A method for strength analysis of a ceramic matrix composite mesoscopic non-periodic structure

Abstract

This invention provides a method for strength analysis of microscopic aperiodic structures in ceramic matrix composites. First, a microscopic geometric model and finite element model are established based on images obtained from X-ray computed tomography (CT) scans to accurately describe the differences in yarn structure in different parts of the microscopic aperiodic structure of the ceramic matrix composite. Then, the mechanical properties of the fiber bundle composite are obtained through experiments and formulas to characterize the yarn mechanical properties. Finally, appropriate constraints and loads are applied, and the load-displacement response of the microscopic aperiodic structure of the ceramic matrix composite is calculated using a progressive damage analysis method. When the load continuously decreases with increasing applied displacement, the structure is considered to have completely failed; the maximum load at this point is the failure load of the structure. This invention overcomes the problem that commonly used macroscopic homogenization methods cannot represent the macroscopic mechanical properties of different regions of the microscopic aperiodic structure, and can accurately predict the strength of such advanced structures.

Description

Technical Field

[0001] This invention belongs to the field of composite material structural strength analysis technology, specifically relating to a method for analyzing the microscopic non-periodic structure strength of ceramic matrix composites based on fiber bundles as the main load-bearing unit. Background Technology

[0002] Continuous fiber reinforced ceramic matrix composites possess numerous advantages, including high specific stiffness, high specific strength, high temperature resistance, corrosion resistance, and low density, making them promising candidates for applications in hot-end components of aero-engines. While advancements in fabrication processes have solved the challenge of achieving net-size molding for complex, irregularly shaped structures, they have also led to inconsistencies in yarn structure across different parts of these structures, resulting in microscopic aperiodicity. Microscopic aperiodicity means that a finite set of parameters cannot characterize all material properties within the structure. For microscopic aperiodic structures, the microstructure continuously changes with location, leading to continuous variations in macroscopic properties. Currently used methods for macroscopic homogenization, which obtain overall macroscopic properties through experiments or simulations, are no longer applicable to these structures. Accurate strength analysis of microscopic aperiodic structures in ceramic matrix composites is impossible, hindering the further application of these advanced structures. Accurate assessment of the mechanical properties of structures is crucial for their design and application. Therefore, strength analysis methods for microscopic aperiodic structures in ceramic matrix composites represent an important and challenging key technology in this field. Summary of the Invention

[0003] To address the shortcomings of existing technologies, this invention proposes a method for strength analysis of microscopic aperiodic structures in ceramic matrix composites, based on fiber bundles as the main load-bearing unit, to meet the needs of performance analysis of microscopic aperiodic structures. The following further elaborates on the invention.

[0004] A method for analyzing the structural strength of ceramic matrix composites under mesoscopic aperiodic structures includes the following steps:

[0005] Step 1: Establish a mesoscopic geometric model of the microscopic aperiodic structure of the ceramic matrix composite material:

[0006] Step 2: Mesh the micro-geometric model from Step 1 to establish a micro-finite element model of the micro-aperiodic structure of ceramic matrix composite material, and establish an auxiliary structural finite element model.

[0007] Step 3: Obtain the mechanical properties of fiber bundle composites with a microscopic non-periodic structure in ceramic matrix composites;

[0008] Step four: The mechanical properties of the fiber bundle composite material from step three are applied to the micro-finite element model from step two. Constraints and initial displacement loads are applied to the micro-finite element model through the auxiliary structural finite element model.

[0009] Step 5: Apply displacement load, solve and record the fixed end support reaction force in the micro-finite element model from Step 4;

[0010] Step 6: Based on the failure criteria and the calculation results of the fixed end support reaction, determine whether the yarn element in the microscopic finite element model has failed.

[0011] Step 7: Continue to apply displacement load. The cumulative failure of the yarn units in Step 6 eventually leads to the overall failure of the microstructure of the ceramic matrix composite material. The maximum load is the failure load of the microstructure of the ceramic matrix composite material.

