JP2014193596A - Coefficient of thermal conductivity prediction method of reinforcement resin, and apparatus of the same - Google Patents

Abstract

PROBLEM TO BE SOLVED: To solve a problem that in a conventional method, physical properties that clearly relate to an average fiber direction at a prescribed place in a sample are usually considered, however, in any amount of a product or the like, a fact that a distribution function is used instead of an average value, thereby a fiber orientation is expressed most favorably is neglected, therefore prediction accuracy of a coefficient of thermal conductivity is low, and high accuracy heat design of the product becomes difficult.SOLUTION: A coefficient of thermal conductivity prediction method of a resin includes: an information acquisition step in which based on numerical simulation and/or experimental analysis, information relating to a fiber in a reinforcement resin, or fiber and spherical type filler orientation angles is obtained; a fitting step in which an accumulation consequence is obtained from a fiber relating to a prescribed region in the fiber reinforcement resin, or the fiber and spherical type filler orientation angles distribution obtained by the information acquisition step, the consequence is fitted to a mathematical formula that expresses a theoretical or experimental model; and a calculation step in which a parameter obtained by the fitting step is used, and the coefficient of thermal conductivity relating to the prescribed region is calculated.

Description

  This invention relates to the field of fiber, or fiber and spherical filler reinforced plastic processing, and in particular the generality of the polymer processing industry (representing some techniques in which injection molding and / or extrusion is used). The present invention relates to a method and an apparatus for predicting the thermal conductivity of a filler (filler) -filled resin produced by using this technique, or the fiber and spherical filler-reinforced portions.

Accurate knowledge of the thermal conductivity of the product, etc. when the thermal insulation property or the high thermal conductivity property is required in a specific direction in the product or part (hereinafter referred to as a product etc.) This is an important step for optimizing the thermal design. Accurate knowledge of the local thermal conductivity in each region of a product or the like enables three-dimensional thermal calculation with numerical calculation software. On the other hand, knowing the lateral thermal conductivity from side to side is useful for predictive evaluation in the pre-design stage.

When fibers or fiber and spherical filler reinforced materials are used, the prediction of thermal conductivity is made difficult by the thermal anisotropy behavior of materials using high thermal conductivity fibers in a low thermal conductivity polymer matrix. . Fiber orientation has a strong effect on directional thermal conductivity, and therefore fiber orientation is an important factor for performing thermal calculations.

  There are several ways to predict fiber orientation during the manufacture of fiber reinforced products and the like. Computational algorithms that describe different means have been developed, most of which are based on individually modified fluid dynamic equation models. Of these, the Folgar-Tucker model is considered to be one of the best models available for modeling fiber or fiber orientation of fibers and spherical filler reinforcing materials (see, for example, Patent Document 1 or 2). ).

In addition, models for predicting some physical properties (for example, mechanical strength, Young's modulus, etc.) of fibers or fibers and spherical filler reinforced parts can be used (for example, Patent Documents 3 to 5 or Non-Patent Documents). References 1 to 3).

Special table 2010-531752 gazette JP-T-2006-523351 Japanese Patent Laid-Open No. 9-237267 Japanese Patent Laid-Open No. 7-304056 JP 2011-758 A

Thermal Conductivity of Misaligned Short-Fiber-Reinforced Polymer Composites, Shao-Yun Fu, Yui-Wing Mai, Journal of Applied Polymer 88. Elastic Modulus and Thermal Conductivity of Injection-Molded Short-Fiber-Reinformed Thermoplastics, C.I. L. Choy, W. P. Leung, K.C. W. Kowk, Polymer Compositions, 1992, Vol. 13, no. 2 Percolation Based Enhancement in Effective Thermal Conductivity of HDPE / LBSMO Composites, Madhusley Kole, D.C. Tripati, T.A. K. Dey, Indian Academy of Sciences, 2012, Vol. 35, no. 4

  However, the above conventional method usually takes into account the physical properties that are clearly related to the average fiber direction at a predetermined location in the sample, but in any quantity such as a product, a distribution function is used instead of the average value. Ignoring the fact that the fiber orientation is best represented by using, so the prediction accuracy of the thermal conductivity is low, making high-precision thermal design of the product difficult.

