JP2013054578A - Method for simulating rubber material - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a method for accurately defining a rubber material model for simulation from an actual rubber material.SOLUTION: A method for simulating a rubber material including filler comprises: an imaging step S1 of acquiring an electron transmission image of a rubber material using a scanning transmission electron microscope; a step S2 of constructing a three-dimensional structure of the rubber material by a tomography method, from the image that has been acquired in the imaging step; and a model setting step of setting a rubber material model from the three-dimensional structure of the rubber material. The model setting step includes: a step S4 of dividing the rubber material into same-shaped basic elements partitioned by regular grids to set an initial rubber material model; a step S5 of setting segmented areas for further dividing the reference element, in a part of the initial rubber material model; and a step S6 of dividing only each element of the segmented area into two or more.

Description

  The present invention relates to a rubber material simulation method, and more particularly to a method capable of accurately defining a rubber material model for simulation from an actual rubber material.

  Rubber materials such as tires are blended with fillers such as carbon black and silica from the viewpoint of reinforcement. It has been found that the dispersibility of the filler in the rubber material largely affects the rubber strength and the like, but the details are not so clear. For this reason, it is important to accurately observe the dispersion state of the filler in the rubber material and perform a simulation using a model based on the dispersion state.

JP 2007-131774 A JP 2008-66057 A JP 2010-108633 A

  The present invention has been devised in view of the above problems. A rubber material model is accurately set from an actual rubber material, and for example, only a part of a region where calculation accuracy is required is subdivided. An object of the present invention is to provide a rubber material simulation method capable of solving the above-described problems by dividing the elements.

  The invention according to claim 1 of the present invention is a method for simulating a rubber material containing a filler, the imaging step of obtaining an electron beam transmission image of the rubber material using a scanning transmission electron microscope, A model setting step including a step of constructing a three-dimensional structure of a rubber material from the image obtained in the imaging step by a tomography method, and a model setting step of setting a rubber material model based on the three-dimensional structure of the rubber material. Is a step of setting an initial rubber material model by dividing by basic elements of the same shape divided by a regular lattice, and setting a subdivision area for further dividing the basic elements in a part of the initial rubber material model And a step of dividing each element of the subdivided region into two or more.

  The invention according to claim 2 is characterized in that the imaging step focuses the scanning transmission electron microscope on a central region of the thickness of the rubber material.

  According to a third aspect of the present invention, the imaging step includes the step of imaging the rubber material in a plurality of angle states with different angles with respect to an optical axis of an electron beam of the scanning transmission electron microscope, and the focus Is matched to the central region of the apparent thickness along the direction of the electron beam crossing the rubber material.

  The invention according to claim 4 is characterized in that the rubber material has a thickness of 200 to 1500 nm.

  The invention according to claim 5 is characterized in that a distance between the rubber material and a transmission electron detector of the scanning transmission electron microscope is 8 to 150 cm.

  In the rubber material simulation method of the present invention, an imaging step of acquiring an electron beam transmission image of the rubber material using a scanning transmission electron microscope, and a three-dimensional rubber material by a tomography method from the image obtained in the imaging step And a model setting step for setting a rubber material model based on the three-dimensional structure of the rubber material, wherein the model setting step is divided by basic elements having the same shape divided by a regular lattice. A step of setting an initial rubber material model, a step of setting a subdivision area for further dividing the basic element in a part of the initial rubber material model, and dividing each element of the subdivision area into two or more Including the step of:

  According to such a method, an accurate rubber material model can be obtained based on the actual rubber material, and an accurate simulation result can be obtained by performing deformation calculation based on the model. In particular, as in the second aspect of the present invention, in the imaging step, it is desirable to focus the electron beam of the scanning transmission electron microscope on the central region of the thickness of the rubber material. By adopting such a method, it is possible to secure a wider focal depth region in which the clear image can be obtained in the rubber material. Therefore, a clear image can be obtained as compared with the prior art, and as a result, the dispersion state of the filler of the rubber material can be grasped more accurately and dropped into the model.

