High efficient composite random fiber generation method suitable for wide volume fraction range

Abstract

The present application relates to a kind of high-efficiency composite random fiber generation method suitable for wide volume fraction range, comprising: step (1) generates high volume fraction random fiber distribution, generates high volume fraction random fiber distribution by random sampling fiber center coordinates and fiber diameter in representative volume element model.Model.Step (2) random fiber encryption improves fiber volume fraction.When fiber volume fraction cannot meet the requirement of the required high volume fraction, the fiber volume fraction of random fiber is improved by fiber encryption, to reach the required high fiber volume fraction.Step (3) generates wide volume fraction range fiber distribution and finite element model, and the fiber distribution under any volume fraction can be obtained by randomly removing fiber, and the finite element model of representative volume element model under this volume fraction.The present application can be carried out subsequent finite element analysis by modifying fiber material properties, and significantly improves calculation efficiency.

Description

TECHNICAL FIELD

[0001] The application belongs to the technical field of aerospace engines, and particularly relates to a high-efficiency composite random fiber generation method suitable for a wide volume fraction range. BACKGROUND

[0002] Fiber-reinforced composite structures have been gradually applied to aerospace structures due to their lightweight and high-strength material properties. Fiber-reinforced composites include fibers, matrices, interfaces, and other key components. The processing of these components results in significant randomness in the fibers, which has a significant impact on the strength and fracture performance of the composite materials. Therefore, it is necessary to develop random fiber generation technology based on the microstructure characteristics of composite materials and establish a random fiber distribution model suitable for a wide volume fraction range, thereby supporting the prediction of the strength and fracture performance of composite materials.

[0003] At present, the random fiber generation method based on Monte Carlo sampling has been established: ① The existing literature "Buryachenko V A, Pagano N J, Kim R Y, et al. Quantitative description and numerical simulation of random microstructures of composites and their effective elastic moduli [J]. International journal of solids and structures, 2003, 40(1): 47-72." obtains random distribution by random sampling of fiber center position and diameter. However, studies have shown that the fiber volume distribution obtained by this method can only reach 54.7%, which cannot meet the demand of high fiber volume fraction fiber distribution. ② The Latin hypercube sequence expansion method established in the existing literature "Zhang L, Xu D, Zhang S F, et al. Effect of random fiber distribution on the longitudinal compression properties of composite materials [J]. Mechanical Strength, 2018, 40(4): 875-881." can realize high volume fraction fiber random distribution, but when the fiber volume fraction changes due to processing technology, the fiber needs to be regenerated by sampling and the finite element modeling needs to be re-meshed, which cannot meet the requirement of high efficiency calculation. In the aspect of invention patent, the existing invention patent "Unidirectional fiber reinforced composite material random fiber distribution generation method" (CN106295062A) proposes a high volume fraction random fiber generation method based on fiber generation by generation. The invention can realize high volume fraction fiber distribution, but the method samples in the whole area of the composite material cross section and does not consider the periodic boundary condition, which is only suitable for single cross section modeling and cannot be applied to RVE modeling. When applied to complex structures, the calculation amount is large and it is difficult to realize engineering application. As can be seen from the above, the existing fiber random distribution generation method cannot meet the demand of wide volume fraction and high efficiency of fiber random distribution in engineering. SUMMARY

[0004] In order to overcome the shortcomings of the prior art, the present application provides a high-efficiency composite material random fiber generation method suitable for a wide volume fraction range, which supports damage evaluation and design of aero-engine composite components.

[0005] In order to achieve the above purpose, the technical scheme adopted by the present application is as follows:

[0006] A high-efficiency composite random fiber generation method suitable for a wide volume fraction range, a high-volume fraction random fiber distribution is generated by random sampling, the fiber volume fraction is increased by random fiber densification to achieve the required high volume fraction, and a fiber distribution under any volume fraction is generated by randomly removing fibers on the basis of the generated high-volume fraction fiber fraction, including the following steps:

[0007] Step (1) generating a high-volume fraction random fiber distribution: generating a high-volume fraction random fiber distribution by randomly sampling fiber center coordinates and fiber diameters in a representative volume element model;

[0008] Step (2) increasing the fiber volume fraction by random fiber densification: When the fiber volume fraction obtained in step (1) cannot meet the required high volume fraction requirement, the random fiber volume fraction is increased by fiber densification to achieve the required high fiber volume fraction;

[0009] Step (3) generating a wide volume fraction range fiber distribution and a finite element model: For the fiber distribution obtained in step (2), a fiber distribution under any volume fraction is obtained by randomly removing fibers, and a representative volume element model finite element model under the volume fraction.

