A parameterized three-dimensional modeling method of a fiber-woven multi-layer heterogeneous c-ring structure

Abstract

A three-dimensional parametric modeling method of a fiber-woven multilayer heterogeneous C-ring structure, which realizes the full three-dimensional modeling of the multilayer heterogeneous matrix, fiber-woven preform and ellipsoidal pores in the fiber-woven multilayer heterogeneous C-ring composite material through a parametric modeling method. The method is suitable for all numerical simulation modeling involved in the composite material with fiber-woven preform, ellipsoidal pores and multilayer heterogeneous matrix. The modeling method steps are as follows: 1. setting the fiber-woven preform curve equation, fiber cross section, woven body layer number and other parameters. 2. establishing the three-dimensional model of the woven preform structure through the parametric method. 3. establishing the ellipsoidal pore model. 4. establishing the C-ring matrix model. 5. judging whether the matrix is a multilayer heterogeneous structure. 6. dividing the matrix layer. 7. deleting the pores in the ceramic matrix and combining the fibers and the ceramic matrix through Boolean operation to complete the modeling of the fiber-woven multilayer heterogeneous C-ring structure.

Description

Technical Field

[0001] This invention belongs to the field of method invention technology, specifically relating to a parametric three-dimensional modeling method for a multi-layer heterogeneous C-ring structure woven from fibers. Background Technology

[0002] Multilayer heterogeneous cyclic ceramic matrix composites possess excellent mechanical and thermodynamic properties. In engineering, silicon carbide fiber-reinforced silicon carbide-based (SiCf / SiC) multilayer heterogeneous cyclic ceramic matrix composites are commonly used as cladding tubes for nuclear fuel, offering advantages such as low density, high specific strength, and corrosion resistance. Structurally, the multilayer heterogeneous cyclic ceramic matrix composite model constructed in this invention includes a metal / ceramic matrix / ceramic fiber structure, taking into account the porosity generated during material preparation. In the composite material preparation process, chemical vapor deposition (CVD) is typically used to combine the metal, ceramic matrix, and fibers. However, CVD usually requires considerable time and resources, and the prepared composite material necessitates extensive experimentation, resulting in long cycles and high costs. Therefore, it is necessary to establish a parametric modeling method suitable for cyclic braided composite materials, using numerical simulation for performance prediction and testing, thereby saving time and money and providing a modeling means and method for the numerical analysis of two-dimensional braided multilayer heterogeneous composite materials.

[0003] Domestic and international research

[0004] In recent years, there has been an increasing number of numerical simulation methods for braided composite materials. Scholars at home and abroad have carried out relevant modeling work and conducted certain performance prediction and analysis studies based on these methods.

[0005] For example, in the paper "A coupled micro–meso-scale study on the damage mechanism of 2DSiC / SiC ceramic matrix composites," the authors used the Representative Volume Elements (RVE) model to model and predict the properties of two-dimensional braided composites. This method assumes that the fibers are unidirectional fiber / matrix composites with a PyC interface layer. However, unlike this invention, this invention is based on modeling cyclic multilayer heterogeneous composites, which contain multiple heterogeneous structures, specifically cyclic structures. The RVE model cannot fully show the effect of loads on the complete C-ring structure, nor can it display the mechanical properties of various matrix material pairs. Therefore, this RVE modeling method is not suitable for analyzing the specific, special-structure composite materials involved in this invention.

[0006] For example, in the paper "Modeling of Pore Defects and Simulation of Tensile Properties of C / C-SiC Satin Braided Composite Material", the pores in the composite material are approximated as regular hexahedrons. The regular hexahedrons at the corresponding positions are deleted to replace the pores. However, in actual engineering applications, most pores in composite materials are flattened ellipsoids. The stress concentration characteristics of ellipsoidal pores are quite different from those of cubic pores. Therefore, this simplification method is not advisable for this invention.

[0007] In summary, there is a limited amount of research literature on crack damage simulation of composite materials both domestically and internationally. Furthermore, most modeling methods used when studying basic mechanical properties employ the RVE model. However, the RVE model has limitations for the fiber-woven multilayer heterogeneous C-ring structure addressed in this invention. It cannot fully reflect the geometric characteristics and stress features of the C-ring structure, nor can it completely simulate the crack damage of this special structural material. Additionally, existing pore simplification methods have certain defects and significant errors. Therefore, it is necessary to develop a modeling method suitable for fiber-woven multilayer heterogeneous C-ring structures. Summary of the Invention

[0008] To address the problems existing in the prior art, the present invention aims to provide a three-dimensional parametric modeling method for fiber-woven multilayer heterogeneous C-ring structures. This method is applicable to modeling composite materials with fiber-woven preforms, ellipsoidal pores, and multilayer heterogeneous matrices, and can achieve three-dimensional parametric modeling with different porosities and fiber weaving densities.

