Method, device, and program for predicting stress-strain characteristics of rubber material, recording medium, and design method

Abstract

To provide a method, device, and a program, capable of accurately predicting stress-strain characteristics of a rubber material in a shorter time and at lower cost, a recording medium, and a design method.SOLUTION: A method for predicting stress-strain characteristics of a rubber material based on an 8-chain model by computer simulation comprises steps of: calculating parameters on the basis of a correlation expression of a molecular chain number n and a segment number N being the parameters of the 8-chain model and at least one of the crosslink density and component formulation amount, created using at least one of the previously-experimentally obtained crosslink density and component formulation amount for a plurality of rubber material samples having different formulations, and previously-experimentally obtained stress-strain characteristics of the rubber material samples, and at least one of the crosslink density and component formulation amount of the rubber material to be analyzed; and predicting the stress-strain characteristics of the rubber material to be analyzed on the basis of the calculated value of the parameters and the 8-chain model.SELECTED DRAWING: Figure 4

Description

[Technical Field]

[0001] The present disclosure relates to a method, an apparatus, a program, a recording medium, and a design method for predicting stress-strain characteristics of a rubber material. [Background technology]

[0002] Computer simulations have been used to predict the stress-strain characteristics (also referred to as "SS characteristics" in this specification) of rubber materials using strain energy density functions such as the Mooney-Rivlin model, the Ogden model, and the Arruda-Boyce model (also referred to as the "8-chain model") as constitutive equations (see, for example, Non-Patent Documents 1 and 2 and Patent Document 1).

[0003] Non-Patent Document 1 describes a method for expressing the mechanical properties of rubber through numerical analysis using various constitutive equations, and describes the relationship between various physical property testing methods for deriving the parameters of various constitutive equations and prediction accuracy.

[0004] Non-Patent Document 2 proposes an eight-chain model, which is a type of molecular chain network theory, as a constitutive formula for rubber materials.

[0005] Patent Document 1 discloses a simulation method for rubber materials that is useful for accurately analyzing the deformation of rubber materials containing rubber, silica, and an interfacial bonding agent that bonds them. In the examples of this document, an eight-chain model is used as a constitutive equation. [Prior art documents] [Patent documents]

[0006] [Patent Document 1] Japanese Patent Application Laid-Open No. 2011-242336 [Non-patent literature]

[0007] [Non-Patent Document 1] Hiroshi Iizuka, Yoshihiro Yamashita, Identification of Mechanical Properties of Rubber Materials and Their Application to FEM Analysis, Journal of the Society of Rubber Science and Technology of Japan, Vol. 77, No. 9, 2004, pp. 306-311 [Non-patent document 2] EM Arruda and MC Boyce, A THREE-DIMENSIONAL CONSTITUTIVE MODEL FOR THE LARGE STRECH BEHAVIOR OF RUBBER ELASTIC MATERIALS, Journal of the Mechanics and Physics of Solids Volume 41, Issue 2, Pages 389-412 (1993) Summary of the Invention [Problem to be solved by the invention]

[0008] In the design and development of rubber materials using numerical analysis as described above, for example, as shown in FIG. 18, after the formulation of the raw rubber composition is considered, samples are prepared and three types of physical property tests (uniaxial extension test, uniaxial constrained uniaxial extension test, and uniform biaxial extension test) are performed (steps S91 to S93). Then, parameters of the constitutive equation are derived from the obtained experimental data, and the physical properties of the rubber material to be analyzed are predicted (steps S94 and S95). If the obtained prediction results meet the desired requirements, the formulation of the rubber material to be analyzed is used to proceed to mass production considerations, etc. (steps S96 and S97). However, if the obtained prediction results do not meet the desired requirements, conventional methods require returning to the formulation of the rubber composition and repeating steps S91 to S94 up to parameter derivation. In particular, as described in Non-Patent Document 1, it is ideal to perform three types of physical property tests to ensure sufficient prediction accuracy, which is a bottleneck in the design and development flow in terms of time, cost, etc.

[0009] However, in the Mooney-Rivlin model and the Ogden model, each parameter is merely a coefficient in an approximate formula and has no physical meaning. Therefore, the information on the calculated values ​​obtained in the parameter derivation process cannot be fed back to the rubber composition formulation study. Therefore, when these models are used as constitutive equations, if the rubber composition formulation is changed, there is essentially no option but to conduct physical property tests again to calculate the parameters, making it difficult to simplify the parameter derivation process.

[0010] In this regard, the eight-chain model is a model derived from polymer network theory, and its parameters have physical meaning. Non-Patent Document 1 describes that the eight-chain model can accurately represent behavior in the high strain range using only the results of uniaxial extension tests. However, neither this document nor Patent Document 1 describes a specific method for simplifying the parameter derivation process.

[0011] Therefore, an object of the present disclosure is to provide a method, device, program, recording medium, and design method that can accurately predict the stress-strain characteristics of a rubber material in a shorter time and at lower cost. [Means for solving the problem]

[0012] In order to solve the above problems, one embodiment of a method for predicting stress-strain characteristics of a rubber material disclosed herein includes: A method for predicting stress-strain properties of a rubber material based on an eight-chain model by computer simulation, comprising: a step of calculating the parameters based on a correlation equation between the number of molecular chains n and the number of segments N, which are parameters of the eight-chain model, and at least one of the crosslink density and the component compounding amount, which is created based on at least one of the crosslink density and the component compounding amount experimentally obtained in advance for a plurality of rubber material samples with different compoundings and the stress-strain characteristics experimentally obtained in advance for the rubber material samples, and at least one of the crosslink density and the component compounding amount of the rubber material to be analyzed; and a step of predicting the stress-strain characteristics of the rubber material to be analyzed based on the calculated values ​​of the parameters and the eight-chain model. It is characterized by:

[0013] The eight-chain model is a type of molecular chain network theory that can phenomenologically calculate energy from the network of a rubber material. After extensive research, the inventors discovered that the eight-chain model parameters, the number of molecular chains n and the number of segments N, correlate with the actual number of crosslinking points in rubber, i.e., the crosslink density, a material index indicating the network density of the rubber material, and the component compounding amount of the rubber material. The relationship between the eight-chain model parameters n and N and at least one of the crosslink density and component compounding amount was modeled as a correlation equation. As a result, even if the rubber material being analyzed undergoes compounding adjustments, such as adjusting the component compounding amount or changing the additives, the values ​​of the parameters n and N can be calculated using the correlation equation as long as at least one of the crosslink density and component compounding amount of the rubber material is known. Furthermore, the stress-strain characteristics of the rubber material can be accurately predicted without molding or physical property testing. In other words, this configuration simplifies the parameter derivation process, which was previously performed in the rubber material development flow, thereby contributing to reducing the man-hours and costs of material design.