In other words, the thermal conductivity used in the conventional method relies on the local value of the fiber orientation predicted in a given cell or region, but in reality the orientation may vary in every part of the product. Confirmed from experiments.

Also, fiber interactions are not fully considered in conventional thermal conductivity algorithms. As a result, it has been confirmed that a large deviation from the true value is reached.

The resin thermal conductivity prediction method according to the present invention includes an information acquisition step for obtaining information relating to a fiber orientation angle in a fiber reinforced resin based on numerical simulation and / or experimental analysis, and a fiber obtained by the information acquisition step. The cumulative information is obtained from the fiber orientation angle distribution related to a predetermined region in the reinforced resin, and the result is applied to a mathematical expression representing a theoretical or experimental model, and a parameter obtained by the fitting process is used to determine the predetermined value. And a calculation step of calculating the thermal conductivity related to the region.

  The present invention enables highly accurate estimation of the thermal conductivity in the fiber reinforced portion even when the shape or material of the molding cavity used in the fiber reinforced product or the like is changed.

It is the flowchart which showed the whole process of the thermal conductivity prediction method of resin which concerns on Embodiment 1 of this invention. It is a figure which shows the state which divided | segmented the main volume into the subvolume. It is a figure which shows the fiber orientation angle using a Cartesian coordinate. It is a figure which shows the mode of the fiber orientation obtained by experiment. It is a figure which shows an example of the cumulative fiber orientation angle distribution obtained from the value simulation data. It is a block diagram which shows an example of the thermal conductivity prediction apparatus of resin which concerns on Embodiment 1 of this invention. It is the flowchart which showed the whole process of the thermal conductivity prediction method of resin which concerns on Embodiment 2 of this invention. It is a thermal conductivity calculation example of the base material composite material when using a plurality of spherical fillers in the thermal conductivity prediction method for a resin according to Embodiment 2 of the present invention.

Embodiment 1 FIG.
Next, embodiments of the present invention will be described with reference to the drawings. In the following description of the drawings, the same or similar parts are denoted by the same or similar reference numerals. However, it should be noted that the drawings are schematic and ratios of dimensions and the like are different from actual ones. Therefore, specific dimensions and the like should be determined in consideration of the following description. Moreover, it is a matter of course that portions having different dimensional relationships and ratios are included between the drawings.

FIG. 1 is a flowchart showing the entire process of the resin thermal conductivity prediction method according to the first embodiment of the present invention. In the figure, first, based on numerical simulation and / or experimental analysis in steps 11 to 13, for example, a thermoplastic resin or a resin belonging to at least one of a thermosetting resin manufactured by an injection molding or extrusion process or the like. An information acquisition process for obtaining information related to the fiber orientation angle in the fiber reinforced resin will be described.

In order to calculate the behavior of the fibers in the mold liquid phase during manufacture, in step 11, the shape data of the product to be analyzed is divided into three-dimensional elements such as tetrahedral elements and hexahedral elements, and fluid dynamic numerical simulation is performed. Is executed. If injection molding is used as the manufacturing method, a numerical simulation of the flow pattern inside the mold cavity is performed at this step. For example, the Navier-Stokes equation is used to model the velocity and pressure distribution in the liquid phase, and the Folgar-Tucker model is used to orient the fibers as they move in the mold. Can be used to calculate routes.

  Next, step 12 is a process of exporting the result obtained in step 11 in the form of numerical data. Here, the fiber orientation tensor represented by Equation 1 below is used to export data describing the three-dimensional fiber orientation of each element (cell).

Next, step 13 is a process of calculating the fiber orientation angle in each direction for each element. FIG. 3 is a diagram illustrating fiber orientation angles using Cartesian coordinates. Using the diagonal component of the fiber orientation tensor a _ij obtained in Step 12, the fiber orientation angle in each direction is 1 axis, 2 axes, and 3 axes of Cartesian axes, Easy to calculate using.