[0009] To achieve the above objectives, the present invention adopts the following technical solution:

[0010] A three-dimensional parametric modeling method for fiber-woven multilayer heterogeneous C-ring structures is disclosed. This method achieves full three-dimensional modeling of the multilayer heterogeneous matrix, ellipsoidal pores, and fiber-woven preforms in the multilayer heterogeneous C-ring structure through parametric methods. This method is applicable to all numerical simulation modeling involving composite materials with fiber-woven preforms, ellipsoidal pores, and multilayer heterogeneous matrices. The modeling method allows for the insertion of fiber-woven preforms and ellipsoidal pores into the multilayer heterogeneous matrix. The specific steps are as follows:

[0011] Step 1: Define the curve equation of the fiber braided preform, the fiber cross-sectional shape, the number of braided layers n, the braiding density, and the outer radius R of the matrix of the multi-layer heterogeneous C-ring structure. 外 , inner radius R 内 The relationship between thickness c, number of multilayer heterogeneous matrix layers k and radius of each layer of heterogeneous matrix, number of ellipsoidal pores α, equatorial radius a and b, polar radius c, wherein: the multilayer heterogeneous C-ring structure is composed of fiber braided preform, ellipsoidal pores and multilayer heterogeneous matrix, the fiber braided preform includes circumferential fibers and longitudinal fibers, and its geometric features are manifested as a ring with a notch from the appearance;

[0012] The curve equation of the circumferential fibers in the fiber braided preform is:

[0013]

[0014] The curve equation of the longitudinal fibers in the fiber braided preform is:

[0015]

[0016] Where:

[0017] t - The independent variable parameter of the circumferential fiber curve equation;

[0018] x - The independent variable parameter of the longitudinal fiber curve equation;

[0019] x t - The equation of the x - coordinate of the circumferential fiber with respect to the parameter t;

[0020] y t - The equation of the y - coordinate of the circumferential fiber with respect to the parameter t;

[0021] y x - The equation of the y - coordinate of the longitudinal fiber with respect to the parameter x;

[0022] r1 - The reference circle radius of the circumferential fiber;

[0023] r2 - The distance from the longitudinal fiber to the center of the reference circle of the circumferential fiber;

[0024] A - The parameter controlling the amplitude of fiber fluctuation;

[0025] T i - The parameter controlling the period of fiber fluctuation, i = 1, 2;

[0026] θ1 - The starting angle of the circumferential fiber curve equation;

[0027] θ2 - The ending angle of the circumferential fiber curve equation;

[0028] K i - The parameter controlling the initial phase, i = 1, 2, 3;

[0029] π - Pi;

[0030] c - The matrix thickness, x < c ensures that the fiber does not exceed the matrix;

[0031] An elliptical fiber cross - section is adopted, and its equation is:

[0032] Among them, the parameter T in the curve equation of the circumferential fibers in the fiber braided preform can change the number of fibers, and the cross-sectional shape of the fibers can change the fiber volume. The two together can regulate the fiber density.

[0033] Step 2: Based on the parameters of the fiber-woven preform set in Step 1, establish the three-dimensional geometric model of the fiber-woven preform through the parametric method. The specific method is as follows: Select the reference plane S1, draw the sweep line L1 on the reference plane according to equation (1), select the reference plane S2 perpendicular to the reference plane S1, draw the sweep line L2 on S2 according to equation (2), create the reference plane S3 at the endpoints of L1 and L2, draw the fiber cross section on S3, use the sweep method, select the fiber cross section as the contour plane, select L1 and L2 as the path respectively, sweep to obtain circumferential fibers and longitudinal fibers, the fiber-woven preform is formed by the orthogonal combination of circumferential fibers and longitudinal fibers, forming a single-layer fiber-woven preform structure, arrange the multi-layer fiber-woven structure according to the radius size to obtain the fiber-woven preform;

[0034] Step 3: Based on the ellipsoidal pore size and number set in Step 1, complete the modeling of the ellipsoidal pores and distribute the ellipsoidal pores at the intersection of the circumferential and longitudinal fibers in a periodic distribution pattern.

