A method for predicting the fracture toughness of graphene and whisker synergistically strengthened ceramic composites

Abstract

A method for predicting the fracture toughness of graphene and whisker synergistically strengthened ceramic composites is proposed. Based on whisker and graphene modeling methods, two-dimensional structural models of whiskers and graphene are sequentially embedded in the ceramic composite matrix to generate the required whisker / graphene / ceramic composite model. A fracture toughness prediction model for the whisker / graphene / ceramic composite is constructed. This model is then imported into Abaqus software to configure material parameters and boundary conditions, and fracture toughness simulation is performed. Finally, the maximum fracture load is extracted, and the fracture toughness of the whisker and graphene synergistically strengthened ceramic composite is calculated using a novel fracture toughness calculation method, thus completing the fracture toughness prediction. This invention can quickly model graphene, whiskers, and the ceramic matrix, efficiently and accurately predict the optimal content of graphene and whiskers, as well as the fracture toughness of the ceramic composite, providing an effective aid to experimental methods.

Description

TECHNICAL FIELD

[0001] The present application relates to the technical field of ceramic composite materials, and particularly relates to a method for predicting the fracture toughness of a graphene and whisker synergistically toughened ceramic composite material. BACKGROUND

[0002] Si3N4 and SiC as representative ceramic materials have been widely used in aerospace, machine tools, high-speed rail and nuclear power and other high-end equipment fields due to their low density, high strength, high temperature resistance, wear resistance and electrical insulation and other characteristics. However, in a complex working environment, the inherent brittleness of ceramic materials becomes a key factor restricting the long-term stable service of high-end equipment. Therefore, improving the toughness of ceramic materials is an important technical approach to solve the above-mentioned bottleneck, which has important significance for the quality and efficiency of tens of thousands of major high-end equipment.

[0003] To improve the toughness of ceramic materials, so far, various toughening technologies such as nanoparticle toughening, fiber toughening, phase transformation toughening and whisker toughening have been developed. Among them, graphene and whisker toughening is considered to be an effective means to solve the toughness deficiency of ceramic materials. For example, studies have shown that a small amount of graphene and whisker doped in Si3N4, SiC and Al2O3 ceramic matrix can significantly improve the strength and toughness of ceramic materials. However, the research on graphene and whisker synergistically toughened ceramic composites mainly relies on experimental methods. In order to obtain the optimal component content and mechanical properties of graphene and whisker, a large number of samples need to be prepared and a large number of experiments need to be carried out. This process is long, low in efficiency, and has great blindness, and some powders in the sample preparation have certain pathogenicity. Therefore, a simulation method that can improve experimental efficiency and purpose and reduce exposure to dangerous powders has become a development trend. At present, the patent application with the patent number CN114913930A only constructs a molecular dynamics model for solving the Si3N4 / TiC interfacial bonding energy, and has not realized the modeling of the microstructure of the multiphase ceramic material; the patent application with the registration number 2013SR111566 mainly realizes the nanoparticle and single reinforcing phase toughened ceramic material, and does not realize the modeling of the multiphase ceramic composite material; the calculation of the fracture toughness (K IC ) is currently mainly based on the extended finite element method, which has a complex calculation process. Therefore, how to realize the modeling of the multiphase reinforcing phase, especially the modeling of the graphene and whisker synergistically toughened ceramic composite material and the more simple fracture toughness prediction has become an urgent problem to be solved. SUMMARY

[0004] In view of the problems existing in the prior art, the purpose of the present application is to provide a method for predicting the fracture toughness of a graphene and whisker synergistically toughened ceramic composite material, which can quickly realize the modeling of graphene, whisker and ceramic matrix, efficiently and accurately predict the optimal content of graphene and whisker and the fracture toughness of the ceramic composite material, and form an effective aid to the experimental method.

[0005] To achieve the above objectives, the technical solution adopted by the present invention is as follows:

[0006] A method for predicting the fracture toughness of graphene and whisker synergistically strengthened ceramic composites includes the following steps:

[0007] (1) Modeling of ceramic composites synergistically toughened by whiskers and graphene:

[0008] Based on the Delaunay triangulation method, the required ceramic composite matrix is ​​constructed; based on the whisker and graphene modeling method, two-dimensional structure models of whiskers and graphene are embedded in the ceramic composite matrix in sequence to generate the required whisker / graphene / ceramic composite model.

