A modeling method of random arrangement continuous carbon fiber reinforced ceramic matrix composite

Abstract

The present application belongs to the technical field of discrete element modeling and numerical simulation, and provides a modeling method of randomly arranged continuous carbon fiber reinforced ceramic matrix composite material. The method comprises the following steps: (1) specifying a modeling area, setting the allowed volume fraction and relative error of carbon fibers in the model, and obtaining the radius and number of carbon fiber models; (2) randomly generating non-coincident carbon fiber end face center coordinates on a certain boundary surface of the modeling area; (3) generating a plurality of carbon fiber cylindrical particles that are bonded along the axial direction of the carbon fiber end face circle; (4) filling ceramic matrix particles; (5) assigning carbon fiber and ceramic matrix model parameters; (6) generating a specified fraction of randomly arranged continuous carbon fiber reinforced ceramic matrix material model. Compared with the sample generated by using an electron microscope photo, the modeling speed of the present application is faster, and the carbon fiber ceramic matrix model with different internal arrangements can be quickly generated. It has certain significance for studying the influence of internal carbon fiber arrangement on the mechanical properties of the material.

Description

Technical Field

[0001] This invention belongs to the field of discrete element modeling and numerical simulation technology, specifically relating to a modeling method for randomly arranged continuous carbon fiber reinforced ceramic matrix composite materials. Background Technology

[0002] Fiber-reinforced silicon carbide composites possess a range of advantages, including high strength, high modulus, high temperature resistance, oxidation resistance, corrosion resistance, radiation resistance, and creep resistance. As high-temperature resistant structures, they have broad application prospects in aerospace, nuclear energy, and other fields. Furthermore, the composition of fiber-reinforced silicon carbide composites is adjustable, making them highly designable and high-performance high-temperature resistant microwave absorbing materials. Therefore, fiber-reinforced silicon carbide composites have become one of the hot research topics both domestically and internationally in recent years.

[0003] Near-net-shape forming techniques are commonly used to fabricate ceramic matrix composites (CMCs), but secondary processing is still required to meet the dimensional accuracy and geometric tolerances of the final assembly. Due to the anisotropy, high hardness, and brittleness of CMCs, the material removal mechanism during processing differs from that of homogeneous materials, and the influence of surface integrity and fatigue performance also differs between the two. Many scholars both domestically and internationally have conducted extensive research on the processing mechanism, damage detection and characterization, surface integrity, and processing technology of CMCs. They have also incorporated special energy field processing technologies, introducing non-traditional processing techniques such as ultrasonic vibration, lasers, water jets, and electrical discharge machining to improve processing efficiency and quality. However, problems such as severe tool wear, low surface quality and processing efficiency, and difficulty in controlling processing damage still exist.

[0004] Rapidly generating randomly arranged continuous carbon fiber reinforced ceramic matrix materials by specifying a volume fraction is significant for studying the influence of the internal arrangement of carbon fibers on the mechanical properties of the material. Summary of the Invention

[0005] Purpose of the invention: This invention provides a modeling method for randomly arranged continuous carbon fiber reinforced ceramic matrix composites. It can quickly generate carbon fiber ceramic matrix models with a specified volume fraction and different internal arrangements through a uniform distribution algorithm, which is of certain significance for the study of continuous carbon fiber reinforced ceramic matrix materials with different carbon fiber distributions.

[0006] Technical solution: This invention includes the following steps:

[0007] (1) Select the required discrete element modeling area size in PFC3D software, set the volume fraction and relative error conditions of carbon fiber in the continuous carbon fiber reinforced ceramic matrix composite model, specify the range of the generation of the end face circle radius of the carbon fiber model, and calculate the number and radius of the carbon fiber model required to satisfy the specified volume fraction and relative error.

[0008] (2) Using the uniform distribution function in the Fish function library, the coordinates of the center of the carbon fiber end face circle are randomly generated with a specified boundary surface of the modeling area as the end face. The area of ​​the carbon fiber model end face circle is obtained by combining the obtained carbon fiber model radius, and the edge of the area of ​​each carbon fiber end face circle is left with at least the distance of one ceramic particle diameter.

