JP5495516B2 - Rubber material deformation behavior prediction apparatus and rubber material deformation behavior prediction method - Google Patents

Description

  The present invention relates to an apparatus for predicting deformation behavior of a rubber material in which rubber and a filler such as carbon black or silica are blended, and a method for predicting the deformation behavior of a rubber material.

Conventionally, it is known that there is a reinforcing effect when a filler such as carbon black or silica is blended with rubber, and rubber materials blended with rubber are widely used in rubber products such as tires and conveyors. .
In such a rubber material, the deformation behavior and the like when a force is applied are measured by experiments, and the measurement results are evaluated to design the blending amount of the filler.

On the other hand, recently, various methods such as the finite element method (FEM) and other numerical analysis methods and the development of computer environments have created various methods for analyzing the deformation behavior etc. by creating a three-dimensional model of the filler region and rubber region of rubber materials. Has been.
For example, it is described that a three-dimensional model in which a rubber material filler region is viewed as a rigid sphere is created, and the stress and strain generated when the rubber material is stretched are analyzed by the finite element method. It has been found that this is consistent with the GOTH equation showing the increase in elastic modulus due to the volume effect of the filler compounded in the rubber material, and the experimental results (see Non-Patent Document 1, for example).

  In addition, it is described that a three-dimensional model in which the shape of the filler region of the rubber material is changed from a sphere to a rod shape and analyzed by a finite element method is used. It is possible to analyze strain and stress distribution (see, for example, Non-Patent Document 2).

  By the way, it is known that the structure of the filler in the actual rubber material forms a complex network structure in which a plurality of fillers are connected, and the filler region of the rubber material is regarded as a sphere or rod. The simple three-dimensional model cannot accurately analyze the deformation behavior of the rubber region and the filler region in the actual rubber material at the micro level.

For this reason, for example, a slice image obtained by slicing a rubber material at a predetermined interval is obtained by a CT scanner (computer tomography scanner), and rubber included in each slice image based on the density value of each pixel constituting the slice image. A three-dimensional model is created by discriminating a portion and a filler portion, layering each slice image in the order of slice positions, and using each pixel constituting each slice image as a lattice region, and using the three-dimensional model, rubber It is considered to analyze the deformation behavior of materials precisely at the micro level.
However, when an analysis is performed using such a three-dimensional model, although the deformation behavior of the rubber material can be analyzed precisely at the micro level, the number of lattice areas of the three-dimensional model becomes enormous, so that the analysis takes time. There is a problem of this.

  Therefore, the present inventors can accurately analyze the deformation behavior of the rubber material and reduce the analysis time, and as a deformation behavior prediction apparatus and method for predicting the deformation behavior of the rubber material, the filler of the actual rubber material The structure of the film is photographed with a transmission electron microscope (TEM), and the obtained data is reconstructed into a three-dimensional basic model by the computer tomography method (CT method), and the deformation behavior of the rubber material is predicted by the finite element method (FEM). The technique which develops is developed (for example, refer patent document 1).

However, the technology for predicting the deformation behavior of a rubber material using a three-dimensional basic model by the transmission electron microscope (TEM) and the computed tomography method (CT method) of the above-mentioned Patent Document 1 is an excellent technology that has never been seen before. However, in a transmission electron microscope (TEM), a continuous inclination of a rubber material is performed by scanning while relatively rotating by a predetermined angle (for example, an interval of 2 degrees) in a range of −60 degrees to +60 degrees. As shown in FIG. 16, the thickness of the rubber material is limited to about several hundred nm, and the primary particle size present in a general rubber material is several tens of nm. It is difficult to accurately represent a complex network structure with several dozen or more fillers, and it is difficult to accurately represent the placement of fillers with a primary particle size of several hundreds of nanometers. There is.
Miho Fukahori, “Polymer Dynamics for Design”, Gihodo, 2000, P188, P340, etc. J. Busfield and Alan Muhr, “Consilitutive Models for Rubber III”, Balkema, 2003, P301. Japanese Patent Laying-Open No. 2006-200937 (Claims, First Embodiment, etc.)

  The present invention is to solve this problem in view of the above-described conventional problems and the present situation, and is a complex in which several tens of fillers having a primary particle size of several tens of nanometers existing in a rubber material are connected. An object of the present invention is to provide a rubber material deformation behavior prediction apparatus and a deformation behavior prediction method capable of accurately analyzing the deformation behavior of a rubber material having a network structure and further reducing the analysis time.

  As a result of intensive studies on the above-described conventional problems and the like, the present inventors perform the configuration of a three-dimensional basic model by a conventional transmission electron microscope (TEM) and a computer tomography method (CT method) by other specific means. Thus, the present inventors have found that a deformation behavior predicting apparatus and a deformation behavior predicting method for the rubber material can be obtained, and have completed the present invention.