[0009] Specifically:

[0010] ① Ceramic composite matrix: Construct a model with length and width B and width H as the random seed distribution range, and use the pseudo-random function (rand()) in Matlab to generate a random seed P in the space of B×H. k This process involves forming a finite set of points in the two-dimensional real number field; then, generating a Delaunay triangulation network based on the Bowyer-Watson algorithm; finally, using the Delaunay triangulation method, generating a polygon set R. k This set represents the ceramic composite matrix, and the average value of the ceramic composite matrix is ​​controlled by controlling the number of seeds sprinkled.

[0011] ② Whisker / ceramic composite material: Based on the model in step ①, the pseudo-random function (rand()) in Matlab is used to generate a matrix with length and width of B. w and H w The rectangle is used to represent the two-dimensional model of the whisker. Boolean operation is performed on the two-dimensional model of the whisker and the model in step ① to generate the whisker / ceramic composite material model. The ratio of the area of ​​the two-dimensional model of the whisker to the total area of ​​the ceramic composite matrix represents the whisker content value.

[0012] ③ Whisker / graphene / ceramic composite material: Based on the model in step ②, randomly select n adjacent polygonal edges, with a total length of L. M Based on this, the corresponding line segment L is generated by offsetting. M’ Connecting line segment L M and L M’ This is used to characterize a two-dimensional graphene model with a certain thickness. Boolean operations are performed on the two-dimensional graphene model and the model in step ② to generate the required whisker / graphene / ceramic composite material model. The ratio of graphene length to the total length of polygon boundaries represents the graphene content value.

[0013] (2) Fracture toughness prediction model and calculation:

[0014] Based on the whisker / graphene / ceramic composite material model, a fracture toughness prediction model for whisker / graphene / ceramic composite materials was constructed. The fracture toughness prediction model for whisker / graphene / ceramic composite materials was imported into Abaqus software to configure material parameters and boundary conditions, and to carry out fracture toughness simulation. Finally, the maximum fracture load was extracted, and the fracture toughness of the whisker and graphene synergistically toughened ceramic composite material was calculated according to a novel fracture toughness calculation method, thus completing the prediction of fracture toughness.

[0015] Specifically:

[0016] ① Fracture toughness prediction model: Based on the whisker / graphene / ceramic composite material model, two fixed rigid support points with a span of l and symmetrical to the center of the model are established at the bottom of the model. Then, a crack with a length of a is prefabricated at the middle position of the bottom of the model, and a load with a velocity of v is applied at the middle position of the upper part of the model.

[0017] ② Fracture toughness calculation: Fracture toughness simulation is carried out using the three-point bending method, and the maximum fracture load F in the simulation results is extracted. max Substitute into the fracture toughness calculation formula K IC =g[10 -6 F max l / (bH 3 / 2 )][1.5(a / H) 1 / 2 / (1-a / H) 3 / 2 In the calculation of the fracture toughness K of the synergistic toughening of whisker and graphene ceramic composite materials, the following is performed. IC Where b is the thickness of the model established in ①, and for a two-dimensional model, b is taken as 1;

[0018] g=1.9472-5.0247(a / H)+11.8954(a / H) 2 -18.0635 (a / H) 3 +14.5986 (a / H) 4 -4.6896(a / H)

[0019] Finally, based on the above fracture toughness calculation formula, the fracture toughness of the synergistic toughening ceramic composite material of whiskers and graphene can be predicted.

[0020] The innovative aspects of this invention:

[0021] By using the Delaunay triangulation method to generate polygon sets, modeling of ceramic composites synergistically toughened by whiskers and graphene was achieved. This method and the generated model are simpler and can quickly and accurately predict the fracture toughness of ceramic composites, thereby obtaining the optimal content of whiskers and graphene. The prediction results are in strong agreement with the experimental results. Attached Figure Description

[0022] Figure 1 This is a schematic diagram of the modeling process for the synergistic toughening of the whisker and graphene ceramic composite material of the present invention.

[0023] Figure 2 This is a schematic diagram of the fracture toughness model of the ceramic composite material synergistically toughened by whiskers and graphene according to the present invention.

[0024] Figure 3 This is a schematic diagram illustrating the optimal content of whiskers and graphene in this invention, as well as the prediction and experimental verification of the fracture toughness of the ceramic composite material. Detailed Implementation

[0025] To achieve rapid and accurate prediction of fracture toughness of multi-reinforcing phases, especially whisker and graphene synergistic toughening ceramic composites, and to effectively assist experimental research and reduce the blindness, time consumption and hazards of experiments, this invention proposes a method for predicting the fracture toughness of whisker and graphene synergistic toughening ceramic composites. The invention will be further described in detail below with reference to the accompanying drawings.