[0009] (3) Generate multiple carbon fiber cylindrical particles along the axial direction of the carbon fiber end face, and set a linear parallel bond model between the carbon fiber cylindrical particles in contact, thereby bonding multiple carbon fiber cylindrical particles to form a continuous carbon fiber discrete element model.

[0010] (4) Within the selected modeling region and outside the generated carbon fiber discrete element model region, use the range fish function to generate densely arranged ceramic matrix spherical particles.

[0011] (5) Set up linear parallel bond contact models for ceramic-based spherical particles-spherical particles and ceramic-based spherical particles-carbon fiber cylindrical particles, and assign corresponding microscopic contact parameters to the particles;

[0012] (6) Finally, a discrete element model of a randomly arranged continuous carbon fiber reinforced ceramic matrix composite material that meets the required volume fraction and relative error conditions is generated.

[0013] The beneficial effects of this invention are as follows: This invention provides a modeling method for randomly arranged continuous carbon fiber reinforced ceramic matrix composites, which can quickly generate a discrete element model of continuous carbon fiber reinforced ceramic matrix with an error not exceeding a specified error value by specifying a volume fraction. It has certain significance for the influence of different carbon fiber arrangements on the mechanical properties of continuous carbon fiber reinforced ceramic matrix materials under the same volume fraction.

[0014] Further: In step (1), the volume fraction and relative error conditions of carbon fibers in the continuous carbon fiber reinforced ceramic matrix composite model are set. In the PFC3D software, the uniform distribution function in the fish function library is called to make the radius of the end face circle of the carbon fiber model. The value should be taken within a reasonable range, and the formula is:

[0015]

[0016] in, This is the minimum value generated for the end face radius of the carbon fiber model. The maximum value generated for the end face radius of the carbon fiber model. This is a uniform distribution function in the fish function library of PFC3D software, which randomly selects values ​​in the range of 0.0-1.0.

[0017] By combining the loop command, the appropriate end-face radius of the carbon fiber model and the appropriate number of carbon fiber models are calculated using formulas. This ensures that the generated randomly arranged continuous carbon fiber reinforced ceramic matrix material achieves a specified volume fraction within a specified error range. The formula is:

[0018]

[0019] in,

[0020] in, The number of carbon fiber models. for The value rounded to the nearest whole number. The length of the modeling region in the x-coordinate direction. The length of the modeling region in the y-coordinate direction. The length of the modeling region in the z-coordinate direction. For the specified volume fraction, For the allowable volume fraction error (when At that time, it is certain that the end face radius of the carbon fiber model can be found that satisfies the volume fraction and relative error conditions of the carbon fiber in the material model. Let be the radius of the end face circle of the carbon fiber model. This represents the axial length of the carbon fiber model.

[0021] The further beneficial effects mentioned above are: by specifying the volume fraction of different carbon fiber distribution models and controlling the volume fraction error range, a better fiber arrangement can be found to improve the mechanical properties and stability of the material.

[0022] Further: In step (2), the uniform distribution function in the Fish function library of PFC software is used to randomly generate the center coordinates of the carbon fiber model end face circle within a specified boundary surface of the area to be modeled. The distance between the center coordinates of the carbon fiber model end face circle and the boundary of the modeling area is at least the sum of the radius of the carbon fiber model end face circle and the diameter of the ceramic-based spherical particle, so that the carbon fiber is wrapped inside the material. The formula for randomly generating the center coordinates of the carbon fiber model end face circle is as follows:

[0023]

[0024] in, The center of the circle on the end face of the carbon fiber model is in the modeling area. Coordinates along the axial direction, For modeling area Length in coordinate direction Let be the radius of the circle at the end face of the carbon fiber model. The radius of the ceramic-based spherical particles is denoted as . This is a uniform distribution function in the fish function library of PFC3D software, which randomly selects values ​​in the range of 0.0-1.0.

