JP2008122154A - Manufacturing method of rubber material analyzing model - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a method for manufacturing a rubber material analyzing model useful for precisely analyzing the deformation state of a rubber material compounded with a filler. <P>SOLUTION: The method for manufacturing the three-dimensional rubber material analyzing model using when the deformation of the rubber material prepared by compounding a matrix rubber with the filler is simulated using a computer includes the step of setting a filler model 4 by dividing the filler having a three-dimensional shape by a limited number of tetrahedron elements e1, the step of setting a first matrix rubber model 5 by dividing the interfacial side part of the filler, which comes into contact with the filler of the matrix rubber and has an arbitrary thickness by a limited number of trigonal prism elements e2 of which the height directions are arranged in a thickness direction D and the step of setting a second matrix rubber model 6 by dividing the region between the outer surface of the first matrix rubber model 5 and a predetermined space V by a limited number of the tetrahedron elements e1. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

  The present invention relates to a method for creating a rubber material analysis model useful for accurately analyzing a deformation state or the like of a rubber material containing a filler.

  Rubber materials that are widely used industrially, including tires, are blended with fillers such as carbon black and / or silica in matrix rubber as a raw material. It is known that the strength is greatly improved. For example, a rubber material compounded with carbon black exhibits a so-called hysteresis (history phenomenon) in which stress during unloading is lower than when loaded, as compared with a rubber material not compounded with carbon black. Such hysteresis closely affects the function of the rubber material. However, experimental observations have been conducted on the detailed mechanism and microscopic deformation behavior inside the material, especially the influence of the carbon black particle and rubber interface, which is considered to have a significant effect on the properties of the rubber material. Because it is difficult, there are still many unclear points.

  Therefore, in recent years, in order to investigate the deformation behavior of the rubber material in more detail, simulation analysis by a finite element method using a computer has been proposed (for example, Patent Documents 1, 2, and 3 listed below and Non-Patent Document 1). reference.).

Japanese Patent No. 3668239 Japanese Patent No. 3668238 JP 2006-138810 A Naito, “Change in influence of microscopic structure on viscoelastic behavior of carbon black-filled rubber by simulation” [No.05-2], Proceedings of the 18th Annual Meeting of Japan Opportunity Society [2005.11.19]・ Tsukuba City] P.365-P.366

  In Non-Patent Document 1, for example, as shown in FIG. 15, a matrix rubber model a obtained by dividing (modeling) a matrix rubber by a tetrahedral element e1, and an example in which filler particles are divided by a tetrahedral element e1. Has proposed a rubber material analysis model c comprising four filler models b.

  Such a rubber material analysis model c has an advantage that it can be created using, for example, general-purpose mesh generation software. In other words, this kind of mesh generation software automatically inputs the elements based on the conditions by inputting the information of the three-dimensional area to be divided in advance and the necessary conditions (for example, the number of divisions and element shapes). Can do. Moreover, many softwares support the division function using tetrahedral elements as a standard. Therefore, by using such a function of the general-purpose software, the matrix rubber and filler regions can be easily divided by the tetrahedral elements.

  However, the matrix rubber model a in which all are divided by tetrahedral elements has the following drawbacks.

  First, in a deformation simulation of a rubber material by a computer, normally, rubber is handled as an incompressible material, that is, a volume that does not change even when deformed. On the other hand, fillers such as carbon black are defined as rigid bodies or hard elastic bodies because they are sufficiently harder than rubber.

  In such a situation, for example, as shown in FIG. 16, when the tetrahedron element e1 of the matrix rubber model a disposed on the outer surface of the filler model b is given a tensile load F to the rubber material model c, for example, The nodes n1 and n2 shared with the filler model b cannot move because the filler model b itself does not substantially deform. Further, because of the incompressible nature described above, the tetrahedron element e cannot be deformed with a volume change, so that the node n3 at the top of the element e follows the tensile load F in spite of it. There arises a disadvantage that it cannot be displaced in the direction (note that the node n3 can be displaced in the left-right direction as indicated by a virtual line). For this reason, in the analysis model c of the conventional rubber material, the deformation of the elements of the matrix rubber model a arranged at the interface with the filler model b is greatly different from the actual behavior, which deteriorates the calculation accuracy. The inventors have found that this is the case.

