CN111951907B - Method and system for predicting nonlinear conductivity characteristics of composite material - Google Patents

Method and system for predicting nonlinear conductivity characteristics of composite material Download PDF

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CN111951907B
CN111951907B CN202010829131.6A CN202010829131A CN111951907B CN 111951907 B CN111951907 B CN 111951907B CN 202010829131 A CN202010829131 A CN 202010829131A CN 111951907 B CN111951907 B CN 111951907B
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伍珈乐
卞星明
宋绪鹏
张依然
刘琳
林俊
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North China Electric Power University
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Abstract

A method and system for predicting nonlinear electrical conductivity characteristics of a composite material, characterized by: the method comprises the following steps: step 1: constructing a geometric model of the composite material; and 2, step: defining peripheral cubic units and internal geometric body area materials in the geometric model; and step 3: setting a boundary condition; and 4, step 4: solving a control equation; and 5: and (5) processing data to obtain the nonlinear conductivity characteristic of the composite material. The method can avoid unnecessary waste of time cost and material cost, improves the adaptability of the conventional random model, and improves the applicability of the calculation model.

Description

Method and system for predicting nonlinear conductivity characteristics of composite material
Technical Field
The present invention relates to a method and a system for predicting nonlinear electrical conductivity of a composite material.
Background
With the improvement of the voltage grade of an electric power system, the importance of the insulation problem of high-voltage electric power equipment and parts thereof is highlighted day by day, and the adoption of a nonlinear voltage-sharing material with the conductivity or dielectric constant changing along with the self-adaption of an external electric field at the key position of the equipment to replace the traditional insulation material is an effective solution.
The research aiming at the nonlinear conductivity characteristics of the composite material is mostly completed through experiments, the whole research period needs to go through the links of experiment design, equipment debugging, sample preparation, test operation, data processing and the like, a large amount of manpower and material resources need to be invested, even a large amount of trial experiments may exist, and unnecessary waste of time cost and material cost is caused. Therefore, a calculation method for predicting the nonlinear conductivity characteristics of the composite material is proposed and established to guide actual production.
At present, in the aspect of establishing a calculation method, a series of researches are carried out by scholars at home and abroad. In the prior art, as in the finite element simulation of dielectric properties of composite dielectrics (Motor and control bulletin, author: huang Zhipeng, etc.), random distribution of filler particles in a matrix is realized by programming, and the alternating current conductivity and dielectric properties of the composite material are calculated by simulation; the research on nonlinear conductivity characteristics and mechanism of polyethylene/inorganic filler composite materials (author: guo Wenmin) calculates the influence of filler concentration and particle size on the DC conductivity characteristics of the composite materials by establishing a random small sphere model simulation; the simulation analysis of dielectric properties under the mechanism of nonlinear insulating medium alternating electric field (author: chen Xin) establishes a random ellipsoid model considering that the shape of the filler is not ideal sphere in practice, and simulates and calculates the influence of the filler doping amount, space orientation, size and other factors on the conductance and dielectric properties of the material under the alternating electric field.
In combination with practical situation analysis, the above prior art has two main disadvantages: firstly, the shape of the filler in the existing method is not considered comprehensively, and only spherical and spheroidal fillers are considered; secondly, the conventional method is not fully considered about the filling scheme of the filler, and only the filling situation of the filler with a single type and a single size is considered. Aiming at the defects, the invention improves the adaptability of the conventional random model and improves the applicability of the calculation model.
Disclosure of Invention
The invention aims to improve the adaptability of the prior similar technology, and mainly aims to solve the two defects of the prior art:
1. the types of the fillers are not considered comprehensively, the actual fillers have different aspect ratios such as ceramic whiskers, carbon nanotubes and the like besides spherical and spheroidal fillers, and flaky materials such as boron nitride, graphene and the like, the existing prediction method assumes the uniform and ideal filler shapes as spherical and spheroidal fillers, cannot realize the prediction of the nonlinear conductivity characteristics of different types of filler filled composite materials, and has insufficient applicability;
2. the filling scheme is not considered comprehensively, for example, the experimental research on the interface and nonlinear conductivity characteristics of the micro-nano SiC/epoxy composite material (author: han Yong forest, etc.) in the prior art shows that the multi-size filler compound filling can effectively improve the conductivity of the composite material in a nonlinear region, the existing prediction method only considers the single-type and single-particle-size filler scheme, cannot realize the prediction of the nonlinear conductivity characteristics of the composite material filled by compounding fillers with different particle sizes or different-type fillers, and has insufficient applicability.
The invention adopts the following technical scheme:
a method for predicting nonlinear electrical conductivity characteristics of a composite material, characterized by: the method comprises the following steps: step 1: constructing a geometric model of the composite material; step 2: defining peripheral cubic units and internal geometric body area materials in a geometric model; and step 3: setting a boundary condition; and 4, step 4: solving a control equation; and 5: and processing data to obtain the nonlinear conductivity characteristic of the composite material.
The invention also discloses a control system for predicting the nonlinear conductivity characteristic of the composite material, which is characterized in that: the calculation method for predicting the nonlinear electrical conductivity characteristic of the composite material is included.
Has the beneficial effects that:
the method comprehensively considers that spherical, flaky and different aspect ratio fillers are possibly used in the actual preparation process of the composite material, can be used for predicting the conductivity characteristics of the composite material filled with more different types of fillers, and is more comprehensive;
the invention comprehensively considers the situations of the compound filling of the fillers with different particle diameters and the compound filling of different types of fillers, more conforms to the current experimental research trend and enlarges the application range of the method.