That is, the present invention resides in the following (1) to (5).
(1) A rubber material having a predetermined shape in which rubber and a filler are blended is etched at a predetermined interval by a focused ion beam, and each etched surface is observed by a scanning electron microscope to obtain a plurality of slices. An acquisition means for acquiring an image;
Conversion means for converting into a binarized image for discriminating between a rubber part and a filler part included in each slice image based on the density value of each pixel constituting each slice image acquired by the acquisition means; ,
A plurality of binarized images converted by the converting means, and a three-dimensional model generating means for generating a three-dimensional model by stacking at a predetermined interval;
Giving means for imparting a structural condition that defines the relationship between strain and stress of rubber or filler based on the binarized value for each lattice region of the three-dimensional model generated by the three-dimensional model generating means When,
Analyzing means for analyzing deformation behavior using the three-dimensional model to which the configuration condition is given by the giving means;
A rubber material comprising: a presenting means for calculating a strain distribution or a stress distribution based on an analysis result by the analyzing means, distinguishing a strain or stress distribution area, specifying a position of each area, and presenting Deformation behavior prediction device.
(2) The apparatus for predicting deformation behavior of a rubber material according to (1), wherein the etching treatment is 0.1 to 100 nm.
(3) The deformation behavior prediction apparatus for a rubber material according to (2), wherein the etching treatment when carbon black and / or silica is used as a filler is 0.1 to 30 nm.
(4) The rubber material according to any one of (1) to (3) above, wherein the deformation behavior of the three-dimensional model is analyzed using a finite element method to which the constituent conditions are given. Deformation behavior prediction device.
(5) A rubber material having a predetermined shape in which rubber and a filler are blended is etched at a predetermined interval by a focused ion beam, and each etched surface is observed by a scanning electron microscope to obtain a plurality of slices. Get an image,
Converted into a binarized image for discriminating between the rubber part and the filler part contained in each slice image based on the density value of each pixel constituting each acquired slice image,
A plurality of binarized images that have been converted are stacked at predetermined intervals to generate a three-dimensional model,
A structural condition that defines a relationship between strain and stress of rubber or filler based on the binarized value is assigned to each lattice region of the generated three-dimensional model,
Analyzing deformation behavior using the three-dimensional model to which the constituent conditions are given,
Deformation of rubber material characterized by calculating strain distribution or stress distribution according to the analysis result, distinguishing strain or stress distribution area, specifying the position of each area, and predicting deformation behavior of rubber material Behavior prediction method.

  According to the present invention, the deformation behavior of a rubber material having a complicated network structure in which dozens of fillers having a primary particle size of several tens of nanometers existing in the rubber material are connected can be accurately analyzed at a micro level. In addition, the analysis time can be further shortened, and the change in physical properties due to strain can also be predicted, whereby the deformation behavior prediction apparatus for rubber material and the deformation behavior prediction method thereof capable of controlling physical properties such as the breaking strength of the rubber material. Is provided.

Hereinafter, embodiments of the present invention will be described in detail with reference to the drawings.
FIG. 1 shows a configuration diagram of a rubber material deformation behavior prediction system as an example of a rubber material deformation behavior prediction device of the present invention.
The rubber material deformation behavior prediction system 10 includes a focused ion beam (FIB) -scanning electron microscope (SEM) apparatus 11 and a computer 12. The FIB-SEM apparatus 11 and the computer 12 are connected by a cable 20.

  The FIB-SEM apparatus 11 includes a transmission electron microscope and a sample stage. The FIB-SEM apparatus 11 performs an etching process using a focused ion beam (FIB) on a rubber material to be analyzed placed on a sample stage and repeatedly performs imaging with a transmission electron microscope. Then, the FIB-SEM apparatus 11 generates slice image data photographed at a predetermined interval.

The computer 12 displays a keyboard 15 for inputting various conditions for analysis, a computer main body 13 for analyzing the deformation behavior of the rubber material in accordance with a pre-stored processing program, and calculation results of the computer main body 13. And a display 14. The computer 12 analyzes the deformation behavior of the rubber material using the slice image data generated by the FIB-SEM apparatus 11.
The computer main body 13 includes a flexible disk drive unit (hereinafter referred to as FDU) 18 into which a flexible disk (hereinafter referred to as FD) 16 as a recording medium can be inserted and removed.

Next, the configuration of the main part of the electrical system of the computer 12 will be described with reference to FIG.
The computer 12 temporarily stores a CPU (central processing unit) 40 that controls the operation of the entire apparatus, a ROM 42 that stores various programs and various parameters including a control program for controlling the computer 12, and various data. Connected to the RAM 48 and the connector 59 connected to the cable 20, an external I / O control unit 60 that acquires slice image data from the FIB-SEM device 11 via the connector 59, and an HDD that stores the acquired slice image data (Hard disk drive) 56, flexible disk I / F unit 52 for inputting / outputting data with FD 16 mounted on FDU 18, display driver 44 for controlling display of various information on display 14, and keyboard 15 And an operation input detection unit 46 for detecting a key operation. There.

  The CPU 40, RAM 48, ROM 42, HDD 56, external I / O control unit 60, flexible disk I / F unit 52, display driver 44, and operation input detection unit 46 are connected to each other via a system bus BUS. . Therefore, the CPU 40 controls access to the RAM 48, ROM 42 and HDD 56, access to the FD 16 mounted on the FDU 18 via the flexible disk I / F unit 52, and control of data transmission / reception via the external I / O control unit 60. Various types of information can be displayed on the display 14 via the display driver 44. Further, the CPU 40 can always grasp key operations on the keyboard 15.