  In the present invention, an initial rubber material model is set by dividing a rubber material by basic elements having the same shape divided by a regular lattice. Thus, by dividing the elements using the regular lattice, an initial rubber material model can be created in a short time. Further, in the present invention, a subdivided region is set in a part of the initial rubber material model, and only each element of the subdivided region is divided into two or more. Since the subdivided region is limited to a part of the initial rubber material model, it is possible to prevent a significant increase in the number of elements and shorten the time for subdividing the elements. In particular, by setting a portion for which the deformation state is to be examined in more detail as a subdivided region, a rubber material model that improves the calculation accuracy while suppressing an increase in the number of elements can be efficiently created.

It is a schematic partial expanded sectional view of the rubber material of this embodiment. It is a flowchart explaining the process sequence of this embodiment. It is the schematic which shows an example of the scanning transmission electron microscope apparatus used by this invention. It is the schematic which shows an example of the scattering angle limiting stop for dark field limitation. It is explanatory drawing of the sample inclination part which inclines a sample. (A), (b) is a side view which shows the positional relationship of the focus and sample in an imaging process. It is a side view which shows the positional relationship of the focus and sample in an imaging process. It is a three-dimensional image of the rubber material obtained from the sample by the method of this embodiment. (A) is the elements on larger scale of a two-dimensional rubber material model, (b) is the principal part enlarged view further. (A) is the elements on larger scale of a two-dimensional rubber material model, (b) is the principal part enlarged view further. It is a typical enlarged view of a part of a three-dimensional rubber material model. It is an enlarged view of the element explaining the subdivision of the element of a cube. It is a slice image in the sample upper part and lower part about Experimental example 1 and 2. FIG. It is a side view explaining the upper part and lower part of a sample. It is a graph which shows the relationship of the stress-strain which shows the result of simulation.

Hereinafter, an embodiment of the present invention will be described with reference to the drawings.
In the present embodiment, as shown in FIG. 1, the object to be analyzed is a rubber material c containing a filler containing a rubber component a as a matrix rubber and a filler b, and the deformation calculation is performed by a computer (illustrated). Is omitted).

  Examples of the rubber component a include natural rubber (NR), isoprene rubber (IR), butyl rubber (IIR), butadiene rubber (BR), styrene butadiene rubber (SBR), styrene isoprene butadiene rubber (SIBR), and ethylene. Examples include propylene diene rubber (EPDM), chloroprene rubber (CR), and acrylonitrile butadiene rubber (NBR). Further, the filler b is not particularly limited, and examples thereof include carbon black, silica, clay, talc, magnesium carbonate, magnesium hydroxide, and the like. The rubber material c may be appropriately mixed with various materials generally used in the rubber industry such as sulfur and a vulcanization accelerator.

  FIG. 2 shows a flowchart for carrying out the simulation method of the present embodiment. First, in the present embodiment, an imaging step of acquiring an electron beam transmission image of the rubber material c using a scanning transmission electron microscope is performed (step S1).

  In the present invention, as an apparatus including a scanning transmission electron microscope, for example, the one shown in FIG. 3 is used. The scanning transmission electron microscope apparatus 100 includes an electron gun 1 and a focusing lens for focusing a primary electron beam 2 emitted from the electron gun 1 at a right angle and below the horizontal plane onto a sample 5 made of the rubber material c. 3 and an X direction scanning coil 4X and a Y direction scanning coil 4Y for scanning the sample 5 in the X direction and the Y direction.

  The sample 5 is fixed to a sample holder 6. The sample holder 6 is provided with an electron beam passage hole 8 through which the transmitted electrons 7 transmitted through the sample 5 pass along the optical axis O of the electron beam at the center. The sample holder 6 is attached to the sample stage 9. The sample 5 has a plate shape having a constant thickness t.

  The sample stage 9 is provided with an electron beam passage hole 10 that is continuous with the electron beam passage hole 8 along the electron beam optical axis O at the center. Further, on the downstream side of the sample stage 9, a scattering angle limiting stop 11 for limiting the passage of the transmitted electrons 7 is provided.

  Furthermore, a scintillator 13 for converting the transmitted electrons 12 into light and a photomultiplier tube 14 for converting the converted light into an electronic signal are provided on the downstream side of the scattering angle restricting stop 11, and thereby, A transmission electron detector 20 is constructed.

  The sample stage 9, the scattering angle limiting aperture 11, the scintillator 13, and the photomultiplier tube 14 are arranged in a sample chamber (not shown) of the scanning transmission electron microscope apparatus main body 100, and the sample holder 6 is placed on the sample stage 9. On the other hand, it is detachably mounted.