[0012] Furthermore, in step one, the microscopic aperiodic structure of the ceramic matrix composite material is composed of interwoven warp and weft yarns. The yarn structure differs in different regions of the microscopic aperiodic structure of the ceramic matrix composite material. Electron microscopy reveals that the yarns and fiber bundle composite materials have the same microscopic composition, i.e., the yarns are fiber bundle composite materials. The fiber bundle composite material consists of fibers, a matrix surrounding the fibers, and the interface between the matrix and the fibers. X-ray computed tomography is used to scan the microscopic aperiodic structure of the ceramic matrix composite material. Based on the direction of the warp and weft yarns, a geometric model of each yarn is established. All the yarn geometric models are combined to form the microscopic geometric model of the microscopic aperiodic structure of the ceramic matrix composite material.

[0013] Furthermore, in step two, the mesoscopic geometric model of the ceramic matrix composite material mesoscopic aperiodic structure described in step one is meshed in the finite element analysis software to establish a mesoscopic finite element model of the ceramic matrix composite material mesoscopic aperiodic structure. All elements in the mesoscopic finite element model are called yarn elements, and the direction of each yarn is used as the main direction to assign a main direction to all yarn elements in the mesoscopic finite element model.

[0014] The auxiliary structural finite element model mentioned in step two is a clamping finite element model of a ceramic matrix composite micro-aperiodic structure, with a contact point set at the contact between the clamp and the micro-aperiodic structure.

[0015] Furthermore, in step three, the mechanical properties of the fiber bundle composite material are obtained through experiments and formula calculations. The direction along the fiber bundle composite material is the longitudinal direction, and the directions perpendicular to the fiber bundle composite material are the transverse and thickness directions, respectively. Tensile tests are performed on the fiber bundle composite material, and the stress-strain curve of the fiber bundle composite material along the longitudinal direction is obtained. The materials and preparation process of the fiber bundle composite material are the same as those of the fiber bundle composite material in the micro-aperiodic structure of the ceramic matrix composite material in step one. The average strain of the fiber bundle composite material is... Equivalent to the average strain of undamaged fiber bundle composite materials Right now:

[0016]

[0017] When the interface between the matrix and fibers of the fiber bundle composite material is completely debonded, the average strain is expressed as follows:

[0018]

[0019] Among them, E f V is the longitudinal elastic modulus of the fiber, L is the crack spacing in the matrix, and V is the longitudinal elastic modulus of the fiber. f σ represents the fiber volume fraction. f For the longitudinal stress of the fiber, σ f0 Let σ be the longitudinal stress of the fiber bundle composite material when it is undamaged, and r be the longitudinal stress of the fiber bundle composite material. f Let λ be the average fiber radius, x be the interfacial slip distance, τ be the interfacial shear stress, d be the length of the debonding region, and α be the average fiber radius. f α is the coefficient of thermal expansion of the fiber. c Let be the coefficient of thermal expansion of the fiber bundle composite, and ΔT be the difference between room temperature and the composite preparation temperature.

[0020] Among them, L, σ f0 , d, α c The value is obtained from the following equation:

[0021]

[0022]

[0023] E c =V f E f +E m V m ,

[0024]

[0025]

[0026] Where D is the matrix crack density, D sat It is the final density of the matrix when it reaches crack saturation. and m m It is a statistical parameter, E c E represents the longitudinal elastic modulus of the fiber bundle composite material. m α is the elastic modulus of the matrix. m V is the coefficient of thermal expansion of the matrix. m E represents the volume fraction of the matrix. m The elastic modulus of the matrix.

[0027] The elastic constants of fiber bundle composites in other directions are expressed as follows:

[0028]

[0029]

[0030]

[0031] Where E 22 E represents the transverse elastic modulus of fiber bundle composites. 33 This represents the elastic modulus in the thickness direction of the fiber bundle composite material. The modulus of elasticity in the transverse direction of the fiber, v 12 v 13 v 23 For the three-directional Poisson's ratio of fiber bundle composite materials, v 12 v represents the strain in direction 2 caused by a unit strain in direction 1. 13 v represents the strain in three directions caused by a unit strain in one direction. 23 This represents the strain in three directions caused by a unit strain in two directions. To enhance the Poisson's ratio of the fiber, v m The matrix represents Poisson's ratio; direction 1 is the longitudinal direction, direction 2 is the transverse direction, and direction 3 is the thickness direction.