  Note that a 3D model generation processing program, an analysis processing program, density value data for discriminating between a rubber part and a filler part of a slice image, a 3D model, and the like described below can be read from and written to the FD 16 using the FDU 18. It is. Therefore, a 3D model generation processing program, an analysis processing program, density value data, a 3D model, and the like, which will be described later, are recorded in the FD 16 in advance, and each processing program recorded in the FD 16 is executed via the FDU 18. Also good. Further, each processing program recorded in the FD 16 may be stored (installed) in the HDD 56 and executed. As the recording medium, there are recording tapes, optical disks such as CD-ROM and DVD, and magneto-optical disks such as MD and MO. When these are used, instead of the FDU 18 or a corresponding read / write device is used. Good.

Next, a detailed description will be given of the operation when the prediction is performed by the rubber material deformation behavior apparatus according to the first embodiment of the present invention.
In the first embodiment of the present invention, a rubber material having a predetermined shape in which a rubber to be analyzed and a filler are blended is placed on a sample table by a user, and a predetermined operation for starting processing is performed on the FIB-SEM apparatus 11. When performed, a slice image generation process described later is executed.
The FIB-SEM apparatus 11 according to the first embodiment has a function of irradiating a rubber material S having a predetermined shape as a sample with a focused ion beam, and irradiating an electron beam onto a sample cross section processed by the focused ion beam. It has an SEM function capable of observing an electron microscope image.
FIG. 3 shows an example (schematic) of the FIB-SEM apparatus 11 used in the first embodiment, in which 11a is a FIB column and 11b is a SEM column. In the FIB column 11a, there are an ion gun 11c, a focusing lens 11d for focusing an accelerated ion beam generated from the ion gun 11c, an objective lens 11e, and a deflector 11f for scanning the ion beam two-dimensionally. Is provided. Note that an electrostatic lens is mainly used as the ion beam focusing lens 11d and the objective lens 11e.

The ion beam generated from the ion gun 11c is finely focused on the rubber material S having a predetermined shape as a sample by the focusing lens 11d and the objective lens 11e, and the irradiation position of the ion beam irradiated on the sample S is deflected. The scanner 11f can scan. These focusing lens 11d, objective lens 11e, and deflector 11f are controlled by the FIB control unit 11g.
For example, when changing the current amount of the ion beam irradiated to the rubber material S having a predetermined shape, the FIB control unit 11g controls the focusing lens 11d and the objective lens 11e, and controls the intensity of each lens to control the ion beam. The amount of ion beam passing through a diaphragm (not shown) provided in the optical path of the ion beam is controlled by changing the degree of focusing of the ion beam. When the ion beam is scanned two-dimensionally or linearly on the sample, a scanning signal is supplied from the FIB control unit 11g to the deflector 11f.

In the SEM column 11b, an electron gun 11h, a focusing lens 11i for focusing an electron beam generated from the electron gun 11h, an objective lens 11j, and a deflector 11k for two-dimensionally scanning the electron beam are provided. Yes.
The electron beam generated from the electron gun 11h is finely focused on the sample S by the focusing lens 11i and the objective lens 11j, and the irradiation position of the electron beam applied to the sample S can be scanned by the deflector 11k. Has been. The focusing lens 11i, the objective lens 11j, and the deflector 11k are controlled by the SEM control unit 11l. Note that electromagnetic lenses are mainly used as the focusing lens 11i for the electron beam and the objective lens 11j.

  For example, when changing the current amount of the electron beam irradiated to the sample S, the focusing lens 11i and the objective lens 11j are controlled by the SEM control unit 11l, and the intensity of each lens is controlled to increase the degree of focusing of the electron beam. The amount of the electron beam passing through a diaphragm (not shown) provided in the optical path of the electron beam is controlled. When the electron beam is scanned two-dimensionally or linearly on the sample S, a scanning signal is supplied from the SEM control unit 11l to the deflector 11k. The SEM control unit 11l and the FIB control unit 11g are controlled by the control computer 11m. The control computer 11m is controlled by a computer 12 serving as a host.

Secondary electrons generated from the sample by irradiation of an electron beam or ion beam onto a rubber material having a predetermined shape as the sample are detected by the secondary electron detector 11n. The signal detected by the detector 11n is amplified by the amplifier 11o and then supplied to the cathode ray tube 11p via the control computer 11m, and a scanning electron microscope image of the slice portion is obtained on the cathode ray tube 11p.
A rubber material S having a predetermined shape as a sample is placed on the stage 11q. The stage 11q is configured to be horizontally two-dimensionally moved, rotated, and tilted by a stage controller 11r. The stage controller 11r is controlled by the control computer 11m. By adjusting the FIB control unit 11g and the stage control unit 11r, the rubber material having a predetermined shape as a sample can be adjusted to an arbitrary depth, angle, and the like, and in the vertical direction and the horizontal direction of the cross-sectional surface layer in units of several nm. Can be processed.