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FIG. 1 is a schematic diagram of voxel selection according to the present invention.
Fig. 2 is a schematic flow chart of the nonlinear conductance characteristic calculation model construction process of the present invention.
FIG. 3 is a flow chart of the method for establishing a randomly distributed geometric model according to the present invention.
FIG. 4 is a three-electrode conductance test system of the present invention.
FIG. 5 is a graph of measured conductance of an epoxy resin material of the present invention.
FIG. 6 is a graph of measured conductance characteristics of a silicon carbide material according to the present invention.
FIG. 7 is a diagram illustrating the setting of boundary conditions according to the present invention.
FIG. 8 is a geometric model of a silicon carbide/epoxy composite constructed in accordance with the present invention.
FIG. 9 is a curve for predicting the electrical conductivity of two different crystal forms of SiC/epoxy resin composite material according to the present invention.
FIG. 10 is a flow chart of the multi-voxel random distribution geometric model building method of the present invention.
FIG. 11 is a schematic view of a geometric model of a silicon carbide/epoxy resin composite material according to different compounding schemes of the present invention.
FIG. 12 is a graph showing the predicted electrical conductivity of a silicon carbide/epoxy resin composite material according to various embodiments of the present invention.
Detailed Description
The technical solutions in the embodiments of the present invention are clearly and completely described below with reference to the embodiments of the present invention, and the embodiments are only a part of the embodiments of the present invention, but not all of the embodiments.
The construction idea of the method for predicting the nonlinear electrical conductivity of the composite material is derived from the concept of Representative Voxel (RVE). As a whole, the electrical property of the composite material is statistically uniform as a continuous medium consisting of a plurality of material points, so that the macroscopic electrical property of the whole sample can be theoretically obtained by measuring only one selected volume unit containing enough microstructure information in the sample.
In general, a composite material sample prepared in a laboratory is a circular piece with a radius of 7cm and a thickness of 0.5cm, and when a geometric model is constructed, as shown in the circle of fig. 1 (a), a cubic unit with a three-dimensional size of 100 × 100 × 100 μm is selected as a representative voxel in the sample for subsequent calculation, and the voxel shape is shown in fig. 1 (b). On a macro scale, the cell size is small enough to be considered as a macro object particle; on a microscopic scale, the cell contains sufficient material information.
The calculation method aims at the prediction of the electric conductivity of the particle-filled composite material, and simultaneously considers the processes of high-speed stirring, particle dispersion and the like in the actual preparation process of the material, so that the particle random distribution model is considered to be closer to the actual internal condition of a composite material sample than the single particle filling model and the particle regular arrangement model, and is the optimal choice for representing voxel modeling.
Generally, the construction of the conductance characteristic prediction method comprises five steps, namely geometric model construction, regional material definition, boundary condition setting, control equation solving and data processing, and the flow is shown in fig. 2.
The above five steps will be further described in the following two parts of the conductivity prediction method of the filling composite material with different shapes and the conductivity prediction method of the compound filling composite material with different particle sizes.
Method for calculating nonlinear conductance of filling composite materials with different fillers
The first step of the nonlinear conductance prediction method for filling composite materials with different shapes is to establish a geometric model. In the preparation of the actual nonlinear conductive material, the possible filler types include zinc oxide ceramic microspheres, silicon carbide, graphene, carbon nanotubes, etc., and the fillers can be roughly divided into 3 types of spherical fillers, flaky fillers and fillers with different aspect ratios (i.e. aspect ratios) according to the shape division, and the specific summary is shown in table 1.
TABLE 1 classification of filler shapes in actual preparation
Figure 176515DEST_PATH_IMAGE001
The following is directed to constructing corresponding geometric models for fillers of different shapes summarized in table 1, and fig. 3 is a flow chart for establishing geometric models, where the flow chart includes 4 steps of inputting geometric parameters, randomly generating position control parameters, generating randomly distributed geometric bodies, determining positions of the geometric bodies, and determining the number of the geometric bodies, and the specific description is as follows:
step 1-1: the geometric parameters are input. Firstly, the side length of a cubic unit for simulating a polymer matrix is inputDIn μm. Then inputting the geometric parameters corresponding to the filling geometric bodies representing the inorganic filler, wherein the geometric parameters corresponding to filling models of fillers with different shapes are specifically summarized as shown in Table 2, and for spherical fillers, the parameter to be input is the spherical radiusRIn μm; for the sheet-like packing, the input parameter is the side length of the square sheetLAnd heightHIn μm; for fillers with different aspect ratios, the parameter to be input is the radius of the bottom surface of the fillerXAnd heightZThe dimensions of the geometric body used for the simulation of the inorganic filler were determined by setting the values of the parameters in table 2. The geometric parameters input here are not set arbitrarily, but are derived from the measurement of the actual size of the filler by a scanning electron microscope, for example, the common particle size of the α -type silicon carbide material is usually 5 μm, 10 μm, 28 μm, 40 μm, etc., the common edge length of the boron nitride microchip is usually 15 μm, 28 μm, etc., and the thickness is 1 to 2 μm; the aspect ratio, namely the ratio of height to radius of the silicon carbide whisker, namely the beta-type silicon carbide material is 20; the carbon nanotubes have an aspect ratio of 1000. Finally setting and predicting filling volume fractionVOL(in vol%) of the corresponding geometric figureNUMThe calculation formula is as follows
Figure 897346DEST_PATH_IMAGE002
（1）
Wherein, the first and the second end of the pipe are connected with each other,V base body Is the total volume of the peripheral cubic unitV Base body =D 3 Calculated in units of μm 3 ；V Base body Is the volume of a single geometric body and has the unit of mum 3 For the spherical filler is composed ofV Base body =4πR 3 Calculated as/3, the platy filler is composed ofV Base body =L 2 HCalculated to obtain fillers with different aspect ratiosV Base body =πX 2 ZAnd (4) calculating.