  The operation of the scanning transmission electron microscope apparatus 100 will be described. First, the sample holder 6 on which the sample 5 is fixed is mounted on the sample stage 9 by the operator.

  Next, the primary electron beam 2 emitted from the electron gun 1 is accelerated by acceleration means (not shown), focused by the focusing lens 3, and scanned on the sample 5 by the X-direction and Y-direction scanning coils 4X and 4Y. To do. By scanning on the sample 5 with such an electron beam, the electrons 7 scattered in the sample 5 or transmitted through the sample 5 without scattering are emitted from the lower surface of the sample 5.

  The acceleration voltage of the electron beam is preferably 100 to 3000 kV. If the accelerating voltage is less than the lower limit, the electron beam does not pass through the sample and thus may not be observed. If the acceleration voltage exceeds the upper limit, damage to the sample 5 may not be observed.

  The transmitted electrons 7 have different intensities and scattering angles depending on the internal state, thickness, and / or atomic species of the sample 5. Further, the scattering angle of the transmitted electrons 7 also changes depending on the acceleration voltage of the electron beam. For example, when the accelerating voltage is lowered, the transmission electron 7 is scattered by the sample 5, and the transmission angle of the transmission electron emitted from the lower surface of the sample 5 is increased from the optical axis O (scattering angle). .

  Further, the transmitted electrons 7 emitted from the lower surface of the sample 5 reach the scattering angle restricting aperture 11 after passing through the electron beam transmitting hole 8 and the electron beam passing hole 10 of the sample holder 6 and the sample stage 9, respectively. The scattering angle limiting aperture 11 is limited in the diameter of the hole opened at the center thereof so that only transmitted electrons having a specific scattering angle can pass therethrough.

  As such a scattering angle restricting stop 11, in addition to the above-described embodiment, as shown in FIG. 4, a scattering angle with a shielding plate that restricts the passage of transmitted electrons 7 by arranging a shielding plate 17 at the center of the hole. A limiting aperture 16 may be employed. In general, when the scattering angle limiting stop 11 is used, the electron beam transmission image forms a bright field image, and when the scattering angle limiting stop 16 with a shielding plate is used, a dark field image is formed.

  The transmitted electrons 12 that have passed through the scattering angle limiting aperture 11 collide with the scintillator 13 and are converted into light, and then are converted into electric signals by the photomultiplier tube 14. This electric signal is amplified by amplifying means (not shown) and sent to display means (both not shown) via an A / D converter. The display means can modulate the luminance of the transmitted signal, display an electron beam transmission image reflecting the internal structure of the sample 5, and obtain a plurality of images according to the scanning position.

  The distance L1 (camera length) between the sample 5 and the scintillator 13 is preferably 8 to 150 cm. If the distance L1 is less than 8 cm or more than 150 cm, the image may become unclear.

  In the present invention, in the imaging step, the rubber material c is imaged in a plurality of angular states with different angles with respect to the optical axis O of the electron beam of the scanning transmission electron microscope apparatus 100. For this purpose, the scanning transmission electron microscope apparatus 100 is provided with a sample tilt portion that tilts (rotates) the sample 5 with respect to the electron beam.

  As shown in FIG. 5, the sample inclined portion can hold the sample 5 while being inclined with respect to the horizontal plane H by an angle θ (θ ≠ 0). The inclined sample 5 is irradiated with the electron beam e, and the electron beam transmitted through the sample 5 becomes a transmitted electron beam e ′. By outputting a control signal from the computer device or the like to the sample tilt portion, the sample 5 is tilted to a predetermined angle.

  For example, the sample 5 is tilted to the measurement start angle by the operator, and an electron beam transmission image is acquired in that state. Here, the first angle θ can be appropriately set by the operator, and is set to +70 degrees in the present embodiment. After the electron beam transmission image is acquired, the steps of tilting the sample 5 and acquiring the image are repeated in units of a predetermined angle until the measurement end angle set by the operator. Thereby, a rotation series image (a plurality of images) is obtained.