Here, α ₁₁ is the fiber orientation angle with respect to one axis of the Cartesian coordinate system, α ₂₂ is the fiber orientation angle with respect to the two axes of the Cartesian coordinate system, and α ₃₃ is the fiber orientation angle with respect to the three axes of the Cartesian coordinate system. Each is shown.

The fiber orientation can be directly known by an experimental method of analyzing a product or the like using means such as X-ray analysis or microscopic observation. FIG. 4 is a diagram showing the state of fiber orientation obtained by such an experiment. Here, S1 is an actual observation result imaged by an image processing algorithm, and S2 is a diagram simply showing fiber orientation based on S1.

Next, a fitting process in which the fiber orientation angle distribution relating to a predetermined region in the fiber reinforced resin obtained by the information acquisition process in steps 14 to 16 is accumulated and the result is applied to a mathematical expression representing a theoretical or experimental model. explain. FIG. 2 is a diagram showing a state in which the main volume is divided into sub-volumes, and is a reference diagram for explaining steps 14 to 16. Here, the main volume refers to the entire shape data used in step 11, and the sub volume refers to an arbitrary area selected from the main volume. In FIG. 2, the main volume and the subvolume are represented by cubes. However, the main volume is actually a product shape to be analyzed, and the subvolume can take any size and shape within the main volume. . A plurality of 3D elements generated in Step 11 are included in the sub-volume selected in the region, but the size of the sub-volume to be selected is at least 50, preferably 100, of the above-described 3D elements. The size included above is good. This is because in Steps 14 to 16 to be described later, the calculation results (fiber orientation angles) of a plurality of three-dimensional elements included in the subvolume are collectively calculated for each subvolume. At this time, if the number of three-dimensional elements included in the subvolume decreases, accurate heat conductivity calculation cannot be executed.

Since the calculation of the thermal conductivity is performed on the subvolume, an area in which the thermal conductivity is to be calculated is selected as the subvolume in the product shape, that is, the main volume. At this time, if it is desired to calculate the thermal conductivity of the entire main volume, the entire main volume is selected as the sub volume, and the main volume and the sub volume are naturally the same.

In addition, the number of sub-volumes to select an area may be one or plural. It is also possible to perform a transient thermal calculation of the entire product after calculating the thermal conductivity, in which case the main volume is divided into any number of sub-volumes and the overall transient is calculated using the thermal conductivity of each sub-volume. Thermal analysis will be performed. When selecting a plurality of subvolumes, they may partially overlap each other in order to increase the number of 3D elements involved.

Step 14 is a step of calculating a cumulative fiber orientation angle distribution in which the fiber orientation angles of the three-dimensional elements included in the subvolume are accumulated for each subvolume. Here, the fiber orientation angle is an angle with respect to three Cartesian coordinate axes, and the cumulative fiber orientation angle distribution is calculated for each of the 1 axis, 2 axes, and 3 axes.
The cumulative fiber orientation angle is calculated in the range of 0 to 90 degrees. Steps 15 and 16 are executed for each of the first, second and third axes of the aforementioned Cartesian coordinates, and the thermal conductivity for each axial direction is calculated.

Step 15 is a fitting process for fitting the cumulative fiber orientation angle distribution obtained in Step 14 with a theoretical or experimental model. This step completely includes several phenomena that lead to a smoothly distributed fiber orientation of the manufactured product or the like. Fiber-fiber or fiber-wall interactions during the manufacturing process, or physical inhomogeneities, contribute to the smooth fiber orientation angle distribution observed experimentally. Is difficult to reproduce. The fitting of the simulation result (cumulative fiber orientation angle distribution in step 14) to the theoretical or experimental model performed in step 15 is performed in order to give the smooth fiber orientation angle distribution of the above-described actual product or the like to the simulation. . This fitting dramatically improves the accuracy of the thermal conductivity calculation results.