TABLE 2 geometric parameters to be input in the construction of filling models with different shapes of fillers
Figure 610219DEST_PATH_IMAGE003
Step 1-2: randomly generating position control parameters and generating a randomly distributed geometry. Random numbers are first generated using a random seed, from which control parameters for determining the position of the geometry are randomly generated. The position control parameters generated by the filling models with different shapes are specifically summarized in table 3, for spherical fillers, the problem of rotation angle does not need to be considered, and the position of a sphere can be determined only by determining the coordinates of the center of the sphere, so the generated control parameters are three-dimensional coordinates of the center of the sphere; for flaky fillers and fillers with different aspect ratios, besides the square starting vertex coordinates and central coordinates for determining positions need to be generated respectively, rotation angle control parameters need to be generated, and in the actual preparation process of the composite material, when no external force (such as electric field force and magnetic field force) acts, the flaky fillers and the fillers with different aspect ratios cannot be arranged in a single orientation. The values of the parameters in table 3 can determine the position and orientation of the geometric bodies in the cubic units used to model the inorganic filler. Based on the geometric parameters input in table 2 and the position control parameters generated in table 3, random placement of a specific geometric object can be achieved in the cubic unit.
TABLE 3 control parameters generated by filling models with different shapes of fillers
Figure 973067DEST_PATH_IMAGE004
Step 1-3: and determining the position of the geometric body. In the process of randomly throwing the geometric bodies, not every geometric body thrown into the device meets the requirement, and whether the geometric body thrown into the device newly meets the principle that the geometric bodies thrown into the device before and the geometric bodies thrown into the device newly meet the contact requirement or not and do not intersect with each other needs to be repeatedly judged. The judgment conditions for different geometries are different, and the intersection judgment conditions for fillers with different shapes are specifically summarized in table 4. For spherical fillers, only the distance between two spherical centers needs to be calculateddWhether the radius is less than two times of the spherical radius or not, and the calculation formula is as follows
Figure 805894DEST_PATH_IMAGE005
（2）
Wherein, the first and the second end of the pipe are connected with each other, (ii) (x 1 ，y 1 ，z 1 ) Is the sphere center coordinate of the sphere 1; (x 2 ，y 2 ，z 2 ) Is the sphere 2 center coordinate, ifd<2RIf the two balls are not in accordance with the rule, the two balls are crossed with each otherd>=2RThe two balls are judged to be in accordance with the principle. The flaky fillers and the fillers with different aspect ratios cannot simply judge whether the fillers are intersected by a coordinate distance, so that a mode of verifying whether the intersection of the geometric bodies is empty is adopted for judging: if the intersection of the two is empty, the two are not intersected; if the intersection of the two is not empty, the geometric bodies are judged to be intersected. The determination of whether the geometric body position meets the principle of contactability but non-intersection can be realized by using the table 4. The geometric bodies meeting the intersection condition in the table 4 do not meet the above-mentioned throwing principle, and need to be abandoned, at this moment, the step 1-2 needs to be returned to regenerate the position control parameters and the corresponding geometric bodies, and the step 1-3 is executed again until the newly generated geometric bodies and the geometric bodies thrown in before meet the contactable but non-intersecting principle, the newly generated geometric bodies are reserved, and the corresponding position control parameters are stored in the control parameter matrix.
TABLE 4 determination conditions for intersection of fillers of different shapes
Figure 448359DEST_PATH_IMAGE006
Step 1-4: and judging the number of the geometric solids. Reserving a geometric body meeting the release principle, and storing corresponding control parameters into a matrix; discarding the geometric bodies which do not meet the throwing principle, regenerating new control parameters and geometric bodies, and then judging the position; continuously repeating the above process by using a loop statement, and counting the number of generated geometric bodies conforming to the principle in real time, if the number of generated geometric bodies does not reach the number of geometric bodies preset in the step 1-1NUMThen it will return to and execute step 1-2 until it is reachedThe number of generated geometric solids reaches the preset number of geometric solidsNUMAnd then outputs the corresponding random geometric model.
And 4 steps are executed to realize the construction of the geometric model. In short, a cubic unit with a limited side length is used for simulating a polymer matrix in an actual composite material, such as epoxy resin, silicon rubber, low-density polyethylene and the like; randomly embedding geometric bodies with different shapes into the cubic unit to simulate the reinforced filling of particle type fillers, such as silicon carbide, boron nitride, zinc oxide and the like; the filling geometry is to be delivered in a manner that the filling geometry is randomly distributed and can contact each other but not intersect each other.
After the geometric model is constructed, a second step of constructing a nonlinear conductance prediction method, namely region material definition, is carried out, wherein the second step comprises two steps of setting a matrix region material and setting a filler region material, and the specific description is as follows:
step 2-1: and setting the material of the base area. Firstly, according to the type of a polymer matrix in the composite material to be predicted, material parameters are set for a cubic unit area in the geometric model obtained in the first step, and the two input material parameters are the relative dielectric constant and the conductivity of the polymer matrix to be simulated respectively.