[0026] A method for predicting the fracture toughness of whisker and graphene synergistically toughened ceramic composites includes the following steps:

[0027] (1) Modeling of ceramic composites synergistically toughened by whiskers and graphene:

[0028] ①Reference Figure 1 (a) Construct a model with length B and width H as the random seed distribution range, and use the pseudo-random function (rand()) in Matlab to generate a certain number of random seeds P within a rectangle of space B×H. k This forms a finite set of points in the two-dimensional real number field; then, a Delaunay triangulation is generated based on the Bowyer-Watson algorithm, referring to... Figure 1 (b); Finally, the Delaunay triangulation method is used to generate a polygon set R. k This set is a model diagram representing the ceramic composite matrix, referencing... Figure 1 (c). For Figure 1 The average particle size of the polygon in (c) can be controlled by controlling the number of seeds sown.

[0029] ② Based on the ceramic composite matrix model established in step ①, continue to use the pseudo-random function (rand()) in Matlab to establish a certain number of models with lengths and widths of B. w and H w A rectangle is used to represent the two-dimensional whisker model, and Boolean operations are used to merge the newly established two-dimensional whisker model with the ceramic composite matrix model to generate a whisker / ceramic composite model. Figure 1(d). The ratio of the total area of ​​the two-dimensional whisker model to the total area of ​​the ceramic composite model represents the whisker content.

[0030] ③ Randomly select n items, such as Figure 1 (d) shows the polygon with adjacent sides, the total length of all sides being L. M With L M Based on this, offset it by a certain distance to generate the corresponding line segment L. M’ Connecting line segment L M and L M’ This is used to characterize a graphene model with a certain thickness, as shown in 1(e). Then, a Boolean operation is performed between the graphene model and the whisker / ceramic composite material model established in step ② to generate the required whisker / graphene / ceramic composite material model, as shown in [reference 1]. Figure 1 (f) Total length of one side of graphene and Figure 1 (c) The ratio of the total length of the polygon boundary indicates the graphene content.

[0031] (2) Fracture toughness model and calculation:

[0032] ① Modeling of fracture toughness prediction model: Based on the modeling method in step (1), a model is constructed. Figure 2 The image shows a model of a ceramic composite material synergistically toughened with whiskers and graphene, with lengths and widths of B and H, respectively. (Refer to...) Figure 2 Two fixed rigid supports, symmetrical to the center of the model, are established at the bottom of the model, with a span of l between them. A crack of length a is prefabricated at the middle position of the bottom of the model, and a load of velocity v is applied at the middle position of the upper part of the model.

[0033] ② Fracture toughness calculation: Refer to Figure 2 Fracture toughness simulation was conducted using the three-point bending method. Then, the maximum fracture load F was extracted from the simulation results. max Incorporate it into the fracture toughness calculation formula K IC =g[10 -6 F max l / (bH 3 / 2 )][1.5(a / H) 1 / 2 / (1-a / H) 3 / 2 The fracture toughness of a ceramic composite material synergistically toughened by whiskers and graphene was calculated. Here, b represents the model thickness; for a two-dimensional model, b is set to 1. g = 1.9472 - 5.0247(a / H) + 11.8954(a / H) 2 -18.0635 (a / H) 3 +14.5986 (a / H) 4 -4.6896(a / H) 5Based on the above modeling and fracture toughness prediction formula, the fracture toughness of multi-reinforced phase ceramic composites can be predicted. Using the prediction results, the experimental workload can be reduced, and the purposefulness and time efficiency of experiments can be improved.

[0034] Fracture toughness test verification:

[0035] Taking the synergistic toughening of Si3N4 ceramic composite material by β-Si3N4 whiskers and graphene as an example, a β-Si3N4 whisker / graphene / Si3N4 ceramic composite material model was constructed according to step (1), and the fracture toughness of the β-Si3N4 whisker / graphene / Si3N4 ceramic composite material model was calculated according to step (2). See [link to relevant documentation]. Figure 3 Curve 2. Based on the graphene and β-Si3N4 whisker content in the β-Si3N4 whisker / graphene / Si3N4 ceramic composite material model, different samples were prepared and fracture toughness tests were conducted. The test results are shown in [reference]. Figure 3 Medium curve 1. Figure 3 In the results, curve 2 shows a good consistency with curve 1, and the predicted optimal content of graphene and β-Si3N4 whiskers is consistent with the experimental results. The average relative change between the predicted and experimental fracture toughness values ​​is 15.44%, indicating a strong consistency between the predicted and experimental results. This fully demonstrates the effectiveness and accuracy of the proposed method for modeling and predicting fracture toughness of ceramic composites with synergistic toughening of graphene and whiskers, thus solving the problem of modeling and rapidly predicting fracture toughness of multi-reinforcing phase toughened ceramic composites.

