Analysis method

Abstract

To provide an analysis method capable of analyzing a characteristic value of a composite material in consideration of contact between particles without implementing a numerical analysis method such as finite element analysis.SOLUTION: An analysis method for analyzing a characteristic value of a composite material includes: a setting step (S3) of setting a characteristic value which includes form specification information and a contact allowable area dimension for each of a plurality of composite materials; a generation step (S6) of generating a filling structure model including a matrix on the basis of the set characteristic values; a first calculation step (S7) of calculating contact volume; and prediction steps (S9, S10) for predicting the magnitude of the characteristic values by comparing the contact volume.SELECTED DRAWING: Figure 5

Description

[Technical Field]

[0001] The present disclosure relates to an analytical method for analyzing property values ​​of a particle-filled composite material containing a plurality of particles. [Background technology]

[0002] Particle-filled composite materials (hereinafter referred to as composite materials) are designed by adjusting various material formulations, measuring their properties, and selecting a formulation that has the best effect (desired property values). This formulation selection requires analyzing the properties that the composite material will exhibit. Since many experiments are required between formulation and analysis, significant experimental costs and time are required. Therefore, in recent years, in order to reduce experimental costs and time, studies have been conducted to analyze the property values ​​of composite materials through simulations using a representative volume element model (RVE). Examples of such analytical techniques are disclosed in, for example, Patent Documents 1 and 2.

[0003] In the analysis method of Patent Document 1, a first model is created by dividing the structure into multiple elements each having multiple nodes, and a second model is created in which nodes are generated at positions symmetrical to the nodes of the first model. The first and second models are then combined to create a third model. The third model is then used as a simulation model, and boundary conditions are set. The first model is a model used to perform deformation analysis using a numerical analysis method such as the finite element method or the finite difference method.

[0004] In the analysis method of Patent Document 2, first and second packed structure models including particles and a matrix that fills the gaps between the particles are generated based on shape-specific information and volume fraction, and finite element analysis is performed on each of the first and second packed structure models. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Patent No. 5771935 [Patent Document 2] Patent Publication No. 2021-60902 Summary of the Invention [Problem to be solved by the invention]

[0006] However, Patent Documents 1 and 2 do not specifically disclose how to generate a packed structure model that takes into account the overlap of particles (fillers). When the overlap of particles is taken into account, a packed structure model generated by a known method may deviate from the actual structure of the composite material. Therefore, when a numerical analysis method such as finite element analysis is used as in the analysis methods of Patent Documents 1 and 2, it may not be possible to accurately analyze the characteristic values ​​of the composite material.

[0007] Furthermore, it is known that the predicted property values ​​of the above-mentioned numerical analysis methods deviate from the experimental values ​​in composite materials with a relatively high particle volume fraction (highly particle-filled composite materials).Furthermore, the above-mentioned numerical analysis methods require relatively high calculation costs and time.

[0008] An object of one aspect of the present invention is to realize an analysis method that can analyze the characteristic values ​​of a composite material while taking into account the overlap of particles and without using the above-mentioned numerical analysis method. [Means for solving the problem]

[0009] An analysis method according to one aspect of the present invention is an analysis method for analyzing characteristic values ​​of a plurality of particle-filled composite materials based on the formulation of the particle-filled composite materials, the analysis method including a setting step of setting, for each of the plurality of particle-filled composite materials, morphology-specific information for specifying the morphology of particles contained in the particle-filled composite material, the volume fraction of the particles, and characteristic values ​​of the particles, the characteristic values ​​including a contact allowance region dimension that indicates the dimension of a contact allowance region that allows overlapping with other particles on the surface of the particle, as defined by the following formula (1); and calculating, for each of the plurality of particle-filled composite materials, a plurality of particle-filled composite materials based on the morphology-specific information, the volume fraction, and the contact allowance region dimension. The method includes a generation step of generating a packed structure model including particles and a matrix that fills the gaps between the particles; a first calculation step of calculating, for each of the plurality of particle-filled composite materials, a contact volume indicating the volume of the portion where the particles overlap from the packed structure model; and a prediction step of predicting the magnitude of a characteristic value of the particle-filled composite material by comparing the contact volumes calculated for each of the plurality of particle-filled composite materials, where equation (1) is expressed as 2t / (d-2t), where t is the dimension of the contact allowable region, and d is the length of the line segment that connects two points on the surface of the particle and passes through the center of gravity of the particle. [Effects of the Invention]

[0010] According to one aspect of the present invention, it is possible to analyze the characteristic values ​​of a composite material while taking into consideration the overlap of particles and without performing the above-mentioned numerical analysis method. [Brief explanation of the drawings]

[0011] [Figure 1] FIG. 1 is a block diagram illustrating an example of an analysis device. [Figure 2] FIG. 1 is a schematic diagram showing an RVE model, which is an example of a filling structure of a modeled composite material. [Figure 3] 10A and 10B are schematic diagrams for explaining a contact allowable region and dimensions of the contact allowable region. [Figure 4] FIG. 1 is a schematic diagram showing a state in which two particles overlap each other. [Figure 5]10 is a flowchart showing an example of a processing flow of a control unit included in the analysis device. [Figure 6] 10 is a graph showing an example of an analysis result. [Figure 7] 10 is a graph showing another example of the analysis results. [Figure 8] FIG. 2 is a schematic diagram for explaining the shape of a particle. [Figure 9] FIG. 2 is a schematic diagram for explaining the shape of a particle. DETAILED DESCRIPTION OF THE INVENTION

[0012] [Embodiment 1] An embodiment of the present invention will be described in detail below. Before describing the analysis device 1 and analysis method of this embodiment, first, a composite material (particle-filled composite material) that is an analysis target of the analysis device 1 and analysis method of this embodiment, and an RVE (Representative Volume Element) model that is an example of the structure of a modeled composite material will be described.