It should be noted that, in order to ensure that the prediction result is more real and effective, the two input parameters are obtained by experimental tests on specific material samples. Wherein, the relative dielectric constant of the specific material sample can be obtained by actual measurement of a dielectric constant tester, for example, the measured value of the epoxy resin material is 2.3, and the measured value of the silicon rubber material is 4.3; unlike the relative dielectric constant, the conductivity of a polymeric material cannot be simply characterized by a fixed value due to the presence of impurities, but rather by a continuous curve, commonly referred to as the conductivity curve. The conductance profile of a particular material sample was obtained using a three-electrode conductance test system as shown in fig. 4, with the specific experimental operation of placing a high voltage electrode connected to a dc voltage source against the top of the material sample for applying a stepped-up dc high voltageU(ii) a The lower surface of the sample is a measuring electrode, and a metal plate for placing the sample is connected with a picoammeter by a test wire and is grounded for measuring eachValue of current flowing through sample at voltage pointIObtained by testingU、IThe value is calculated by the formula (3) to obtain the electric field intensityEElectrical conductivity ofγ Material Will beE、γ Material Drawing the conductivity characteristic curve of the material sample in one-to-one correspondenceγ Material (E) And performing exponential fitting on the curve to obtain a functional relation, namely the conductivity of the polymer material needing to be input.
Figure 366636DEST_PATH_IMAGE007
（3）
Wherein the content of the first and second substances,Lis the material sample thickness;Sis the surface area of the portion of the material sample in contact with the bottom metal plate.
Fig. 5 shows that the function relation (4) of the conductivity of the epoxy resin material and the electric field intensity is obtained by performing exponential fitting on the conductance characteristic curve of the epoxy resin material actually measured in the laboratory by using the three-electrode system according to the experimental operation in the second step 2-1. If the matrix material to be simulated is an epoxy resin material, the cubic unit area is only required to input the material with the relative dielectric constant of 2.3 and the conductivity input of the expression in the expression (4)γ Epoxy resin And (4) finishing.
Figure 533175DEST_PATH_IMAGE008
（4）
In the above, by taking the simulation of the epoxy resin matrix material as an example, if it is desired to simulate other types of matrix materials, the setting of the step 2-1 on the matrix area material can be completed only by inputting the relative dielectric constant measured value and the conductivity fitting expression of the corresponding matrix material instead.
Step 2-2: and setting the material of the filler area. And (3) according to the type of the inorganic filler in the composite material to be predicted, setting material parameters of the internal geometric body area in the geometric model obtained in the first step, wherein the input material parameters are the relative dielectric constant and conductivity measured value of the inorganic filler to be simulated, the experimental measurement method is the same as the polymer matrix material test method described in the step 2-1, and the test sample is only required to be replaced by the inorganic filler sample to be simulated in the experimental process, which is not repeated herein.
Fig. 6 shows a conductance characteristic curve of the silicon carbide material obtained by actual measurement using the three-electrode system, and the function equation (5) of the conductivity of the silicon carbide material and the electric field intensity can be obtained by performing exponential fitting on the curve. If the inorganic filler to be simulated is the silicon carbide material, the measured value of the relative dielectric constant of the silicon carbide material is only required to be input into the geometric body area and 10 is input into the fitting relational expression of the conductivityγ Silicon carbide And (4) finishing.
Figure 968311DEST_PATH_IMAGE009
（5）
In the above, for example, the silicon carbide filler is simulated, and if it is desired to simulate other types of filler materials, the setting of the filler region material in step 2-2 can be completed only by inputting the relative permittivity measured value and the conductivity fitting expression of the corresponding filler.
The definition of the zone material can be realized by performing the above 2 steps. In short, materials are respectively defined for corresponding geometric regions according to the polymer matrix type (such as epoxy resin, silicon rubber and cross-linked polyethylene) and the filler type (such as silicon carbide and zinc oxide) of the composite material to be simulated, and a relative dielectric constant measured value and a conductivity fitting expression corresponding to the material to be simulated are input.
After the material definition is completed, the third step of nonlinear conductance prediction model construction, namely boundary condition setting, is carried out. The schematic diagram of boundary condition setting is shown in fig. 7, which includes 3 steps of applying excitation, setting ground and setting electrical isolation, and is described as follows:
step 3-1: an excitation is applied. As shown in FIG. 7, a DC voltage which was stepped up in steps of 100V was applied to the upper surface of the moldUThe voltage amplitude range is 0-1kV.
Step 3-2: and (4) setting the grounding. As shown in FIG. 7, the lower surface potential holding of the model was setU 0 And =0, i.e. the analog ground state.
Step 3-3: an electrically insulating arrangement. As shown in fig. 7, the peripheral surface of the mold is set to pass no current, i.e., to maintain an electrically insulated state.
And (3) completing the 3 steps to complete the setting of boundary conditions, and aiming at carrying out equivalence on experimental environments and simulating the actual measurement of the conductivity characteristics of the composite material in a computer.
And then, carrying out the fourth step of constructing a nonlinear conductance prediction model, namely solving a control equation, wherein the fourth step comprises 3 steps of electric field intensity calculation, current density calculation and conductivity calculation.
Step 4-1: and calculating the electric field intensity. Sequentially calculating the electric field intensity acting on the whole cubic model under different direct current voltages applied in the step 3-1 of the third stepE
Figure 296524DEST_PATH_IMAGE010
（6）
Wherein the content of the first and second substances,Dis the distance between the upper and lower plates, i.e. the side length of the cubic unit representing the polymer matrix as set in the first step, step 1-1.
