Modeling and strength prediction method for SiC / SiC composite material tubular member

Abstract

The invention discloses a SiC / SiC composite material tubular component modeling and strength prediction method, and particularly relates to the field of composite material tubular component modeling and performance simulation, and the method comprises the steps: building a spiral line equation about a weaving angle; fitting by utilizing a spiral line equation to obtain a weaving path of a single fiber, establishing a prefabricated body model of the tubular component, establishing a matrix model, performing Boolean operation on the matrix model and the prefabricated body model to obtain a unit cell model, performing service behavior simulation on the unit cell model, and combining with an elastic modulus to obtain a stress-strain curve; and obtaining the strength of the tubular member according to the stress-strain curve. According to the method, a spiral line equation is established according to the weaving angle of the tubular component, then the weaving path of fibers is fitted, establishment of a SiC / SiC composite material cladding tube model at any angle and with any number of layers is achieved, and the strength distribution of the SiC / SiC composite material cladding tube can be analyzed and predicted.

Description

Technical Field

[0001] The present application relates to the field of modeling methods, and in particular to a modeling and strength prediction method for SiC / SiC composite tubular components. Background Art

[0002] SiC / SiC composite material is a ceramic-based composite ceramic material with strengthening and toughening properties obtained by adding a continuous fiber reinforcement phase to the ceramic matrix for exogenous toughening and matching with an appropriate weak interface phase. With the help of strengthening and toughening mechanisms such as fiber bridging and interface crack deflection, SiC / SiC composite materials overcome the inherent brittleness of traditional SiC ceramics and are not prone to catastrophic damage under nuclear reactor accident conditions. In addition, SiC / SiC composite materials also have a small neutron absorption cross section, excellent high-temperature chemical inertness (resistance to high-temperature water vapor oxidation, low hydrogen production rate), and excellent high-temperature mechanical properties. They are recognized as ideal candidate materials for accident-resistant nuclear fuel cladding tubes.

[0003] On a macro scale, the SiC / SiC composite cladding tube has a complex structure, and the braided structure of the fiber preform has a great influence on the macro mechanical properties of the cladding tube. On a micro scale, the SiC / SiC composite cladding tube is mainly composed of two main structural units, SiC fiber and SiC matrix. Although both components are SiC, their mechanical properties are quite different. Therefore, in the process of finite element modeling and strength prediction of SiC / SiC composite cladding tubes, the following problems are often encountered: 1. Due to the complex weaving structure path of the fiber preform, the SiC / SiC composite cladding tube model often cannot include the fiber weaving preform structure; 2. The refinement and accuracy of the fiber preform modeling inside the cladding tube will affect the calculation amount and calculation accuracy in the finite element calculation and strength prediction process. Directly establishing a macro-refined model of the structure will cause a series of problems such as the model being too complex and difficult to generate, the meshing being difficult, and the calculation cost being high; 3. The existing SiC / SiC composite material strength prediction model is often only applicable to components of flat structure, ignoring the influence of curvature factors, which will affect the prediction of the axial and circumferential mechanical properties of the components; 4. The modeling method does not take into account the nonlinear factors of the material, so it is impossible to carry out strength prediction analysis of SiC / SiC composite cladding tubes. Summary of the invention

[0004] The main purpose of the present application is to provide a modeling and strength prediction method for SiC / SiC composite tubular components, aiming to solve the problem that the cladding tube model in the prior art is often unable to establish a fiber braided preform structure.

[0005] To achieve the above-mentioned purpose, the present application provides a modeling method for a SiC / SiC composite tubular component, comprising: combining a cylindrical helix equation and an exponential elliptical wave equation to establish a helix equation about a braiding angle; using the helix equation to fit a braiding path of a single fiber; establishing a first helical fiber and a second helical fiber according to the braiding path of the single fiber; wherein the first helical fiber and the second helical fiber have opposite helical directions; and translating and replicating the first helical fiber and the second helical fiber respectively along the axial direction of the tubular component to obtain a preform model of the tubular component.

[0006] Optionally, after obtaining the prefabricated model of the tubular component, the method includes: When it is determined that there is interference inside the preform model of the tubular component, the sizes of the first spiral fiber and the second spiral fiber are adjusted, and the first spiral fiber and the second spiral fiber are translated and replicated along the axial direction of the tubular component again until there is no interference inside the preform model of the tubular component.

[0007] Alternatively, the helix equation is:

[0008]

[0009]

[0010] In the formula, is the winding spiral angle, h is the fiber bundle thickness, ω is the fiber bundle width, c is the spacing between fiber bundles, p is the bending coefficient, r0 is the inner diameter of the preform model, x tow is the x-coordinate in the exponential elliptic wave equation, β is a period of length 2π, and θ is the braiding angle.