FIG. 5 is a diagram showing an example of a cumulative fiber orientation angle distribution obtained from numerical simulation data (a solid line indicates simulation data and a dotted line indicates fitting data). In the figure, the X axis represents the orientation angle, the Y axis represents the cumulative frequency for each orientation angle, the solid line S1 represents the cumulative fiber orientation angle distribution obtained from the simulation data, and the dotted line S2 represents the solid line S1 as a theoretical or experimental model. The results of fitting to each are shown.

An example of a theoretical or experimental model used in the fitting of step 15 is obtained from the Halpin-Tsai equations by using laminate theory. This is given by Equation 3 (Choy, Leung et al).

ここで、αはデカルト軸に対する繊維の角度を表わし、λは繊維配向の度合いを特徴づけているパラメータである。ステップ１５において、ステップ１４で得られた累積繊維配向角度分布を数式３へフィッティングすることで、各デカルト座標軸に対するパラメータλが得られる。

Here, α represents the angle of the fiber with respect to the Cartesian axis, and λ is a parameter characterizing the degree of fiber orientation. In step 15, the parameter λ for each Cartesian coordinate axis is obtained by fitting the cumulative fiber orientation angle distribution obtained in step 14 to Equation 3.

Next, a calculation process for calculating the thermal conductivity related to the predetermined region using parameters obtained by the fitting process will be described. Step 16 is a process of calculating the thermal conductivity of the sub-volume using the material characteristics and the parameter λ obtained in Step 15. A specific calculation of thermal conductivity can use, for example, the Halpin-Tsai equations for thermal conductivity. They can be expressed by Equation 4.

Here, K _{c, i} is the thermal conductivity of the sub-volume in the Cartesian coordinate i-axis (i = 1, 2, 3) direction, and V _i is the Cartesian coordinate i-axis (i = 1, 2, 3). Μ ₁ is a coefficient related to heat conduction in the fiber long axis direction, μ ₂ is a coefficient related to heat conduction in the fiber short axis direction, and K _f1 is a parameter representing the degree of fiber orientation in the fiber long axis direction. K _f2 is the thermal conductivity of the fiber itself in the minor axis direction of the fiber, K _m is the thermal conductivity of the base resin, and ν is the average ratio of the major axis length to the minor axis length (average aspect ratio). the ratio), K ₁ is the thermal conductivity of the fiber length direction of the fiber filled resin, K ₂ is the thermal conductivity of the fibers minor axis direction of the fiber filled resin, VF denotes a packing volume fraction of fibers. K _f1 , K _f2 , K _m , and ν are values specific to the material to be used, and μ ₁ and μ ₂ can be calculated from these values. Next, K ₁ and K ₂ can be calculated from the obtained μ ₁ and μ ₂ and the volume fraction VF and K _m of the fibers in the material. Finally, the thermal conductivity K _{c, i} for each Cartesian coordinate axis can be calculated from λ corresponding to each Cartesian coordinate axis obtained in Step 15 and K ₁ and K _2.

The fiber-fiber interaction can be determined by using the method proposed by Fu and Mai, which consists of a two-step iterative method. In the first stage calculation, VF in Equation 4 is calculated as VF / (2-VF), and K _{c, i} is obtained. In the second stage calculation, K _{c, i} obtained in the first stage is set as the thermal conductivity K _{m of the} base resin, and VF is calculated as VF / 2. By performing the above two-stage iterative method, the thermal conductivity of the sub-volume considering the fiber-fiber interaction can be calculated.

The process described in the above viewpoint includes a hard disk and a ROM memory 301 for recording data and codes / programs through a process of inputting a parameter 21 such as a molding process and material characteristic values and a part / product shape data 22. The calculation is performed by a computer 31 comprising a central processing unit 302 for analyzing input data, a RAM memory 303 used for assigning temporarily stored data or main codes / programs, and the obtained thermal conductivity is calculated. Output to an output device 41 such as a display or printer. An example of such an apparatus is shown in FIG. The output system 41 may include a number of devices that visualize the results and / or an interface that transfers the resulting data to a different location or device.