[0032]

[0033]

[0034] G 12 G 13 G 23 Let be the shear modulus of the fiber bundle composite material in three directions, representing the ratio of shear stress to shear strain in the 1-2 plane, 1-3 plane, and 2-3 plane, respectively. To enhance fiber shear modulus, G m This represents the matrix shear modulus.

[0035] Furthermore, in step four, the mechanical properties of the fiber composite material obtained from the experiments and calculations in step three are applied to all the yarn elements in the micro-finite element model of the ceramic matrix composite material micro-aperiodic structure described in step two, and the corresponding material parameters are set for the clamped finite element model, and an initial displacement load dL is applied.

[0036] Furthermore, in step five, the support reaction force results obtained from the two iterations of the micro-finite element model under the same displacement load are compared. If the difference is less than a predetermined value, it is determined that the calculation result under the displacement load has converged. If the difference is greater than the predetermined value, it is determined whether the yarn unit has been damaged. The data is then statistically analyzed as the strain calculation result of the yarn unit.

[0037] Furthermore, in step six, based on the strain calculation results of the yarn unit obtained in step five, if the yarn unit completely fails, the material stiffness suddenly degrades according to the reduction factor X; if the yarn unit does not completely fail, it continuously degrades according to the stress-strain curve of the fiber bundle composite material, and the cumulative damage of the yarn is statistically calculated; if the yarn unit is not damaged, the displacement load ΔL is increased and step five is repeated.

[0038] Furthermore, in step seven, as the displacement load increases, the cumulative failure of yarn units eventually causes the overall failure of the micro-aperiodic structure of the ceramic matrix composite material. When the load continues to decrease, it is determined that the micro-aperiodic structure of the ceramic matrix composite material has completely failed, the calculation ends, and the maximum load value is read. Otherwise, the displacement load ΔL is increased and the solution is continued. The calculation results are statistically analyzed to obtain the load-displacement curve of the micro-aperiodic structure of the ceramic matrix composite material.

[0039] The beneficial effects of this invention are as follows:

[0040] 1. This invention provides a method for analyzing the strength of a microscopic non-periodic structure of ceramic matrix composites based on fiber bundles as the main load-bearing unit. This method can accurately describe the differences in yarn structure in different parts of a complex structure formed by integral conforming of 2.5D / 3D composite materials.

[0041] 2. The method proposed in this invention solves the problem that commonly used macroscopic homogenization methods cannot represent the macroscopic mechanical properties of different regions of microscopic aperiodic structures. It can accurately predict the load-displacement response of microscopic aperiodic structures of ceramic matrix composites, which is helpful for the design and optimization of such advanced structures.

[0042] 3. The method proposed in this invention uses yarn as the basic load-bearing unit and endows the yarn with the constitutive structure of fiber bundle composite material, which reflects the material parameter differences in different parts of the microscopic non-periodic structure of ceramic matrix composite material. The progressive damage analysis method can more accurately analyze the damage in different parts of the structure. Attached Figure Description

[0043] Figure 1 This is a general roadmap for the analysis of the strength of the microstructure of ceramic matrix composites with aperiodic structure.

[0044] Figure 2This is a front view of a 2.5D woven tenon structure obtained using X-ray computed tomography.

[0045] Figure 3 It is a bottom view of a 2.5D woven tenon structure obtained by X-ray computed tomography.

[0046] Figure 4 It is a 2.5D micro-geometric model of the woven tenon structure;

[0047] Figure 5 This is a 2.5D micro-finite element model of a woven tenon structure and the applied boundary conditions, where A is the displacement load, B is the non-separation contact, C is the fixed support, and D is the frictionless support.