[0013] <Composite materials> A composite material is a material designed to achieve desired characteristics by mixing multiple particles and a resin. Specifically, a composite material is a material containing multiple particles and a matrix that fills the gaps between the particles. A composite material may contain particles with different volumes. In this case, the multiple particles can be classified in descending order of volume, such as large particles, medium particles, and small particles. However, the volume types of particles contained in a composite material are not limited to three types consisting of large particles, medium particles, and small particles, and may be classified into two or four or more types. The raw materials for the particles are, for example, inorganic materials such as metals, metal oxides, and metal nitrides, or carbon-based materials. The raw materials for the particles are, for example, alumina or aluminum nitride. The raw materials for the matrix are, for example, polymer resins such as epoxy resins or acrylic resins.

[0014] <RVEモデル> FIG. 2 is a schematic diagram showing an RVE model, which is an example of a packed structure of a modeled composite material. The RVE model is an example of a packed structure model including a plurality of particles and a matrix that fills the gaps between the particles. Reference numeral 1001 in FIG. 2 indicates an example of an RVE model including large particles CP (Coarse Particles), small particles FP (Fine Particles), and a matrix PM (Polymer Matrix). Reference numeral 1002 in FIG. 2 is a diagram showing an example of an RVE model in which only large particles CP are extracted from the RVE model shown by reference numeral 1001.

[0015] The RVE model is a cubic or rectangular parallelepiped model that defines the packing structure of a composite material using unit cells (representative volume elements) equivalent in the X-, Y-, and Z-axis directions (three axes). The RVE model is generated by setting the length of one side, the size of each particle, the shape of each particle, and the volume fraction of each particle, and then distributing and arranging the particles, starting with the largest particle, using Monte Carlo simulation until the specified volume fraction is reached. In the RVE model of this embodiment, each particle is arranged while allowing overlap between particles within the specified contact tolerance area dimensions (described below). Digimat-FE by MSC Software Corporation can be used to generate the RVE model.

[0016] All boundaries of the generated RVE model are assumed to have cyclic symmetry, and the interfaces between multiple particles and the matrix included in the RVE model are assumed to be completely bonded.

[0017] In the RVE model, the volume fraction of the target particle is calculated as "(volume of the target particle) / (volume of all particles + volume of the matrix)". For example, in the RVE model of reference numeral 1001 in Fig. 2, if the volume of the large particle CP is Vc, the volume of the small particle FP is Vf, and the volume of the matrix MP is Vp, the volume fraction Vfc of the large particle CP and the volume fraction Vff of the small particle FP are given by Vfc=Vc / (Vc+Vf+Vp) Vff=Vf / (Vc+Vf+Vp) It is expressed as:

[0018] <Purpose of this application> Properties involving mass transfer, such as thermal or electrical conduction, are manifested by the interconnection of individual particles. Therefore, when analyzing properties such as thermal or electrical conductivity, composite materials with a high density of particles of different sizes are typically used. Numerous control factors are also required. Therefore, when analyzing the properties of composite materials through trial and error based on the experimenter's experience, the analysis requires significant time and effort. Therefore, predicting specific values ​​using simulations is useful for such analyses. As mentioned above, in order to reduce experimental costs and time, the use of numerical analysis methods such as finite element analysis using the RVE model has been considered.

[0019] However, as described above, the inventors have found that when overlapping of particles in a composite material is taken into account, the particle state in a packing structure model generated by a known method deviates from the actual particle state, making it impossible to accurately analyze the property values ​​of the composite material. The inventors have found that the above-mentioned numerical analysis method is particularly unable to accurately analyze properties (such as thermal conduction or electrical conduction) that arise from overlapping of particles. Furthermore, it is known that property values ​​obtained by the above-mentioned numerical analysis method deviate from experimental values, particularly in composite materials with a high particle filling rate.

[0020] Based on these findings, the inventors have devised the following analysis device 1 and analysis method. The analysis device 1 and analysis method will be described below.

[0021] <Configuration of the analysis device> 1 is a block diagram showing an example of an analysis device 1. The analysis device 1 includes, for example, an input unit 11, a display unit 12, a control unit 13, and a storage unit 14. The analysis device 1 is a device that analyzes the characteristic values ​​of a composite material from the blend (structure) of a plurality of composite materials. The analysis device 1 may be realized by, for example, a general computer such as a personal computer.

[0022] The input unit 11 is a device that receives various inputs from a user and outputs them to the control unit 13. The input unit 11 may be an input device such as a keyboard or a mouse. The display unit 12 is a display that displays various information such as analysis results. The control unit 13 is a control device that controls the operation of the analysis device 1. The functions of the control unit 13 will be described later.

[0023] The memory unit 14 is a storage device that stores data necessary for control by the control unit 13. The memory unit 14 stores, for example, a material DB (Data Base) 141. The material DB 141 stores information about raw materials that can be constituent materials (particles and matrix) of the composite material. The information about the raw materials includes, for example, information such as characteristic values ​​of the raw materials that can be the constituent materials.