  In the FIB-SEM apparatus 11 configured as described above, first, a rubber material S having a predetermined shape, which is a sample by FIB, is processed. In processing the sample, an ion beam is generated from the ion gun 11c in the FIB column 1, and this ion beam is finely focused on the sample S by the focusing lens 11d and the objective lens 11e, and the ion beam is lined by the deflector 11f. To scan. This focused ion beam is obtained by finely focusing the ion beam from the ion source and irradiating the processed sample S to etch any surface of the sample. After the processing is completed, the sample is immediately etched without moving the sample. The cross section is observed with an SEM image. In this FIB-SEM apparatus 11, an ion beam is normally applied from above the sample S for etching, and an electron beam is applied to the cross section at an angle of 30 ° from the sample surface to observe the structure of the cross section. . The sample S processed by the ion beam forms a cross section perpendicular to the sample surface, and the cross section is cut out almost perpendicular to the sample surface, although it depends on the current amount of the ion beam and the probe diameter. The FIB-SEM apparatus 11 is not only capable of observing the SEM without moving the sample immediately after processing by the FIB, but also simultaneously monitoring the progress of processing by the FIB and the depth of the processing surface in the SEM. Can do.

In this FIB-SEM apparatus 11, the surface of a rubber material S having a predetermined shape as a sample is etched at a predetermined interval by a focused ion beam, and each etched surface is irradiated with an electron beam, and the surface is scanned by a scanning electron microscope. Observation is to obtain a continuous image (a plurality of slice images) of the rubber material. In the present embodiment, a wide range of, for example, 3 μm × 3 μm × 0.2 μm can be grasped by one measurement as compared with a conventional transmission electron microscope (TEM), and positioning is facilitated.
Here, the rubber material of a predetermined shape which is the sample S of the present embodiment is a rubber material in which a rubber component such as natural rubber and / or synthetic rubber and a filler such as carbon black or silica are blended. The rubber material has a complicated network structure in which several tens of fillers having a primary particle size of several tens of nanometers are connected. Therefore, in order to examine the network structure, an etching process is preferably performed. The thickness is preferably adjusted to 0.1 to 100 nm, more preferably 0.1 to 50 nm, and particularly preferably 0.1 to 30 nm.
Furthermore, the etching treatment when carbon black and / or silica is used as the filler is preferably 0.1 to 30 nm, more preferably 0.1 to 20 nm, and particularly preferably 0. 1-10 nm.
If this etching treatment is less than 0.1 nm, adjustment becomes difficult. On the other hand, if it exceeds 100 nm, a complicated network structure such as a filler may not be obtained, which is not preferable.

  In the FIB-SEM apparatus 11 configured as described above, as shown in FIGS. 4A and 4B, image data of captured images (image data of 150 images in this embodiment) is used. Then, slice images S1 sliced at a predetermined interval parallel to each surface are generated, and a three-dimensional model is generated as described later. The generated slice image data is output to the computer 12 via the cable 20. The computer 12 stores the slice image data acquired via the cable 20 in the HDD 56.

When the user performs a predetermined operation for starting 3D model generation via the keyboard 15, the computer 12 executes 3D model generation processing described later. In a three-dimensional model generation process to be described later, a three-dimensional model of a rubber material is generated based on slice image data stored in the HDD 56. Thereafter, the computer 12 generates a three-dimensional model indicating the rubber material based on the three-dimensional image generated by executing the three-dimensional model generation process. The generated three-dimensional model is stored in the HDD 56.
Further, when the user designates a three-dimensional model to be analyzed and an analysis condition via the keyboard 15 and a predetermined operation for starting the analysis is performed, the computer 12 performs an analysis process to be described later for analysis. It will be.
In the analysis processing according to the present embodiment, the direction in which the three-dimensional model is changed and the rate of change in which the three-dimensional model is expanded, compressed, or sheared in that direction can be specified as analysis conditions. In the analysis process, a 3D model of a rubber material is specified as an analysis condition, and the strain value, internal stress distribution, and stress value of the 3D model as a whole are analyzed when the stretch, compression or shear is applied in the direction. Can be displayed on the display 14.

Note that, in the analysis processing according to the present embodiment, up to the first order term of the MOONEY-RIVLIN equation, which defines the relationship between strain and stress, is used as the constituent condition of the rubber region of the three-dimensional model. In addition, since the filler is sufficiently harder than rubber, the measured value obtained by measuring the hardness of the filler in advance through experiments or the like as the constituent condition of the filler region of the three-dimensional model, or the crystal part of the filler And an estimated value calculated from the ratio of the amorphous part (a value of about 10 [GPa] to 100 [GPa]) is used. Note that the Young's modulus that is a predetermined multiple (1000 times in this embodiment) of the Young's modulus (elastic modulus) obtained from the constituent conditions specified in the rubber region may be used as the constituent condition of the filler region of the three-dimensional model. Good.
Further, as a constituent condition of the rubber region of the three-dimensional model, the temperature dependence and elastic strain dependence of the elastic modulus shown in the generalized OGDEN equation and the following formula (1) disclosed by the present applicant (Japanese Patent Laid-Open No. 2005-345413) A constitutive equation representing the above may be used.