[0048] Figure 6 This is the calculated load-displacement curve of the 2.5D woven tenon structure;

[0049] Figure 7 This is an approximate schematic diagram of the cross-sections of the warp and weft yarns. Detailed Implementation

[0050] To more clearly demonstrate the technical solution and advantages of the present invention, the present invention will be further described in detail below with reference to the accompanying drawings and embodiments:

[0051] A method for strength analysis of mesoscopic aperiodic structures in ceramic matrix composites based on fiber bundles as the main load-bearing units is applied to the strength analysis of tenon structures in ceramic matrix composites exhibiting mesoscopic aperiodicity. The tenon structure is integrally formed from a 2.5D ceramic matrix composite material. Due to the gradually changing thickness of the tenon structure, the yarn structure differs in different regions. For example... Figure 1 The diagram shown is an overall roadmap of the method of the present invention, which includes the following steps:

[0052] Step 1: Establish a microscopic geometric model of the non-periodic structure of ceramic matrix composites:

[0053] like Figure 2 and Figure 3As shown, the microscopic aperiodic structure of the ceramic matrix composite material is composed of interwoven warp and weft yarns, and the yarn structure differs in different regions of the microscopic aperiodic structure. Electron microscopy revealed that the yarns have the same microscopic composition as fiber bundle composite materials; therefore, the yarns can be considered as fiber bundle composite materials. The fiber bundle composite material consists of fibers, a matrix surrounding the fibers, and the interface between the matrix and the fibers. The fiber bundle composite material also consists of SiC fibers, a SiC matrix surrounding the fibers, and a pyrolytic carbon interface between the matrix and the fibers. Based on images obtained from X-ray computed tomography, the cross-sections of the warp and weft yarns are approximated as rectangular, elliptical, racetrack-shaped, or double-convex lens-shaped, etc. Figure 7 As shown, in this embodiment, the cross-sections of the warp and weft yarns are approximated as rectangular and double-sided convex lens shapes, respectively. Then, based on the direction of the warp / weft yarns, a geometric model of each yarn is established. All yarn geometric models are combined to form a complete model. Figure 4 The model shown is a microscopic geometric model of the aperiodic structure of a ceramic matrix composite material. This microscopic geometric model reasonably approximates and accurately describes the actual yarn geometry and orientation of the tenon structure, reflecting the differences in fiber structure in different regions of the tenon structure.

[0054] Step 2: Establish a micro-finite element model of the aperiodic structure of the ceramic matrix composite material:

[0055] In the finite element analysis software, the mesoscopic geometric model of the ceramic matrix composite tenon structure described in step one is meshed. Each yarn is a yarn element, and the direction of each yarn is assigned as the principal direction to all yarn elements in the finite element model. To meet the needs of finite element analysis, a necessary finite element model of the fixture auxiliary structure is also established. Contacts are set at the contact points between the fixture and the mesoscopic aperiodic structure. Contact types include binding contact, friction contact, and non-separation contact, selected according to the actual contact conditions. This embodiment ultimately establishes a mesh as follows: Figure 5 The finite element model shown.

[0056] Step 3: Obtain the mechanical properties of the fiber bundle composite material:

[0057] The mechanical properties of fiber bundle composites were obtained through experiments and formulas. The direction along the fiber bundle composite is the longitudinal direction, and the directions perpendicular to the fiber bundle composite are the transverse and thickness directions, respectively. Fiber bundle composites were prepared using the same process as the tenon structure, and tensile tests were conducted to obtain the stress-strain curves of the fiber bundle composites along the longitudinal direction.

[0058] Fiber bundle composites can be considered transversely isotropic materials, and their constitutive models must be based on the damage mechanisms of their microstructure components. Regarding fiber / matrix interface slip, the shear hysteresis model directly uses mathematical methods to describe the role of interfacial shear stress in the force balance between the fiber and the matrix. Regarding matrix cracking, probabilistic statistical methods are one of the most commonly used theories for matrix cracking in ceramic matrix composites. Based on the above models and methods, the longitudinal stress-strain curve of fiber bundle composites can be calculated using equations (1) and (2).

[0059] Average strain of fiber bundle composites Considered as the average strain of an undamaged fiber bundle composite material Right now:

[0060]

[0061] When the interface is completely debonded, the average strain is expressed as follows:

[0062]

[0063] Among them, E f V is the longitudinal elastic modulus of the fiber, L is the crack spacing in the matrix, and V is the longitudinal elastic modulus of the fiber. f σ represents the fiber volume fraction. f For the longitudinal stress of the fiber, σ f0 Let σ be the longitudinal stress of the fiber bundle composite material when it is undamaged, and r be the longitudinal stress of the fiber bundle composite material. f Let λ be the average fiber radius, x be the interfacial slip distance, τ be the interfacial shear stress, d be the length of the debonding region, and α be the average fiber radius. f α is the coefficient of thermal expansion of the fiber. c Let be the coefficient of thermal expansion of the fiber bundle composite, and ΔT be the difference between room temperature and the composite preparation temperature.