[0014] Preferably, the rubber material contains a filler, the correlation equations include a first correlation equation between the number n of molecular chains and the crosslink density, and a second correlation equation between the number N of segments and the blending amount of the filler component, In the step of calculating the parameters, the number n of molecular chains is calculated based on the crosslink density of the rubber material to be analyzed and the first correlation equation, and the number N of segments is calculated based on the content of the filler component in the rubber material and the second correlation equation; As the elongation ratio λ in the eight-chain model, λ' expressed by the following formula (1) is used, which takes into consideration the compounding amount of the filler component in the rubber material.

[0015] λ'=[(λ-1) / a]+1 (1) (In formula (1), a is the volume fraction of the polymer in the rubber material.) As a result of extensive research, the inventors of the present application have found that when a rubber material contains a filler, as the amount of filler increases, the degree of freedom of the molecular chain decreases, the number of segments N, one of the parameters of the eight-chain model, decreases, and local strain increases as the amount of rubber per unit volume decreases. By calculating the parameters n and N using the first and second correlation equations and correcting the elongation ratio λ of the eight-chain model taking into account the amount of filler (amount of polymer), it is possible to improve the prediction accuracy of the stress-strain characteristics of filler-containing rubber materials.

[0016] The filler is preferably carbon black.

[0017] Preferably, the crosslink density is obtained by a combination of a toluene swelling test and pulse NMR measurement.

[0018] According to this configuration, it is possible to obtain information on crosslink density with high accuracy regardless of the compounding of the rubber material.

[0019] One aspect of the stress-strain characteristic prediction device for a rubber material disclosed herein is An apparatus for predicting the stress-strain characteristics of a rubber material based on an eight-chain model by computer simulation, a calculation unit that calculates the parameters based on a correlation equation between the number of molecular chains n and the number of segments N, which are parameters of the 8-chain model, and at least one of the crosslink density and the component compounding amount, which correlation equation is created based on at least one of the crosslink density and the component compounding amount experimentally obtained in advance for a plurality of rubber material samples with different compoundings and the stress-strain characteristics experimentally obtained in advance for the rubber material samples, and on at least one of the crosslink density and the component compounding amount of the rubber material to be analyzed; a prediction unit that predicts the stress-strain characteristics of the rubber material to be analyzed based on the calculated values ​​of the parameters and the eight-chain model. It is characterized by:

[0020] One embodiment of the stress-strain property prediction program for a rubber material disclosed herein is: A program for predicting the stress-strain characteristics of a rubber material based on an eight-chain model by computer simulation, On the computer, a step A of calculating the parameters based on at least one of crosslink density and component compounding amount experimentally obtained in advance for a plurality of rubber material samples with different compoundings and stress-strain characteristics experimentally obtained in advance for the rubber material samples, and a correlation equation between the number of molecular chains n and the number of segments N, which are parameters of the 8-chain model, and at least one of the crosslink density and the component compounding amount, and based on at least one of the crosslink density and the component compounding amount of the rubber material to be analyzed; and a procedure B for predicting the stress-strain characteristics of the rubber material to be analyzed based on the calculated values ​​of the parameters and the eight-chain model. It is characterized by:

[0021] One aspect of the recording medium disclosed herein is: A computer-readable recording medium having recorded thereon the above-mentioned program for predicting the stress-strain characteristics of rubber materials.

[0022] One aspect of the method for designing a rubber material disclosed herein is to A method for designing a rubber material, comprising a method for predicting stress-strain characteristics of the rubber material based on an eight-chain model by computer simulation, determining the formulation of a basic rubber material; a step of creating a correlation equation between the number of molecular chains n and the number of segments N, which are parameters of the 8-chain model, and at least one of the crosslink density and the component compounding amount, based on at least one of the crosslink density and the component compounding amount experimentally obtained in advance for a plurality of rubber material samples having a compounding amount different from that of the basic rubber material, and on stress-strain characteristics experimentally obtained in advance for the plurality of rubber material samples; determining a compounding ratio of a rubber material to be analyzed; calculating the parameters based on the correlation equation and at least one of the crosslink density and the component blending amount of the rubber material to be analyzed; a step of predicting the stress-strain characteristics of the rubber material to be analyzed based on the calculated values ​​of the parameters and the eight-chain model; and a step of determining whether or not the predicted stress-strain characteristics of the rubber material to be analyzed satisfy desired requirements, in this order; When it is determined in the determining step that the desired requirements are not satisfied, the process returns to the step of determining the composition of the rubber material to be analyzed, and the steps from the step of determining the composition of the rubber material to be analyzed to the determining step are repeated until it is determined that the predicted stress-strain characteristics of the rubber material to be analyzed satisfy the desired requirements. It is characterized by:

[0023] According to the above configuration, the parameter derivation process that has conventionally been performed in the development flow of rubber materials can be simplified, which contributes to reducing the number of steps and costs involved in material design. [Effects of the Invention]

[0024] As described above, according to the present disclosure, the parameter derivation process that has conventionally been performed in the development flow of rubber materials can be simplified, thereby contributing to reducing the man-hours and costs of material design. [Brief explanation of the drawings]