When using the above thermal conductivity analysis method for the filler-filled resin, there is no particular limitation on the base material resin to be used, one of thermoplastic resin or thermosetting resin, or two or more May be combined.
Specific examples of the thermoplastic resin include polypropylene, polyacetal, liquid crystal resin, polybutylene terephthalate, polyethylene terephthalate, polyphenylene sulfide, polyamide, and the like.
Specific examples of thermosetting resins include, for example, epoxy resins, vinyl ester resins, unsaturated polyester resins, phenol resins, benzoxazine resins, urethane resins, urea resins, melamine resins, maleimide resins, cyanate resins, diallyl phthalate resins, etc. Is mentioned.

Although there is no restriction | limiting in particular in a filler material, Glass, carbon, a metal, or a ceramic can be used. The shape is not particularly limited, but is preferably cylindrical or needle-like. The base material resin and the filler material may each be a single material, or two or more materials may be combined.

The results using the above method may be used to represent the average thermal conductivity of the product / part, or the calculated subvolume thermal conductivity can be imported into the thermal analysis software and used. May be.
In the latter case, two-dimensional / three-dimensional steady / unsteady condition analysis using the thermal conductivity of each sub-volume becomes possible.

The method for predicting the thermal conductivity of the resin according to the embodiment of the present invention is generally shown as follows. The fiber orientation of a fiber reinforced resin product or the like is a fluid dynamic numerical simulation using a plurality of three-dimensional elements created from product shape data, and a theoretical or experimental model of an existing fiber orientation (for example, Folger Tucker, Calculated by the model (Folgar-Tucker model).

  The product shape data used in the previous process is divided into one or more sub-volumes in which the fiber orientation distribution is calculated on each Cartesian coordinate axis. The cumulative fiber orientation angle distribution of all three-dimensional elements contained in the region-selected subvolume is fitted to an experimental or theoretical model to approximate the fiber orientation angle distribution of the actual product.

There are various logical models for representing the fiber orientation distribution. The model used for explaining the present invention is a model represented by the following formula.

このモデルによるフィッティング・パラメターはλとなる。ただ、様々なモデルが存在するため、一般的な「理論的なモデル」という言語で表現する。
前の工程で得られたフィッティング・パラメータ、は、各デカルト座標軸について実験的または理論的な熱伝導率の計算式を用いて所定のサブボリュームの熱伝導率を計算するために、連続相で使用される。熱伝導率に対する繊維相互作用の寄与は、フー（Ｆｕ）とマイ（Ｍａｉ）によって提案される方法を用いて加えることができる。

The fitting parameter according to this model is λ. However, since there are various models, it is expressed in a general language called “theoretical model”.
The fitting parameters obtained in the previous step are used in the continuous phase to calculate the thermal conductivity of a given sub-volume using an experimental or theoretical thermal conductivity formula for each Cartesian coordinate axis Is done. The contribution of fiber interaction to thermal conductivity can be added using the method proposed by Fu and Mai.

  This process is repeated for each subvolume so that interpolation between different subvolumes is used to increase the spatial resolution of the method. The number of 3D elements at the start must be chosen as large as possible to increase the accuracy of the analysis. When calculating one numerical value for the thermal conductivity in one direction from one end to the other, the product shape data may be used as one subvolume.

Embodiment 2. FIG.
In the first embodiment, the method for predicting the thermal conductivity of the fiber reinforced resin has been described. In the second embodiment, the method for predicting the thermal conductivity of the fiber and the spherical filler reinforced resin using the fiber and the spherical filler as a reinforcing material. Will be described. In the figure, the portions denoted by the numbers shown in the first embodiment are the same as the configurations described in the first embodiment, and thus the description thereof is omitted here.