[0064]

[0065]

[0066] E c =V f E f +E m V m (5)

[0067]

[0068]

[0069] Where D is the matrix crack density, D sat It is the final density of the matrix when it reaches crack saturation. and mm It is a statistical parameter, E c E represents the longitudinal elastic modulus of the fiber bundle composite material. m α is the elastic modulus of the matrix. m V is the coefficient of thermal expansion of the matrix. m E represents the volume fraction of the matrix. m This is the elastic modulus of the matrix.

[0070] The following mixing law is used to calculate the elastic constants of fiber bundle composites in other directions:

[0071]

[0072]

[0073]

[0074]

[0075]

[0076] Among them, E ij G ij v ij (i, j = 1, 2, 3) represent the elastic modulus, shear modulus, and Poisson's ratio, respectively. The subscripts 1, 2, and 3 represent the longitudinal, transverse, and thickness directions of the fiber / fiber bundle composite material, respectively. In the above formula: E 22 E represents the transverse elastic modulus of fiber bundle composites. 33 This represents the elastic modulus in the thickness direction of the fiber bundle composite material. The modulus of elasticity in the transverse direction of the fiber, v 12 v 13 v 23 For the three-directional Poisson's ratio of fiber bundle composite materials, v 12 v represents the strain in direction 2 caused by a unit strain in direction 1. 13 v represents the strain in three directions caused by a unit strain in one direction. 23 This represents the strain in three directions caused by a unit strain in two directions. To enhance the Poisson's ratio of the fiber, v m G represents the matrix Poisson's ratio; direction 1 is the longitudinal direction, direction 2 is the transverse direction, and direction 3 is the thickness direction. 12 G 13 G 23 Let be the shear modulus of the fiber bundle composite material in three directions, representing the ratio of shear stress to shear strain in the 1-2 plane, 1-3 plane, and 2-3 plane, respectively. To enhance fiber shear modulus, G m This represents the matrix shear modulus.

[0077] The basic mechanical properties of the fiber and matrix in this example are shown in Table 1, and the mechanical properties of the fiber bundle composite material in other directions can be calculated.

[0078] Table 1 Fiber and matrix properties

[0079]

[0080] Step 4: Assign the mechanical properties of the fiber bundle composite material described in Step 3 to all yarn elements in the micro-finite element model of the ceramic matrix composite tenon structure. Set the material parameters of 45 steel for the finite element model of the fixture auxiliary structure required for finite element analysis. Set the constraints as shown in Figure 5 and apply an initial displacement load dL = 0.1 mm.

[0081] Step 5: Solve and record the support reaction force at the fixed end of the clamp in the micro-finite element model of the ceramic matrix composite tenon structure described in Step 4. Compare the support reaction force results obtained from two iterations of the finite element model under the same displacement load. If the difference is less than 10N, it is determined that the calculation result converges under that displacement load; otherwise, it is determined whether the yarn unit has been damaged.

[0082] Step Six: Based on the corresponding failure criteria and the obtained strain calculation results of the yarn unit, determine whether the yarn unit has failed. This example uses the maximum strain criterion. Only tensile failure in the longitudinal direction, compressive failure in the thickness direction, and shear failure in the 1-2, 1-3, and 2-3 planes are assessed. The corresponding failure strains are shown in Table 2. If the yarn unit completely fails, the material stiffness suddenly degrades according to the reduction factor of 0.01. If the yarn unit does not completely fail, the stress-strain curve of the fiber bundle composite material continuously degrades to reflect the cumulative damage of the yarn. If the yarn unit is not damaged, the displacement load ΔL = 0.1 mm is increased to continue the solution.