  The present invention has been devised in view of the above problems, and the filler interface side portion of the matrix rubber that contacts the filler and has an arbitrary thickness is aligned in the thickness direction in the height direction. A method for creating a rubber material analysis model capable of expressing an appropriate deformation of the filler interface side portion and thus preventing a decrease in calculation accuracy is provided based on the division by a finite number of triangular prism elements. The main purpose.

  The invention described in claim 1 of the present invention is a method for creating a three-dimensional rubber material analysis model used when a deformation of a rubber material in which a filler is mixed with a matrix rubber is simulated using a computer. A step of setting a filler model by dividing the filler having a three-dimensional shape by a finite number of tetrahedral elements, a filler interface side portion that contacts the filler and has an arbitrary thickness of the matrix rubber A step of setting a first matrix rubber model by dividing it by a finite number of triangular prism elements whose height direction is aligned in the thickness direction, and an outer surface of the first matrix rubber model and a predetermined space; A step for setting the second matrix rubber model by dividing the region between the two by a finite number of tetrahedral elements. Characterized in that it comprises a.

  The invention according to claim 2 is the method for creating a rubber material analysis model according to claim 1, wherein the first matrix rubber model has a thickness of 1 to 100% of a particle size of the filler model.

  A third aspect of the present invention is the rubber material analysis model creation method according to the first or second aspect, wherein a plurality of the first matrix rubber models are stacked in the thickness direction.

  In the method of the present invention, a filler model is set by dividing a three-dimensional filler by a finite number of tetrahedral elements. Such processing can be easily performed using, for example, general-purpose mesh generation software. In the present invention, the filler interface side portion of the matrix rubber that contacts the filler and has an arbitrary thickness is divided by a finite number of triangular prism elements whose height direction is aligned with the thickness direction. 1 matrix rubber model is set. Such a triangular prism element can be deformed by extending in the height direction without causing a volume change by deforming the area of the triangle. Therefore, deformation at the time of tension can be expressed without deviating from actual behavior. Therefore, it is possible to prevent a reduction in simulation calculation accuracy. Furthermore, since the second matrix rubber model is also divided by a finite number of tetrahedral elements as in the filler model, it is possible to easily join the first matrix rubber model.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
The present invention is for creating a three-dimensional rubber material analysis model used when simulating deformation of a rubber material (vulcanized rubber) in which fillers such as carbon black and silica are blended with matrix rubber using a computer. Is the method. In this embodiment, as shown in FIG. 1, a procedure for generating a three-dimensional rubber material analysis model (simulation model) of vulcanized rubber 1 in which a plurality of fillers (filler particles) 3 are blended with matrix rubber 2. Is explained. All or most of this procedure is performed using a computer device (not shown).

  The vulcanized rubber 1 shown in FIG. 1 has a predetermined constant volume, and four fillers 3 forming a smooth spherical shape are dispersed therein. For example, carbon black has primary particles with a diameter of about several tens of nanometers. Moreover, the filler 3 of this embodiment contains two types from which an outer diameter differs, and all the outer sides of each filler 3 are covered with the matrix rubber 2. FIG. The shape, arrangement, and / or number of fillers 3 are not limited to the illustrated form.

  Next, as shown in FIGS. 2 and 3, in the present embodiment, the filler model 4 is set by dividing each of the four fillers 3 using only the tetrahedral element e1. As shown in FIG. 4, the tetrahedral element e1 of the present embodiment is a primary tetrahedral element having four planar triangles t, four nodes n, and six sides s, and is also referred to as a “tetra element”. There is a case. Such a tetrahedron element e1 is preferable in that a complicated three-dimensional region can be easily divided by using so-called automatic mesh generation software (automatic mesher) or the like even if it has a complicated shape. The primary tetrahedral element is preferable in that the memory consumption specified for calculation can be reduced as compared with the secondary element (10-node element).

  In the software, for example, the center coordinates of each filler 3 in FIG. 1 and the radius of the particle are specified to specify the region to be divided (three-dimensional region), and these are input together with the mesh division condition, Filler model 4 is set. The number of elements of the filler model 4 is appropriately set based on the calculation accuracy desired to be acquired, the processing capability of the computer, and the like.

  In addition, since each surface of the tetrahedral element e1 is a flat surface, the spherical surface of the filler 3 cannot be completely reproduced. Therefore, as shown in FIG. 3, each side s of all tetrahedral elements e1 arranged on the outer surface 4o of the filler model 4 is shared with one side s of other adjacent tetrahedral elements e1. It is desirable to place each tetrahedral element. Thereby, the tetrahedron element e1 having the node n protruding without being joined to other elements does not appear on the outer surface 4o. Therefore, the outer surface of the filler model 4 can be smoothed as much as possible. Further, the filler model 4 having such an outer surface shape is desirable in terms of facilitating the setting of the first matrix rubber model (described later).