[0024] In this embodiment, the characteristic value of the constituent material is thermal conductivity, which represents a thermal property, or electrical conductivity, which represents an electrical property. That is, in this embodiment, the characteristic value of the composite material to be analyzed is thermal conductivity or electrical conductivity. As described above, properties such as thermal conduction and electrical conduction are manifested by the overlap of particles, and it has been difficult to accurately analyze these characteristic values ​​using known methods. The analysis device 1 analyzes the characteristic values ​​of composite materials taking into account the overlap of particles, and is therefore particularly effective in analyzing the characteristic values ​​of properties manifested by the overlap of particles. In other words, the analysis device 1 makes it possible to accurately analyze thermal conductivity or electrical conductivity.

[0025] However, the characteristic values ​​of the constituent materials and composite materials are not limited to thermal conductivity or electrical conductivity, and may be the coefficient of linear expansion representing thermomechanical properties, Young's modulus or Poisson's ratio representing mechanical properties (elastic properties), or the like.

[0026] The control unit 13 includes, for example, a setting unit 131, a model generation unit 132, a first calculation unit 133, a prediction unit 134, and a second calculation unit 135. However, the control unit 13 does not necessarily need to include the second calculation unit 135.

[0027] The setting unit 131 sets the raw materials of the constituent materials (particles and matrix) for each of the multiple composite materials. Furthermore, the setting unit 131 sets, for each of the multiple composite materials, form specifying information that specifies the form of the particles contained in the composite material, the volume fraction of the particles, and characteristic values ​​of the particles. Furthermore, the setting unit 131 sets characteristic values ​​of the matrix for each of the multiple composite materials. Based on input from the user via the input unit 11, the setting unit 131 sets the raw materials of the constituent materials that make up the composite material, the shape of the particles, the size of the particles, the volume fraction of the particles, etc.

[0028] The particle shape may be selected from various shapes, such as spherical, fibrous (cylindrical), polyhedral, etc. The particle size is set, for example, as the diameter if the particle shape is spherical, as the diameter and length if the particle shape is fibrous (cylindrical), or as the length of one side if the particle shape is polyhedral. The particle shape and size are examples of the form-specifying information.

[0029] Furthermore, the setting unit 131 sets the property values ​​of the particles and the matrix with reference to the material DB 141. In this embodiment, the setting unit 131 sets the thermal conductivity or the electrical conductivity as the property values ​​of the particles and the matrix.

[0030] The setting unit 131 further sets the contact-tolerance area dimension as a characteristic value of the particle. The contact-tolerance area dimension is the dimension of the contact-tolerance area on the surface of the particle that allows overlap with other particles. FIG. 3 is a schematic diagram for explaining the contact-tolerance area and the contact-tolerance area dimension. FIG. 3 is a schematic diagram showing a cross section of a spherical particle including its center. As shown in FIG. 3, the contact-tolerance area CA is a layer having a predetermined thickness (a predetermined length from the surface toward the inside of the particle along the normal or perpendicular line to the surface of the particle) that is set perpendicularly inward to the surface over the entire surface of the particle. This thickness is the contact-tolerance area dimension t. Furthermore, the area inside the contact-tolerance area CA of the particle is a non-contact area NCA that does not allow overlap with other particles.

[0031] The contact allowable area dimension t is, for example, 2t / (d-2t) …Equation (1) where d is the length of a line segment connecting two points on the surface of a particle and passing through the center of gravity of the particle. d is a value corresponding to the size of the particle described above. Since the particle of this embodiment is spherical, d is the diameter of the sphere (particle size) as shown in FIG. 3. Equation (1) is the ratio of the contact tolerance area dimension t to the dimension of the non-contact-tolerance area NCA (dimension defined as "d-2t"). d may be the longest line segment connecting two points on the surface of a particle and passing through the center of gravity of the particle.

[0032] The contact allowable region dimension t is set as a value when formula (1) satisfies the following predetermined value. The predetermined value is set, for example, by comparing the characteristic value of the composite material obtained by the analysis device 1 with the characteristic value of the composite material obtained by experiment. The predetermined value can be set at least regardless of the particle size. For example, the predetermined value is set to 0.01 to 0.3, and preferably 0.05 to 0.1. When the raw material is alumina, the predetermined value can be set within the above numerical range, and for example, 0.058 can be set as an appropriate value. Setting the contact allowable region dimension t within the above numerical range enables the prediction unit 134 to accurately compare the magnitude of the characteristic value of the composite material.

[0033] When the raw material contains multiple types of particles (particles having different sizes), the setting unit 131 sets form specifying information for each of the multiple types of particles based on input from the user via the input unit 11. The multiple types of particles may be particles having the same component composition (for example, alumina particles having different sizes), or particles having different component compositions (for example, alumina and aluminum nitride).

[0034] Furthermore, based on an input from the user via the input unit 11, the setting unit 131 sets the size of the packed structure model to be generated by the model generation unit 132, for example, the length of one side of a cube.

[0035] The model generation unit 132 generates a packed structure model including a plurality of particles and a matrix for each of the plurality of composite materials, based on the various information set by the setting unit 131. The model generation unit 132 generates the above-mentioned RVE model for each of the plurality of composite materials.

[0036] The first calculation unit 133 calculates a contact volume, which indicates the volume of the portion where particles overlap, for each of the multiple composite materials from the packing structure model generated by the model generation unit 132. FIG. 4 is a schematic diagram showing a state in which two particles overlap. FIG. 4 is a schematic diagram showing a cross section including the center of each of two spherical particles. As shown in FIG. 4, the volume of the area CAij where the contact allowance area CAi of one particle and the contact allowance area CAj of the other particle overlap is the contact volume V contact i / j is.

[0037] The first calculation unit 133 calculates the contact volume V contact i / j For example, V contact i / j =(V j* -V j j ) / V j …Formula (2) and / or V contact i / j =(V j j -V i-j j ) / V j ...Formula (3) It is calculated as follows.