[0083] Table 2. Yarn Failure Strain

[0084]

[0085] Step 7: As the displacement load increases, the cumulative failure of yarn units eventually leads to the overall failure of the tenon structure. When the load continues to decrease, the tenon structure is considered to have completely failed. If the tenon structure has completely failed, the calculation ends, and the maximum load value is read. Otherwise, the displacement load is increased, and the solution continues. The statistical calculation results are obtained as follows: Figure 6 The load-displacement curve of the ceramic matrix composite tenon structure is shown. In this example, the tenon structure completely fails when the displacement load is 2.5 mm, therefore the calculated failure load of the ceramic matrix composite tenon structure is 16.8 kN.

[0086] The above are merely preferred embodiments of the present invention. The scope of protection of the present invention is not limited to the above embodiments. All technical solutions falling within the scope of the present invention's concept are within the scope of protection of the present invention. It should be noted that for those skilled in the art, any improvements and modifications made without departing from the principle of the present invention should be considered within the scope of protection of the present invention.

Claims

1. A method for strength analysis of the microstructure of aperiodic ceramic matrix composites, characterized in that, Includes the following steps, Step 1: Establish a mesoscopic geometric model of the microscopic aperiodic structure of the ceramic matrix composite material: Step 2: Mesh the micro-geometric model from Step 1 to establish a micro-finite element model of the micro-aperiodic structure of ceramic matrix composite material, and establish an auxiliary structural finite element model. Step 3: Obtain the mechanical properties of fiber bundle composites with a microscopic non-periodic structure in ceramic matrix composites; Step four: The mechanical properties of the fiber bundle composite material from step three are applied to the micro-finite element model from step two. Constraints and initial displacement loads are applied to the micro-finite element model through the auxiliary structural finite element model. Step 5: Apply displacement load, solve and record the fixed end support reaction force in the micro-finite element model from Step 4; Step 6: Based on the failure criteria and the calculation results of the fixed end support reaction force, determine whether the yarn element in the microscopic finite element model has failed. Step seven: Continue applying displacement loads. The cumulative failure of the yarn units in step six eventually leads to the overall failure of the microscopic aperiodic structure of the ceramic matrix composite material. The maximum load is the failure load of the microscopic aperiodic structure of the ceramic matrix composite material. In step one, the microscopic aperiodic structure of the ceramic matrix composite material is composed of interwoven warp and weft yarns. The yarn structure differs in different regions of the microscopic aperiodic structure of the ceramic matrix composite material. Electron microscopy reveals that the yarns and fiber bundle composite materials have the same microscopic composition, i.e., the yarns are fiber bundle composite materials. The fiber bundle composite material consists of fibers, a matrix surrounding the fibers, and the interface between the matrix and the fibers. Using X-ray diffraction (XRD)... The ceramic matrix composite material is subjected to computed tomography (CT) scans to obtain a microscopic aperiodic structure. Then, based on the orientation of the warp and weft yarns, a geometric model of each yarn is established. All yarn geometric models are combined to form a microscopic geometric model of the ceramic matrix composite material's microscopic aperiodic structure. In step two, the microscopic geometric model of the ceramic matrix composite material's microscopic aperiodic structure described in step one is meshed in finite element analysis software to establish a microscopic finite element model of the ceramic matrix composite material's microscopic aperiodic structure. All elements in the microscopic finite element model are referred to as yarn elements, and each yarn's orientation is assigned a primary orientation to all yarn elements in the microscopic finite element model.

2. The method for strength analysis of the microstructure of aperiodic ceramic matrix composites according to claim 1, characterized in that, The auxiliary structural finite element model mentioned in step two is a clamping finite element model of a ceramic matrix composite micro-aperiodic structure, with a contact point set at the contact between the clamp and the micro-aperiodic structure.