  The set filler model 4 is stored in the storage device of the computer as numerical data. Specifically, the position of each node in the XYZ coordinate system of each tetrahedral element e1 constituting the filler model 4 and the material characteristics defined for each element are stored. In the present embodiment, the filler model 4 is handled as an elastic body. For this reason, the longitudinal elastic modulus, the Poisson's ratio, and the density are stored as material characteristics of each tetrahedral element e1 constituting the filler model 4.

  Further, as shown in FIG. 1, the matrix rubber 2 can be divided into a filler interface side portion 2A that contacts the filler 3 and has an arbitrary thickness D, and a base portion 2B outside thereof (however, The materials are the same.) In order to examine the change in rubber physical properties due to the filler 3, it is important to deform the filler interface side portion 2A more accurately. Therefore, in the present invention, as shown in FIGS. 5 and 6, the first matrix rubber model 5 is set by dividing the filler interface side portion 2A by a finite number of triangular prism elements e2.

  As shown in an enlarged view in FIG. 7, the triangular prism element e2 is formed by two opposing faces t made of a plane triangle, three quadrilateral faces h connecting between them, and six nodes n. Sometimes called. The facing triangles t and t do not have to be parallel to each other, and need not be the same shape. In addition, the distance from the surface t of one triangle to the surface t of the other triangle is the height of the triangular prism element e2 (in the case of accurate measurement, the distance between the centers of gravity of the triangular surfaces), and the direction is the height direction. And

  In the first matrix rubber model 5 of the present embodiment, five triangular prism elements e2 are overlapped in the thickness direction. In FIG. 8, the innermost triangular prism element e2 is indicated by a virtual line. The triangular prism element e2 is divided so that the height direction thereof is along the thickness direction of the filler interface side portion 2A. This is to the extent that the side s extending between the quadrilateral surfaces h and h of the triangular prism element e2 extends in the thickness direction, and the height direction of the triangular prism element e2 is the thickness of the filler interface side portion 2A. It does not mean that it is completely parallel to the vertical direction.

  The innermost triangular prism element e2 has a triangular inner surface t1 that shares a node n with each triangular surface t of the tetrahedral element e1 appearing on the outer surface 4o of the filler model 4. And it extends from the inner surface t1 to the outer surface t2 outside in the thickness direction (substantially radial direction). Such a triangular prism element e2 is arranged outside the filler model 4 without any gaps, and in the present embodiment, is stacked in five layers as shown in FIG. 9, whereby the first corresponding to the thickness D of the filler interface side portion 2A. The matrix rubber model 5 is formed.

  In such a first matrix rubber model 5, for example, the triangular prism element e <b> 2 can be formed by extending a triangular surface t appearing on the outer surface 4 o of the filler model 4 outward in the normal direction. It should be noted that the first matrix rubber model 5 and the filler model 4 can obtain the same effect by setting a constraint condition so that the relative distance between the first matrix rubber model 5 and the filler model 4 is not displaced at the boundary surface without sharing the nodes. it can.

  The first matrix rubber model 5 set in this way is also stored in the storage device of the computer as numerical data. Specifically, like the filler model 4, the position of each node of each triangular prism element e2 constituting the first matrix rubber model 5 and the material characteristics of each element are included. The defined material properties can include density, viscoelastic properties indicating the relationship between stress and strain, and deformation rate dependence.

  Here, the thickness D of the first matrix rubber model 5 is determined to be several angstroms in consideration of the minimum degree of deformation of the first matrix rubber model 5, that is, the intermolecular distance of the rubber molecules. desirable. Since the particle diameter of the filler is usually several tens of nanometers, the thickness D of the first matrix rubber model is desirably 1% or more of the particle diameter of the filler model. Further, the maximum value of the thickness D of the first matrix rubber model 5 is determined in consideration of the distance between the filler models 4 and 4 and the like, but the range in which the stress change near the particles is large corresponds to the distance between the fillers. Often within range. For this reason, the maximum value of the thickness of the first matrix rubber model is preferably 100% of the filler particle diameter.