[0035] Step 4: Based on the parameters of the matrix set in Step 1, establish a three-dimensional geometric model of the annular matrix, delete the matrix in the annular matrix that forms an angle between γ° and -γ° with the center of the circle, and obtain a C-ring matrix, so that the matrix can completely wrap all the fibers.

[0036] Step 5: Determine whether the matrix is ​​a multilayered heterogeneous material. The specific method is as follows:

[0037] If the number of layers k in the multilayer heterogeneous matrix is ​​greater than 1, then the matrix is ​​a multilayer heterogeneous material, and steps 6 and 7 are completed.

[0038] If the number of layers k in the multilayer heterogeneous matrix is ​​1, then the matrix is ​​a single-layer ceramic material, and we skip to step 7.

[0039] Step 6: On the C-ring matrix obtained in Step 4, divide the matrix layers according to the radius relationship of each heterogeneous matrix layer in the multilayer heterogeneous C-ring in Step 1 to obtain a multilayer heterogeneous C-ring matrix;

[0040] Step 7: Set the ellipsoidal pores as the deletion object, delete the ellipsoidal pores in the matrix, and merge the fiber braided prefabricated body with the multilayer heterogeneous C-ring matrix through Boolean operation to complete the modeling of the fiber braided multilayer heterogeneous C-ring structure.

[0041] Compared with the prior art, the present invention has the following advantages:

[0042] 1. The modeling method of this invention is applicable to the modeling of cyclic, fiber-woven, and multi-layered heterogeneous matrix composite materials, and can achieve full three-dimensional parametric modeling of different fiber preform weaving densities and different porosities.

[0043] 2. The modeling method of this invention retains the composite material fiber preform weaving structure, multi-layer heterogeneous matrix structure, and pores. The holistic modeling can restore the research object that conforms to the actual engineering application to the greatest extent and improve accuracy.

[0044] 3. Independent model and innovative method: The method of this invention is a parametric modeling method. The model can be changed by simply changing the relevant parameters according to the algorithm. It can obtain fibers with different cross sections and has strong applicability.

[0045] 3. The modeling method of this invention does not limit the number of heterogeneous layers in the matrix and can be extended from two-layer heterogeneous metal / ceramic matrices to n-layer heterogeneous matrices, making it widely applicable.

[0046] The present invention proposes a parametric modeling method for a multilayer heterogeneous two-dimensional braided C-ring structure, which is applicable to the modeling of various composite materials. The ideas and methods mentioned are also applicable to the modeling of all complex composite shell tubes involving fiber braided preforms and matrix. Attached Figure Description

[0047] Figure 1 This is a flowchart of the three-dimensional parametric modeling method for the fiber-woven multilayer heterogeneous C-ring structure proposed in this invention.

[0048] Figure 2 This is a half-section diagram of a three-dimensional model of the fiber-woven bilayer heterogeneous C-ring composite material established using this invention. Detailed Implementation

[0049] The following is in conjunction with the appendix Figure 1 The present invention will be described in further detail below. The modeling method proposed in the present invention mainly includes the following steps:

[0050] Step 1: Define the curve equation of the fiber braided preform, the fiber cross-sectional shape, the number of braided layers n=2, the braiding density, and the outer radius R of the matrix of the multi-layer heterogeneous C-ring structure. 外 =4mm, inner radius R 内=2mm and thickness c=4mm, number of heterogeneous matrix layers k=2 and the radius relationship of each heterogeneous matrix layer (maximum radius of metal matrix layer is 2.7mm, maximum radius of ceramic matrix is ​​4mm), number of ellipsoidal pores α=52, equatorial radius of ellipsoidal pores a=0.1mm and b=0.05mm, polar radius c=0.05mm, the multilayer heterogeneous C-ring structure is composed of fiber braided preform, ellipsoidal pores and multilayer heterogeneous matrix. The fiber braided preform includes circumferential fibers and longitudinal fibers. From the appearance, its geometric features are manifested as a ring with a certain gap.

[0051] The curve equation for the circumferential fibers in the fiber-woven preform is:

[0052]

[0053] The curve equation for the longitudinal fibers of the fiber-woven preform is:

[0054]

[0055] First layer fiber braiding structure parameters:

[0056] r1=3.1mm, r2=3.35mm, A=0.05mm, T1=16, T2=4,

[0057] K1 = K2 = 1, θ1=0.33, θ2=-0.33, c=3.8mm.