[0025] [Figure 1] FIG. 1 is a diagram for explaining the relationship between the parameters of the eight-chain model and the crosslink density in an actual rubber material. [Figure 2] A diagram to explain the bond points and parameters of the 8-chain model in (a) low crosslink density pure rubber material, (b) high crosslink density pure rubber material, and (c) CB compound rubber. [Figure 3] FIG. 1 is a block diagram showing an apparatus for predicting stress-strain characteristics of a rubber material according to an embodiment. [Figure 4]1 is a flowchart showing a method for designing a rubber material according to an embodiment. [Figure 5] 2 is a graph showing true stress-elongation ratio curves obtained by uniaxial tensile tests on the rubber material samples of Production Examples 1 to 6. [Figure 6] 1 is a graph showing the relationship between the crosslink density and the sulfur content obtained by a toluene swelling test of the rubber material samples of Production Examples 1 to 11. [Figure 7] 1 is a graph showing the relationship between the crosslink density of the rubber material samples of Production Examples 1 to 6 and the parameters n and N of the 8-chain model. [Figure 8] 1 is a graph showing true stress-elongation ratio curves obtained by uniaxial tensile tests on rubber material samples of Production Examples 3 and 7 to 11. [Figure 9] FIG. 9 is an enlarged view of the true stress-elongation ratio curves of Production Examples 3 and 9 shown in FIG. 8. [Figure 10] FIG. 1 is a diagram for explaining the strain generated in the polymer phase of pure rubber and CB-blended rubber. [Figure 11] Graph showing the results of pulse NMR measurement of the rubber material formulation of Production Example 10. [Figure 12] 1 is a graph showing the relationship between the crosslink density obtained by a toluene swelling test of the rubber material samples of Production Examples 1 to 6 and 1 / T2HS obtained by pulse NMR measurement. [Figure 13] 12. A graph showing the relationship between the crosslink density and the sulfur content calculated from the crosslink density obtained by a toluene swelling test of the rubber material samples of Production Examples 1 to 6, the 1 / T2HS obtained by pulse NMR measurement of the rubber material samples of Production Examples 7 to 11, and correlation formula I of FIG. [Figure 14] 13 is a graph showing the relationship between the crosslink density and the parameter n calculated from 1 / T2HS obtained by pulse NMR measurement of the rubber material samples of Production Examples 1 to 6 and correlation formula I of FIG. [Figure 15] 1 is a graph showing the relationship between the CB volume fraction and the parameter N of the rubber material samples of Production Examples 7 to 11. [Figure 16] Graph showing the results of verification test 1. [Figure 17] Graph showing the results of verification test 2. [Figure 18]1 is a flowchart showing a conventional method for designing a rubber material. DETAILED DESCRIPTION OF THE INVENTION

[0026] Hereinafter, embodiments of the present disclosure will be described in detail with reference to the accompanying drawings. The following description of the preferred embodiments is merely exemplary in nature and is not intended to limit the present disclosure, its applications, or its uses.

[0027] (Embodiment 1) <Rubber materials> The rubber materials to be analyzed in the present disclosure are not particularly limited and include commonly known rubber parts, rubber products, and rubber materials used therein. Specific examples of rubber parts and rubber products include various vibration-damping rubbers, vibration-damping pads, mounts, belts, tires, etc. Applications of rubber parts and rubber products include, for example, vehicle parts such as automobile parts, rocket and aircraft parts, precision machinery components, industrial product components, building materials, and sporting goods. Specific examples of automobile parts include suspension bushings, engine mounts, muffler hangers, brake hoses, water hoses, fuel hoses, filler hoses, fan belts, oil seals, weatherstrips, wipers, tires, etc.

[0028] The unvulcanized rubber composition, which is the raw material for rubber materials, contains a polymer as the main component, a vulcanizing agent such as sulfur, and, as necessary, optional fillers such as carbon black (also referred to as "CB") and silica. The polymer is not particularly limited, and commonly known materials can be used. Specific examples include rubber components consisting of one or a mixture of two or more of natural rubber (NR), isoprene rubber (IR), ethylene propylene rubber (EPDM), styrene butadiene rubber (SBR), butadiene rubber (BR), butyl rubber (IIR), chloroprene rubber (CR), and nitrile rubber (NBR). The rubber composition may also contain other additives commonly used in known rubber compositions, such as zinc oxide, stearic acid, and vulcanization accelerators. The specifications and content of the additives are not particularly limited, and commonly used conditions can be used. These additives can be added alone or in combination.

[0029] The average particle size of the filler is not particularly limited and can be any average particle size commonly used in rubber materials. The average particle size of the filler can be determined as the volume average particle size or number average particle size by determining the D50 value, which is the 50% value of the particle size distribution, using, for example, a laser diffraction particle size analyzer. When CB is used as the filler, the average particle size may be calculated in accordance with ASTM D3849-22. The average particle size of CB (in accordance with ASTM D3849-22) is, but is not intended to be limited to, for example, greater than 30 nm, preferably 70 nm or more and 90 nm or less. When the average particle size of CB is 30 nm or less, an occluded rubber phase, which is a polymer phase trapped between aggregated CB particles, is likely to occur, which increases the impact on the CB / polymer volume fraction and may tend to reduce prediction accuracy.

[0030] <Relationship between parameters of the 8-chain model and cross-link density> In this disclosure, the eight-chain model, a type of molecular chain network theory that can phenomenologically calculate the energy from the network of a rubber material, is adopted as a constitutive equation for predicting the SS properties of a rubber material. Below, we will explain the relationship between the parameters of the eight-chain model and the crosslink density of an actual rubber material.

[0031] As shown on the left side of Figure 1, actual rubber has a three-dimensional network structure (molecular chain network structure) in which many polymer chains are entangled and connected to each other at cross-linking points (bonding points) formed by covalent bonds. Cross-linking density is an example of a material index that indicates the density of the network. The cross-linking density can be controlled by the amount of vulcanizing agent (amount of sulfur) blended into the unvulcanized rubber composition, which is the raw material for the rubber material.

[0032] According to Non-Patent Document 2, the eight-chain model is a model that assumes that molecular chains extend from one bond point at the center of a cube to eight bond points at each vertex, as shown in the center of Figure 1, and represents the stress of each molecular chain in eight axial directions. Macroscopically, rubber materials are assumed to be made up of a structure formed by an assembly of many such cubes. The relationship between true stress and elongation ratio in the eight-chain model is expressed by the following formula (2).

[0033]

number

[0034] In equation (2), k and T are constants, σ ​​and λ(λc) are experimental values ​​obtained by physical property tests, and n and N are parameters determined to match the results of physical property tests.

[0035] When a molecular chain connecting two adjacent bond points is considered to be one molecular chain, the parameter n represents the number of molecular chains per unit volume. The number of monomer units (=segments) that make up one molecular chain is represented by the parameter N, which is called the number of segments. The number of segments N is a value corresponding to the length of the polymer between the crosslinking points of the rubber material.

[0036] The number of molecular chains n and the number of segments N vary depending on the number of bonding points.