Step 4-2: and (4) calculating the current density. Current density flowing through the interior of the model under the action of DC voltageJCan be obtained by solving differential equations including Poisson's equation, current continuity equation and auxiliary equation
Figure 967677DEST_PATH_IMAGE011
（7）
Wherein, firstly, the electric field intensity in the model is obtained by solving the formula 1 Poisson equation in (7)E ’ ，φIs an electric potential;γ material The material conductivity expression obtained by actual measurement in the steps 2-1 and 2-2 is obtained, and the specific expression is changed according to the type of the material; the obtained internal electric field intensityE ’ Substituting into parallel simultaneous solution current continuity equation (formula 2) and auxiliary equation (formula 3) to obtain current densityJ。
Step 4-3: and (6) calculating the conductivity.The conductivity of the entire composite model can be calculated by the following equation
Figure 423060DEST_PATH_IMAGE012
（8）
Wherein the content of the first and second substances,σi.e. the predicted conductivity value. During solving, the corresponding conductivity at each voltage point needs to be calculated in sequence, a conductivity characteristic curve of the composite material can be drawn through post data processing, and two key parameters for representing the nonlinear conductivity characteristic of the material can be further obtained: threshold electric field and nonlinear coefficient.
After the 3 steps are executed, the solution of the control equation can be realized, and then the fifth step of constructing the nonlinear conductance prediction model, namely data processing, is carried out, wherein the fifth step comprises 3 steps of log-log coordinate drawing, threshold electric field calculation and nonlinear coefficient calculation.
Step 5-1: and (5) drawing a log-log coordinate. And (4) correspondingly drawing the conductivity and electric field data which are obtained by calculation in the fourth step and correspond to each voltage point in a log-log coordinate graph one by one, wherein the drawn curve is the nonlinear conductivity characteristic curve of the composite material to be predicted.
Step 5-2: and calculating a threshold electric field. The nonlinear conductivity characteristic curve of the composite material is in a form of intersection of two straight lines, the left side of the intersection point is called as an ohmic region, and the influence of an electric field on the conductivity of the composite material in the region is small; the right side of the intersection point is called a nonlinear region, and the conductivity of the material in the region is increased sharply with the increase of an external electric field; the abscissa value corresponding to the intersection point of the two straight lines is the threshold electric field value of the composite material.
Step 5-3: and calculating a nonlinear coefficient. The prior art studies show that, as the prior art: research on epoxy resin surface charge accumulation and inhibition method based on high-voltage direct current GIS basin-type insulator substrate (Tianjin university, 2019, author: li Ang) on composite material conductivityσAnd the electric field intensityEHas the following functional relationship
Figure 230479DEST_PATH_IMAGE013
（9）
Wherein the content of the first and second substances,αis connected with electricityA coefficient related to;βnamely the nonlinear coefficient of the material, and represents the change of the direct current conductance along with the applied electric field. Taking the logarithm based on 10 from both sides of the pair formula (9) at the same time, have
Figure 995173DEST_PATH_IMAGE014
（10）
It can be seen that the slope of the straight line in the nonlinear region (i.e. the straight line on the right side of the intersection point) is the nonlinear coefficient of the composite materialβThe calculation formula is as follows:
Figure 638775DEST_PATH_IMAGE015
（11）
wherein the content of the first and second substances, (ii) (E 1 ，σ 1 ）、（E 2 ，σ 2 ) Is the coordinate of any two points on the straight line.
The data processing is completed after the above 3 steps are executed.
At this moment, the five steps which need to be executed by the nonlinear conductance prediction method for filling composite materials with different shapes are completely described, the final aim of the method is to simulate the structure and experimental environment of the composite material according to the actual performance design requirement, and two key parameters of the nonlinear conductance characteristic prediction curve and the measurement characteristic of the filling composite materials with different shapes are calculated and obtained: threshold electric field and nonlinear coefficient.
The practical application and effect verification of the calculation method are carried out by taking the alpha-type silicon carbide and the beta-type silicon carbide single-filling epoxy resin composite material with the filling volume fraction of 10vol% as research objects respectively.
Firstly, the difference between the alpha-type silicon carbide and the beta-type silicon carbide is mainly caused by the difference of crystal forms when a geometric model is constructed. Under the observation of an electron scanning microscope, the alpha-type silicon carbide is in a hexagonal crystal form, so that a sphere is used for simulating and filling during model construction; the beta-type silicon carbide is in a whisker shape and has a certain aspect ratio, so that the beta-type silicon carbide is filled by a cylinder in the model construction. Fig. 8 is a geometric model of a silicon carbide/epoxy composite constructed in accordance with the first flow procedure. FIG. 8 (a) is a schematic view ofFigure of an alpha-silicon carbide filled geometric model in which the peripheral cubes simulate an epoxy matrix with side lengthsDSet to 100 μm; the sphere in the cubic unit simulates alpha-type silicon carbide filling, and the size setting is based on the actual observation value under an electron scanning microscopeR=10 μm; fractional fill volumeVOL=10vol%, and the number of filled pellets is calculated by the following equation (1)NUM24, then the output result of the first step 1-4 is fig. 8 (a). FIG. 8 (b) is a model view of a beta-type silicon carbide filling, the same, peripheral cube simulating an epoxy matrix with side lengthsDSet to 100 μm; the cylinders in the cubic units simulate beta-type silicon carbide filling, the size is set according to the actual observation value under an electron scanning microscopeX=4μm，Z=80 μm, aspect ratio ofZ/X=20; fractional volume of fillVOL=10vol%, and the number of filled cylinders was calculated by the following equation (1)NUMAnd 24, then the output result of the first step 1-4 is fig. 8 (b). The function of the geometric model in fig. 8 is to perform geometric processing on the two different crystal forms of the silicon carbide filled epoxy resin material, so as to lay a foundation for the next step of regional material definition.