[0025] Before generating the center of the next carbon fiber model end face circle, the loop command is used to determine the distance to the center of all already generated carbon fiber model end face circles. If the condition is met, the model is generated. The determination formula is as follows:

[0026]

[0027] in, The center of the next carbon fiber model end face circle is located in the modeling area. Coordinates in the direction of coordinates, The center of the next carbon fiber model end face circle is located in the modeling area. Coordinates in the direction of coordinates, The center of the circle on the end face of the generated carbon fiber model is located in the modeling area. Coordinates in the direction of coordinates, The center of the circle on the end face of the generated carbon fiber model is located in the modeling area. Coordinates in the direction of coordinates, Let be the radius of the end face circle of the carbon fiber model. denoted as the radius of the ceramic-based spherical particle.

[0028] When the number of generated carbon fiber model end face center coordinates reaches the number of carbon fiber models required to satisfy the specified volume fraction and relative error, the generation of carbon fiber model end face center coordinates will stop.

[0029] Further: In step (4), the rblock.inside instruction of the fish function library in PFC3D software is used to detect whether the ceramic-based spherical particles are inside the carbon fiber cylindrical particles. Combined with the range fish instruction for generating ceramic-based spherical particles, the generation range of ceramic-based spherical particles is made to be outside the carbon fiber cylindrical particles. Combined with the box instruction for generating ceramic-based spherical particles, the generation range of ceramic-based spherical particles is made to be within the required discrete element modeling area.

[0030] The further beneficial effects mentioned above are: the absence of ceramic matrix particles inside the carbon fiber model is conducive to the stability of the entire model and is also more in line with reality.

[0031] Further: In step (5), all contact models are assigned as Linear Parallel Bond contact models, and bond gap parameters are assigned respectively to emod, kratio, pb_emod, pb_kratio, pb_ten, pb_coh, dp_nratio, and firc between linear contacts of carbon fiber cylindrical particles and between contacts of ceramic-based circular particles.

[0032] The further beneficial effects mentioned above are: more effectively simulating the forces generated by various adhesions and particle contacts within the material, which is beneficial for studying the influence of internal particle arrangement on mechanical properties under certain conditions. Attached Figure Description

[0033] The accompanying drawings, which are included to provide a further understanding of embodiments of the invention and form part of this application, do not constitute a limitation thereof. In the drawings:

[0034] Figure 1 This is a flowchart of a modeling method for randomly arranged continuous carbon fiber reinforced ceramic matrix materials provided in an embodiment of the present invention;

[0035] Figure 2 This is an end view of a randomly arranged continuous carbon fiber reinforced ceramic matrix material according to an embodiment of the present invention;

[0036] Figure 3 This is a discrete element model diagram of a continuous carbon fiber reinforced ceramic matrix material randomly arranged according to an embodiment of the present invention;

[0037] Figure 4 This is a three-dimensional diagram of a randomly arranged continuous carbon fiber reinforced ceramic matrix material according to an embodiment of the present invention;

[0038] Figure 5 This is a cross-sectional view of a randomly arranged continuous carbon fiber reinforced ceramic matrix material according to an embodiment of the present invention. Specific implementation methods

[0039] To make the objectives, technical solutions, and advantages of the present invention clearer, the present invention will be further described in detail below with reference to the embodiments and accompanying drawings. The illustrative embodiments and descriptions of the present invention are only used to explain the present invention and are not intended to limit the present invention.

[0040] This invention provides a modeling method for randomly arranged continuous carbon fiber reinforced ceramic matrix composites, such as... Figure 1 As shown, it includes the following steps:

[0041] 1. In PFC3D software, select the required discrete element modeling region size, set the volume fraction and relative error conditions of carbon fibers in the continuous carbon fiber reinforced ceramic matrix composite model, specify the generation range of the end face circle radius of the carbon fiber model, and calculate the number and radius of the carbon fiber model required to satisfy the specified volume fraction and relative error.

[0042] 2. Using the uniform distribution function in the Fish function library, randomly generate the center coordinates of the carbon fiber end face circle with a specified boundary surface of the modeling area as the end face, and combine it with the obtained carbon fiber model radius to obtain the area of ​​the carbon fiber model end face circle, and ensure that the edge of the area of ​​each carbon fiber end face circle leaves at least the distance of one ceramic particle diameter.