[0038] i and j are particle numbers. Equation (2) is an equation for calculating the contact volume between the particle with particle number i and the particle with particle number j when i = j. That is, it is an equation for calculating the contact volume when the sizes of the particles are the same. In the following description, the particle with particle number i is referred to as particle i, and the particle with particle number j is referred to as particle j. Equation (3) is an equation for calculating the contact volume between particle i and particle j when i ≠ j (specifically, i < j). That is, it is an equation for calculating the contact volume when the sizes of the particles are different.

[0039] Therefore, when the composite material contains particles of the same size, the first calculation unit 133 applies Equation (2), and when the composite material contains particles of different sizes, the first calculation unit 133 applies Equation (3). Therefore, when particles of the same size and particles of different sizes are mixed in the composite material, the first calculation unit 133 applies both Equation (2) and Equation (3). In addition, the first calculation unit 133 calculates the contact volume in order from the particle with the largest volume.

[0040] The definitions of the symbols in Equations (2) and (3) are as follows. ·V i : The volume per particle of particle i. ·V j : The volume per particle of particle j. Here, when i ≤ j, V i ≥V j shall be the case. ·V i* : The total value (theoretical value) of the volume of the contact allowable region of particle i when all particles i included in the filling structure model are not in contact with each other. ·V j* : The total value (theoretical value) of the volume of the contact allowable region of particle j when all particles j included in the filling structure model are not in contact with each other. ·V i i: When focusing on particles i included in a packing structure model, the total volume (actual value) of the contact allowable regions of particles i in a state where there is at least one pair of particles i in which two particles i partially overlap each other. This packing structure model may be generated using only particles i. ·V j j : When focusing on particles j included in a packing structure model, the total volume (actual value) of the contact allowable regions of particles j in a state where there is at least one pair of particles j in which two particles j partially overlap each other and have a partial overlap. This packing structure model may be generated using only particles j. ·V i-j i : When focusing on particles i and j included in the packing structure model, the total volume of the part of particle i that overlaps with particle j. ·V i-j j : When focusing on particles i and j included in the packing structure model, the total volume of particle j that overlaps with particle i.

[0041] The first calculation unit 133 calculates V i , V j , V i* , V j* The first calculation unit 133 calculates V based on the shape specification information and the contact allowable area dimensions set by the setting unit 131. i i , V j j 、 V i-j i , V i-j j is calculated using the RVE model generated by the model generation unit 132.

[0042] When i=j, the first calculation unit 133 calculates n different contact volumes. In the case of an RVE model filled with three particles, the first calculation unit 133 calculates three different contact volumes. Specifically, the first calculation unit 133 calculates Contact volume V at i=j=1 contact1 / 1 =(V 1* -V1 1 ) / V 1 Contact volume V at i=j=2 contact 2 / 2 =(V 2* -V2 2 ) / V 2 Contact volume V at i=j=3 contact 3 / 3 =(V 3* -V3 3 ) / V 3 Calculate.

[0043] When i≠j (i≦j), the first calculation unit 133 calculates n In the case of an RVE model in which three particles are packed, the first calculation unit 133 calculates 3C2=3 contact volumes. Specifically, the first calculation unit 133 calculates Contact volume V for i=1, j=2 contact 1 / 2 =(V2 2 -V 1-2 2 ) / V 2 Contact volume V for i=1, j=3 contact 1 / 3 =(V3 3 -V 1-3 3 ) / V 3 Contact volume V at i=2, j=3 contact 2 / 3 =(V3 3 -V 2-3 3 ) / V 3 Calculate.

[0044] In this embodiment, the first calculation unit 133 makes the contact volume dimensionless by using formulas (2) and (3). However, the first calculation unit 133 may calculate only the numerators of formulas (2) and (3) to determine the contact volume.

[0045] Furthermore, when a composite material contains multiple types of particles with different component compositions, the first calculation unit 133 calculates the contact volume between the particles with different component compositions. That is, the first calculation unit 133 calculates the contact volume of the multi-component system. Therefore, it is possible to analyze the characteristic values ​​of a composite material using the contact volume not only for composite materials containing particles with the same component composition, but also for composite materials containing particles with different component compositions.

[0046] The prediction unit 134 predicts the magnitude of the characteristic value of each composite material by comparing the contact volumes calculated for each of the multiple composite materials by the first calculation unit 133. As will be described later, there is a correlation between the contact volume and the characteristic value (thermal conductivity in the example described later). Therefore, the prediction unit 134 can predict the magnitude relationship of the characteristic values ​​of the composite materials by comparing the contact volumes.

[0047] In this way, the control unit 13 can predict the magnitude relationship of the characteristic values ​​of the composite material by setting the contact allowance region dimensions and calculating the contact volume from the packed structure model. Therefore, the control unit 13 can predict the magnitude relationship of the characteristic values ​​of the composite material by taking into account the overlap of particles. Furthermore, by setting the contact allowance region dimensions and calculating the contact volume, the control unit 13 can predict the magnitude relationship of the characteristic values ​​of the composite material without applying finite element analysis to the packed structure model. Therefore, the control unit 13 can analyze the characteristic values ​​of the composite material by taking into account the overlap of particles and without requiring the calculation cost and time required by finite element analysis.

[0048] The second calculation unit 135 calculates the characteristic values ​​of the composite material by applying finite element analysis to the filled structure model generated by the model generation unit 132. The second calculation unit 135 specifies the characteristic values ​​of the contact allowance region within a predetermined range and performs the finite element analysis. In this embodiment, thermal conductivity or electrical conductivity is specified as this characteristic value. The setting unit 131 may set the characteristic values ​​of the contact allowance region by accepting a user input via the input unit 11, thereby causing the second calculation unit 135 to specify the characteristic values ​​of the contact allowance region.