[0010] Further, the specific steps of step (1) are:

[0011] ① Randomly sample the center coordinates (x1, y1) of the first fiber in the central region of the representative volume element model, and randomly sample the diameter d1 of the first fiber.

[0012] ② Randomly sample the diameter d2 of the second fiber, establish a polar coordinate system with the center of the first fiber as the coordinate origin, and obtain the center coordinates (x1, y1) of the second fiber by randomly sampling the polar coordinate radius r and angle θ, wherein the polar coordinate radius sampling range is [0.5d1+0.5d2+l min ,0.5d1+0.5d2+l max ] and the angle sampling range is [0, 2π);

[0013] ③ If the newly generated fiber overlaps with the existing fiber, return to step ② to regenerate the fiber until there is no overlap between two fibers.

[0014] ④ If the newly generated fiber exceeds the boundary of the representative volume element model, the fiber exceeding the boundary is cut off and placed on the opposite boundary to ensure that the result meets the periodic boundary condition; if the fiber on the opposite boundary overlaps with the existing fiber or the minimum distance between the two fibers is less than l minIf necessary, return to step ② and regenerate fibers until no two fibers overlap and the minimum distance is greater than l. min ;

[0015] ⑤ Repeat steps ②-③ to generate the diameter d3 and center coordinates (x3, y3) of the third fiber;

[0016] ⑥ Repeat steps ②-④ until the first fiber can no longer generate new fibers;

[0017] ⑦ Repeat steps ②-⑤ for the i-th fiber to obtain the fiber diameter d. i and fiber center coordinates (x i ,y i ), where i = 2, 3, ...;

[0018] ⑧ Repeat steps ②-⑥ until no new fibers can be generated, obtain the number of fibers M, and calculate the fiber volume fraction V at this point. max1 .

[0019] Furthermore, the specific steps of step (2) are as follows:

[0020] ① Find the directly adjacent fiber for the i-th fiber, denoted as F. ij , where i = 1, 2, 3, ..., M; j = 1, 2, 3, ..., N; directly adjacent fibers indicate that the line connecting the fiber to the center of the i-th fiber does not pass through other fibers, and N represents the number of directly adjacent fibers;

[0021] ② Calculate the center distance Fd between the i-th fiber and its directly adjacent fiber. ij When Fd ij >l min +d i +d ij At that time, a new fiber is obtained by randomly sampling along the line connecting the i-th fiber and its directly adjacent fiber j, and the diameter dd is determined by randomly sampling the fiber diameter. k ;

[0022] ③ If the newly generated fiber overlaps with the existing fiber, return to step ② and regenerate the fiber until no two fibers overlap.

[0023] ④ If the newly generated fiber exceeds the boundary of the volume element model, the fiber exceeding the boundary is cut off and placed on the boundary opposite to the boundary, thus ensuring that the result satisfies the periodic boundary condition; if the fiber on the boundary opposite to the boundary overlaps with the existing fiber or the minimum distance between two fibers is less than l min If necessary, return to step ② and regenerate fibers until no two fibers overlap and the minimum distance is greater than l. min ;

[0024] ⑤ Repeat steps ②-④ until the i-th fiber can no longer generate new fibers, obtaining the number of newly added fibers K, at which point the fiber volume fraction V is obtained. max2 This is the maximum achievable fiber volume fraction; based on the fiber distribution obtained in step (2), finite element modeling and mesh generation are performed to obtain a representative volume element model finite element model, which is then used to calculate the subsequent strength performance.

[0025] Furthermore, the specific steps of step (3) are as follows:

[0026] ① Calculate the number of fibers to be removed, num. Remove num points as Scheme 1, and remove num-1 points as Scheme 2.

[0027] ② For Scheme 1 and Scheme 2, the optimal Latin hypercube method is used to generate num and num-1 points respectively within the representative volume element model;

[0028] ③ For points num and num-1 generated in step ②, determine the nearest fiber, which is the fiber that needs to be removed; if the nearest fibers are the same, select the second nearest fiber as the fiber that needs to be removed; and so on.

[0029] ④ Calculate the fiber volume fraction after removing fibers in step ③. The fiber volume fractions for Scheme 1 and Scheme 2 are denoted as V1 and V2 respectively. Choose the option with V... a The closest scheme will be used as the final fiber distribution scheme;

[0030] ⑤ Repeating steps ①-④ will yield the fiber distribution for any target volume.

[0031] Furthermore, in step (3), the specific method for generating a finite element model representing a wide volume fraction range is as follows: the fibers randomly removed in step (2) are assigned the properties of the matrix, and the finite element model is obtained directly.