The geometric model of fig. 8 is then subjected to regional material definition. Simulating an epoxy resin matrix in the peripheral cube in the geometric model, selecting the peripheral cube according to the description of the step 2-1 in the second step during material definition, and inputting a relative dielectric constant measured value of 2.3 and a conductivity formula (4) of the epoxy resin material; the simulation of the internal geometry (sphere and cylinder) in the geometric model is the silicon carbide filler, and during the material definition, all the internal geometry is selected according to the description of the second step 2-2, and the measured value of the relative dielectric constant of the silicon carbide material 10 and the conductivity formula (5) are input.
And sequentially executing the third step of boundary condition setting and the fourth step of control Cheng Qiujie on the two geometric models after the area material definition is finished, and drawing the calculated conductivity and electric field intensity data in a log-log graph in a one-to-one correspondence manner to obtain nonlinear conductivity characteristic prediction curves of two different crystal silicon carbide filled epoxy resin materials with the filling volume fraction of 10vol%, as shown in fig. 9. The purpose of drawing this curve is to calculate two key parameters characterizing the nonlinear behavior of the material: threshold electric field and non-linear coefficient. FIG. 9 (a) is a predicted curve of conductance characteristics for a 10vol% α -type silicon carbide single fill, which is subjected to data processing according to the fifth steps 5-2 and 5-3, and key characterization parameter values of the 10vol% α -type silicon carbide/epoxy resin composite material can be calculated, as shown by the symbols in FIG. 9 (a), the abscissa value corresponding to the intersection point of two straight lines is the threshold electric field, and the value is 4.8kV/mm; two coordinates are taken from a straight line on the right side of the intersection point to replace the formula (11) to calculate the slope of the straight line, namely the nonlinear coefficient, and the value of the slope is 1.6. FIG. 9 (b) is a predicted curve of the electrical conductivity characteristic of the 10vol% β -type silicon carbide single pack, and the threshold electric field of the 10vol% β -type silicon carbide/epoxy resin composite material was calculated to be 2.6kV/mm and the nonlinear coefficient thereof to be 4.96 by the same data processing method.
The acquisition of the prediction curves of the electrical conductivity characteristics of the single-filled epoxy resin composite material of alpha-type silicon carbide and beta-type silicon carbide and the corresponding key parameters in fig. 9 means that the calculation method described in the calculation method of the nonlinear electrical conductivity of the filling composite material with different shapes can actually realize the nonlinear electrical conductivity prediction of the filling composite material with different shapes.
(II) nonlinear conductance calculation method of composite material under different compound filling schemes
In the former part, only the filling situation of a single type and a single size of filler is considered, and in fact, experimental research shows that the compound filling of the multi-size filler or the compound of the multi-type filler can effectively improve the conductivity of the composite material in a nonlinear region, so that a nonlinear conductivity characteristic calculation model of the composite material under different compound filling schemes needs to be established.
The method for calculating the nonlinear conductivity characteristics of the composite material under the different compound filling schemes comprises five steps of geometric model construction, regional material definition, boundary condition setting, control equation solving and data processing, wherein the latter four steps are the same as the method for calculating the nonlinear conductivity of the filler filled composite material with different shapes in the step (I), and the difference is that the improvement of the first step of geometric model construction needs to consider the feeding of two geometric bodies at the same time.
Fig. 10 is a flow chart of a first step of establishing a geometric model with multi-voxel random distribution, which comprises 2 steps, namely main filler feeding and reinforcing filler feeding. The details are as follows
Step 1a: and (4) putting main filler. In the actual preparation experiment of the compound composite material, the filler filled firstly is the main filler and is also called as the skeleton filler, and the filler filled later is the reinforcing filler and mainly plays a gap filling role. In the geometric modeling process, by taking the filling rule as reference, firstly, part of geometric bodies are put into the cubic matrix to serve as main fillers, the putting flow of the geometric bodies is carried out according to the flow on the left side of the dotted line in fig. 10, the step can be regarded as putting of single-type single-size fillers, and the step can be executed according to 4 steps of the first-step geometric model construction in the nonlinear conductance calculation method for filling the composite materials with the fillers in the (first) different shapes, and the details are not repeated.
Step 2a: and (4) putting the reinforcing filler. After the main filler is randomly put in, the reinforcing filler needs to be put in. Because the spherical filler reinforcing filler is usually selected in practical experiments, the method is adopted in the modeling process, and the spherical filler with large particle size, the flaky filler and the filler with different aspect ratios are used as main fillers and are reinforced by the spherical filler with small particle size. The process of adding the reinforcing filler is carried out according to the process on the right side of the dotted line in fig. 10, and comprises 4 steps of inputting geometric parameters and the number of spherical reinforcing fillers, randomly generating position control parameters of the spherical reinforcing fillers, judging the positions of geometric bodies of the reinforcing fillers and judging the number of the geometric bodies of the reinforcing fillers.