  FIG. 7 is a flowchart showing the entire process of the resin thermal conductivity prediction method according to Embodiment 2 of the present invention. In the figure, first, based on numerical simulation and / or experimental analysis in steps 511 to 513, for example, a thermoplastic resin or a resin belonging to at least one of a thermosetting resin manufactured by an injection molding or extrusion molding process or the like. For step 51, which is an information acquisition step for obtaining information related to the fiber and the fiber orientation angle in the spherical filler reinforced resin, a method similar to the method described in the first embodiment can be used. Is omitted

  Step 52 is a process of predicting the thermal conductivity of the resin reinforced with only the spherical filler, considering only the spherical filler and the base resin in the fiber and the spherical filler reinforced resin. Step 521 is a process for obtaining the thermal conductivity, density, and volume fraction of the spherical filler and the base material resin. Here, the thermal conductivity and density of the spherical filler and the base material resin may be obtained from literature or may be obtained experimentally. When the volume fraction of the spherical filler and the base material resin is known at the stage of material blending, the value is used. When only the mass fraction of each material is known at the material blending stage, the volume fraction of the spherical filler can be obtained by the following formula 6.

ここで、ρ_ｓｆとρ_ｂａｓｅは、それぞれ球状フィラーと母材樹脂の密度を、ＭＦ_ｓｆは球状フィラーの質量分率を、ＶＦ_ｓｆは球状フィラーの体積分率をそれぞれ示す。ステップ５２２は、ステップ５２１で得られた球状フィラーおよび母材樹脂の特性値から球状フィラーのみで強化された樹脂（以下、母材複合材又は母材複合材料と記載する場合がある）の熱伝導率を理論的な方程式から計算する工程である。理論的な方程式は、球状フィラー強化樹脂の熱伝導率の予測式であって、既知の方程式を用いることができる。好ましくは以下の数式７に示すＢｒｕｇｇｅｍａｎｎの式が良い。

Here, ρ _sf and ρ _base represent the density of the spherical filler and the base material resin, MF _sf represents the mass fraction of the spherical filler, and VF _sf represents the volume fraction of the spherical filler, respectively. Step 522 is the heat conduction of the resin reinforced with only the spherical filler from the characteristic values of the spherical filler and the base resin obtained in Step 521 (hereinafter, may be referred to as a base material composite or a base material composite material). This is the process of calculating the rate from a theoretical equation. The theoretical equation is a prediction formula of the thermal conductivity of the spherical filler reinforced resin, and a known equation can be used. The Bruggemann's formula shown in the following formula 7 is preferable.

ここで、Ｋ_ｓｆとＫ_ｂａｓｅは、球状フィラーおよび母材樹脂の熱伝導率を示し、Ｋ_ｍａｔは母材複合材料の熱伝導率を示す。

Here, K _sf and K _base indicate the thermal conductivity of the spherical filler and the _base material resin, and K _mat indicates the thermal conductivity of the base material composite material.

  Step 523 is a process of obtaining the thermal conductivity of the base material composite material from the result calculated by the prediction formula of Step 522.

  Steps 54 to 57 are steps for predicting the thermal conductivity of the fiber and the spherical filler reinforced resin from the fiber orientation obtained in Step 51 and the thermal conductivity of the base material composite material obtained in Step 52. Here, the method described in the first embodiment can be used by replacing the characteristics of the base material described in the first embodiment with the characteristics of the base material composite material obtained in step 52. Here, although there is no restriction | limiting in particular in a spherical filler material, Various organic fillers, such as inorganic fillers, such as glass, a metal, or a ceramic, or carbon can be used.

  Moreover, the spherical filler may be one type or a plurality of types. When a plurality of kinds of spherical fillers are used, a stepwise calculation method including steps 61 and 62 shown in FIG. That is, in step 62, the first thermal conductivity of the first base material composite is calculated from the characteristic values of only the first spherical filler and the base material resin. Next, in step 61, from the first thermal conductivity of the first base material composite material obtained in step 62 and the characteristic value of the second spherical filler, the second base material composite material Calculate the thermal conductivity.

  In addition, when there are many types of spherical fillers, this step may be repeated for the number of types of spherical fillers. From the thermal conductivity of the resin reinforced with the obtained plurality of spherical fillers and the fiber orientation obtained in step 51 shown in FIG. 7, the thermal conductivity of the fibers and the spherical filler reinforced resin by the method described in the first embodiment. Can be predicted.