[0032] The advantages of this invention compared to existing technologies are:

[0033] (1) The present invention can generate high volume fraction of composite random fibers, and the generation process is more computationally efficient and can obtain a higher fiber volume fraction compared with the Monte Carlo method.

[0034] (2) The present invention can generate random fibers of composite materials with a wide volume fraction range, and the generated random fiber distribution does not require re-finite element modeling. Subsequent finite element analysis can be performed by modifying the fiber material properties, which significantly improves the calculation efficiency. Attached Figure Description

[0035] Figure 1A flow chart of a high-efficiency composite random fiber generation method suitable for a wide volume fraction range according to the present application;

[0036] Figure 2 A schematic diagram of volume fraction random fiber generation; wherein (a) is a first fiber generation schematic diagram, (b) is a second fiber generation schematic diagram, and (c) is a third fiber generation schematic diagram;

[0037] Figure 3 A periodic boundary condition judgment method; wherein (a) is a schematic diagram of a fiber exceeding the boundary of a representative volume element model, and (b) is a schematic diagram of cutting off the fiber exceeding the boundary at the opposite boundary;

[0038] Figure 4 Increasing the volume fraction of random fibers by densification;

[0039] Figure 5 The highest fiber volume fraction that can be achieved by an embodiment of the present application. DETAILED DESCRIPTION

[0040] The technical solutions of the present application will be further described below with reference to the accompanying drawings.

[0041] As shown in the drawings, Figure 1 a high-efficiency composite random fiber generation method suitable for a wide volume fraction range according to the present application includes the following steps:

[0042] Step 1: Generate a high-volume fraction random fiber distribution.

[0043] First, assume that the fiber diameter D follows a normal distribution with a mean of d and a standard deviation of dsig, i.e. D ~ N(d, dsig 2 ), which is obtained by microscopic image statistics. The minimum distance between fibers is l min , which is determined by the interface layer thickness, and in the present application, the minimum distance l min = 0.07D / 2 is taken. The maximum distance between fibers is l max , and in the present application, the maximum distance l min = 0.08D / 2 is taken. The representative volume element (representative volume element model) has a cross-sectional size of L and W, and the coordinates of the four vertices in the representative volume element model are (0, 0), (L, 0), (0, W), and (L, W), respectively, and in the present application, L = 100 and W = 100 are taken for illustration. The specific steps are as follows:

[0044] ① Randomly sample the center coordinates (x1, y1) of the first fiber in the central region of the representative volume element model Figure 2(a)). The central region has an abscissa range of [0.45L, 0.55L] and a ordinate range of [0.45W, 0.55W]. Random sampling means uniform sampling within the abscissa and ordinate ranges. The diameter d1 of the first fiber is determined by random sampling of the fiber diameter.

[0045] ② The diameter d2 of the second fiber is determined by random sampling of the fiber diameter. Figure 2 (b) A polar coordinate system is established with the center of the first fiber as the origin. The coordinates (x1, y1) of the center of the second fiber are obtained by randomly sampling the polar radius r and angle θ. The sampling range of the polar radius is [0.5d1 + 0.5d2 + l]. min ,0.5d1+0.5d2+l max The angle sampling range is [0, 2π].

[0046] ③ If the newly generated fiber overlaps with the existing fiber, return to step ② and regenerate the fiber until no two fibers overlap.

[0047] ④ If the newly generated fiber exceeds the boundary of the volume element model, the fiber exceeding the boundary is cut off and placed on the boundary opposite to the boundary, thus ensuring that the result satisfies the periodic boundary condition. Figure 3 In (a), (b)); if the fiber on the boundary opposite to the boundary overlaps with the existing fiber or the minimum distance between the two fibers is less than l min If necessary, return to step ② and regenerate fibers until no two fibers overlap and the minimum distance is greater than l. min .

[0048] ⑤ Repeat steps ②-③ to generate the diameter d3 and center coordinates (x3, y3) of the third fiber. Figure 2 (c) in the middle.

[0049] ⑥ Repeat steps ②-④ until the first fiber can no longer generate new fibers.

[0050] ⑦ Repeat steps ②-⑤ for the i-th (i = 2, 3, ...) fiber to obtain the fiber diameter d. i and fiber center coordinates (x i ,y i ).

[0051] ⑧ Repeat steps ②-⑥ until no new fibers can be generated, obtain the number of fibers M, and calculate the fiber volume fraction at this point.