[0037] Specifically, Figures 2(a) and 2(b) show schematic diagrams of low-crosslink density and high-crosslink density materials, respectively, in pure rubber that does not contain fillers such as CB. As shown in Figure 4(a), for example, when considering a low-crosslink density material with four bond points per unit volume, the number of molecular chains n and the number of segments N are both 4. Considering the high-crosslink density material shown in Figure 4(b), which uses this structure as a base and has increased crosslink density, if the number of bond points increases to 9, the number of molecular chains n increases to 12. Meanwhile, as the number of bond points increases, the distance between bond points decreases, and the number of segments N decreases to 2. In other words, the number of molecular chains n and the number of segments N can be considered to be correlated with the actual number of crosslink points in rubber, i.e., the crosslink density mentioned above.

[0038] Therefore, if we can model the relationship between the parameters n and N in the eight-chain model and the crosslink density, which is a material index that indicates the network density of a rubber material, we can calculate the values ​​of the parameters n and N from the crosslink density of the rubber material even if we adjust the blending amounts of components or change the additives. This makes it possible to accurately predict the stress-strain characteristics of rubber materials without having to perform molding or physical property tests.

[0039] <Stress-strength property prediction device for rubber materials> FIG. 3 shows a configuration example of a rubber material SS property prediction device 100 (hereinafter also referred to as "prediction device 100") according to this embodiment. The prediction device 100 is a device that predicts the SS property of a rubber material using numerical analysis such as the finite element method through computer simulation. The prediction device 100 in FIG. 3 is merely an example of a device according to the present disclosure, and the device configuration is not limited to this example.

[0040] The prediction device 100 is a CAE (Computer Aided Engineering) system whose basic configuration includes a computer 110. The computer 110 includes a storage unit 120, such as a ROM, RAM, and hard disk, and a processor 130, such as a CPU. The prediction device 100 also includes a display unit 140, such as a display, an input unit 150, such as a keyboard, and a reading unit 160 for acquiring various information stored in a recording medium 170. At least one of the storage unit 120 and the recording medium 170 stores information such as programs for arithmetic processing, analytical model information, a constitutive equation of the 8-chain model, correlation equations (described later), and various other analytical data. The processor 130 can function as an analytical model creation unit, an analytical condition setting unit, a calculation unit, a prediction unit, and the like. The processor 130 performs various arithmetic processing based on the information stored in the storage unit 120, information input via the input unit 150, and information acquired from the recording medium 170 via the reading unit 160. The device 100 is configured to be able to communicate with external devices via an interface (not shown).

[0041] The analytical model creation unit divides shape data, such as 3D CAD data that defines the shape of the rubber material, into multiple tiny elements to create an analytical model for numerical analysis. Commercially available automatic mesh creation software can be used as the analytical model creation unit. The shape and size of the elements are not particularly limited and are set appropriately depending on the product specifications, material composition, calculation efficiency, and calculation accuracy level.

[0042] The analysis condition setting unit sets, as preconditions for analysis, material property data relating to the types of components contained in the rubber composition, blending, additives, various physical property values, etc. as analysis conditions.

[0043] The calculation unit calculates parameters of the eight-chain model based on a correlation equation, which will be described later, and at least one of the crosslink density and the component blending amount of the rubber material to be analyzed.

[0044] The prediction unit predicts the SS characteristics of the rubber material to be analyzed based on the calculated values ​​of the parameters calculated by the calculation unit and the eight-chain model.

[0045] <Rubber material design method and SS property prediction method> FIG. 4 is a flowchart showing an example of a method for designing a rubber material, including an example of a method for predicting the SS characteristics of a rubber material according to the present disclosure (hereinafter also referred to as the "prediction method").

[0046] As shown in FIG. 4, the design method includes a basic rubber material composition determination step S1, a correlation equation creation step S2, an analytical rubber material composition determination step S3, a parameter calculation step S4, an SS characteristic prediction step S5, an SS characteristic evaluation step S6, and a mass production study rubber material composition determination step S7.

[0047] The correlation equation creating step S2 includes a rubber material sample creating step S21, a testing step S22, and a correlation equation deriving step S23.

[0048] This prediction method is a method for predicting the stress-strain characteristics of a rubber material using an eight-chain model through computer simulation, and is carried out using, for example, the above-mentioned device 100. This prediction method includes at least a parameter calculation step S4 and an SS characteristic prediction step S5, and may include, for example, steps from the correlation equation derivation step S23 to the SS characteristic prediction step S5 in FIG.

[0049] [Basic rubber material composition determination process] First, in the basic rubber material blending determination step S1, the blending of the basic rubber material is determined. That is, this step is a step in which specific raw materials such as a polymer containing a rubber component as the main component, a vulcanizing agent, and a filler component if a filler is included, and the blending amounts of these components are considered and determined. The blending amounts of components determined at this stage are the component blending amounts that serve as the basis for creating a correlation equation.

[0050] [Correlation equation creation process] As described above, the correlation equation creating step S2 includes the sample creating step S21, the testing step S22, and the correlation equation deriving step S23.

[0051] -Sample production process- In the sample preparation step S21, a plurality of rubber material samples are prepared, each containing a basic rubber material formulation but with a different component blending amount from the basic rubber material formulation. That is, first, a basic rubber material sample having the basic rubber material formulation is prepared. In addition, a plurality of rubber material samples for creating a correlation equation, each having the same components as the basic rubber material sample but with a different component blending amount, are prepared, preferably two or more types (three or more types in total including the basic rubber material sample).

[0052] Then, unvulcanized rubber compositions having the blends of these rubber material samples for creating a correlation equation are prepared, and test pieces made of vulcanized rubber are produced by actual molding to be subjected to the next test step S22.

[0053] -Testing process- In the testing step S22, physical property tests and material analysis tests are carried out on the plurality of rubber material samples for creating a correlation equation.

[0054] In the description of this embodiment, the rubber material will be mainly pure rubber that does not contain filler.

[0055] <Physical property testing> The physical property test is not limited as long as it can measure the stress-strain characteristics of a rubber material sample, but is preferably a uniaxial tensile test, which can be performed by a generally known method.

[0056] Specifically, for example, this can be carried out by the uniaxial tensile test method of the Experimental Examples described later. As an example of the test results obtained, true stress-elongation ratio curves obtained by the uniaxial tensile test of the rubber material samples of Production Examples 1 to 6 described later are shown in Figure 5.

[0057] ≪Material analysis≫ Material analysis is a test for determining the crosslink density of a rubber material sample. The type of material analysis is not particularly limited as long as it can calculate the crosslink density. Specific examples of material analysis include a toluene swelling test, pulse NMR measurement, thiolamine method, toluene swelling / small-angle X-ray scattering, and dynamic viscoelasticity measurement.