However, G represents Young's modulus, S represents entropy change at the time of rubber deformation, P and Q represent coefficients related to elastic modulus, I ₁ represents invariant of strain, and T represents absolute temperature. β is equal to 1 / (kΔT), k represents the Boltzmann constant, and ΔT represents the difference from the glass transition temperature of the rubber.

Next, the operation of the slice image generation process executed by the FIB-SEM apparatus 11 will be described in detail with reference to FIG. FIG. 5 is a flowchart showing the flow of the slice image generation processing program.
In step 100 of FIG. 5, as an initial process, the sample table on which a rubber material having a predetermined shape is placed and the scanning electron microscope are relatively moved to set the positional relationship to the initial position. In the next step 102, the sample surface is cleaned by an etching process of several nm, and then the rubber material is photographed with a scanning electron microscope to obtain an image of the rubber material.

In the next step 104, etching is performed at a depth (0.1 to 100 nm, 20 nm in this embodiment) set by the ion beam, and an image of the rubber material is acquired by photographing the rubber material with a scanning electron microscope. . In this step, it is determined whether or not imaging with the scanning electron microscope is completed. If the determination is affirmative, the etching process is repeated until the set depth is reached, and imaging of the rubber material is repeatedly performed with the scanning electron microscope a predetermined number of times. After the end, the process proceeds to step 108, and in the case of a negative determination, photographing of the rubber material is performed again. In this embodiment, each etching process is 20 nm and the number of times of photographing is 150 times.
On the other hand, in step 108, since the set imaging has been completed, a three-dimensional basic model is generated by the CT method from the image data obtained by imaging.

  In the next step 110, a plurality of (150 in this embodiment) slice images representing the cross-sectional shape including the internal structure when the generated three-dimensional basic model is sliced at predetermined intervals are generated. In the next step 112, the slice image data of the generated slice image is output to the computer 12 via the cable 20. In addition, this predetermined space | interval can be changed with the filler mix | blended with a rubber material.

Here, FIG. 6 shows an example of one slice image generated by the FIB-SEM apparatus 11 according to the present embodiment.
In the slice image shown in FIG. 6, since the luminance of the rubber constituting the rubber material and the filler are materially different, the filler portion is dark (density value is large) and the rubber portion is thin (density value is small). It is shown. In addition, the rubber material which concerns on this embodiment is mix | blended with the silica as a filler. As shown in FIG. 6, in the slice image, since the luminance of the silica and the rubber component are also physically different, the rubber component and the filler portion are shown as different concentrations. Therefore, the rubber portion and the filler portion of the slice image can be determined based on the density of each pixel of the slice image. The density value by which the rubber part and the filler part of the slice image can be discriminated can be determined in advance by experiments or the like.

Next, the operation of the three-dimensional model generation process executed by the computer 12 will be described in detail with reference to FIG. FIG. 7 is a flowchart showing the flow of the three-dimensional model generation processing program.
In step 150 of FIG. 7, a threshold value h is set as a threshold value for discriminating between a rubber part and a filler part of a slice image that is determined in advance by experiments or the like. In the next step 152, 1 is set to the counter n. In the next step 154, slice image data indicating the nth slice image is read from the HDD 58. In the next step 156, the density value of each pixel of the slice image indicated by the read slice image data is compared with a threshold value h to generate binary image data of a binary image obtained by binarizing each pixel. To do. FIG. 8 shows a binarized image obtained by binarizing the slice image shown in FIG.

  In the slice image generation process, the density value of each pixel of the slice image is set to a threshold value h in order to more accurately extract the filler portion by distinguishing the filler in the rubber material from other blended members. In comparison, a binarized image in which each pixel in a portion where a predetermined number (for example, five or more) of pixels having a density value equal to or higher than the threshold value h is continuous in black, and the other pixels are white. The binarized image data is generated.

In the next step 158, the format of the binarized image data is converted into binarized image data in which the value of the black portion of the binarized image is “1” and the values of the other pixels are “0”. To do. FIG. 8 shows binarized image data obtained by converting each image of the binarized image shown in FIG. 6 into a numerical value as an image including the array.
In the next step 160, it is determined whether or not the processing from reading to format conversion has been completed for all slice image data (in this embodiment, each slice image data of 150 slice images). If the determination is affirmative, the process proceeds to step 164. If the determination is negative, the process proceeds to step 162. In step 162, the counter n is incremented by 1, and the process proceeds to step 154 to read the next slice image data.

  On the other hand, in step 164, based on each binarized image data subjected to format conversion, the binarized images are stacked in the order of the slice positions of each slice image and at the above-described predetermined intervals to form a three-dimensional structure. Then, a three-dimensional model determined as a mesh (lattice region) having each pixel in each binarized image as a single element is generated. In this three-dimensional model, a portion where the pixel value is “1” is a filler portion, and a portion where the pixel value is “0” is a rubber portion. In the next step 166, the generated three-dimensional model data of the rubber material is stored in the HDD 56.