3. The method for strength analysis of the microstructure of aperiodic ceramic matrix composites according to claim 1, characterized in that, In step three, the mechanical properties of the fiber bundle composite material are obtained through experiments and formula calculations. The direction along the fiber bundle composite material is the longitudinal direction, and the directions perpendicular to the fiber bundle composite material are the transverse and thickness directions, respectively. Tensile tests are performed on the fiber bundle composite material, and the stress-strain curve of the fiber bundle composite material along the longitudinal direction is obtained. The materials and preparation process of the fiber bundle composite material are the same as those of the fiber bundle composite material in the micro-aperiodic structure of the ceramic matrix composite material in step one. The average strain of the fiber bundle composite material is... Equivalent to the average strain of undamaged fiber bundle composite materials ,Right now: ， When the interface between the matrix and fibers of the fiber bundle composite material is completely debonded, the average strain is expressed as follows: ， in, This refers to the longitudinal elastic modulus of the fiber. The distance between matrix cracks. This represents the fiber volume fraction. For fiber longitudinal stress, The longitudinal stress of the fiber bundle composite material when it is undamaged. For the longitudinal stress of fiber bundle composite materials, The average radius of the fiber. This refers to the interface sliding distance. For interfacial shear stress, The length of the debonding region. The coefficient of thermal expansion of the fiber. The coefficient of thermal expansion of the fiber bundle composite material is given. It is the difference between room temperature and the composite material preparation temperature. in, , , , The value is obtained from the following equation: ， ， ， ， ， in, The matrix crack density. It is the final density of the matrix when it reaches crack saturation. and These are statistical parameters. The longitudinal elastic modulus of the fiber bundle composite material. The matrix elastic modulus. The coefficient of thermal expansion of the matrix is ​​denoted as . The volume fraction of the matrix. The elastic modulus of the matrix. The elastic constants of fiber bundle composites in other directions are expressed as follows: ， ， ， in This represents the transverse elastic modulus of fiber bundle composites. This represents the elastic modulus in the thickness direction of the fiber bundle composite material. This represents the elastic modulus in the transverse direction of the fiber. , , The Poisson's ratio in three directions for fiber bundle composite materials. This represents the strain in direction 2 caused by a unit strain in direction 1. This represents the strain in three directions caused by a unit strain in one direction. This represents the strain in three directions caused by a unit strain in two directions. , To enhance the Poisson's ratio of the fiber, The matrix represents Poisson's ratio; direction 1 is the longitudinal direction, direction 2 is the transverse direction, and direction 3 is the thickness direction. ， ， , , Let be the shear modulus of the fiber bundle composite material in three directions, representing the ratio of shear stress to shear strain in the 1-2 plane, 1-3 plane, and 2-3 plane, respectively. , To enhance fiber shear modulus, This represents the matrix shear modulus.

4. The method for strength analysis of the microstructure of aperiodic ceramic matrix composites according to claim 1, characterized in that, In step four, the mechanical properties of the fiber composite material obtained from the experiments and calculations in step three are applied to all the yarn elements in the mesoscopic finite element model of the ceramic matrix composite material mesoscopic aperiodic structure described in step two. Corresponding material parameters are then set for the clamped finite element model, and an initial displacement load is applied. .

5. The method for strength analysis of the microstructure of aperiodic ceramic matrix composites according to claim 1, characterized in that, In step five, the support reaction force results obtained from the two iterations of the micro-finite element model under the same displacement load are compared. If the difference is less than a predetermined value, it is determined that the calculation result under the displacement load has converged. If the difference is greater than the predetermined value, it is determined whether the yarn unit has been damaged. The data is statistically analyzed as the strain calculation result of the yarn unit.

6. The method for strength analysis of the microstructure of aperiodic ceramic matrix composites according to claim 1, characterized in that, In step six, based on the strain calculation results of the yarn unit obtained in step five, if the yarn unit completely fails, the material stiffness suddenly degrades according to the reduction factor X; if the yarn unit does not completely fail, it continuously degrades according to the stress-strain curve of the fiber bundle composite material, and the cumulative damage of the yarn is statistically calculated; if the yarn unit is not damaged, the displacement load is increased. Repeat step five.

7. The method for strength analysis of the microstructure of aperiodic ceramic matrix composites according to claim 1, characterized in that, In step seven, as the displacement load increases, the cumulative failure of yarn units eventually leads to the overall failure of the microstructure of the ceramic matrix composite material. When the load continues to decrease, the microstructure of the ceramic matrix composite material is determined to have completely failed, the calculation ends, and the maximum load value is read; otherwise, the displacement load is increased. The solution process was continued, and the statistical results were obtained to obtain the load-displacement curves of the microstructure of the ceramic matrix composite non-periodic structure.

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