  Here, the unit of the angle at which the sample 5 is inclined (the angle at which the sample is inclined at each inclination step of the sample inclined portion) is preferably 0.5 to 4 degrees, more preferably 1 to 2 degrees. If the unit of the angle is less than 0.5 degrees, the imaging time becomes long and the sample 5 may be damaged. Conversely, if the unit of the angle exceeds 4 degrees, the slice image after reconstruction ( (Described later) may become unclear.

  Further, the angle θ of the sample 5 is not particularly limited, but as a theoretical ideal obtained by processing the sample into a rod shape, it is preferable to measure in the entire range of −180 degrees to +180 degrees. It is desirable to measure in the range of −90 degrees to +90 degrees, more preferably −70 degrees to +70 degrees.

  Further, in the imaging process of the present embodiment, as shown in an enlarged view in FIG. 6A, in the imaging process, the focus F of the scanning transmission electron microscope apparatus 100 is set to the thickness of the sample 5 (rubber material). To the central region C of FIG.

  In the conventional imaging process, as shown in FIG. 7, the focus F of the electron beam e is adjusted to the upper surface 5 a of the sample 5. However, in such a method, there is a problem that a clear image cannot be obtained on the lower surface 5b of the sample 5. For example, in the case where the actual thickness t of the sample 5 is t = 1000 nm and the distance G = 600 nm (focus depth f = 1200 nm) where the focus of the electron microscope is focused, when the focus F is aligned with the surface 5a of the sample 5, the lower surface side of the sample 5 A clear image cannot be obtained in the region B of 400 nm. In particular, such a problem is likely to occur when the thickness t of the sample increases.

  On the other hand, as in the present embodiment, by positioning the focal point F in the central region C of the thickness of the sample 5 (rubber material), a range where a clear image can be obtained, that is, a region having a focal depth f. A wider area can be secured inside the sample 5 (in this example, f = t).

  FIG. 6A shows a mode in which the upper surface 5a and the lower surface 5b of the sample 5 are orthogonal to the horizontal plane, that is, orthogonal to the optical axis O of the electron beam e. In this case, the thickness of the sample 5 is equal to the actual thickness t in the direction perpendicular to the upper surface 5a and the lower surface 5b. The central region C does not have to be a complete center position of the thickness of the sample 5, but is preferably a region of 30% of the thickness centering on the center position of the thickness. More preferably, the area is 20%, more preferably 10%.

  FIG. 6B shows a mode in which the upper surface 5a and the lower surface 5b of the sample 5 are inclined with respect to the horizontal plane, that is, are not orthogonal to the optical axis O of the electron beam e. The thickness of the sample 5 in this case is determined as an apparent thickness t ′ along the optical axis direction of the electron beam e that crosses the sample 5. The central region C is determined based on the apparent thickness t ′. The apparent thickness t ′ is easily calculated by t / cos θ using the thickness t of the sample 5 and the inclination angle θ. As described above, when the actual thickness direction of the sample 5 is not orthogonal to the optical axis O of the electron beam, the sample region 5 is determined by determining the central region C based on the apparent thickness t ′. A clear electron transmission image can be obtained even when tilted.

  The focus F can be performed using the focus adjustment mechanism of the scanning transmission electron microscope apparatus 100, and can be performed by adjusting the focusing lens 3, the sample stage 9, and the like.

  Note that the thickness t of the sample 5 is not particularly limited. That is, the thickness t may be less than 200 nm or 200 nm or more according to the custom. According to this embodiment, the dispersion state of the filler can be satisfactorily observed with any sample thickness. The thickness t is preferably 200 to 1500 nm, more preferably 500 to 1000 nm. By being able to observe up to 1500 nm, the observation accuracy of the aggregated structure of the filler of the sample of 200 nm or more can be improved, and the accurate dispersion state of the filler can be analyzed.

  Next, in the present embodiment, a process of constructing a three-dimensional structure of a rubber material by a tomography method from the image obtained in the imaging process is performed (step S2). That is, in the imaging step, the sample 5 of the rubber material containing the filler is irradiated and scanned with the electron beam focused using the scanning transmission electron microscope to obtain a plurality of electron beam transmission images. At this time, the sample 5 is tilted with respect to the electron beam by a predetermined angle unit, and an electron beam transmission image is acquired for each angle, so that the acquired electron beam transmission image is obtained by using the tomography method. Reconstructed as a dimensional structure, a three-dimensional image of the dispersed state of the filler in the rubber material is generated. An example of such a three-dimensional structure is shown in FIG. 8, and is stored on a computer as numerical data.