  According to the above embodiment, the fiber orientation is considered as one distribution in particular, so that several phenomena that lead to dispersion during product manufacture can be taken into account indirectly. In addition, it can be predicted with high accuracy by considering the relationship of the fiber interaction to the heat conduction mechanism.

11 Fluid dynamic simulation 12 Export simulation results 13 Calculate fiber orientation in each direction for each element 14 Calculate cumulative fiber orientation distribution 15 Theoretical / experimental function / model fitting 16 Material properties and previously obtained fitting parameters Calculate the thermal conductivity using the 21 parameter input (process settings, material properties, ...)
22 Part / product shape data 31 Computer 301 Hard disk, ROM memory 302 Central processing unit 303 RAM memory 41 Thermal conductivity 51 Fiber orientation calculation step 511 Fluid dynamic simulation step 512 Export simulation result 513 Each element in each direction Step 52 for calculating the fiber orientation Step 521 for determining the characteristics of the base material composite material Step 521 for obtaining the physical properties of the spherical fillet and the base material resin 522 Step 523 for fitting to a theoretical equation Step 523 for determining the thermal conductivity of the base material composite material Step 55 of calculating cumulative fiber orientation distribution Step of fitting theoretical / experimental function / model 56 Step of calculating thermal conductivity using material properties and previously obtained fitting parameters 57 of fiber and spherical filler reinforced resin Obtaining thermal conductivity Degree 61 second to obtain the characteristics of the matrix composite material step 62 first step of obtaining a characteristic of the matrix composite

Claims (8)

A thermal conductivity prediction method for predicting the thermal conductivity of a fiber reinforced resin,
An information acquisition step for obtaining information on the fiber orientation angle in the fiber reinforced resin based on numerical simulation and / or experimental analysis;
A fitting step of obtaining the accumulated information from the fiber orientation angle distribution relating to the predetermined region in the fiber reinforced resin obtained by the information acquisition step, and fitting the result to a mathematical expression representing a theoretical or experimental model;
Using the parameters obtained by the fitting step, a calculation step for calculating the thermal conductivity related to the predetermined region;
A method for predicting thermal conductivity. A thermal conductivity prediction method for predicting the thermal conductivity of fibers and spherical filler reinforced resin,
An information acquisition step for obtaining information on the fiber orientation angle in the fiber and the spherical filler reinforced resin based on numerical simulation and / or experimental analysis;
Calculating a composite thermal conductivity in a composite system comprising a spherical filler and a resin contained in the fiber and the spherical filler reinforced resin; and
Fitting step of obtaining cumulative information from the fiber orientation angle distribution relating to the predetermined region in the fiber and spherical filler reinforced resin obtained by the information acquisition step, and fitting the result to a mathematical expression representing a theoretical or experimental model When,
A calculation step of calculating a thermal conductivity according to the predetermined region using the parameters obtained by the fitting step and the composite thermal conductivity;
A method for predicting thermal conductivity.   The fiber reinforced resin, or the fiber and the spherical filler reinforced resin are divided into the predetermined regions, and the thermal conductivity of each predetermined region is calculated for each coordinate axis direction of Cartesian coordinates. Item 3. The thermal conductivity prediction method according to any one of Items 2.   4. The fiber reinforced resin, or the fiber and the spherical filler reinforced resin, is a resin belonging to at least one of a thermoplastic resin or a thermosetting resin. 5. The thermal conductivity prediction method described in 1.   The thermal conductivity prediction method according to any one of claims 1 to 4, wherein the fibers belong to at least one of glass, carbon, metal, and ceramic.   The thermal conductivity predicting method according to any one of claims 2 to 4, wherein the spherical filler belongs to at least one of glass, carbon, metal, and ceramic.   The thermal conductivity prediction method according to claim 1, wherein the fiber has a cylindrical shape or a needle shape.   The thermal conductivity prediction apparatus according to claim 1, wherein software according to the thermal conductivity prediction method according to claim 1 is executed using hardware resources.

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