[0052] Step 2: Random fiber encryption increases fiber volume fraction, such as... Figure 4 As shown. When the fiber volume fraction V obtained in the first step max1When the required high fiber volume fraction cannot be met, the random fiber volume fraction is increased by densifying the fiber to achieve the desired high fiber volume fraction. The specific steps are as follows:

[0053] ① For the i-th (i = 1, 2, 3, ..., M) fiber, find its direct neighbor fiber, denoted as F. ij (j = 1, 2, 3, ..., N). Directly adjacent fibers are those whose line of connection to the center of the i-th fiber does not pass through any other fiber, and N represents the number of directly adjacent fibers.

[0054] ② Calculate the center distance Fd between the i-th fiber and its directly adjacent fiber. ij When Fd ij >l min +d i +d ij At that time, a new fiber is obtained by randomly sampling along the line connecting the i-th fiber and its directly adjacent fiber j, and the diameter dd is determined by randomly sampling the fiber diameter. k .

[0055] ③ If the newly generated fiber overlaps with the existing fiber, return to step ② and regenerate the fiber until no two fibers overlap.

[0056] ④ If the newly generated fiber exceeds the boundary of the volume element model, the fiber exceeding the boundary is cut off and placed on the boundary opposite to the boundary, thus ensuring that the result satisfies the periodic boundary condition; if the fiber on the boundary opposite to the boundary overlaps with the existing fiber or the minimum distance between two fibers is less than l min If necessary, return to step ② and regenerate fibers until no two fibers overlap and the minimum distance is greater than l. min .

[0057] ⑤ Repeat steps ②-④ until the i-th (i = 1, 2, 3, ..., M) fiber can no longer generate new fibers, and obtain the number of newly added fibers K, at which point the fiber volume fraction is obtained. V max2 This represents the maximum fiber volume fraction achievable by this method. This invention utilizes this method to obtain composite materials with a wide volume fraction range of 0–67% for random fiber distribution. Figure 5 As shown.

[0058] Based on the fiber distribution obtained in the second step, finite element modeling and mesh generation are performed to obtain a representative volume element model, which can be used for subsequent strength performance calculations.

[0059] Third step: generating fiber distribution of wide volume fraction range and finite element model. For the fiber distribution obtained in the second step, the fiber distribution under any volume fraction can be obtained by randomly removing fibers; at the same time, the properties of the removed fibers are assigned to the matrix, and the finite element model of the representative volume element model under any volume fraction can be obtained. Assuming that the target volume is V a The specific steps are as follows:

[0060] ① Calculate the number of fibers to be removed Where [ ] represents rounding up. The scheme one is recorded as removing num points, and the scheme two is recorded as removing num-1 points.

[0061] ② For scheme one and scheme two, num and num-1 points are generated in the range [0, L] x [0, W] of the representative volume element model by the optimal Latin hypercube method.

[0062] ③ For the num and num-1 points generated in step ②, the nearest fiber is determined, which is the fiber to be removed. If the nearest fibers are the same, the second nearest fiber is selected as the fiber to be removed. In this way.

[0063] ④ Calculate the fiber volume fraction after removing the fiber in step ③. The fiber volume fractions of scheme one and scheme two are respectively: And Select the scheme closest to V a as the final fiber distribution scheme.

[0064] ⑤ Repeating steps ①-④ can obtain the fiber distribution under any target volume, and the properties of the randomly removed fibers are assigned to the matrix, so that the finite element model can be directly obtained without re-meshing, effectively simplifying the calculation.

[0065] Those skilled in the art will readily understand that the above description is only a preferred embodiment of the present application and is not intended to limit the present application. Any modification, equivalent replacement and improvement made within the spirit and principle of the present application shall be included in the protection scope of the present application.