  Next, in this embodiment, the process of acquiring the slice image of the rubber material c from the said three-dimensional structure is performed (step S3). Since such a slice image has already obtained the three-dimensional structure of the sample 5 (rubber material c), it can be easily output from the computer by designating the position of the cross section.

  Next, in the present embodiment, a step of setting an initial rubber material model from the slice image of the rubber material c is performed (step S4). This step includes a step of performing image processing on the slice image to divide all areas of the slice image into at least a rubber portion and a filler portion. Such image processing is already known, and by setting a threshold value for information such as brightness and luminance of the image in advance, the computer converts each area of the slice image into a rubber part and a filler part. Identify automatically.

  Next, in the image processing, the slice image is divided into a rubber part and a filler part, and then this slice image is divided into basic elements of the same shape that are divided by a regular lattice. The model is set.

  In FIG. 9A, a part of the initial rubber material model 5a of the present embodiment is visualized. FIG. 9B shows a partially enlarged view thereof. As shown in an enlarged view in FIG. 9B, the regular lattice is composed of a lattice GD of vertical lines L1 and horizontal lines L2 arranged at the same pitch P on the x-axis and the y-axis. Each square divided by the vertical line L1 and the horizontal line L2 constitutes one basic element eb. More specifically, the basic element eb is a square element (a quadrilateral element) having nodes n at four corners arranged at the intersections of the vertical line L1 and the horizontal line L2.

  The initial rubber material model 5a of the present embodiment includes a rubber model 21 simulating the rubber part a and a filler model 22 simulating the filler b.

  The filler model 22 is colored and displayed in FIG. 9A for easy understanding. The filler model 22 is set by discretizing the filler b using a finite number of basic elements eb.

  The rubber model 21 is set by discretizing the rubber part a of the rubber material c with a finite number of basic elements eb.

  In such element division, for example, using the computer, a regular lattice is set on the slice image that has been subjected to image processing, and either the rubber a or the filler b has a larger area for each basic element eb. The occupancy is calculated. Based on the calculation result, it is determined whether each basic element eb belongs to the rubber model 21 or the filler model 22. As described above, the initial analysis model can be created in a short time by using only the basic element eb divided by the regular lattice, and the slice image of the three-dimensional structure of the rubber material 5 photographed with high accuracy is used. Are set as being very close to the object to be analyzed.

  In the basic element eb, information necessary for numerical analysis by simulation is defined. The numerical analysis means a numerical analysis method such as a finite element method. The information necessary for the analysis includes at least the number of the node n constituting each basic element eb and the coordinate value of the node n. Further, each basic element eb defines a material characteristic (physical property value) of a portion represented by each element. That is, material constants corresponding to the physical properties of the filler and rubber are defined in the basic elements eb of the rubber model 21 and the filler model 22, respectively. These pieces of information are all input and stored in the computer.

  Next, in the present embodiment, a subdivision area 23 for further dividing the basic element eb is set in a part of the initial rubber material model 5a (step S5).

  The said subdivision area | region 23 is a part comprised by the element smaller than the basic element eb among the rubber material models 5a. Therefore, in the subdivided region 23, the deformation behavior can be examined in more detail, and high calculation accuracy can be obtained. Therefore, it is desirable to set the subdivided area 23 in a portion that meets such requirements.

  In the case of the rubber material c in which the filler is blended, as shown in FIG. 1, large strain and stress are likely to be generated in the rubber part a1 between the adjacent filler particles b. Therefore, in this embodiment, the rubber part sandwiched between the filler models 22 and 22 is set as the subdivided region 5 so as to include the rubber part a1 at least in part.

  For example, a range of the subdivided area 23 may be designated by the user using an input unit such as a keyboard or a mouse. Predetermined information is added to the elements of the area designated as the subdivided area 23 and input to the computer.

  Further, the subdivided region 23 may be determined by other methods. For example, first, a deformation simulation is performed using the initial rubber material model 5a and based on predetermined deformation conditions. Then, from the result of the deformation simulation, a large deformation region including the largest stress or strain portion of the initial rubber material model 5a is specified, and a region including at least a part of the large deformation region is determined as the subdivided region 23. May be.