[0043] 3. Generate multiple carbon fiber cylindrical particles along the axial direction of the carbon fiber end face, and set a linear parallel bond contact model between the contacting carbon fiber cylindrical particles to bond the multiple carbon fiber cylindrical particles into a continuous carbon fiber discrete element model.

[0044] 4. Within the selected modeling region and outside the region of the generated carbon fiber discrete element model, use the range fish function to generate densely arranged ceramic matrix spherical particles.

[0045] 5. Set up linear parallel bond contact models for ceramic-based spherical particles-spherical particles and ceramic-based spherical particles-carbon fiber cylindrical particles, and assign corresponding microscopic contact parameters to the particles;

[0046] 6. Finally, a discrete element model of a randomly arranged continuous carbon fiber reinforced ceramic matrix composite material that meets the required volume fraction and relative error conditions is generated.

[0047] Step 1 of this embodiment of the invention is specifically as follows:

[0048] 1-1. In PFC3D software, select the required discrete element modeling region size, and set the volume fraction of carbon fibers and relative error conditions in the continuous carbon fiber reinforced ceramic matrix composite model.

[0049] 1-2. In PFC3D, call the uniform distribution function from the fish function library to adjust the radius of the end face circle of the carbon fiber model. The value should be taken within a reasonable range, and the formula is:

[0050]

[0051] in, This is the minimum value generated for the end face radius of the carbon fiber model. The maximum value generated for the end face radius of the carbon fiber model. This is a uniform distribution function in the fish function library of PFC3D software, which randomly selects values ​​in the range of 0.0-1.0.

[0052] 1-3. In PFC3D software, use the loop command to input the radius of the end face of the carbon fiber model randomly obtained within a reasonable range in 1-2, and calculate the number of carbon fiber models. The formula is as follows:

[0053]

[0054] in, This represents the ideal number for the carbon fiber model. The length of the modeling region in the x-coordinate direction. The length of the modeling region in the y-coordinate direction. The length of the modeling region in the z-coordinate direction. For the specified volume fraction, Let be the cross-sectional radius of the carbon fiber model. This represents the axial length of the carbon fiber model.

[0055] 1-4. Since the number of carbon fibers can only be an integer, the rounded value of the carbon fiber model is calculated and substituted into the formula to obtain the error of the volume fraction under the conditions of the end face radius of the carbon fiber model obtained in 1-2 and the volume fraction of carbon fiber in the continuous carbon fiber reinforced ceramic matrix composite model set in 1-1. The formula is as follows:

[0056]

[0057] in, This represents the ideal number for the carbon fiber model. for The value rounded to the nearest whole number. The length of the modeling region in the x-coordinate direction. The length of the modeling region in the y-coordinate direction. The length of the modeling region in the z-coordinate direction. For the allowable volume fraction error, Let be the cross-sectional radius of the carbon fiber model. This represents the axial length of the carbon fiber model.

[0058] 1-5. If the allowable volume fraction error can be met, set the value of the end face radius of the carbon fiber model that satisfies the volume fraction and relative error conditions of carbon fiber in the material model as the end face radius of the carbon fiber model, and set the rounded value of the carbon fiber quantity as the number of carbon fiber models to be generated in the next step.

[0059] Step 2 of this embodiment of the invention is specifically as follows:

[0060] 2-1. Use the uniform distribution function from the fish function library in PFC3D software to randomly generate the coordinates of the center of the carbon fiber model's end face circle within a specified boundary surface of the modeling area. The distance between the center of the carbon fiber model's end face circle and the boundary of the modeling area should be at least the sum of the radius of the carbon fiber model's end face circle and the diameter of the ceramic-based spherical particle, ensuring the carbon fiber is encased within the material. The formula for randomly generating the center coordinates of the carbon fiber model's end face circle is as follows:

[0061] in, The center of the circle on the end face of the carbon fiber model is in the modeling area. Coordinates along the axial direction, For modeling area Length in coordinate direction Let be the radius of the circle at the end face of the carbon fiber model. The radius of the ceramic-based spherical particles is denoted as . This is a uniform distribution function in the fish function library of PFC3D software, which randomly selects values ​​in the range of 0.0-1.0.