[0049] The predetermined range may be, for example, a range from 0 to the characteristic value of the particle, or a range from the characteristic value of the matrix to the characteristic value of the particle, or, if voids are present on the surface of the composite material, a range from the characteristic value of the void to the characteristic value of the particle.

[0050] As described above, the control unit 13 can predict the magnitude relationship of the characteristic values ​​of the composite material. On the other hand, the control unit 13 can also predict the characteristic values ​​of the composite material using finite element analysis by setting the dimensions of the contact allowance region and specifying the characteristic values ​​of the contact allowance region. In other words, the control unit 13 can predict the characteristic values ​​of the composite material by taking into account the overlap between particles and using finite element analysis.

[0051] As described above, the model generation unit 132 generates a packed structure model based on the raw materials of the constituent materials, the shape specification information, the particle volume fraction, the particle characteristic values, and the size of the packed structure model set by the setting unit 131. The second calculation unit 135 divides the generated packed structure model into elements to generate a finite element model. Then, the second calculation unit 135 calculates the characteristic values ​​of the composite material by performing finite element analysis, for example, as follows.

[0052] The second calculation unit 135 divides the packed structure model into a plurality of elements using, for example, a free mesh method. Tetrahedral elements smaller in size than the packed structure model are used as the elements. The shape of the elements is not limited to tetrahedrons, and other polyhedrons such as pentahedrons and hexahedrons may also be used.

[0053] The second calculation unit 135 sets boundary conditions for a finite element model obtained by dividing the filling structure model into elements. When the analysis target is thermal conductivity, the second calculation unit 135 sets the temperature at each boundary of the finite element model as the boundary condition. When the analysis target is electrical properties, the second calculation unit 135 sets the electric potential at each boundary of the finite element model as the boundary condition. When the analysis target is mechanical properties, the second calculation unit 135 sets the displacement amount at each boundary of the finite element model as the boundary condition.

[0054] The second calculation unit 135 constructs simultaneous linear equations based on the boundary conditions set for the finite element model, finds solutions to the simultaneous linear equations using a solver, and calculates the characteristic values ​​of the composite material based on the solutions. For a packed structure model in which particles are randomly dispersed, the second calculation unit 135 can calculate the characteristic values ​​in each of the three axial directions, but in this case, it calculates the average of the characteristic values ​​in each of the three axial directions as the characteristic value of the composite material.

[0055] <Analysis method> 5 is a flowchart showing an example of the processing flow (analysis method) of the control unit 13. The setting unit 131 sets the morphology specification information of particle i, volume fraction information of particle i, and characteristic value information of particle i as physical property values ​​for generating a packing structure model (S1, S2, S3; setting steps). In S3, the setting unit 131 sets the contact allowance region size of particle i as the characteristic value of particle i.

[0056] The setting unit 131 determines whether all of this information has been set (S4). If the setting unit 131 determines that any of the information has not been set (NO in S4), the process returns to S1. The order of the processes from S1 to S3 is not limited to this, and they may be performed in any order. Furthermore, if the composite material contains multiple types of particles with different sizes, the setting unit 131 sets the information shown in S1 to S3 for each of the multiple types of particles.

[0057] When it is determined that all of the above-mentioned information has been set (YES in S4), the setting unit 131 sets the matrix information (for example, characteristic values ​​of the matrix) as physical property values ​​for generating a filling structure model (S5).

[0058] After the setting unit 131 sets the various information, the model generation unit 132 generates a packing structure model including a plurality of particles and a matrix based on the various information (S6; generation step). The first calculation unit 133 calculates the contact volume from the packing structure model generated by the model generation unit 132 (S7; first calculation step).

[0059] The control unit 13 determines whether the model generation unit 132 has generated a filling structure model and the first calculation unit 133 has calculated a contact volume for each of the multiple composite materials to be compared (S8). If the control unit 13 determines that not all filling structure models to be compared have been generated and not all contact volumes to be compared have been calculated (NO in S8), the process returns to S1. As a result, a contact volume is calculated for each of the multiple composite materials to be compared.

[0060] When the control unit 13 determines that all packing structure models to be compared have been generated and all contact volumes to be compared have been calculated (YES in S8), the prediction unit 134 compares the contact volumes calculated by the first calculation unit 133 (S9; part of the prediction step).The prediction unit 134 then predicts the magnitude of the characteristic value for each of the multiple composite materials based on the comparison (S10; part of the prediction step).

[0061] Although not shown, for example, after the processing of S6 (generation of the filled structure model), the second calculation unit 135 may calculate the characteristic value of the composite material by applying finite element analysis to the filled structure model (second calculation step).

[0062] <Example> Fig. 6 is a graph showing an example of the analysis results, which is a graph showing the relationship between the volume fraction of particles in a composite material and the thermal conductivity of the composite material. Fig. 6 includes the following graphs. A packed structure model is generated for a composite material in which the contact allowable region is defined as described above, and a graph (labeled "this embodiment" in the figure) plots the thermal conductivity of the composite material calculated by the second calculation unit 135. The particle volume fraction in this case is the total volume fraction of the contact allowable region and the non-contact region. A graph plotting the thermal conductivity of a composite material obtained by generating a filled structure model for a composite material that does not specify a contact tolerance region and performing finite element analysis ("Comparative Example" in the figure). A graph plotting the measured thermal conductivity of composite materials ("Example of Experimental Results" in the figure).