[0058] From the viewpoints of accuracy in calculating the crosslink density and ease of testing, it is preferable to use the toluene swelling test for pure rubber materials that do not contain fillers. The toluene swelling test is a method in which the mass of a test piece is measured before and after swelling with toluene and in the dried state after swelling, and the crosslink density is calculated using the modified Flory-Rehner equation described below. The toluene swelling test has the advantage of being able to directly obtain the value of crosslink density.

[0059] The relationship between the crosslink density obtained by the toluene swelling test of the rubber material samples of Production Examples 1 to 11, which will be described later, and the amount of sulfur compounded in the rubber composition is shown in Figure 6. As shown in Figure 6, for the pure rubbers of Production Examples 1 to 6, a nonlinear correlation is obtained in which the crosslink density increases as the sulfur content increases.

[0060] Although details will be described later in embodiment 2, in the case of filler-blended rubber materials containing fillers, it is difficult to evaluate the crosslink density of a rubber material sample using only a toluene swelling test, and it is preferable to use a combination of a toluene swelling test and pulse NMR measurement.

[0061] -Correlation equation derivation process- Based on the SS characteristic results of the rubber material samples obtained by physical property testing, the number of molecular chains n and the number of segments N, which are parameters of the 8-chain model for each rubber material sample, are identified. Specifically, the parameters n and N of the 8-chain model are determined for each rubber material sample using the least squares method or the like so that the SS characteristic curve expressed by the 8-chain model matches the measured SS characteristic curve for each rubber material sample obtained as a result of uniaxial tensile testing. This work is substantially the same as the work performed in the SS characteristic prediction step S5 described below, and can be performed using, for example, commercially available CAE analysis software exemplified in the SS characteristic prediction step S5.

[0062] Furthermore, since the crosslink density for each rubber material sample is obtained by material analysis, the values ​​of the parameters n and N for each rubber material sample determined by the above-described method are plotted against the crosslink density value.

[0063] Then, curve fitting is performed on the obtained data points, and a correlation equation can be obtained between the crosslink density of the rubber material and the parameters n and N when the basic rubber material formulation and its component formulation amounts are changed.

[0064] Specifically, Fig. 7 shows the relationship between the crosslink density obtained as described above and the parameters n and N of the 8-chain model for the rubber material samples of Production Examples 1 to 6. It can be seen that for each of the parameters n and N, correlation formulas IIa and IIb can be obtained, which are consistent with the relationship between the crosslink density and the parameters n and N considered using Fig. 2 (as the crosslink density increases, the number of molecular chains n tends to increase and the number of segments N tends to decrease).

[0065] [Rubber material composition determination process for analysis] In the step S3 of determining the composition of the rubber material to be analyzed, the composition of the rubber material to be analyzed is determined. In the first iteration of the design method flow in Fig. 4, the composition of the rubber material to be analyzed may be the composition of the basic rubber material, or may be a composition obtained by adjusting the composition amounts of the components from the composition of the basic rubber material within the range in which the above correlation equation can be used.

[0066] [Parameter calculation process] In the parameter calculation step S4, the parameters n and N are calculated based on the crosslink density of the rubber material to be analyzed and the correlation equation derived in the above-mentioned correlation equation derivation step S23. If the crosslink density of the rubber material to be analyzed can be obtained from known information, that information can be used, and if it is unknown, it can be calculated by performing the above-mentioned material analysis.

[0067] [SS characteristics prediction process] In the SS characteristic prediction step S5, the stress-strain characteristics of the rubber material to be analyzed are predicted based on the calculated values ​​of the parameters n and N calculated in the parameter calculation step S4 and the constitutive equation (Equation (2)) of the 8-chain model described above. Specifically, the analytical model creation unit described above creates an analytical model from 3D data of the shape of the rubber material to be analyzed. In addition, the analytical condition setting unit sets the analytical conditions. Then, the prediction unit calculates the deformation of the analytical model for each infinitesimal element and each time step. This step is not particularly limited, and can be performed using commercially available CAE analysis software capable of structural analysis of rubber materials, specifically, for example, Abaqus by Dassault Systèmes or Ansys Mechanical by Ansys, Inc., or homemade CAE analysis software with similar functions.

[0068] [SS characteristic evaluation process] The SS characteristic evaluation step S6 is a step of determining whether or not the SS characteristic prediction result obtained in the SS characteristic prediction step S5 satisfies a desired range of SS characteristics (desired requirements).

[0069] If the prediction result is NG in the SS characteristic evaluation step S6 (if the desired requirements are not met), proceed to NO and return to the analytical rubber material blend determination step S3. Then, the component blend amounts and the like are adjusted, and the parameter calculation step S4 to the SS characteristic evaluation step S6 are performed again. The blend adjustment step S3 to the SS characteristic evaluation step S6 are repeated until a rubber material that meets the desired SS characteristic range is obtained.

[0070] [Rubber material compounding process for mass production consideration] If the prediction result is OK in the SS characteristic evaluation step S6, proceed to YES, and the final rubber material composition is determined in the rubber material composition determination step S7 for mass production consideration. Mass production of the rubber material of the composition is considered taking into account, for example, other conditions.

[0071] <Action and effect> In the above configuration, the relationship between the parameters n and N in the eight-chain model and the crosslink density, which is a material index that indicates the network density of a rubber material, is modeled as a correlation equation. As a result, even if the rubber material being analyzed undergoes formulation adjustments such as adjusting the component blending amounts or changing additives, the values ​​of the parameters n and N can be calculated using the correlation equation as long as the crosslink density of the rubber material is known. This makes it possible to accurately predict the stress-strain characteristics of the rubber material without molding or physical property testing. In other words, the above configuration simplifies the parameter derivation process that was previously performed in the rubber material development flow, thereby contributing to reducing the man-hours and costs of material design.

[0072] <Program for predicting stress-strain characteristics of rubber materials and its recording medium> At least some of the steps of the present prediction method are programmed as a stress-strain property prediction program for a rubber material. That is, the stress-strain property prediction program for a rubber material according to this embodiment is a program that causes a computer to execute at least the parameter calculation step S4 (step A) and the SS property prediction step S5 (step B) among the steps described above. The program may also be configured to execute other steps in addition to the steps described above. Specifically, for example, the desired SS property range may be predetermined in the SS property evaluation step S6, and the rubber material composition determination step S3 for analysis may be automated to adjust the rubber material composition so that the prediction results satisfy the predetermined range. In this case, the program may be configured to execute each step from the correlation equation derivation step S23 to the composition determination step S7 shown in FIG. 4. The program may be stored in the storage unit 120, for example, and executed by the processor 130. The program may also be stored in various well-known computer-readable recording media 170, such as optical disk media or magnetic tape media. The program can be executed by loading such a recording medium 170 into the reading unit 160 and reading out the program.