[0058] Second layer fiber braiding structure parameters:

[0059] r1=3.5mm, r2=3.6mm, A=0.05mm, T1=16, T2=4,

[0060] K1=K2=-1, K3=2, θ1=0.33, θ2=-0.33, c=3.8mm.

[0061] In the formula:

[0062] x t —The equation for the x-coordinate of the circumferential fiber with respect to parameter t;

[0063] y t —The equation for the y-coordinate of the circumferential fiber with respect to parameter t;

[0064] t—the independent variable parameter of the circumferential fiber curve equation;

[0065] x — Independent variable parameter of the longitudinal fiber curve equation;

[0066] π — Pi (the mathematical constant of a circle).

[0067] This invention uses an elliptical fiber cross-section, the equation of which is:

[0068] Among them, the parameter T of the curve equation of the circumferential fibers in the fiber braided preform can change the number of fibers, the cross-sectional shape of the fibers can change the fiber volume, and the two together can change the fiber density.

[0069] Step 2: Based on the parameters of the fiber-woven prefabricated body set in Step 1, establish a three-dimensional geometric model of the fiber-woven prefabricated body structure through a parametric method. The specific method is as follows: Select the reference plane S1, draw the sweep line L1 on the reference plane according to equation (1), select the reference plane S2 perpendicular to the reference plane S1, draw the sweep line L2 on S2 according to equation (2), create the reference plane S3 at the endpoints of L1 and L2, draw the fiber cross section on S3, use the sweep method, select the fiber cross section as the contour plane, select L1 and L2 as the path respectively, and sweep to obtain the circumferential fiber FiberX and the longitudinal fiber FiberY. The fiber-woven prefabricated body is formed by the orthogonal combination of the circumferential fiber and the longitudinal fiber, forming a single-layer fiber-woven prefabricated structure. Repeat the operation using the parameters of the second layer fiber-woven prefabricated structure, and combine the two layers of fiber-woven prefabricated structures according to the radius to obtain the fiber-woven prefabricated body.

[0070] Step 3: Based on the ellipsoidal pore size and number set in Step 1, complete the modeling of the ellipsoidal pores and distribute the ellipsoidal pores at the intersection of the circumferential and longitudinal fibers in a periodic distribution pattern.

[0071] Step 4: Based on the parameters of the matrix set in Step 1, establish a three-dimensional geometric model of the annular matrix, delete the matrix between 18° and -18° in the annular matrix to obtain a C-ring matrix, and make the matrix completely cover all fibers.

[0072] Step 5: Determine whether the matrix is ​​a multilayered heterogeneous matrix. The specific method is as follows:

[0073] If k = 2 > 1, then the matrix is ​​a multilayer heterogeneous matrix, and we continue to complete step 5.

[0074] Step 6: On the C-ring matrix obtained in Step 4, divide the matrix layers according to the radius relationship of each heterogeneous matrix layer in the multilayer heterogeneous C-ring in Step 1 to obtain a multilayer heterogeneous C-ring matrix.

[0075] Step 7: Set the ellipsoidal pores as the deletion object, delete the ellipsoidal pores in the matrix, and merge the fiber-woven prefabricated body with the multilayer heterogeneous C-ring matrix through Boolean operations to complete the modeling of the fiber-woven multilayer heterogeneous C-ring structure. The established model is as follows: Figure 2 As shown.

[0076] The modeling method involved in this invention can ultimately achieve the modeling of multi-layer heterogeneous two-dimensional braided C-ring structures, and can be applied to the corresponding numerical simulation process.

[0077] The above description is a further detailed explanation of the present invention in conjunction with specific preferred embodiments. It should not be considered that the specific embodiments of the present invention are limited to this. For those skilled in the art, several simple deductions or substitutions can be made without departing from the concept of the present invention, and all such deductions or substitutions should be considered to fall within the scope of patent protection determined by the submitted claims.