  Next, in this embodiment, subdivision is performed to divide each basic element of the subdivision area 5 into two or more (step S6).

  The subdivision step S6 can be performed, for example, by reducing the pitch P of the vertical lines L1 and / or the horizontal lines L2 of the regular lattice passing through the subdivision area 23 to reduce the basic element eb. In this embodiment, as shown in FIG. 10 (a) and FIG. 10 (b) which is a partially enlarged view, only the pitch of the horizontal line L2 of the regular lattice passing through the subdivided region 23 is the initial rubber material model 5a. For example, the pitch P is reduced to ½ of the pitch P determined at the time. Thereby, the basic element eb of the rubber part sandwiched between the filler models 22 and 22 is divided into two equal parts in the y direction. That is, each basic element eb of the subdivision area 23 is divided into small rectangular elements es having the same x dimension and the y dimension of 1/2 as the original basic element eb.

  Therefore, by performing deformation simulation using the analysis model 5b that has undergone the subdivision step S6, it is possible to improve the calculation accuracy of the rubber portion (subdivision region 23) between the filler models 22 and 22. Further, the deformation behavior of the rubber part can be examined in more detail. In addition, the change of the pitch at the time of subdividing is not limited to the above 1/2, and can be set to various values. Further, the subdivision step S3 may be repeated a plurality of times until a necessary element resolution is obtained.

  In the above embodiment, the two-dimensional rubber material model 5a has been described as an example. However, as shown in FIG. 11, the present invention can be applied to a three-dimensional rubber material model 5c. It goes without saying that it can be done with. In this case, modeling can be performed directly from the three-dimensional structure of the rubber material c without using a slice image. In the case of the three-dimensional model 5c, the basic element eb divided by the regular lattice is a rectangular parallelepiped element.

  The step of subdividing the three-dimensional rubber material model 5c includes, for example, a basic element eb similar to the basic element eb inside the cubic basic element eb as shown in the upper diagram of FIG. One cubic small element es smaller than eb is set so that the centers of gravity are aligned with each other. Next, as shown in the lower diagram of FIG. 12, each node ns of the small element eb is assigned to the corresponding node of the basic element eb. Each nb is connected with a side s. Thereby, the basic element eb can be divided into one cubic small element es and six hexahedral elements ea surrounding it.

  Although the present invention has been described in detail above, it is needless to say that the present invention is not limited to the above-described embodiment, and can be implemented in various forms.

  In order to confirm the effect of the present invention, the following experiment was conducted. However, the present invention is not limited to these examples.

Various chemicals and devices used in the experiment are as follows. That is, according to the composition shown below, materials other than sulfur and a vulcanization accelerator were kneaded for 4 minutes under the condition of a discharge temperature of 160 ° C. using a Banbury mixer to obtain a kneaded product. Next, sulfur and a vulcanization accelerator were added to the obtained kneaded product, and kneaded for 2 minutes at 100 ° C. using an open roll to obtain an unvulcanized rubber composition. Furthermore, the obtained unvulcanized rubber composition was vulcanized at 175 ° C. for 30 minutes to obtain a vulcanized rubber.
[Rubber compounding] (Unit: parts by mass)
SBR 100
Silica 53.2
Silane coupling agent 4.4
Sulfur 0.5
Vulcanization accelerator A 1
Vulcanization accelerator B 1
[Chemicals]
SBR: SBR1502 manufactured by Sumitomo Chemical Co., Ltd.
Silica: 115Gr made by Rhodia Japan
Silane coupling agent: Si69 manufactured by Degussa
Sulfur: Powder sulfur manufactured by Tsurumi Chemical Co., Ltd. Vulcanization accelerator A: Noxeller NS manufactured by Ouchi Shinsei Chemical Co., Ltd.
Vulcanization accelerator B: Noxeller D manufactured by Ouchi Shinsei Chemical Industry Co., Ltd.
[apparatus]
Microtome: Ultramicrotome EM VC6 manufactured by LEICA
Electron microscope: Transmission electron microscope JEM2100F manufactured by JEOL Ltd.

  Next, a sample (section) having a thickness of 500 nm was produced from the obtained vulcanized rubber using a microtome.