Claims

1. A method for predicting the fracture toughness of graphene and whisker synergistically toughened ceramic composites, characterized in that, Comprising the following steps: Step (1), modeling of whisker and graphene synergistically toughened ceramic composite material: Based on the Delaunay triangulation method, the required ceramic composite material matrix is constructed; based on the whisker and graphene modeling method, the whisker and graphene two-dimensional structure model is sequentially embedded in the ceramic composite material matrix to generate the required whisker / graphene / ceramic composite material model; Step (2), fracture toughness prediction model and calculation: Based on the whisker / graphene / ceramic composite material model, the fracture toughness prediction model of the whisker / graphene / ceramic composite material is constructed; the fracture toughness prediction model of the whisker / graphene / ceramic composite material is imported into the Abaqus software to carry out material parameter and boundary condition configuration, and to carry out fracture toughness simulation; finally, the maximum fracture load is extracted and the fracture toughness of the whisker and graphene synergistically toughened ceramic composite material is calculated according to the new fracture toughness calculation method, and the fracture toughness prediction is completed.

2. The method of fracture toughness prediction of graphene and whisker synergistically toughened ceramic composites according to claim 1, wherein Step (1) is specifically: ① Ceramic composite matrix: The length and width of the component are respectively B and H The model is used as the random seed distribution range, and pseudo-random functions in Matlab are used in the space. B × H Generate random seed internally P k First, a finite set of points is formed in the two-dimensional real number field. Then, a Delaunay triangulation is generated based on the Bowyer-Watson algorithm. Finally, a set of polygons is generated using the Delaunay triangulation method. R k This set represents the ceramic composite matrix, and the average value of the ceramic composite matrix is ​​controlled by controlling the number of seeds sprinkled. ②Whisker / ceramic composite material: based on the model of step ①, the pseudo-random function in Matlab is used to generate a rectangle with length and width of B w and H w to represent the two-dimensional model of the whisker, and the Boolean operation is performed on the two-dimensional model of the whisker and the model in step ① to generate the model of the whisker / ceramic composite material, and the total area ratio of the two-dimensional model of the whisker to the ceramic composite material matrix represents the whisker content value; ③ Whisker / graphene / ceramic composite material: based on the model of step ②, randomly select n a total length of L M , and the corresponding line segment is generated by offsetting L M’ , and the line segment L M and L M’ , which represents a two-dimensional model of graphene with a certain thickness. Perform a Boolean operation on the two-dimensional graphene model and the model in step ② to generate the required whisker / graphene / ceramic composite material model. The ratio of graphene length to total length of polygon boundary represents the graphene content value.

3. The method of fracture toughness prediction of graphene and whisker synergistically toughened ceramic composites according to claim 2, characterized in that, Step (2) is specifically: ① Fracture toughness prediction model: based on the whisker / graphene / ceramic composite material model, a new type of fracture toughness prediction model is constructed at the bottom of the model The model is symmetric to the model center and the span is l Two fixed rigid support points, then in the model bottom middle position pre length a The crack is applied to the upper middle position of the model with a load of v The speed is ② Fracture toughness calculation: the three-point bending method is used to carry out fracture toughness simulation, and the maximum fracture load is extracted from the simulation results Maximum breaking load F max , substituted into the fracture toughness calculation formula K IC = g [10 -6 F max l / ( bH 3 / 2 )][1.5( a / H ) 1 / 2 / (1- a / H ) 3 / 2 ] to calculate the fracture toughness of whisker and graphene synergistically toughened ceramic composite materials K IC ; wherein, b is the established model thickness, for a two-dimensional model, b is taken as 1; H is the width of the model; g =1.9472-5.0247( a / H )+11.8954( a / H ) 2 -18.0635( a / H ) 3 +14.5986( a / H ) 4 -4.6896( a / H ) 5 Finally, according to the above fracture toughness calculation formula, the fracture toughness of the whisker and graphene synergistically toughened ceramic composite material can be predicted.

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