Claims

1. A three-dimensional parametric modeling method for a fiber-woven multilayer heterogeneous C-ring structure, characterized in that: This method realizes the full three-dimensional modeling of multi-layer heterogeneous matrix, ellipsoidal pores and fiber braided preforms in a multi-layer heterogeneous C-ring structure through parameterization. This method is applicable to all numerical simulation modeling involved in composite materials with fiber braided preforms, ellipsoidal pores and multi-layer heterogeneous matrix. This modeling method realizes the insertion of fiber braided preforms and ellipsoidal pores into the multi-layer heterogeneous matrix. The specific steps are as follows: Step 1: Define the curve equation of the fiber braided preform, the fiber cross-sectional shape, the number of braided layers n, the braiding density, and the outer radius R of the matrix of the multi-layer heterogeneous C-ring structure. 外 , inner radius R 内 The relationship between thickness c, number of multilayer heterogeneous matrix layers k and radius of each layer of heterogeneous matrix, number of ellipsoidal pores α, equatorial radius a and b, polar radius c, wherein: the multilayer heterogeneous C-ring structure is composed of fiber braided preform, ellipsoidal pores and multilayer heterogeneous matrix, the fiber braided preform includes circumferential fibers and longitudinal fibers, and its geometric features are manifested as a ring with a notch from the appearance; The curve equation of the circumferential fibers in the fiber braided preform is: The curve equation of the longitudinal fibers in the fiber braided preform is: In the formula: t - The independent variable parameter of the circumferential fiber curve equation; x - The independent variable parameter of the longitudinal fiber curve equation; x t —The equation for the x-coordinate of the circumferential fiber with respect to parameter t; y t —The equation for the y-coordinate of the circumferential fiber with respect to parameter t; y x —The equation for the longitudinal fiber's y-coordinate with respect to the parameter x; r1 - The reference circle radius of the circumferential fibers; r2 - The distance from the longitudinal fibers to the center of the reference circle of the circumferential fibers; A - The parameter controlling the fiber fluctuation amplitude; T i —Parameters that control the fiber oscillation period, i = 1, 2; θ1 - The starting angle of the circumferential fiber curve equation; θ2 - The ending angle of the circumferential fiber curve equation; K i —Control the initial phase parameters, i = 1, 2, 3; π - Pi; c - The matrix thickness, x < c ensures that the fibers do not exceed the matrix; Using an elliptical fiber cross-section, its equation is: a>b>0 Among them: The parameter T in the curve equation of the circumferential fibers in the fiber braided preform and the curve equation of the circumferential fibers in the fiber braided preform can change the number of fibers, and the fiber cross-sectional shape can change the fiber volume. The two work together to regulate the fiber density; Step 2: According to the various parameters of the fiber braided preform set in Step 1, establish a three-dimensional geometric model of the fiber braided preform through the parameterization method. The specific method is as follows: Select the reference plane S1, draw the sweeping line L1 on this reference plane according to Equation (1), select the reference plane S2 perpendicular to the reference plane S1, draw the sweeping line L2 on S2 according to Equation (2), create the reference plane S3 at the endpoints of L1 and L2, draw the fiber cross-section on S3, use the sweeping method, select the fiber cross-section as the profile plane, and select L1 and L2 as the paths respectively to sweep to obtain the circumferential fibers and longitudinal fibers. The fiber braided preform is composed of the orthogonal combination of the circumferential fibers and longitudinal fibers to form a single-layer fiber braided preform structure. Arrange the multi-layer fiber braided structures according to the radius size to obtain the fiber braided preform; Step 3: According to the ellipsoidal pore size and pore number set in Step 1, complete the modeling of the ellipsoidal pores, and distribute the ellipsoidal pores at the intersections of the circumferential fibers and longitudinal fibers in a periodic distribution manner; Step 4: According to the parameters of the matrix set in Step 1, establish a three-dimensional geometric model of the circular ring matrix, delete the matrix between the angles of γ° to -γ° with the center line in the circular ring matrix to obtain the C-ring matrix, and make the matrix completely wrap all the fibers; Step 5: Judge whether the matrix is a multi-layer heterogeneous material. The specific method is as follows: If the number of layers k of the multi-layer heterogeneous matrix > 1, then the matrix is a multi-layer heterogeneous material, and complete Steps 6 and 7; If the number of layers k of the multi-layer heterogeneous matrix = 1, then the matrix is a single-layer ceramic material, and jump to Step 7; Step 6: On the C-ring matrix obtained in Step 4, divide the matrix layer according to the radius relationship of each layer of heterogeneous matrix in the multi-layer heterogeneous C-ring in Step 1 to obtain the multi-layer heterogeneous C-ring matrix; Step 7: Set the ellipsoidal pores as the deletion object, delete the ellipsoidal pores in the matrix, and merge the fiber braided prefabricated body with the multilayer heterogeneous C-ring matrix through Boolean operation to complete the modeling of the fiber braided multilayer heterogeneous C-ring structure.

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