[0073] (Embodiment 2) Other embodiments of the present disclosure will be described in detail below. In the description of these embodiments, the same parts as those in the first embodiment will be denoted by the same reference numerals, and detailed description thereof will be omitted.

[0074] In the first embodiment, the case where the rubber material is pure rubber containing no filler has been mainly described, but in this embodiment, the case where the rubber material is a filler, preferably a filler-blended rubber containing CB, will be described.

[0075] <Relationship between the parameters of the 8-chain model and the crosslink density and filler content> FIG. 8 is a graph showing true stress-elongation ratio curves obtained by uniaxial tensile tests on rubber material samples of Production Examples 3 and 7 to 11 described below, and FIG. 9 is an enlarged view of the true stress-elongation ratio curves of Production Example 3 (pure rubber) and Production Example 9 (CB-blended rubber) shown in FIG.

[0076] As shown in Figure 9, the CB-blended rubber, which contains CB as a filler, shows a larger increase in stress with respect to the elongation ratio than pure rubber. This indicates that the CB particles promote the full elongation of the molecular chains.

[0077] There are two possible reasons for the molecular chain stretching effect of CB particles.

[0078] First, as shown in Figure 2(c), the degree of freedom of the molecular chain is reduced and its movement is suppressed when CB particles come into contact with the molecular chain. This is thought to result in a decrease in the effective number of segments N. In other words, it is thought that the number of segments N decreases as the proportion of CB particles in CB-blended rubber increases.

[0079] The second is the change in strain experienced by the polymer phase. In other words, as shown in Figure 10, it is thought that the local strain increases in the CB-blended rubber due to the decrease in the amount of rubber per unit volume compared to pure rubber.

[0080] From the above considerations, in filler-blended rubber, the number of segments N is affected by the amount of filler blended, so it is considered desirable to define the relationship between the number of segments N and the amount of filler blended as a correlation equation for the number of segments N. Also, in filler-blended rubber, the presence of filler affects the elongation ratio λ, so it is possible to modify the elongation ratio λ in the constitutive equation of the 8-chain model (the above equation (2)) so that the amount of filler blended can be taken into account.

[0081] The number of molecular chains n is thought to tend to increase from the perspective of increasing interactions with molecular chains that were not involved in elongation due to the inclusion of filler particles in a unit volume, but to tend to decrease from the perspective of increasing the number of molecular chains extruded from a unit volume. Therefore, due to these two opposing trends, the effect of filler incorporation on the number of molecular chains n is thought to be significantly smaller than the effect of filler incorporation on the number of segments N and the elongation ratio λ (the effect of fully elongating molecular chains). Furthermore, the effect of filler incorporation on the number of molecular chains n can ultimately be considered to be included in the correction of the elongation ratio λ.

[0082] <Rubber material design method and SS property prediction method> [Correlation equation creation process] -Testing process- ≪Material analysis≫ While the toluene swelling test has the advantage of being able to directly obtain values ​​for crosslink density, the accuracy of the obtained crosslink density value can be reduced due to the influence of the filler in filler-compounded rubber. In particular, in CB-compounded rubber, which contains carbon black as a filler, the influence of the bound rubber phase formed at the interface between the rubber component and the CB particles becomes a problem.

[0083] In fact, as shown in Figure 6, in the CB compounded rubbers of Production Examples 7 to 11, the crosslink density decreased as the sulfur content increased, and the accuracy of the crosslink density of the polymer phase decreased compared to the pure rubbers of Production Examples 1 to 6.

[0084] In this regard, by combining the toluene swelling test with pulsed NMR measurement, the crosslink density of filler-blended rubber can be calculated with high accuracy.

[0085] Pulse NMR measurement enables analysis focused on the polymer phase by measuring transverse relaxation using the Hahn echo method. Specifically, pulse NMR measurement can be performed by the method described in "Iwabuki, Jin, Nuclear Magnetic Resonance (NMR) Spectroscopy in Soft Material Analysis (2) The Role of Pulse NMR in Soft Material Analysis, Journal of the Society of Rubber Science and Technology of Japan, Vol. 87, No. 5, 2014, pp. 195-202" (referred to as "Non-Patent Document 3").

[0086] Figure 11 shows the pulse NMR measurement results for the rubber material compound of Production Example 10. Curve fitting was performed on these measurement results to obtain the 1 / T 2HS Calculate the value of

[0087] FIG. 12 shows the crosslink density obtained by the toluene swelling test of the rubber material samples of Production Examples 1 to 6 and the 1 / T 2HS 12 is a graph showing the relationship between the two. As shown in Fig. 12, it can be seen that there is a good linear correlation between the two. The approximation formula for the data points in Fig. 12 is referred to as correlation formula I.

[0088] 1 / T obtained by pulse NMR measurement of the rubber material samples of Production Examples 7 to 11 2HS The crosslink density calculated from correlation formula I in Figure 12 is plotted against the sulfur content as shown in Figure 13. When curve fitting is performed including the crosslink densities obtained by the toluene swelling test of the rubber material samples of Production Examples 1 to 6, the coefficient of determination R 2 = 0.9863. This means that for filler-blended rubber, the crosslink density of the polymer phase can be calculated with high accuracy by combining the toluene swelling test and pulse NMR measurement.

[0089] -Correlation equation derivation process- As for the number of molecular chains n, as in the first embodiment, the value of the number of molecular chains n for each rubber material sample is plotted against the crosslink density of the rubber material sample obtained by material analysis, and correlation formula IIa is created as a first correlation formula. As mentioned above, since the influence of filler compounding on the number of molecular chains n is considered to be small, correlation formula IIa may be created using either the crosslink density of pure rubber or the crosslink density of filler-compounded rubber. An example of correlation formula IIa in this embodiment is shown in FIG. 14. In FIG. 14, 1 / T obtained by pulse NMR measurement of the rubber material samples of Production Examples 1 to 6 is shown. 2HS and the crosslink density calculated from correlation formula I in FIG. 12 is used.