  In the next step 168, image processing for forming a three-dimensional region in which the pixels having the same value are integrated as the same element between the respective binarized images is performed on the three-dimensional model generated in step 164, and the rubber material 3D is generated, and the 3D image is displayed on the display 14.

  Here, FIG. 9 shows an example of a stereoscopic image displayed on the display 14. As shown in FIG. 9, the filler forms a network structure inside the rubber material and has a complicated three-dimensional structure. Since the stereoscopic image shown in FIG. 9 is reconstructed within the range of the rubber material acquired as a slice image, the rubber material up to the boundary of the acquired slice image is displayed. For this reason, when the rubber material continues across the slice images, the boundary portion is cut by a predetermined plane. In the present embodiment, when there is a filler on the cut surface, it is assumed that the concentration increases toward the inside of the filler, and the difference is shown.

Next, the operation of the analysis process executed by the computer 12 will be described in detail with reference to FIG. FIG. 10 is a flowchart showing the flow of the analysis processing program.
In step 200, initial processing for performing this processing is performed. First, a three-dimensional model designated by the user is set as a three-dimensional model to be analyzed. Next, analysis conditions in this analysis process are set. The analysis condition corresponds to any of the type of energy applied to the three-dimensional model to be analyzed, the method of applying energy, the type of structure or state that changes or occurs after the application of energy, and the acquisition method thereof.

  In the present embodiment, as the type of energy to be applied, the pressure or stress for compression or extension is made to correspond, and the application direction is also made to correspond. Further, the pressure distribution and the stress distribution are made to correspond as the fluctuation after the energy application. These settings may be performed by user input in advance or may be defined in advance on a program. As a result, the direction in which the three-dimensional model is changed, the pressure and stress for changing the three-dimensional model to expand or compress, the change amount and the change rate, and their distribution can be set as the analysis conditions. The analysis condition includes setting the configuration condition of the rubber part of the three-dimensional model to be the first-order term of the generalized MOONEY-RIVLIN equation described above. Moreover, setting the Young's modulus calculated | required from the said measured value or an estimated value as the structural conditions of the mesh of a filler part is also included.

In step 202, the 3D model data of the 3D model to be analyzed set in step 200 is read from the HDD 56.
Next, in step 204, the analysis condition set in step 200 is given as the constituent condition of each mesh of the rubber part and the filler part of the three-dimensional model indicated by the three-dimensional model data read from the HDD 56, and the three-dimensional model Reconstruct the data.
In the next step 206, distortion of the three-dimensional model, internal stress distribution, and stress value in the entire three-dimensional model when the three-dimensional model is changed using the reconstructed three-dimensional model data under the configuration conditions set in step 200. Is analyzed by the finite element method.

In the next step 208, the strain state of the three-dimensional model, the internal stress distribution obtained by the analysis, the stress value in the entire three-dimensional model are displayed on the display 14, and the processing is completed.
FIG. 11 and FIG. 12 show examples of analysis results obtained by the analysis processing according to the first embodiment. 11 and 12 show the analysis results of the strain state and the stress distribution when the analysis is performed to extend the entire three-dimensional model by 10% in the Z direction using the three-dimensional model data. In the stress distribution, the higher the stress value, the higher the concentration.

  FIG. 11 shows a strain state on one surface (XY surface) of a binarized image layered when generating a three-dimensional model and a stress distribution in each mesh constituting the surface. FIG. 12 shows a strain state in a cross section (XZ plane) in a direction orthogonal to the plane of the binarized image of the three-dimensional model, and a stress distribution in each mesh constituting the cross section.

  As described above, according to the above-described embodiment, it is possible to analyze the stress and strain state at the micro level by using the three-dimensional model generated from the actual rubber material. By analyzing the stress and strain state at the micro level, it is possible to optimize the blending amount of the filler in the rubber material and to control the performance of the rubber material with higher accuracy.

  On the other hand, FIG. 13 shows the relationship between the expansion ratio and the stress value of the entire three-dimensional model when the analysis is performed by changing the expansion ratio in the Z direction using the three-dimensional model data. Line A in FIG. 13 shows the elongation ratio and analysis results when the entire three-dimensional model is stretched in the Z direction by 10%, 20%, and 30%, respectively, using the three-dimensional model data of the rubber material containing the filler. The relationship with the stress value is shown. Further, line B in FIG. 13 shows that the entire three-dimensional model is 1% in the Z direction using the three-dimensional model data of the rubber material not containing the filler (that is, all meshes of the three-dimensional model are rubber parts). It shows the relationship between the elongation rate when stretched to ˜30% and the stress value of the analysis result.

FIG. 14 shows FIG. 13 as a relationship between the elongation rate [%] and the Young's modulus (= stress / elongation rate) [MPa].
According to the analysis processing according to this embodiment, as shown in FIGS. 13 and 14, the effect of increasing the stress and Young's modulus (elastic modulus) due to the blending of the rubber material with the rubber material is also reproduced in the analysis result. We were able to.