[0062] 2-2. Before generating the center coordinates of the next carbon fiber model end face circle, use the loop command to determine the distance to the center of all already generated carbon fiber model end face circles. If the condition is met, then generate the next carbon fiber model end face circle. The determination formula is as follows:

[0063] in, The center of the next carbon fiber model end face circle is located in the modeling area. Coordinates in the direction of coordinates, The center of the next carbon fiber model end face circle is located in the modeling area. Coordinates in the direction of coordinates, The center of the circle on the end face of the generated carbon fiber model is located in the modeling area. Coordinates in the direction of coordinates, The center of the circle on the end face of the generated carbon fiber model is located in the modeling area. Coordinates in the direction of coordinates, Let be the radius of the end face circle of the carbon fiber model. denoted as the radius of the ceramic-based spherical particle.

[0064] 2-3. When the number of center coordinates of the end face circles of the generated carbon fiber model reaches the number of carbon fiber models required to satisfy the specified volume fraction and relative error, the generation of center coordinates of the end face circles of the carbon fiber model will stop.

[0065] Step 3 of this embodiment of the invention is specifically as follows:

[0066] 3-1. Call the loop instruction of the fish function library in PFC3D to generate multiple carbon fiber cylindrical particles along the axial direction based on the center of the end face circle of the generated carbon fiber model and the carbon fiber radius that meets the conditions.

[0067] 3-2. A linear parallel bond model is set between the contacting carbon fiber cylindrical particles to bond multiple carbon fiber cylindrical particles together to form a bond such as... Figure 3 The continuous carbon fiber discrete element model is shown.

[0068] Step 4 of this embodiment of the invention is specifically as follows:

[0069] 4-1. Define a function in PFC3D software that calls the rblock.inside instruction in the fish function library of PFC3D software to detect whether the ceramic-based spherical particles are inside the carbon fiber cylindrical particles. When the ceramic-based spherical particles are inside the carbon fiber cylindrical particles, the function output value is 1.

[0070] 4-2. In PFC3D software, the range fish command in sphere generation is used to make the generated range of ceramic-based spherical particles outside the area where the function value output in 4-1 is 1;

[0071] 4-3. In PFC3D software, use the box command in sphere generation. The length, width, and height of the box are equal to the length, width, and height of the discrete element modeling region. Fill the discrete element modeling region with ceramic matrix particles.

[0072] 4-4. Ultimately, the ceramic matrix particles are filled outside the carbon fiber cylindrical particles and within the required discrete element modeling area.

[0073] 4-5. Construct walls at the edge of the modeling region, with length, width, and height equal to the length, width, and height of the discrete element modeling region;

[0074] 4-6. Use the solve command in PFC3D software to make the particles densely arranged;

[0075] 4-7. The final result is as follows Figure 4 The diagram shows a discrete element model of a continuous carbon fiber reinforced ceramic matrix material.

[0076] Step 5 of this embodiment of the invention is specifically as follows:

[0077] All contact models are assigned the Linear Parallel Bond contact model, and bond gap parameters are assigned respectively to emod, kratio, pb_emod, pb_kratio, pb_ten, pb_coh, dp_nratio, and firc between linear carbon fiber contacts and between ceramic matrix particles.