[0090] As mentioned above, the number of segments N is affected by the amount of filler blended, so the value of the number of segments N is plotted against the amount of filler blended, and correlation equation III is created as a second correlation equation. An example of correlation equation III is shown in Figure 15. Figure 15 is a graph plotting the number of segments N against the CB volume fraction of the rubber material samples of Production Examples 7 to 11. Correlation equation III was created by curve fitting the data points.

[0091] [Parameter calculation process] In the parameter calculation step S4 of this embodiment, the number of molecular chains n is calculated based on the crosslink density of the rubber material to be analyzed and correlation formula IIa, and the number of segments N is calculated based on the content of the filler component in the rubber material to be analyzed and correlation formula III.

[0092] [SS characteristics prediction process] In the SS characteristic prediction step S5 of this embodiment, the elongation ratio λ in the constitutive equation of the 8-chain model (the above equation (2)) is λ' expressed by the following equation (1) taking into account the amount of filler component compounded in the rubber material.

[0093] λ'=[(λ-1) / a]+1 (1) (In formula (1), a is the volume fraction of the polymer in the rubber material.) <Action and effect> According to the above configuration, the parameters n and N are calculated using correlation formula IIa and correlation formula III, respectively, and the elongation ratio λ of the 8-chain model is corrected taking into account the filler blending amount (polymer blending amount), thereby improving the prediction accuracy of the stress-strain characteristics of the filler-blended rubber material.

[0094] (Other embodiments) It is believed that the correlation equations IIa, IIb, and III of the first and second embodiments are applicable to compounding adjustments such as changing the compounding amounts of rubber material components, adding or not adding additives, and changing them. When making a major compounding change to the rubber material, such as changing the type of polymer component, it is desirable to start over with the design method flow in Figure 4 and create the correlation equation again. Note that, even if the polymer component is changed, the correlation equation may be applicable if the crosslink density value and increase rate relative to the sulfur content are similar between different polymer components.

[0095] (Experimental example) Next, specific experimental examples will be described.

[0096] <Calculation> All calculations in the following experimental examples, including curve fitting and verification results, were performed using the functions and solver functions of the spreadsheet software. Deformation calculations were performed on a single-element model. It has been confirmed that the calculation of the true stress-elongation ratio curve for Verification Test 1, described below, also yields results similar to those obtained using the spreadsheet software when using commercially available CAE analysis software (Abaqus, manufactured by Dassault Systèmes).

[0097] <Rubber material sample> Rubber material samples were produced in Production Examples 1 to 11 (sometimes denoted by symbols E1 to E11). Tables 1 and 2 show the formulations and the specific gravities of the components.

[0098] [Table 1]

[0099] [Table 2]

[0100] The raw materials used for the rubber material samples are as follows:

[0101] [Raw materials] (1) Polymer component (polyisoprene rubber (IR)) (2) Carbon black (average particle size: 85 nm) The average particle size of CB is a value measured in accordance with ASTM D3849-22.

[0102] (3) Two types of zinc oxide (4) Stearic acid (5) Vulcanization accelerator (sulfenamide vulcanization accelerator) (6) Vulcanizing agent (fine sulfur) <Uniaxial tensile test> Dumbbell-shaped specimens (JIS K 6251 dumbbell No. 3, thickness: 2.0 ± 0.2 mm, width: 5.0 ± 0.1 mm, gauge length: 20.0 ± 0.5 mm, total length: 100 mm, width at both ends: 25 mm) were cut from the rubber material samples to prepare test specimens. Tensile tests were performed on the test specimens using a tensile testing machine (Shimadzu Autograph AGS-X) at a temperature of 23°C, a relative humidity of 50%, a chuck distance of 50.0 ± 0.5 mm, and a pulling rate of 30 mm / min, to measure the change in true stress versus elongation ratio. The results are shown in Figures 5 and 8. <Toluene swelling test> A test piece weighing approximately 0.3 g was taken from the sample and immersed in toluene at 40°C for 22 hours. The weight of the test piece was measured before and after swelling, and after drying. The crosslink density was calculated using the modified Flory-Rehner equation shown in Equation (3) below. The results are shown in Table 1 and Figure 6.

[0103] [Measurement conditions] Test piece weight: approx. 0.3g Swelling solvent: toluene Immersion conditions: 40±2℃ x 22 hours Drying conditions: Under reduced pressure, 40±2°C x 72 hours [Modified Flory-Rehner equation]

[0104]

number

[0105] ν: Network chain concentration (crosslinking density) [mol / m 3 ] g: Volume fraction of rubber in the test piece before swelling V: Molar volume of swelling solvent (molecular weight ÷ density) [m 3 / mol] μ: Interaction constant between sample rubber and swelling solvent V R : Volume fraction of rubber in the test piece after swelling [Calculation conditions] Molecular weight of toluene: 92.14 [g / mol] Density: 0.867[g / ml] Interaction constant between sample rubber and swelling solvent: 0.39 Density of each material: See Table 1 <Pulse NMR measurement> Pulsed NMR measurements and their analysis were carried out according to the method described in Non-Patent Document 3 above.

[0106] Specifically, a rubber material sample was collected, placed in a test tube, and placed in a pulsed NMR measurement device (JNM-MU25 manufactured by JEOL Ltd., resonance frequency 25 MHz), after which the transverse relaxation was measured by the Hahn echo method. The measurement results for Production Example 10 are shown in Figure 11.

[0107] The transverse relaxation measurement results were subjected to curve fitting as shown in Figure 11. 2HS / T 2HL , F HS / F HL , W HS was calculated from the fitting results. 2HS The values ​​were calculated and the results are shown in Table 1.

[0108] <Correlation Equation I> For the pure rubber material samples (Production Examples 1 to 6), 1 / T calculated from the pulse NMR measurement results 2HS The crosslink density values ​​obtained by the toluene swelling test were plotted against the values ​​of . The graph is shown in Figure 12. The approximate linear equation obtained by fitting was designated as correlation equation I.

[0109] The crosslink density obtained by the toluene swelling test of the rubber material samples of Production Examples 1 to 6 and the 1 / T 2HS The relationship between the crosslink density and the sulfur content calculated from correlation formula I in FIG. 12 is shown in FIG.

[0110] <Correlation Equation II> The number of molecular chains n and the number of segments N, which are parameters of the constitutive equation of the 8-chain model (the above equation (2)), were calculated for each rubber material sample so as to satisfy the elongation ratio-true stress curve in Figure 5 obtained by uniaxial tensile tests of the pure rubber rubber material samples (Production Examples 1 to 6).

