axis of the fiber bundle, is the ratio of pi.

5. The method for pore classification modeling of ceramic matrix composite materials according to claim 4, characterized in that: The process of first modeling the single pore is: S1, randomly selected interlayer positions of the ceramic matrix composite as the pore center; S2, establishing a distance equation, and selecting tetrahedrons from the matrix tetrahedron as the tetrahedrons of the pore, and determining whether the total volume of the tetrahedrons in the pore is equal to the original volume; the original volume is the volume obtained after fitting the pores after extracting the pores; S3, if the total volume of the tetrahedrons in the pore is equal to the original volume, continue to judge whether the pore is a single pore, until all pores are judged, recorded and stored; If the total volume of the tetrahedrons in the pore is smaller than the original volume, the pore size is proportionally enlarged, and steps S2 and S3 are repeated until the total volume of the tetrahedrons in the pore is equal to the original volume; Wherein, judging whether the pore is a single pore includes: S301, randomly select any tetrahedron in the pore; S302, screening tetrahedrons in other pores adjacent to the tetrahedron until all are screened and marked; S303, calculating whether the marked tetrahedron is equal to the pore volume, and judging whether the pore is separated by the fiber bundle. If the marked tetrahedron is equal to the pore volume, the pore is not separated by the fiber bundle, and the pore is a single pore; if the marked tetrahedron is smaller than the pore volume, the pore is separated by the fiber bundle, and it is necessary to regenerate the pore under the corresponding parameters by rotating or adjusting the pore center, and repeating this step until the volume of the generated pore is equal to the original volume, then it is confirmed that the generated pore is a single pore; Wherein, the distance equation is determined by the following formula: ； Where a, b, c are the lengths of the pore in the x, y and z directions respectively, and n is the shape index of the pore. ( , , ) represents the coordinates of the pore center, Represents the distance function of the base tetrahedron vertices.

6. The method for pore classification modeling of ceramic matrix composite materials according to claim 5, characterized in that: After the first modeling of the single pores, it is necessary to determine whether there is overlap between the single pores and perform modeling, including: S1, generating individual pores in descending order of volume; S2, judging whether the pore overlaps with other pores; if so, returning to step S1 to generate a single pore with corresponding parameter values, and repeating steps S1 and S2 until the single pore with corresponding parameter values ​​obtained does not overlap with other pores; S3, determining whether the volume of all pores satisfies the total volume under a given porosity, if not, continuing to repeat steps S1, S2 and S3 until the volume of all pores satisfies the total volume under a given porosity, thereby completing the modeling of multiple pores; Wherein, judging whether the pore overlaps with other pores includes: S201, screening matrix tetrahedrons with adjacent outer surface triangles in the single pore tetrahedron generated in step S1, and marking them; S202, when the marked tetrahedron overlaps with the tetrahedron of other pores, the pores under the corresponding parameter values ​​are regenerated, and steps S201 and S202 are repeated until the tetrahedron marked again has no intersection or overlap with other pores, and it is determined that the regenerated pores do not overlap with other pores.

7. The method for pore classification modeling of ceramic matrix composite materials according to claim 6, characterized in that: After the second modeling, the method further includes defining a second critical volume corresponding to the aspect ratio according to the first critical volume after the second modeling, and performing a third modeling on the pores, wherein the third modeling includes: S1, determining the aspect ratio of the pores according to the parameter values ​​of the pores; for the 2.5D ceramic matrix composite material, the aspect ratio of the pores is determined by the following formula: ； in, is the aspect ratio of the pore, and is the parameter value of the pores, is the length of the pore in the x-axis direction, is the length of the pore in the y-axis direction, is the length of the pore in the z-axis direction; (•) means taking the maximum value, (•) means taking the minimum value; For 2D ceramic matrix composites, the aspect ratio of the pores is determined by the following formula: ； in, is the aspect ratio of the pore, and is the parameter value of the pores, is the length of the pore in the x-axis direction, is the length of the pore in the y-axis direction, (•) means taking the maximum value, (•) means taking the minimum value; S2, fixing the second critical volume of the pore and determining the values ​​of other parameters of the pore except the volume; S3, statistically fit the aspect ratio of the actual pores to determine the value of the aspect ratio when modeling the pores. When the aspect ratio of the pores obtained in S2 is judged to meet the aspect ratio required for modeling according to the aspect ratio formula of the pores in step S1, the pores are modeled inside the unit cell according to the corresponding parameter values. When the aspect ratio of the pores does not meet the actual aspect ratio of the pores, continue to return to step S2 to redetermine the remaining parameter values ​​of the pores except the volume, and repeat steps S2 and S3 until the third modeling is completed.

8. A modulus prediction method, characterized in that: The method for pore classification modeling of ceramic matrix composite materials according to any one of claims 1 to 7, after the second modeling is completed, further comprising: Structural discretization is performed on the modeled geometric region to obtain multiple units; Establish the unit equation through the displacement function of any node in the unit and solve the unit stiffness matrix; Assemble the units, add boundary conditions to the nodes, and obtain the node displacement and support reaction force; Determine the unit strain stress according to the node displacement and the support reaction force, and obtain the stress vector and strain vector of the homogeneous equivalent body; The elastic matrix of the homogeneous equivalent body is obtained according to the stress vector and the strain vector. The elastic matrix of the homogeneous equivalent body is the elastic matrix of the unit cell.

9. The modulus prediction method according to claim 8, characterized in that: After obtaining the elastic matrix of the homogeneous equivalent body, the method further includes: Obtaining a first normalized value and a second normalized value of the elasticity matrix of the unit cell; Obtaining the standard deviation of the first normalized value and the second normalized value respectively, and re-determining the value of the first critical volume or the second critical volume; According to the re-determined value of the first critical volume or the second critical volume, the macropores are accurately fitted and modeled according to the actual morphology of the pores, and the small pores are modeled according to the statistical values ​​of the fitting parameters to obtain a unit cell model, and the macro boundary conditions are applied to the unit cell model to obtain the modulus of the macro material; Wherein, the first normalized value is determined by the following formula: ； in, is the first normalized value, C n represents the stiffness matrix obtained after pore classification modeling, C0 represents the initial stiffness matrix, represents the two-norm of the matrix; The second normalized value is determined by the following formula: ； in, is the second normalized value, C n represents the stiffness matrix obtained after pore classification modeling, C0 represents the initial stiffness matrix, Represents the infinity norm of a matrix.

10. The modulus prediction method according to claim 9, characterized in that: The re-determining the value of the first critical volume or the second critical volume includes: The minimum value of the first normalized value and the second normalized value, and the minimum value of the standard deviation of the first normalized value and the standard deviation of the second normalized value are determined, and the critical volume corresponding to the elastic matrix of the unit cell is used as the new first critical volume or the second critical volume.

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