[0063] To create the graph in Figure 6, a composite material containing large alumina particles with a diameter of 20 μm and small alumina particles with a diameter of 4 μm was used. A polymer resin was used as the matrix. The model ratio (maximum particle diameter / length of one side of the packed structure model) was 0.6, and the number of failures was 50,000.

[0064] Furthermore, for composite materials with a defined contact allowance region, the thermal conductivity of the contact allowance region was 7.5 [W / mK], the thermal conductivity of the non-contact region (core region) was 36 [W / mK], and the thermal conductivity of the polymer resin was 0.18 [W / mK]. The dimensions of the contact allowance region were determined when equation (1) satisfied 0.058. For composite materials without a defined contact allowance region, the thermal conductivity of the particles (corresponding to the non-contact region) was 36 [W / mK], and the thermal conductivity of the polymer resin was 0.18 [W / mK].

[0065] As shown in Figure 6, the experimental result example shows that the thermal conductivity of the composite material tends to increase as the volume fraction increases. In this example, as in the experimental result example, the thermal conductivity of the composite material also tends to increase as the volume fraction increases.

[0066] In the comparative example, the thermal conductivity of the composite material also increases as the volume fraction increases, but it can be seen that as the volume fraction increases, the thermal conductivity tends to deviate from the experimental results. On the other hand, in this example, even as the volume fraction increases, it can be seen that the values ​​tend to be closer to the experimental results than the comparative example. In particular, in this example, it can be seen that even at volume fractions of 50% or more, the values ​​are closer to the experimental results than the comparative example.

[0067] From the above, it can be said that the analysis device 1 of this embodiment can accurately predict the thermal conductivity of a composite material over a wide range of volume fractions by defining the contact allowance region. In particular, it can be said that the thermal conductivity of a composite material can be accurately predicted even when the volume fraction of the particles to be filled in the composite material is 50 volume % or more.

[0068] FIG. 7 is a graph showing another example of the analysis results. Reference numeral 1011 in FIG. 7 is a graph showing the relationship between the volume ratio of large particles to small particles contained in a composite material and the thermal conductivity of the composite material. Reference numeral 1012 in FIG. 7 is a graph showing the relationship between the volume ratio of large particles to small particles contained in a composite material and the contact volume in the composite material. Reference numeral 1012 in FIG. 7 shows the contact volume between large particles (represented by "V contact L / L "), the contact volume between the large particle and the small particle ("V contact L / S ") and the contact volume between small particles ("V contact S / S 7) and 8), graphs are shown for each volume ratio. In FIG. 7, the horizontal axis shows the particle size ratio between large particles and small particles as the volume ratio between large particles and small particles.

[0069] In creating the graph in Figure 7, the thermal conductivity of the contact allowable region was set to 7.5 [W / mK], the thermal conductivity of the non-contact region (core region) to 36 [W / mK], and the thermal conductivity of the polymer resin to 0.18 [W / mK] for the composite material with a defined contact allowable region. The volume fraction of the large particles and the volume fraction of the small particles were each set to 30% by volume. Polymer resin was used as the matrix. The model ratio (= maximum particle diameter / length of one side of the packed structure model) was set to 0.6, and the number of failures was set to 50,000. The dimensions of the contact allowable region were determined by the formula (1) being 0.058(t r = 0.058). The dotted line at 1012 in Fig. 7 indicates the calculated value (approximately 1.3 [W / mK]) of the thermal conductivity of the composite material when there is no overlap of particles.

[0070] In addition, when creating the graph in FIG. 7, the following four types of composite materials containing large particles and small particles were prepared. ·Diameter 20μm(d L = 20 μm) and large particles of alumina with a diameter of 4 μm (d S A composite material containing small particles of alumina (particle size ratio (d L / d S ) is 5. ·Diameter 20μm(d L= 20 μm) and large particles of alumina with a diameter of 6 μm (d S A composite material containing small particles of alumina (particle size ratio (d L / d S ) is about 3.3. ·Diameter 20μm(d L = 20 μm) and large particles of alumina with a diameter of 8 μm (d S A composite material containing small particles of alumina (particle size ratio (d L / d S ) is 2.5. ·Diameter 20μm(d L = 20 μm) and large particles of alumina with a diameter of 10 μm (d S A composite material containing small particles of alumina with a particle size ratio (d L / d S ) is 2.

[0071] As shown by reference numeral 1011 in Fig. 7, it can be seen that the thermal conductivity of the composite material tends to decrease as the particle size ratio decreases. Also, as shown by reference numeral 1012 in Fig. 7, at least the contact volume (V contact L / S ) and the contact volume between small particles (V contact S / S ) and (2), it can be seen that the contact volume becomes smaller as the particle size ratio becomes smaller. From these relationships, it can be seen that the thermal conductivity of the composite material tends to decrease as the contact volume becomes smaller.

[0072] From the above, it can be seen that the contact volume is a parameter correlated with the thermal conductivity of the composite material. Therefore, it can be seen that the prediction unit 134 can predict the magnitude of the thermal conductivity of the composite material in each filling structure model by comparing the contact volumes of each filling structure model calculated by the first calculation unit 133.

[0073] <Modification> The analysis device 1 sets contact allowance area dimensions for each particle contained in each composite material, calculates the contact volume of the overlapping portion of the particles, and compares the contact volumes of each composite material to compare the magnitude of the characteristic values ​​of each composite material. Alternatively, the prediction unit 134 of the analysis device 1 may predict the characteristic values ​​of each composite material.