Claims

1. A modeling method of randomly arranged continuous carbon fiber reinforced ceramic matrix composite, the modeling steps are as follows: (1) selecting the required discrete element modeling area size in PFC3D software, setting the volume fraction of carbon fiber in the continuous carbon fiber reinforced ceramic matrix composite model and the relative error condition, specifying the carbon fiber model end face circle radius generation range, calculating the required number and radius of carbon fiber models that meet the specified volume fraction and relative error; (2) using the uniform distribution function in the Fish function library of PFC3D software to randomly generate the carbon fiber model end face circle center coordinates within a specified boundary surface of the required modeling area, the distance between the carbon fiber model end face circle center coordinates and the boundary of the modeling area is at least the sum of the radius length of the carbon fiber model end face circle and the diameter length of the ceramic matrix spherical particle, so that the carbon fiber is wrapped inside the material, the formula for randomly generating the carbon fiber model end face circle center coordinates is as follows: wherein is the radius length of the end face circle of the carbon fiber model is the coordinate direction length of the modeling area is the coordinate direction length of the modeling area is the coordinate direction length of the modeling area is the radius length of the end face circle of the carbon fiber model is the radius length of the ceramic-based spherical particles is the uniform distribution function of the fish function library in the PFC3D software, which randomly takes values in the value range of 0.0-1.0; Before generating the center of the next carbon fiber model end face circle, the loop cycle instruction is used to judge the distance from all the generated carbon fiber model end face circle centers, and if the condition is met, the carbon fiber model end face circle is generated, the judgment formula is as follows: wherein, is the center of the end face circle of the next carbon fiber model in the modeling area is the coordinate of the coordinate direction, is the center of the end face circle of the next carbon fiber model in the modeling area is the coordinate of the coordinate direction, is the center of the end face circle of the carbon fiber model that has been generated in the modeling area is the coordinate of the coordinate direction, is the center of the end face circle of the carbon fiber model that has been generated in the modeling area is the coordinate of the coordinate direction, is the radius length of the end face circle of the carbon fiber model, is the radius length of the ceramic-based spherical particle; When the number of generated carbon fiber model end face circle center coordinates reaches the required number of carbon fiber models that meet the specified volume fraction and relative error, the generation of carbon fiber model end face circle center is stopped; (3) generating multiple carbon fiber cylindrical particles along the axial direction of the carbon fiber end face circle, and setting a linear parallel key contact model between the contacting carbon fiber cylindrical particles, so as to bond the multiple carbon fiber cylindrical particles to form a continuous carbon fiber discrete element model; (4) generating densely arranged ceramic matrix spherical particles in the selected modeling area outside the generated carbon fiber discrete element model area by using the range fish function; (5) setting the ceramic matrix spherical particle-spherical particle, ceramic matrix spherical particle-carbon fiber cylindrical particle linear parallel key contact model, and assigning the corresponding particle mesoscopic contact parameters; (6) finally generating a randomly arranged continuous carbon fiber reinforced ceramic matrix composite discrete element model that meets the required volume fraction and relative error condition.

2. The modeling method of randomly arranged continuous carbon fiber reinforced ceramic matrix composites according to claim 1, characterized in that: In the step (1), the uniform distribution function in the fish function library is called in the PFC3D software to make the end surface circle radius of the carbon fiber model The formula is: wherein, rmin is the minimum value of the radius of the end face circle of the carbon fiber model, rmax is the maximum value of the radius of the end face circle of the carbon fiber model, is a uniform distribution function of the fish function library in the PFC3D software, which randomly takes values in the value range of 0.0-1.0; Combined with the loop cycle instruction, the appropriate carbon fiber model end face circle radius and the appropriate number of carbon fiber models are calculated by the formula, so that the randomly arranged continuous carbon fiber reinforced ceramic matrix material generated meets the specified volume fraction and is within the specified error range, the formula is as follows: wherein wherein, is the number of carbon fiber models, is the number of carbon fiber models, is the rounded value, is the length of the modeling region in the x coordinate direction, is the length of the modeling region in the y coordinate direction, is the length of the modeling region in the z coordinate direction, is the specified volume fraction, is the allowed volume fraction error, when is the radius of the end face circle of the carbon fiber model that satisfies the volume fraction and relative error conditions of the carbon fiber in the material model, is the radius of the end face circle of the carbon fiber model, is the axial length of the carbon fiber model.

3. The modeling method of randomly arranged continuous carbon fiber reinforced ceramic matrix composites according to claim 1, characterized in that: In the step (4), the rblock.inside instruction of the fish function library in the PFC3D software is used to detect whether the ceramic matrix spherical particle is inside the carbon fiber cylindrical particle, combined with the range fish instruction for generating the ceramic matrix spherical particle, the ceramic matrix spherical particle generation range is outside the carbon fiber cylindrical particle, combined with the box instruction for generating the ceramic matrix spherical particle, the ceramic matrix spherical particle generation range is within the required discrete element modeling area.

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