(1) Inputting geometric parameters and number of spherical reinforcing fillers: radius of sphererThe parameter still comes from the measurement value of the scanning electron microscope on the actual size of the filler, for example, the common particle size of the ceramic zinc oxide is usually 1 μm, 5 μm, 10 μm, etc.; setting and reinforcing filler fill volume fractionvol(in vol%) of the corresponding geometric figurenumThe calculation formula is
Figure 147117DEST_PATH_IMAGE016
（12）
WhereinV Reinforcing filler For a single spherical enhancement of the volume of the geometry, from 4 pir 3 And/3 is calculated.
(2) Randomly generating position control parameters of the spherical reinforcing filler: and (4) carrying out random placement of the reinforcing filler in the cubic unit according to the input geometric parameters and the generated position control parameters by using the sphere center three-dimensional coordinates.
(3) And (3) carrying out position judgment on the geometric body of the reinforcing filler: compared with the prior art, the feeding principle to be followed is more complex, and can be summarized as that the reinforcing filler and the main filler can be in contact with each other but not intersect each other, and the reinforcing filler can be in contact with each other but not intersect each other.
Figure 543463DEST_PATH_IMAGE017
（13）
Wherein the content of the first and second substances,Ris the main packing sphere radius;rto enhance the spherical radius of the filler;d master-boost The distance between the spherical centers of the main filler and the reinforced filler;d enhancement-enhancement In order to enhance the distance between the centers of the filler spheres, the distance calculation formula refers to formula (2). For different shapes of compound cases, the disjoint fillers need to satisfy the following judgment rule. The reinforcing filler satisfying formula (14) is considered to be in compliance with the dosing principle, the geometry is retained and the control parameters are stored in a matrix.
Figure 229791DEST_PATH_IMAGE018
（14）
(4) Judging the number of the geometric bodies of the reinforcing filler: if the number of the generated geometric bodies of the reinforcing filler does not reach the number of the geometric bodies preset in the step 2a (1)numThen, it is necessary to return to and execute step 2a (2) until the number of generated geometric objects reaches the preset numberNumber of geometric solidnumAnd then outputs the corresponding random geometric model.
And (3) after the steps 1a-2a are executed, the construction of geometric models under different compound filling schemes can be completed. And the subsequent four steps: the definition of the regional material, the setting of boundary conditions, the solving of a control equation and the data processing are all the same as the partial description of the nonlinear conductance calculation method of the first filling composite material filled with different shapes, and the calculation method is directly executed according to the nonlinear conductance calculation method of the filling composite material filled with different shapes.
So far, five steps which need to be executed by the composite material nonlinear conductivity prediction method under different compound filling schemes are completely described. The final objective of the method is to simulate the composite material structure and the experimental environment according to the actual performance design requirements, and calculate and obtain two key parameters of the nonlinear conductance characteristic prediction curve and the measurement characteristic of the composite material under different compound filling schemes: threshold electric field and nonlinear coefficient.
The silicon carbide/epoxy resin composite materials with the total filling volume fraction of 11vol% and different compounding schemes are taken as research objects respectively, and the calculation method is subjected to practical application and effect verification.
FIG. 11 is a geometric model of a silicon carbide/epoxy composite under a different compounding scheme constructed according to the procedure of FIG. 10. FIG. 11 (a) is a geometric model of an epoxy composite filled with a combination of alpha-type silicon carbide particles of different particle sizes, in which the peripheral cubes simulate an epoxy matrix with side lengthsDSet to 100 μm; the spheres in the cubic units are filled by simulating alpha-type silicon carbide materials, wherein the large spheres are main fillers and are set to have the sizeR=15 μm, filling volume fractionVOL=10vol%, and the number of large balls filled is calculated by using the formula (1)NUM7 in number; the small balls are reinforcing filler and are arranged in sizer=5 μm, filling volume fractionvol=1vol%, and the number of filled pellets was calculated by the following equation (12)numThe number of the cells is 19. FIG. 11 (b) is a geometric model of a silicon carbide composite filled with epoxy resin of different crystal forms, in which a peripheral cube simulates an epoxy resin matrix with a side lengthDSet to 100 μm; in cubic cellsThe cylinder simulates the filling of beta-type silicon carbide material and is a main filling material with the size set asX=4μm，Z=80 μm, filling volume fractionVOL=10vol%, and the number of filling cylinders was calculated by the following equation (1)NUM24 in number; the sphere simulates the filling of alpha-type silicon carbide material, is a reinforcing filler and is set in sizer=5 μm, filling volume fractionvol=1vol%, and the number of filled pellets was calculated by the following equation (12)numThe number of the cells is 19. The function of the geometric model in fig. 11 is to perform geometric processing on the silicon carbide/epoxy resin composite material obtained under two different compounding schemes, so as to lay a foundation for the next regional material definition.
The geometric model of fig. 11 is then subjected to regional material definition. Simulating an epoxy resin matrix in a peripheral cube simulation in a geometric model, selecting the peripheral cube according to the description of the step 2-1 in the nonlinear conductance calculation method for filling the composite material by the fillers in different shapes during material definition, and inputting a relative dielectric constant measured value 2.3 and a conductivity formula (4) of the epoxy resin material; the simulation of the internal geometry in the geometric model is the silicon carbide filler, and when the material is defined, all the internal geometries generated in the step 2a are selected according to the description of the step 2-2 in the nonlinear conductance calculation method of the composite material under different compound filling schemes, and the relative dielectric constant measured value 10 and the conductivity formula (5) of the silicon carbide material are input.