  Next, the obtained sample was placed on a mesh, set in a sample chamber of an electron microscope, a camera length of 150 cm, and an acceleration voltage for electron beam irradiation were set to 200 kV. In the STEM mode, the electron beam was scanned at various rotation angles (−60 degrees to +60 degrees), and each STEM image was acquired.

  In the imaging process, in Experimental Example 1, the focal point was adjusted to the center position of the thickness of the sample. In Experimental Example 2, the focal point was adjusted to the upper surface of the sample. Each sample was tilted in units of 1 degree, and STEM images in the rotation angle range were acquired. In addition, by reconstructing all the obtained STEM images by a computer tomography method, a slice image of each cross section was obtained, and a three-dimensional image of the sample was obtained with the rubber component being black and the filler being white.

  FIG. 13 shows slice images of the upper part A1 and the lower part A2 of the three-dimensional structural diagrams obtained in Experimental Examples 1 and 2. As shown in FIG. 14, the upper part A1 and the lower part A2 of the sample are respectively located at a distance z of 40 nm inside the sample from the upper surface and the lower surface of the sample, respectively. As is clear from FIG. 13, in the experimental example 2 in which the focus is adjusted to the upper surface of the sample, the slice image at the lower part of the sample is blurred, but in the experimental example 1 in which the focus is adjusted to the center of the sample, A clear image was also obtained for the slice image of the lower surface of the sample.

  Next, based on the lower slice image of Experimental Example 1, two types of two-dimensional rubber material models of the comparative example and the example were set. In the comparative example, the slice image is divided by square basic elements. In the example, the basic material of the rubber portion between the filler particles in the rubber material model of the comparative example is further divided into halves only in the y direction.

  And the simulation of the tensile deformation was performed about the rubber material model of these Examples and Comparative Examples. For comparison, the actual vulcanized rubber was also subjected to a tensile test under the same conditions. Main test conditions are, for example, as disclosed in JP 2010-205165 A, using a homogenization method, applying a tensile deformation at a speed of 100 mm / min to a macroscopic area 20 mm × 20 mm, and a maximum deformation amount 3 mm (strain 15%). It was.

  The result of the test is shown in FIG. Although the Example has a high correlation with the actual vulcanized rubber, it can be confirmed that the difference from the result of the actual vulcanized rubber is large in the comparative example.

DESCRIPTION OF SYMBOLS 1 Electron gun 2 Primary electron beam 3 Focusing lens 4X X direction scanning coil 4Y Y direction scanning coil 5 Sample 5a, 5b, 5c Rubber material model 6 Sample holder 7, 12, 15 Transmission electron 8, 10 Electron beam passage hole 9 Sample stage 11, 16 Scattering angle limiting aperture 13 Scintillator 14 Photomultiplier tube 17 Shield plate 21 Rubber model 22 Filler model 23 Subdivision area 100 Scanning transmission electron microscope apparatus

Claims (5)

A method for simulating a rubber material containing a filler,
An imaging step of acquiring an electron beam transmission image of the rubber material using a scanning transmission electron microscope;
A step of constructing a three-dimensional structure of a rubber material by a tomography method from the image obtained in the imaging step;
A model setting step of setting a rubber material model based on the three-dimensional structure of the rubber material,
The model setting step is a step of setting an initial rubber material model by dividing by basic elements of the same shape divided by a regular lattice;
A rubber material comprising: setting a subdivision area for further dividing the basic element in a part of the initial rubber material model; and dividing each element of the subdivision area into two or more. Simulation method.   2. The rubber material simulation method according to claim 1, wherein the imaging step focuses the scanning transmission electron microscope on a central region of the thickness of the rubber material. The imaging step includes the step of imaging the rubber material in a plurality of angular states with different angles with respect to the optical axis of the electron beam of the scanning transmission electron microscope,
The rubber material simulation method according to claim 1, wherein the focal point is adjusted to a central region of an apparent thickness along a direction of an electron beam crossing the rubber material.   The rubber material simulation method according to claim 1, wherein the rubber material has a thickness of 200 to 1500 nm.   The method for simulating a rubber material according to any one of claims 1 to 4, wherein a distance between the rubber material and a transmission electron detector of the scanning transmission electron microscope is 8 to 150 cm.