  On the other hand, FIG. 15 shows the results of experimental measurements of the elongation rate and Young's modulus of an actual rubber material (see line D in FIG. 15), and the rubber material deformation behavior according to the present embodiment with respect to the rubber material. The result of analysis using the prediction system 10 (see line C in FIG. 15) is shown. Note that the line C in FIG. 14 shows the Young's value from the stress value of the analysis result when the entire three-dimensional model is stretched in the Z direction by 10%, 20%, and 30% using the three-dimensional model data generated from the rubber material. This is the result of obtaining the rate (= stress / elongation rate).

  As shown in FIG. 15, a difference of about 20% is recognized between the stress-strain curve (line D in FIG. 15) of the experimental measurement result and the stress-strain curve of the analysis result (line C in FIG. 15). It is considered that the analysis result almost represents the measurement result in the approximate range using up to the first order term of the MOONEY-RIVLIN equation given as the constituent condition of the rubber part.

なお、応力の最大値と摩耗速度は、ゴム材料Ａを基準とした相対値で示されている。このゴム材料Ａ、ゴム材料Ｂ及びゴム材料Ｃは、同一ゴム及び充填剤を同じ量だけ配合しており、材料の構成が同一となっている。ゴム材料Ｃは３つの中で最も充填剤の分散の良く（充填剤が一様に分布している）、ゴム材料Ｂは３つの中で充填剤の分散が悪い（充填剤の分布が偏っている）。 On the other hand, in Table 1 below, the rubber material A, the rubber material B, and the rubber material C are obtained from the stress distributions obtained as a result of performing the analysis processing using the rubber material deformation behavior prediction system 10 according to the present embodiment. The maximum value of the stress of the rubber part and the wear rate when the friction test is performed on the rubber material A, the rubber material B, and the rubber material C are shown.

Note that the maximum value of stress and the wear rate are shown as relative values based on the rubber material A. The rubber material A, the rubber material B, and the rubber material C are blended with the same amount of the same rubber and the same filler, and have the same material structure. Rubber material C has the best filler dispersion among the three (the filler is uniformly distributed), and rubber material B has the poor filler dispersion among the three (the filler distribution is biased). )

  It is considered that the rubber material is likely to be consumed quickly because the rubber portion tends to crack when the maximum value of the stress distribution is large. Therefore, it is predicted that the rubber material B having a poor dispersion of the filler among the three materials will be consumed earlier even if the rubber material C has the same configuration. This coincides with the experimental result of the friction experiment shown in Table 1 above, and the wear rate of the rubber material can be predicted from the maximum value of the stress distribution obtained by the analysis process.

  As described above, according to the present embodiment, the computer 12 etches the surface at a predetermined interval with the focused ion beam (FIB), and observes the etched surface with a scanning electron microscope (SEM). A plurality of slice image data of the acquired rubber material is acquired from the external I / O control unit 60 via the cable 20. When the three-dimensional model generation process is executed, the CPU 40 converts each slice image into a binary image based on the density value of each pixel of the slice image and the threshold value h. Further, in the three-dimensional model generation process, the CPU 40 stacks a plurality of converted binarized images in the order of slice positions of each slice image at a predetermined interval, and sets each pixel in the binarized image as a single element. A three-dimensional model determined as a mesh to be generated is generated. When the analysis process is executed, the CPU 40 assigns a structural condition that defines the relationship between strain and stress of the rubber or filler to the generated mesh of the three-dimensional model, and analyzes the deformation behavior. Thereby, the deformation | transformation behavior of the rubber | gum part of an actual rubber material and a filler part can be precisely analyzed at a micro level. In addition, a change in physical properties due to strain can also be predicted, which makes it possible to control physical properties such as the breaking strength of the rubber material.

The deformation behavior predicting apparatus and the deformation behavior predicting method of the rubber material of the present invention are not limited to the above embodiment, and can be changed in various forms without changing the gist of the present invention.
For example, in the above-described embodiment, the analysis process is performed in all regions of the generated three-dimensional model. For example, the volume ratio of the filler actually blended in the rubber material is input from the keyboard 15, and the analysis process is performed. A region of the three-dimensional model in which the volume ratio of the filler portion becomes the actual volume ratio of the filler may be set as the analysis target region. As a result, the analysis can be performed using the three-dimensional model of the volume ratio region of the filler of the actual rubber material, so that the elastic modulus and the stress distribution corresponding to the actual amount of the filler are appropriately analyzed. be able to.

The configurations of the FIB-SEM apparatus 11 and the computer 12 described in the above embodiment are merely examples, and it goes without saying that they can be changed as appropriate without departing from the gist of the present invention.
Further, the flow of slice image generation processing, three-dimensional model generation processing, and analysis processing (see FIGS. 5, 7, and 10) described in the above embodiment is an example, and does not depart from the gist of the present invention. Needless to say, it can be appropriately changed.
Furthermore, in this embodiment, the case where the computer 12 is connected to the FIB-SEM apparatus 11 via the cable 20 to acquire slice image data has been described. However, the present invention is not limited to this, for example, recording The configuration may be such that the data is acquired via a recording medium such as a tape, an MO, a memory card, or a CD-ROM. When these are used, a read / write device corresponding to the computer 12 may be provided.