Sequentially executing the third step of boundary condition setting and the fourth step of control Cheng Qiujie in the first step on two geometric models after the area material definition is completed, and drawing the calculated conductivity and electric field intensity data in a log-log graph in a one-to-one correspondence manner, so as to obtain a silicon carbide/epoxy resin composite material nonlinear conductivity characteristic prediction curve under different compounding schemes with the total filling volume fraction of 11vol%, as shown in fig. 12, the curve is drawn for the purpose of calculating two key parameters representing the nonlinear characteristic of the material: threshold electric field and non-linear coefficient. Fig. 12 (a) is a conductance characteristic prediction curve of a mixed filling situation of 10vol% large-particle-size alpha-type silicon carbide and 1vol% small-particle-size alpha-type silicon carbide, data processing is performed on the curve according to a fifth step 5-2~5-3 in a nonlinear conductance calculation method for filler filled composite materials of different shapes, key characterization parameter values of the alpha-type silicon carbide compound filled epoxy resin composite materials of different particle sizes can be calculated, as shown by the marks in fig. 12 (a), an abscissa value corresponding to an intersection point of two straight lines is a threshold electric field, and the value is 3.5kV/mm; and (3) two coordinates are taken on the right side straight line of the intersection point to replace the formula (11) to calculate the slope of the straight line, namely the nonlinear coefficient, and the value of the slope is 1.43. FIG. 12 (b) is a predicted curve of the conductance characteristics of the mixed filling situation of 10vol% beta-type silicon carbide and 1vol% small-particle-size alpha-type silicon carbide, and the threshold electric field of the silicon carbide composite filling epoxy resin composite material with different crystal forms can be calculated to be 2.5kV/mm and the nonlinear coefficient to be 4.91 by adopting the same data processing method for the curve.
The acquisition of the prediction curves of the conductivity characteristics of the silicon carbide mixed filling epoxy resin composite material with different grain sizes and different crystal forms and the corresponding key parameters in fig. 12 means that the calculation method described in the calculation method of the nonlinear conductivity of the composite material under (II) different compound filling schemes can really realize the prediction of the nonlinear conductivity of the composite material under different compound filling schemes.
The invention provides a calculation method for predicting the nonlinear conductivity characteristics of a particle-filled composite material. The method combines the experimental preparation research trend of the current composite material, and the modeling process comprehensively considers the situations that spherical, flaky and different aspect ratio fillers, fillers with different particle sizes and fillers with different types are compounded and filled in the actual preparation process of the composite material. In practical application, according to the performance design requirement of the composite material, the actually measured material parameters (relative dielectric constant and conductivity) of the filler and the matrix in the composite material to be simulated are input into the corresponding region of the model, the boundary conditions equivalent to the experimental environment are set, and the nonlinear conductivity characteristic of the composite material under different types of filler filling and different compounding schemes can be predicted by solving a control equation and processing data.
The foregoing shows and describes the general principles, essential features, and advantages of the invention. It will be understood by those skilled in the art that the present invention is not limited to the embodiments described above, which are merely illustrative of the principles of the invention, but that various changes and modifications may be made without departing from the spirit and scope of the invention, which fall within the scope of the invention as claimed. The scope of the invention is defined by the appended claims and equivalents thereof.

Claims (1)

1. A method for predicting nonlinear electrical conductivity characteristics of a composite material, characterized by: the method comprises the following steps:
step 1: constructing a geometric model of the composite material: inputting geometric parameters of a cubic matrix and a filling geometric body in the composite material to be predicted, randomly generating position control parameters of the filling geometric body, realizing random putting of the geometric body, judging whether the position of the put geometric body meets the principle of contactability but non-intersection, judging whether the number of the put geometric bodies reaches a preset value, and outputting a geometric model if the positions of the put geometric bodies meet the preset value;
step 2: defining peripheral cubic unit and internal geometric body area materials in the geometric model: setting material parameters of the cubic unit area in the geometric model obtained in the step (1) according to the type of a polymer matrix in the composite material to be predicted, and inputting the relative dielectric constant and conductivity of the matrix material acquired in the experiment; according to the types of zinc oxide ceramic microspheres, silicon carbide, graphene and carbon nano tube inorganic fillers in the composite material to be predicted, material parameters are set for a filling geometric body area in the geometric model obtained in the step 1, and the relative dielectric constants and conductivities of spherical fillers, flaky fillers and 3 types of fillers with different aspect ratios acquired in an experiment are input;
and 3, step 3: setting a boundary condition; setting boundary conditions on the geometric model obtained in the step 1 according to an actual experimental environment, simulating actual measurement in a computer, sequentially applying direct-current voltage of 0-1kV to the upper surface of the cubic unit, setting the lower surface of the cubic unit to be in a grounding state, and setting the periphery of the cubic unit to be in an electric insulation state;
and 4, step 4: solving a control equation: sequentially calculating the integral electric field intensity of the cubic model under the action of different direct-current voltages; calculating the current density flowing through the model by solving a differential equation; dividing the obtained current density by the whole electric field intensity to calculate the conductivity of the whole composite material model under the action of different direct-current voltages;
and 5: and (3) processing data to obtain the nonlinear conductivity characteristic of the composite material: and (4) correspondingly drawing the electric field intensity data and the conductivity data obtained by the calculation in the step (4) in a double logarithmic coordinate graph in a one-to-one manner in a manner that an abscissa is the electric field intensity data and an ordinate is the conductivity data, wherein the drawn curve is a nonlinear conductivity characteristic curve of the composite material to be predicted, the curve is in an intersecting form of two straight lines, wherein the abscissa value corresponding to the intersecting point is a threshold electric field value, and the slope of the straight line on the right side of the intersecting point is calculated to obtain a nonlinear coefficient.
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