[0074] As described above, the thermal conductivity of a composite material is correlated with the contact volume. In other words, it can be said that there is a correlation between the characteristic value of the composite material to be analyzed and the contact volume. Therefore, data (a correlation table) showing the correlation between the contact volume and the characteristic value of the composite material can be stored in the storage unit 14. Then, the prediction unit 134 can predict the characteristic value of the composite material by referring to the correlation table and identifying the characteristic value corresponding to the contact volume calculated by the first calculation unit 133.

[0075] The correlation table can be created by, for example, repeatedly analyzing the characteristic values ​​using finite element analysis. For example, the correlation table may be created by associating the contact volume calculated by the first calculation unit 133 with the characteristic values ​​of the composite material calculated by the second calculation unit 135. After a correlation table containing enough data to predict the characteristic values ​​of the composite material has been created, the prediction unit 134 can predict the characteristic values ​​in subsequent predictions without having to calculate the characteristic values ​​of the composite material using finite element analysis by the second calculation unit 135.

[0076] [Embodiment 2] Other embodiments of the present invention will be described below. For ease of explanation, the same reference numerals will be used to designate components having the same functions as those described in the above embodiment, and the description thereof will not be repeated.

[0077] In the first embodiment, a method for analyzing the characteristic values ​​of a composite material using spherical particles has been described. The analysis method described in the first embodiment can be applied to any particle shape as long as the particle has a surface area that can be calculated. Examples of such particle shapes (other than spherical) are shown below.

[0078] 8 and 9 are schematic diagrams for explaining the shape of particles. Reference numeral 1021 in Fig. 8 is a diagram showing an example of a cylindrical particle. Reference numeral 1021 in Fig. 8 shows the appearance of a cylindrical particle, a cross section of the particle cut along a plane parallel to the bottom surface ("planar cross section" in the figure), and a cross section of the particle cut along a plane passing through the center of the bottom surface and perpendicular to the bottom surface ("side cross section" in the figure).

[0079] As described above, the contact-tolerance area CA is a layer having a predetermined thickness that is set perpendicularly inward to the surface over the entire surface of the particle. Therefore, for a cylindrical particle, the contact-tolerance area dimension t is defined as indicated by reference numeral 1021 in FIG. 8 . The length d is defined, for example, as the diameter of the circle that forms the base of the cylinder. The symbol h in the figure indicates the sum of the contact-tolerance area dimension t on both sides and the thickness of the non-contact area NCA in a cross section taken along a plane that passes through the center of the base of the cylinder and is perpendicular to the base. The length d may be defined, for example, as the length indicated by the symbol h.

[0080] Reference numeral 1022 in FIG. 8 shows an example of an elliptical particle. Reference numeral 1022 in FIG. 8 shows the appearance of the elliptical particle and a cross section of the particle cut along a plane including the major axis. For the elliptical particle, a contact allowance area CA having a contact allowance area dimension t is set over the entire surface of the particle. The length d is, for example, the minor axis of the ellipse. The length d may also be, for example, the major axis of the ellipse.

[0081] Reference numeral 1023 in FIG. 8 shows an example of a rectangular parallelepiped particle. Reference numeral 1023 in FIG. 8 shows the appearance of the rectangular parallelepiped particle and a cross section of the particle cut along a plane parallel to one of its planes. For the rectangular parallelepiped particle, a contact allowance area CA having a contact allowance area dimension t is set over the entire surface of the particle. The length d is, for example, the length of one of the sides.

[0082] Reference numeral 1031 in FIG. 9 is a cross-sectional view showing an example of a polyhedral particle. Reference numeral 1031 in FIG. 9 shows an example in which the cross-sectional shape of a polyhedral particle when cut along a plane passing through the center is a regular hexagon. Polyhedral particles also include regular polyhedral particles. For polyhedral particles, a contact allowance area CA having a contact allowance area dimension t is set over the entire surface of the particle. The length d may be any line segment connecting two points on the surface and passing through the center.

[0083] The particle may have a three-dimensional shape other than those described above. For example, as shown by reference numeral 1032 in Fig. 9, the particle may have a shape including a plurality of irregularities on its surface. Even with such a shape, a contact allowance area CA having a contact allowance area dimension t can be set over the entire surface of the particle, and the length d can be specified.

[0084] [Software implementation example] The functions of the analysis device 1 (hereinafter referred to as the "device") can be realized by a program that causes a computer to function as the device, and a program that causes a computer to function as each control block of the device (particularly each part included in the control unit 13).

[0085] In this case, the device includes a computer having at least one control device (e.g., a processor) and at least one storage device (e.g., a memory) as hardware for executing the program. The control device and storage device execute the program, thereby realizing the functions described in each of the above embodiments.

[0086] The program may be non-transitory and may be recorded on one or more computer-readable recording media. The recording media may or may not be included in the device. In the latter case, the program may be supplied to the device via any wired or wireless transmission medium.

[0087] Furthermore, some or all of the functions of the control blocks can be realized by logic circuits. For example, an integrated circuit in which a logic circuit that functions as each of the control blocks is formed is also included in the scope of the present invention. In addition, the functions of the control blocks can also be realized by, for example, a quantum computer.

[0088] Furthermore, each process described in each of the above embodiments may be executed by AI (Artificial Intelligence). In this case, the AI ​​may run on the control device or on another device (for example, an edge computer or a cloud server).