Claims

1. A method for generating random fibers in composite materials with high efficiency applicable to a wide volume fraction range, characterized in that, A high-volume-fraction random fiber distribution is generated through random sampling, and the fiber volume fraction is increased by random fiber densification to achieve the desired high volume fraction. Based on the generated high-volume-fraction fiber distribution, fiber distributions with arbitrary volume fractions are generated by randomly removing fibers. The steps include the following: Step (1) Generate a high volume fraction random fiber distribution: Generate a high volume fraction random fiber distribution by randomly sampling the fiber center coordinates and fiber diameter in the representative volume cell model; Step (2) Random fiber densification to increase fiber volume fraction: When the fiber volume fraction obtained in step (1) cannot meet the required high volume fraction, the random fiber volume fraction is increased through fiber densification to achieve the required high fiber volume fraction, including: ① Randomly sample the central coordinates of the first fiber in the central region of the representative volume element model. x 1, y 1) Random sampling means uniformly sampling within the range of the horizontal and vertical axes. For example, randomly sampling the fiber diameter to determine the diameter of the first fiber. d 1; ② Determine the diameter of the second fiber by randomly sampling the fiber diameter. d 2. Establish a polar coordinate system with the center of the first fiber as the origin, and then adjust the polar coordinate radius. r and angle θ The coordinates of the center of the second fiber were obtained by random sampling. x 1, y 1), where the sampling range of polar coordinate radius is The angle sampling range is ; ③ If the newly generated fiber overlaps with the existing fiber, return to step ② and regenerate the fiber until no two fibers overlap. ④ If the newly generated fiber exceeds the boundary of the volume element model, the fiber exceeding the boundary is cut off and placed on the boundary opposite to the boundary, thus ensuring that the result satisfies the periodic boundary condition; if the fiber on the boundary opposite to the boundary overlaps with the existing fiber or the minimum distance between two fibers is less than the boundary condition, the fiber will be removed from the boundary. l min If necessary, return to step ② and regenerate fibers until no two fibers overlap and the minimum distance is greater than 1. l min ; ⑤ Repeat steps ②-③ to generate the diameter of the 3rd fiber. d 3 and center coordinates (( x 3, y 3); ⑥ Repeat steps ②-④ until the first fiber can no longer generate new fibers; ⑦ Repeat steps ②-⑤ for the i-th fiber to obtain the fiber diameter. d i and fiber center coordinates ( x i , y i ), where i = 2, 3, ...; ⑧ Repeat steps ②-⑥ until no more new fibers can be generated, and obtain the number of fibers. M And calculate the fiber volume fraction at this time. V max1 ; Step (3) Generate fiber distribution and finite element model with a wide volume fraction range: For the fiber distribution obtained in step (2), fiber distribution with arbitrary volume fraction is obtained by randomly removing fibers, and a finite element model representing the volume element model with that volume fraction is generated, including: ① Calculate the number of fibers that need to be removed num Complete, remove num Let the points be denoted as Scheme 1, and remove... num The scheme with a value of -1 is designated as Scheme Two; ② For Scheme 1 and Scheme 2, the optimal Latin hypercube method is used to generate the model within the representative volume element range, respectively. num and num- 1 point; ③ Regarding the generation in step ② num and num -1 points are used to determine the nearest fiber, which is the fiber that needs to be removed; if the nearest fibers are the same, the second nearest fiber is selected as the fiber that needs to be removed; and so on. ④ Calculate the fiber volume fraction after removing fibers in step ③. The fiber volume fractions for Scheme 1 and Scheme 2 are denoted as follows: V 1 and V 2. Choose and V a The closest scheme will be used as the final fiber distribution scheme; ⑤ Repeat steps ①-④ to obtain the fiber distribution under any target volume.

2. The method for generating random fibers in high-efficiency composite materials applicable to a wide volume fraction range according to claim 1, characterized in that, The specific steps of step (2) are as follows: ① Regarding the first i The root fiber finds its directly adjacent fiber, denoted as... F ij ,in i =1,2,3,... M ; j =1,2,3,…, N Directly adjacent fibers indicate that the fiber is adjacent to the first fiber. i The line connecting the centers of the root fibers does not pass through other fibers. N Indicates the number of directly adjacent fibers; ②Calculate the first i Distance between the center of the root fiber and the center of the directly adjacent fiber Fd ij ,when At that time, in the i Root fiber and directly adjacent fiber j New fibers are obtained by random sampling along the line, and the diameter of the fibers is determined by random sampling. dd k ; ③ If the newly generated fiber overlaps with the existing fiber, return to step ② and regenerate the fiber until no two fibers overlap. ④ If the newly generated fiber exceeds the boundary of the volume element model, the fiber exceeding the boundary is cut off and placed on the boundary opposite to the boundary, thus ensuring that the result satisfies the periodic boundary condition; if the fiber on the boundary opposite to the boundary overlaps with the existing fiber or the minimum distance between two fibers is less than the boundary condition, the fiber will be removed from the boundary. l min If necessary, return to step ② and regenerate fibers until no two fibers overlap and the minimum distance is greater than 1. l min ; ⑤ Repeat steps ②-④ until the i-th fiber can no longer generate new fibers, and obtain the number of newly added fibers. K At this point, the fiber volume fraction V max2 This is the maximum achievable fiber volume fraction; based on the fiber distribution obtained in step (2), finite element modeling and mesh generation are performed to obtain a representative volume element model finite element model, and subsequent strength performance calculations are realized.

3. The method for generating random fibers in high-efficiency composite materials applicable to a wide volume fraction range according to claim 2, characterized in that, In step (3), the specific method for generating a finite element model representing a wide volume fraction range is as follows: the fibers randomly removed in step (2) are assigned the properties of the matrix, and the finite element model is obtained directly.

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