  Further, the number of layers of the first matrix rubber model 5 (the number of triangular prism elements e2 stacked in the thickness direction) is not particularly limited. This is determined within the constraints on the total number of elements. However, when the number of layers of the triangular prism element e2 is increased within the limited thickness of the first matrix rubber model, the aspect ratio of each triangular prism element e2 tends to be too large. For this reason, the aspect ratio of the triangular prism element e2 is preferably about 1/10 or less. Note that the aspect ratio of the triangular prism element e2 is obtained by dividing the height by the representative length of the triangular surface t. The representative length of the triangular surface t is the length of the smallest side of the surface.

  Next, as shown in FIG. 5, a region j between the outer surface 5o of the first matrix rubber model 5 and the predetermined three-dimensional space V (that is, the base portion 2B of the matrix rubber 2) is set to a finite number. By dividing by the tetrahedral element e1, the second matrix rubber model 6 as shown in FIG. 10 is set. As a result, a rubber material model 10 in which the filler model 4, the first matrix rubber model 5, and the second matrix rubber model 6 are set in the space V is created (set).

  The predetermined three-dimensional space V can be set as appropriate based on conditions for performing simulation. In the present embodiment, the space V is set as a cube having X, Y, and Z of 100 nanometers each.

  Further, since the second matrix rubber model 6 is formed entirely of tetrahedral elements e1, as with the filler model 4, the mesh generation software is used to specify the region J to be divided in FIG. These are automatically set by inputting them together with the division conditions. At this time, as shown in FIG. 10, it is preferable to share all the nodes at the boundary surface between the second matrix rubber model 6 and the first matrix rubber model 5. However, even if the nodes are not shared, the same effect can be obtained by setting the constraint conditions so that the relative distances are not displaced at the boundary surface.

  The set second matrix rubber model 6 is stored as numerical data in a storage device of the computer. Specifically, the position of each node of each tetrahedron element e1 constituting the second matrix rubber model 6 and the material characteristics of each element are included. The defined material properties can include density, viscoelastic properties indicating the relationship between stress and strain, and deformation rate dependence. Each element of the second matrix rubber model 5 is also treated as incompressible.

  The rubber material model 10 thus obtained is preferably subjected to an overall deformation simulation based on, for example, a homogenization method (asymptotic expansion homogenization method). In the homogenization method, if the analysis target area is composed of repetitions of arbitrary microscopic structures and the repetition degree is very dense, the analysis target area cannot be discretized directly by the finite element method. This is a method for approximating the deformation of the microscopic structure itself by analyzing the whole by substituting and returning the analysis result to the microscopic structure at an arbitrary point, which is suitable for the analysis of rubber materials .

  Specifically, in the homogenization method, as shown in FIG. 11, xi expressing the entire material M having the rubber material model 10 periodically as a microscopic structure (also referred to as a unit cell); Two independent variables with yi representing the microscopic structure are used. By asymptotically expanding each independent variable in different scale fields, a microscopic scale and a macroscopic scale, the average mechanical response of the entire material M reflecting the structure of the rubber material model 10 as a unit cell is obtained. obtain.

  The operation of the rubber material model 10 configured as described above will be described. As shown in FIG. 12, for example, it is assumed that a deformation simulation for applying a tensile load F to the rubber material model 10 is performed. In the triangular prism element e2 of the first matrix rubber model 5, the nodes n1 and n2 shared with the filler model 4 are not displaced because the filler model b itself is sufficiently harder than the matrix rubber models 5 and 6. In addition, since the triangular prism element e2 of the first matrix rubber model 5 is defined as incompressible as a characteristic of rubber, a volume change cannot occur. However, the tetrahedral element e1 can extend in the tensile direction without causing a volume change by deforming the area of the outer triangular surface t2 to be small. This is useful for expressing the deformation of the filler interface side portion 2A during tension without deviating from the actual behavior. Therefore, a decrease in the calculation accuracy of the simulation is prevented.

  A deformation simulation was performed using the rubber material model (Example 1) shown in FIG. 10, and the calculation accuracy of the simulation was evaluated. The rubber material model is a 100 × 100 × 100 nanometer cubic space in which four filler models with a radius of 20 nanometers and four filler models with a radius of 15 nanometers are dispersed and arranged in a staggered manner. A first matrix rubber model and a second matrix rubber model were arranged (filler volume ratio about 20%). The average length of one side of the tetrahedral element used in the filler model and the second matrix rubber model is 2.5 nanometers. The first matrix rubber model has a thickness of 2.0 nanometers by stacking five triangular prism elements having a height of 0.4 nanometers.