[0089] 〔summary〕 An analysis method according to a first aspect of the present disclosure is an analysis method for analyzing characteristic values ​​of a plurality of particle-filled composite materials based on their formulations, the analysis method including: a setting step for setting, for each of the plurality of particle-filled composite materials, morphology-specific information for identifying the morphology of particles contained in the particle-filled composite material, the volume fraction of the particles, and characteristic values ​​of the particles, the characteristic values ​​including a contact allowance region dimension that indicates the dimension of a contact allowance region on the surface of the particle that allows overlap with other particles, as defined by Equation (1); a generation step for generating, for each of the plurality of particle-filled composite materials, a packed structure model including a plurality of particles and a matrix that fills gaps between the particles, based on the morphology-specific information, the volume fraction, and the contact allowance region dimension; a first calculation step for calculating, from the packed structure model, a contact volume that indicates the volume of the portion where the particles overlap, for each of the plurality of particle-filled composite materials; and a prediction step for predicting the magnitude of the characteristic value of the particle-filled composite material by comparing the calculated contact volumes for each of the plurality of particle-filled composite materials.

[0090] In the analysis method according to aspect 2 of the present disclosure, in addition to aspect 1, the characteristic value is thermal conductivity or electrical conductivity.

[0091] In the analysis method according to a third aspect of the present disclosure, in the first or second aspect, the contact allowable region dimension is a value when the formula (1) is 0.01 to 0.3.

[0092] In the analysis method according to aspect 4 of the present disclosure, in any of aspects 1 to 3, in the setting step, the morphology-specific information is set for each of multiple types of particles, and in the first calculation step, the contact volume of the multi-component system is calculated using equations (2) and (3).

[0093] The analysis method according to aspect 5 of the present disclosure, in any of aspects 1 to 4, further includes a second calculation step of calculating characteristic values ​​of the particle-filled composite material by applying finite element analysis to the filled structure model, and in the second calculation step, specifying characteristic values ​​of the contact tolerance region within a predetermined range.

[0094] A sixth aspect of the present disclosure relates to an analysis method according to any one of the first to fifth aspects, wherein the particle-filled composite material contains particles with a volume fraction of 50% by volume or more.

[0095] [Additional Notes] The present invention is not limited to the above-described embodiments, and various modifications are possible within the scope of the claims. Embodiments obtained by appropriately combining the technical means disclosed in different embodiments are also included in the technical scope of the present invention. [Explanation of symbols]

[0096] 1 Analysis device 131 Setting section 132 Model Generation Unit 133 First Calculation Section 134 Prediction Department 135 Second Calculation Unit S1, S2, S3 setting steps S6 Generation Step S7 First calculation step S9,S10 prediction steps

Claims

1. 1. An analysis method for analyzing characteristic values ​​of a particle-filled composite material from a blend of the particle-filled composite material, comprising: a setting step of setting, for each of the plurality of particle-filled composite materials, morphology-specific information for identifying the morphology of particles contained in the particle-filled composite material, the volume fraction of the particles, and characteristic values ​​of the particles, the characteristic values ​​including a contact allowance area dimension that indicates the dimension of a contact allowance area on the surface of the particle that allows overlapping with other particles, as defined by Equation (1); a generation step of generating, for each of the plurality of particle-filled composite materials, a packed structure model including a plurality of particles and a matrix filling gaps between the particles, based on the morphology specifying information, the volume fraction, and the contact allowance region dimensions; a first calculation step of calculating, for each of the plurality of particle-filled composite materials, a contact volume indicating a volume of a portion where the particles overlap with each other from the packed structure model; a prediction step of predicting the magnitude of a characteristic value of the particle-filled composite material by comparing the contact volumes calculated for each of the plurality of particle-filled composite materials, The analysis method, wherein the formula (1) is expressed as 2t / (d-2t), where t is the size of the contact allowable area, and d is the length of a line segment connecting two points on the surface of the particle and passing through the center of gravity of the particle.

2. The analysis method according to claim 1 , wherein the characteristic value is thermal conductivity or electrical conductivity.

3. 3. The analysis method according to claim 1, wherein the contact allowable area size is a value when the formula (1) is 0.01 to 0.

3.

4. In the setting step, the form specifying information is set for each of a plurality of types of particles; In the first calculation step, the contact volume of the multi-component system is calculated using Equations (2) and (3), The formula (2) is V contact i / j = (V j* -V j j ) / V j is expressed as The formula (3) is V contact i / j = (V j j -V i-j j ) / V j is expressed as i, j are particle numbers, V i is the volume per particle of particle i, ・V j is the volume per particle of particle j, ・V i* is the total volume of the contact allowable region of particle i when all particles i included in the packing structure model are not in contact with each other, ・V j* is the total volume of the contact allowable region of particle j when all particles j included in the packing structure model are not in contact with each other, ・V i i is the total volume of the contact allowable region of particle i when focusing on particle i included in the packing structure model, and there is at least one pair of two particles i in which two particles i partially overlap each other, and ・V j j is the total volume of the contact allowable region of particle j when, with respect to particle j included in the packing structure model, there is at least one pair of particles j in which two particles j partially overlap each other, and ・V i-j i is the total volume of the overlapping portion of particle i with particle j when particles i and j are included in the packing structure model, and ・V i-j j 3. The analysis method according to claim 1, wherein, when particles i and j included in the packing structure model are considered, ρ is the sum of the volumes of the portions of particle j that overlap with particle i.

5. and a second calculation step of calculating a characteristic value of the particle-filled composite material by applying finite element analysis to the packed structure model, The analysis method according to claim 1 or 2, wherein the characteristic value of the contact allowable region is designated within a predetermined range in the second calculation step.

6. 3. The analysis method according to claim 1, wherein the particle-filled composite material has a volume fraction of filled particles of 50% by volume or more.

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