[0011] The present invention also provides a strength prediction method for a SiC / SiC composite material tubular component. The tubular component is obtained by the modeling method of the SiC / SiC composite material tubular component described in the claim, comprising: establishing a matrix model, performing Boolean operations on the matrix model and the preform model to obtain an initial unit cell model; meshing the initial unit cell model; setting boundary conditions, reducing the size of the initial unit cell model after meshing to obtain a unit cell model; determining a damage factor of the material of the tubular component, and determining the elastic modulus after fiber failure according to the damage factor; simulating the service behavior of the unit cell model, and obtaining a stress-strain curve in combination with the elastic modulus; and obtaining the strength of the tubular component according to the stress-strain curve.

[0012] Optionally, the rotation angle of the matrix model is determined according to the rotation period of the preform model and the number of braided fibers, and the axial length of the matrix model is determined according to the rotation angle of the preform model and the inner diameter of the preform model.

[0013] Optionally, the boundary conditions include relative displacement boundary conditions of two symmetrical surfaces in the unit cell model.

[0014] Optionally, the relative displacement boundary conditions of the two symmetrical surfaces include axial relative displacement boundary conditions of the two side wall surfaces and circumferential relative displacement boundary conditions of the two end surfaces: the relative displacements of the two side wall surfaces in the axial, radial and thickness directions in the unit cell model are equal to the product of the axial length of the unit cell and the axial macroscopic equivalent displacement, and the relative displacements of the two end surfaces in the axial, radial and thickness directions in the unit cell model are zero.

[0015] Optionally, the boundary condition also includes that the displacement of any vertex in the unit cell model in the axial, radial and thickness directions is zero.

[0016] Optionally, the damage factor is determined using the Hashin criterion.

[0017] Optionally, the elastic modulus after fiber failure is determined using Matzenmiller's damage factor-based progressive stiffness degradation method.

[0018] Compared with the prior art, the present invention has the following beneficial effects: The modeling method of the SiC / SiC composite tubular component of the present invention establishes a helical line equation according to the braiding angle of the tubular component, and fits the braiding path of the fiber according to the helical line equation, and finally can realize the establishment of a SiC / SiC composite cladding tube model with any angle and number of layers.

[0019] The strength prediction method of the SiC / SiC composite tubular component of the present invention performs fiber interference inspection during modeling and establishes a unit cell model for "model scale reduction", thereby avoiding the problem of difficult grid division during finite element calculation. The calculation amount of the established cladding tube reduction unit cell model is greatly reduced (reduced by 90%), and the boundaries of the calculation result array are completely closed after the macroscopic size, and the accuracy is guaranteed; the fiber weaving path is determined by a curve fitting method, and a SiC / SiC composite cladding tube reduction model with a 2 / 2 twill weaving structure is established, and the model can take into account the influence of curvature and weaving structure on the mechanical properties of the cladding; considering the nonlinear characteristics of the fiber and the matrix material, the strength distribution of the SiC / SiC composite cladding tube can be analyzed and predicted. BRIEF DESCRIPTION OF THE DRAWINGS

[0020] Figure 1 A schematic diagram of a flow chart of a method for modeling and strength prediction of a SiC / SiC composite tubular component of the present application; Figure 2 A physical diagram of a modeling method for a SiC / SiC composite tubular component of the present application; Figure 3 A CT scan image used in a modeling method for a SiC / SiC composite tubular component of the present application; Figure 4 A fiber path diagram obtained by fitting a modeling method for a SiC / SiC composite tubular component of the present application; Figure 5 A model diagram obtained by a modeling method for a SiC / SiC composite tubular component of the present application; Figure 6 A unit cell model diagram with different braided structural characteristics obtained by a modeling method of a SiC / SiC composite tubular component in this application; Figure 7 A mesh division diagram of a unit cell model obtained by a modeling method for a SiC / SiC composite tubular component of the present application; Figure 8 A schematic diagram of the surface naming rules of a unit cell model obtained by a modeling method for a SiC / SiC composite tubular component of the present application; Fig. 9 A cloud diagram of calculation results under axial tensile load for a strength prediction method of a SiC / SiC composite tubular component in this application; Fig.10 This is a prediction result diagram of a strength prediction method for a SiC / SiC composite tubular component in the present application.