  For comparison, a similar deformation simulation was performed for a rubber material model (comparative example) in which the first matrix rubber model portion was also divided by tetrahedral elements. The average length of one side of the tetrahedral element of this model is 2.5 nanometers.

  Further, a vulcanized rubber containing about 20% by volume of carbon black was actually molded, and a tensile test was performed on this. Next, the tensile test was similarly simulated using the above two types of rubber material models. For the simulation, analysis application software of “ABAQUS v6.5” manufactured by HKS was used. The calculation parameters of the matrix rubber model were set so as to coincide with the tensile test (strain rate: 0.0589) of vulcanized rubber not containing carbon black. Each true stress-elongation curve is shown in FIG.

  As is clear from FIG. 13, in the comparative example, the deviation from the actual measurement result is large, and a very large stress value is shown. That is, the material is hard. As described in FIG. 16, when the tetrahedral element is arranged around the filler model, if the node on the apex side of the tetrahedral element tries to be deformed in the tensile direction, this is a large amount for preventing volume change. This is probably because the resistance force is calculated.

  On the other hand, since the triangular prism element is used as the first matrix rubber model in Example 1, the volume change is not caused by extending in the tensile direction while deforming (smaller) the outer triangle in the thickness direction. Real deformation behavior can be reproduced. Therefore, it is presumed that a calculation result very close to the actual measurement result was obtained while mainly using tetrahedral elements.

  It is also conceivable to use hexahedral elements for the filler model and the matrix rubber model. However, in order to divide the spherical filler particles into hexahedral elements, unless the number of divisions is increased, the surface becomes uneven and there is a tendency that sufficient calculation accuracy cannot be obtained. On the other hand, when the number of divisions is increased, the calculation time tends to be long and the analysis efficiency tends to decrease. However, in the present invention, such a problem does not occur.

  FIG. 14 shows the result of a true stress-elongation curve when the same tensile test is performed using models having different specifications of the first matrix rubber model. In the examples of FIGS. 14A and 14B, the thickness of the first matrix rubber is 2.0 nanometers, but Example 2 is divided by triangular prism elements having a height of 2.0 nanometers, and Example 3 is high. Each of the triangular prism elements having a length of 0.2 nanometer is divided so as to overlap in the height direction. As is clear from FIG. 14, it was confirmed that the calculation accuracy is higher when a plurality of triangular prism elements are stacked in the height direction even if the thickness is the same.

It is sectional drawing of a rubber material. It is sectional drawing which visualizes and shows a filler model. It is a perspective view which visualizes and shows a filler model. FIG. 6 is a perspective view of a tetrahedral element. It is sectional drawing which visualizes and shows a filler model and a 1st matrix rubber model. It is the A section enlarged view. It is a perspective view explaining a triangular prism element. It is the elements on larger scale explaining the 1st matrix rubber model. It is the elements on larger scale explaining the 1st matrix rubber model. It is a diagram which shows a rubber material model. It is a diagram explaining a homogenization method. It is the schematic explaining the effect | action of the rubber material model of this embodiment. It is a graph which shows the relationship of the true stress-strain which shows the simulation result of a rubber material model. It is a graph which shows the relationship of the true stress-strain which shows the simulation result of a material model as another Example. It is sectional drawing of the conventional rubber material model. It is the principal part enlarged view.

Explanation of symbols

1 Rubber material 2 Matrix rubber 2A Interface side part 2A
2B base portion 3 filler 4 filler model 5 first matrix rubber model 6 first matrix rubber model 10 rubber material model e1 tetrahedral element e2 triangular prism element

Claims (3)

A method for creating a three-dimensional rubber material analysis model used when simulating deformation of a rubber material in which filler is mixed with matrix rubber using a computer,
Setting a filler model by dividing the filler in a three-dimensional shape by a finite number of tetrahedral elements;
A first matrix rubber is obtained by dividing a filler interface side portion in contact with the filler and having an arbitrary thickness among the matrix rubber by a finite number of triangular prism elements whose height direction is aligned with the thickness direction. Setting a model, and setting a second matrix rubber model by dividing a region between an outer surface of the first matrix rubber model and a predetermined space by a finite number of tetrahedral elements A method for creating a rubber material analysis model.   The rubber material analysis model creation method according to claim 1, wherein the first matrix rubber model has a thickness of 1 to 100% of a particle size of the filler model.   The rubber material analysis model creation method according to claim 1 or 2, wherein a plurality of the first matrix rubber models are stacked in the thickness direction.

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