In the present invention configured as described above, a wide range of images can be obtained as compared with a conventional transmission electron microscope (TEM), and positioning can be easily performed during lamination, which is present in the rubber material. The deformation behavior of rubber materials with a complex network structure with several dozen or more fillers with a primary particle size of several tens of nanometers can be analyzed precisely and the analysis time can be further shortened. A prediction device and a deformation behavior prediction method thereof are provided.
Further, the slice image obtained by photographing the actual rubber material by the FIB-SEM device 11 is binarized based on the threshold value h, and a three-dimensional model is generated with each pixel of the binarized image as a mesh. Therefore, a three-dimensional model having a structure close to the structure of an actual rubber material can be generated.
Furthermore, by analyzing by the finite element method using a three-dimensional model of a structure close to the structure of the actual rubber material, it is possible to precisely analyze the elastic modulus and stress distribution inside the rubber material. The wear rate according to the distribution degree of the contained filler can also be predicted.

It is a whole block diagram which shows an example of the rubber material deformation | transformation behavior prediction apparatus (system) of this invention. It is a block diagram which shows an example of a structure of the electric system of the computer used for the rubber material deformation behavior prediction apparatus of this invention. It is the schematic which shows an example of the FIB-SEM apparatus used for this invention. It is explanatory drawing explaining a slice image generation process, (a) is the schematic which shows the state which laminated | stacked the slice image, (b) is a schematic three-dimensional transmission figure of a three-dimensional model. It is a flow which shows the flow of a process of a slice image generation process program. It is a figure which shows an example of a slice image. It is a flow which shows the flow of a process of a three-dimensional model generation process program. It is a figure which shows the binarized image which binarized the slice image. It is a figure which shows an example of a three-dimensional model. It is a flow which shows the flow of a process of an analysis processing program. It is a figure which shows an example of the cross-sectional image of the analysis result displayed on a display. It is a figure which shows an example of the cross-sectional image from the side surface of the analysis result displayed on a display. It is a figure which shows the relationship between the elongation rate of the whole three-dimensional model, and a stress value. FIG. 14 is a diagram illustrating the relationship between the elongation rate and the Young's modulus in the relationship illustrated in FIG. 13. It is a figure which shows the result of having measured the elongation rate and Young's modulus of an actual rubber material by experiment, and the result of having generated and analyzed the 3 time period model using the said rubber material. It is the schematic which shows the outline | summary which comprises a three-dimensional model by the conventional transmission electron microscope (TEM) and the computer tomography method (CT method).

Explanation of symbols

10 Rubber Material Deformation Behavior Prediction System 11 FIB-SEM Device 12 Computer (Deformation Behavior Prediction Device)
40 CPU (discriminating means, 3D image generating means, 3D model generating means, condition assigning means, analyzing means)
60 External I / O control unit (acquisition means)

Claims (3)

A rubber material having a predetermined shape in which rubber and a filler using carbon black and / or silica are blended is focused at a predetermined interval in a range of 0.1 to 30 nm by a focused ion beam of a focused ion beam- scanning electron microscope apparatus. Etching the surface, obtaining means for observing the surface of each etched surface with a scanning electron microscope to obtain a plurality of slice images,
Conversion means for converting into a binarized image for discriminating between a rubber part and a filler part included in each slice image based on the density value of each pixel constituting each slice image acquired by the acquisition means; ,
A plurality of binarized images converted by the converting means, and a three-dimensional model generating means for generating a three-dimensional model by stacking at a predetermined interval;
Giving means for imparting a structural condition that defines the relationship between strain and stress of rubber or filler based on the binarized value for each lattice region of the three-dimensional model generated by the three-dimensional model generating means When,
Analyzing means for analyzing deformation behavior using the three-dimensional model to which the configuration condition is given by the giving means;
A rubber material comprising: a presenting means for calculating a strain distribution or a stress distribution based on an analysis result by the analyzing means, distinguishing a strain or stress distribution area, specifying a position of each area, and presenting Deformation behavior prediction device. 2. The rubber material according to claim 1, wherein the deformation behavior of the three-dimensional model is analyzed using a finite element method to which the constituent conditions are given , and the etching treatment is 0.1 to 20 nm . Deformation behavior prediction device. A rubber material having a predetermined shape in which rubber and a filler using carbon black and / or silica are blended is focused at a predetermined interval in a range of 0.1 to 30 nm by a focused ion beam of a focused ion beam- scanning electron microscope apparatus. Etching the surface, observing the surface of each etched surface with a scanning electron microscope to obtain multiple slice images,
Converted into a binarized image for discriminating between the rubber part and the filler part contained in each slice image based on the density value of each pixel constituting each acquired slice image,
A plurality of binarized images that have been converted are stacked at predetermined intervals to generate a three-dimensional model,
A structural condition that defines a relationship between strain and stress of rubber or filler based on the binarized value is assigned to each lattice region of the generated three-dimensional model,
Analyzing deformation behavior using the three-dimensional model to which the constituent conditions are given,
Deformation of rubber material characterized by calculating strain distribution or stress distribution according to the analysis result, distinguishing strain or stress distribution area, specifying the position of each area, and predicting deformation behavior of rubber material Behavior prediction method.

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