[0021] The realization of the purpose, functional features and advantages of this application will be further explained in conjunction with embodiments and with reference to the accompanying drawings. DETAILED DESCRIPTION

[0022] In order to make the purpose, technical solutions and advantages of this application clearer, the technical solutions in this application will be clearly and completely described below in conjunction with the drawings in this application. Obviously, the described embodiments are part of the embodiments of this application, not all of them. Based on the embodiments in this application, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of this application.

[0023] The first embodiment of the present invention provides a modeling method for a SiC / SiC composite tubular component, such as Figure 1 As shown, the specific steps include: Step S1, combining the cylindrical helix equation and the exponential elliptical wave equation to establish a helix equation, the helix equation has exponential elliptical wave characteristics and can describe the fiber path; the helix equation is:

[0024]

[0025]

[0026] In the formula, is the braiding angle, h is the fiber bundle thickness, ω is the fiber bundle width, c is the spacing between fiber bundles, p is the bending coefficient, r0 is the inner diameter of the tubular component, x tow is the x-coordinate in the exponential elliptical wave equation, β is a period of length 2π, and θ is the inclination angle of the current point relative to the starting point.

[0027] Specifically, the spiral equation is obtained as follows: Since the tubular component (cladding tube) of this embodiment is cylindrical, the braiding path of the fiber can be realized based on the cylindrical helix equation, which is as follows:

[0028] In the formula, when z takes a positive sign, it is the equation of the right helix, and when z takes a negative sign, it is the equation of the left helix. Since the cylindrical helix equation is obtained based on the braiding angle, the braiding paths of fibers with different braiding angles can also be obtained based on the cylindrical helix equation. Figure 2 Physical picture ( Figure 2 The braiding angle of the tubular member in a is 30°. Figure 2 The braiding angle of the tubular member in b is 45°. Figure 2 The braiding angle of the tubular member in c is 60°) and Figure 3 ( Figure 3 The braiding angle of the tubular member in a is 30°. Figure 3 The braiding angle of the tubular member in b is 45°. Figure 3 From the CT scan of the tubular component in c (the braiding angle is 60°), it can be seen that the cylindrical helix should be used as the center line, and the fiber path floats up and down along the center line. The specific floating position can be determined according to the exponential elliptical wave equation, which is as follows:

[0029] Convert the above formula into an expression based on the x coordinate:

[0030] By combining the cylindrical helix equation and the transformed exponential elliptic wave equation, we can get the helix equation.

[0031] Step S2, using the helix equation to fit the braiding path of a single fiber in the Texgen modeling software, the braiding path of the right helical fiber obtained in this embodiment is shown in Figure 4 ; Step S3, since the fiber bundle has a periodic feature in spatial structure, a first spiral fiber and a second spiral fiber can be established according to the weaving path of a single fiber; wherein the spiral directions of the first spiral fiber and the second spiral fiber are opposite; Step S4, replicating the first spiral fiber and the second spiral fiber 18 times respectively along the axial direction of the tubular component, and translating them according to the spacing between the fiber bundles to obtain a prefabricated body model of the initial tubular component; Step S5, determine whether there is interference inside the preform model of the initial tubular component. If interference occurs, the model will fail to be drawn, that is, interference exists, adjust the size of the first spiral fiber and the second spiral fiber (the major axis radius and the minor axis radius of the fiber), and return to step S4 until there is no interference inside the preform model of the tubular component, and obtain a preform model of the tubular component with 18 braided roots and a braiding angle of 45°. Figure 5 ( Figure 5 a is the main view of the model, Figure 5 b is a stereogram of the model).

[0032] Since the SiC / SiC composite cladding tube is a multi-layer tube, the prefabricated model of a single-layer tubular component is obtained in step S1-5. Therefore, according to the actual number of cladding tube layers X, steps S1-5 are repeated for the corresponding number of times, and the inner diameter of the tubular component of each layer is ,in The second embodiment of the present invention provides a method for predicting the strength of a SiC / SiC composite tubular component, wherein the tubular component is obtained by the above-mentioned SiC / SiC composite tubular component modeling method, and comprises the following steps: Step S6: After obtaining the prefabricated body model in the same modeling software, a base model is established, and Boolean operations are performed on the base model and the prefabricated body model to obtain an initial unit cell model. Figure 6 a- Figure 6 f, where Figure 6 a is a single-layer unit cell model with a weaving angle of 45°. Figure 6 b is a double-layer unit cell model with a weaving angle of 45°. Figure 6 c is a three-layer unit cell model with a weaving angle of 45°. Figure 6 d is a unit cell model with a weaving angle of 30°. Figure 6 e is a unit cell model with a weaving angle of 45°. Figure 6 e is a unit cell model with a braiding angle of 60°); according to the periodic characteristics of the tubular component, the periodicity of braiding along the axial direction is used, and a preset angle is selected in the circumferential direction, so as to ensure the periodic characteristics of the unit cell model along the circumferential direction; The method for establishing the matrix model is as follows: draw the radial section of the matrix and perform a rotation operation to form the matrix model. The thickness of the radial section of the matrix model is the same as the thickness of the tubular component. The rotation angle of the matrix model is determined according to the rotation period of the preform model and the number of braided fibers in one direction. The calculation formula is as follows:

[0033] The axial length of the matrix model is determined according to the rotation angle of the matrix model, the inner diameter of the preform model, and the braiding angle. The calculation formula is as follows:

[0034] In the formula, is the number of braided fibers in one direction, n is the number of rotation cycles (should be a positive integer, such as 1, 2, 3...), L0 is the preset axial length, and γ is the preset angle.

[0035] Step S7, use the automatic meshing function in the finite element software to mesh the initial unit cell model. When the mesh size is inappropriate, the mesh generation will fail (a mesh that is too large will cause mesh distortion). At this time, the mesh can be adjusted to fine-tune the mesh size and regenerate the mesh until the meshing of the initial unit cell model is successful. Figure 7 ; Step S8, setting boundary conditions, reducing the size of the initial unit cell model after meshing, and obtaining a unit cell model; Specifically, Figure 8 As shown in a, the unit cell model has periodicity along the cylindrical coordinate system zr-ρ. For the surface naming of the unit cell model, see Figure 8 b. The boundary conditions include the relative displacement boundary conditions of two symmetrical surfaces in the unit cell model. In the figure, surfaces A and B have axial symmetry, and surfaces C and D have circumferential symmetry.

[0036] Furthermore, the relative displacement boundary conditions of the two symmetrical surfaces include the axial relative displacement boundary conditions of surface A and surface B:

[0037] In the formula, is the displacement of surface A in the Z direction, is the displacement of surface B in the Z direction, is the displacement of surface A in the r direction, is the displacement of surface B in the r direction, is the displacement of surface A in the ρ direction, is the displacement of surface B in the ρ direction, L is the axial length of the unit cell, is the macro equivalent displacement in the Z direction.

[0038] Circumferential relative displacement boundary conditions of C and D surfaces:

[0039] In the formula, is the displacement of surface C in the Z direction, is the displacement of surface D in the Z direction, is the displacement of surface C in the r direction, is the displacement of surface D in the r direction, is the displacement of surface C in the ρ direction, is the displacement of surface D in the ρ direction.

[0040] Since the E and F surfaces are not symmetrical, the reduced unit cell is set as a free surface in the radial direction. When considering setting relative displacement boundary conditions in the finite element software, over-constraints will be generated at the edges and vertices. Therefore, the edges where two surfaces intersect and the vertices where three surfaces intersect need to be excluded from the surface and additional boundary conditions are set. The relative displacement boundary conditions at the edges and vertices can be set through the boundary conditions of the corresponding surfaces. In order to prevent the rigid body displacement of the model, this embodiment adds the displacement boundary condition edge of any vertex in the unit cell model:

[0041] In the formula, represents the displacement of node 1 in the Z direction, represents the displacement of node 1 in the r direction, represents the displacement of node 1 in the ρ direction. Step S9, determining the damage factor of the material of the tubular component, and determining the elastic modulus of the fiber after failure according to the damage factor; Specifically, the SiC fiber and the matrix material of this embodiment are both ideal linear elastic materials, the transversely isotropic constitutive model, and the damage factor is determined by the Hashin criterion, and the formula is as follows: Damage factors for fiber tensile failure:

[0042] Damage factors for fiber compression failure: Damage factor for transverse fiber tensile failure:

[0043] Damage factor for transverse fiber compression failure:

[0044] In the formula, , , , , , They are respectively the tensile stress in the fiber X direction, the tensile stress in the Y direction, the tensile stress in the Z direction, the shear stress in the fiber XY direction, the shear stress in the fiber XZ direction, and the shear stress in the fiber YZ direction; is the tensile strength of the fiber in the axial direction (X direction), is the fiber axial (X direction) compressive strength, is the fiber transverse (YZ direction) tensile strength, is the fiber transverse (YZ direction) compressive strength, , They are the shear strength of the fiber in the XY, XZ, and YZ directions respectively.

[0045] The elastic modulus after fiber failure is determined by Matzenmiller's progressive stiffness degradation method based on damage factor. The formula is as follows:

[0046]

[0047]

[0048] Where: , , is the modulus of the fiber before failure, , , is the fiber modulus after failure; is the damage coefficient under different damage modes, and the calculation formula is as follows:

[0049] In the formula, m is the reduction factor, the default value is 0.2, is the damage factor corresponding to different failure modes, and e is a natural constant.

[0050] Step S10, setting mechanical boundary conditions, simulating the service behavior of the unit cell model under the mechanical boundary conditions, and obtaining a stress-strain curve in combination with the elastic modulus; like Fig. 9 As shown in Figure 1, under axial tensile load, the matrix stress is mainly concentrated in the area where the yarns are interlaced, and the inner surface stress is higher than the outer surface. In this case, the matrix fails first, and then the fiber fails. Based on the material parameters obtained in the experiment, the stress-strain curve of the composite cladding tube is predicted, as shown in Figure 1. Fig.10 As shown in the figure, the stress-strain curve and strength value obtained by simulation are in good agreement with the overall trend of the actual experimental results.

[0051] Step S11, obtaining the strength of the tubular component according to the stress-strain curve.

[0052] The above are only preferred embodiments of the present application, and are not intended to limit the patent scope of the present application. Any equivalent structure or equivalent process transformation made using the contents of the present application specification and drawings, or directly or indirectly applied in other related technical fields, are also included in the patent protection scope of the present application.

Claims

1. A modeling method for a SiC / SiC composite tubular component, characterized in that: include: The helix equation about the braiding angle is established by combining the cylindrical helix equation and the exponential elliptic wave equation. The helical line equation is used to fit the braiding path of a single fiber; establishing a first spiral fiber and a second spiral fiber according to a braiding path of the single fiber; Wherein, the spiral directions of the first spiral fiber and the second spiral fiber are opposite; The first spiral fiber and the second spiral fiber are respectively translated and copied along the axial direction of the tubular component to obtain a prefabricated model of the tubular component.

2. The modeling method of the SiC / SiC composite tubular component according to claim 1, characterized in that: After obtaining the prefabricated model of the tubular component, the method comprises: When it is determined that interference exists inside the preform model of the tubular component, the sizes of the first spiral fiber and the second spiral fiber are adjusted, and the first spiral fiber and the second spiral fiber are translated and replicated along the axial direction of the tubular component again until there is no interference inside the preform model of the tubular component.

3. The modeling method of a SiC / SiC composite tubular component according to claim 1, characterized in that: The helix equation is: In the formula, is the braiding angle, h is the fiber bundle thickness, ω is the fiber bundle width, c is the spacing between fiber bundles, p is the bending coefficient, r0 is the inner diameter of the preform model, x tow is the x-coordinate in the exponential elliptical wave equation, β is a period of length 2π, and θ is the inclination angle of the current point relative to the starting point.

4. A method for predicting the strength of a SiC / SiC composite tubular component, characterized in that: The prefabricated body model of the tubular component is obtained by the modeling method of the SiC / SiC composite tubular component according to any one of claims 1 to 3, comprising: Establishing a matrix model, performing Boolean operations on the matrix model and the prefabricated body model to obtain an initial unit cell model; Meshing the initial unit cell model; Set boundary conditions and reduce the size of the initial unit cell model after meshing to obtain a unit cell model; determining a damage factor of the material of the tubular component, and determining an elastic modulus after fiber failure according to the damage factor; Performing a service behavior simulation on the unit cell model and obtaining a stress-strain curve in combination with the elastic modulus; The strength of the tubular component is obtained according to the stress-strain curve.

5. The strength prediction method of SiC / SiC composite tubular component according to claim 4, characterized in that: The rotation angle of the base model is determined according to the rotation period of the preform model and the number of braided fibers, and the axial length of the base model is determined according to the rotation angle, the inner diameter of the preform model and the braiding angle.

6. The strength prediction method of SiC / SiC composite tubular component according to claim 4, characterized in that: The boundary conditions include relative displacement boundary conditions of two symmetrical surfaces in the unit cell model.

7. The strength prediction method of SiC / SiC composite tubular component according to claim 6, characterized in that: The relative displacement boundary conditions of the two symmetrical surfaces include the axial relative displacement boundary conditions of the two side wall surfaces and the circumferential relative displacement boundary conditions of the two end surfaces: the relative displacements of the two side wall surfaces in the axial, radial and thickness directions in the unit cell model are equal to the product of the axial length of the unit cell and the axial macroscopic equivalent displacement, and the relative displacements of the two end surfaces in the axial, radial and thickness directions in the unit cell model are zero.

8. The strength prediction method of SiC / SiC composite tubular component according to claim 4, characterized in that: The boundary conditions also include that the displacement of any vertex in the unit cell model in the axial, radial and thickness directions is zero.

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