[0111] Figure 7 shows a graph in which the calculated number of molecular chains n and number of segments N are plotted against the crosslink density calculated by a toluene swelling test. Curve fitting was performed on the plot, and the resulting polynomial approximation curve was designated correlation equation II. For convenience, the correlation equation between the number of molecular chains n and crosslink density is designated correlation equation IIa (first correlation equation, solid line in Figure 7), and the correlation equation between the number of segments N and crosslink density is designated correlation equation IIb (dashed line in Figure 7).

[0112] Furthermore, for the verification test described later, the number of data points in FIG. 7 was reduced by several points and curve fitting was performed to obtain the polynomial approximation curve equations of the following equations (4) and (5), which were used as correlation equations IIa and IIb for verification, respectively.

[0113] n=2.5×10 15 x 2 +4.3×10 17 x+7.8×10 18 ···(4) N=19415x ―1.164 ···(5) <Correlation Equation III> For the rubber material samples of CB-blended rubber (Production Examples 7 to 11), the elongation ratio λ in the constitutive equation of the 8-chain model (the above equation (2)) was replaced with λ' shown in the following equation (1), where a is the polymer volume fraction in the CB-blended rubber.

[0114] λ'=[(λ-1) / a]+1 (1) The number of molecular chains n and the number of segments N, which are parameters of the constitutive equation of the modified 8-chain model that reflects the above formula (1) in the above formula (2), were calculated for each rubber material sample so as to satisfy the elongation ratio-true stress curve of Figure 8 obtained by uniaxial tensile testing of rubber material samples of CB-blended rubber (Production Examples 7 to 11).

[0115] The calculated number of molecular chains n was plotted against the crosslink density calculated from the pulse NMR measurement results and correlation formula I (not shown). Curve fitting was performed on the plot, and the obtained polynomial approximation curve equation was defined as correlation formula IIa'. Note that correlation formula IIa' may be the same as correlation formula IIa obtained for a rubber material sample of pure rubber. Correlation formula IIa' may also be correlation formula IIa'' created from the crosslink density calculated from the pulse NMR measurement results obtained for the rubber material sample of pure rubber and correlation formula I, and the value of the number of molecular chains n obtained for the rubber material sample of pure rubber. An example of correlation formula IIa'' is shown in Figure 14. Correlation formula IIa'' is expressed by the following formula (6).

[0116] Furthermore, for the purpose of verification testing, the number of data points in FIG. 15 was reduced by several points and curve fitting was performed to obtain the polynomial approximation curve equation of the following equation (7) as correlation equation III (second correlation equation) for verification.

[0117] n=2.5×10 15 x 2 +4.3×10 17 x+8.1×10 18 ···(6) N=401.31y ―0.933 ···(7) <Verification test 1: Prediction of SS properties of pure rubber> Using the correlation equations IIa (equation (4)) and IIb (equation (5)) for verification, n and N for the two types of rubber materials shown below were calculated. Low crosslink density material (crosslink density: 68.0mol / m 3 , n: 4.9 × 10 19 , N:143) Highly crosslinked density material (crosslinked density: 125.7mol / m 3 , n: 1.0 × 10 20 , N:70) For the above rubber materials, true stress-elongation ratio curves were obtained using the above calculation method.

[0118] The results of the uniaxial tensile tests and analysis of the above rubber materials are shown in Figure 16. It was found that the SS characteristics could be predicted with high accuracy for both rubber materials.

[0119] <Verification test 2: Prediction of SS properties of CB compounded rubber> Using correlation formula IIa″ (formula (6)) and correlation formula III (formula (7)) for verification, n and N of the rubber material shown below were calculated. CB compound rubber material (crosslink density: 81.8 mol / m 3 , Polymer content: 88.1 vol%, CB content: 8.9 vol%, n: 6.0 × 10 19 , N:52) For the above rubber material, the true stress-elongation ratio curve was obtained by the above calculation method, with the elongation ratio λ being λ' calculated by the above formula (1).

[0120] The results of the uniaxial tensile test and analysis of the above rubber material are shown in Figure 17. It was found that the SS characteristics of this rubber material can be predicted with high accuracy.

Claims

1. A method for predicting stress-strain properties of a rubber material based on an eight-chain model by computer simulation, comprising: a step of calculating the parameters based on a correlation equation between the number of molecular chains n and the number of segments N, which are parameters of the eight-chain model, and at least one of the crosslink density and the component compounding amount, which is created based on at least one of the crosslink density and the component compounding amount experimentally obtained in advance for a plurality of rubber material samples with different compoundings and the stress-strain characteristics experimentally obtained in advance for the rubber material samples, and at least one of the crosslink density and the component compounding amount of the rubber material to be analyzed; and a step of predicting the stress-strain characteristics of the rubber material to be analyzed based on the calculated values ​​of the parameters and the eight-chain model. A method for predicting stress-strain characteristics of a rubber material, comprising:

2. In claim 1, the rubber material contains a filler, the correlation equations include a first correlation equation between the number n of molecular chains and the crosslink density, and a second correlation equation between the number N of segments and the blending amount of the filler component, In the step of calculating the parameters, the number n of molecular chains is calculated based on the crosslink density of the rubber material to be analyzed and the first correlation equation, and the number N of segments is calculated based on the content of the filler component in the rubber material and the second correlation equation; As the elongation ratio λ in the eight-chain model, λ' expressed by the following formula (1) is used, which takes into account the compounding amount of the filler component in the rubber material. λ'=[(λ-1) / a]+1...(1) (wherein, a in formula (1) is the volume fraction of the polymer in the rubber material) A method for predicting stress-strain characteristics of a rubber material, comprising:

3. In claim 2, The filler is carbon black. A method for predicting stress-strain characteristics of a rubber material, comprising:

4. In claim 2 or claim 3, The crosslink density is obtained by combining a toluene swelling test and pulse NMR measurement. A method for predicting stress-strain characteristics of a rubber material, comprising:

5. An apparatus for predicting the stress-strain characteristics of a rubber material based on an eight-chain model by computer simulation, comprising: a calculation unit that calculates the parameters based on a correlation equation between the number of molecular chains n and the number of segments N, which are parameters of the 8-chain model, and at least one of the crosslink density and the component compounding amount, which correlation equation is created based on at least one of the crosslink density and the component compounding amount experimentally obtained in advance for a plurality of rubber material samples with different compoundings and the stress-strain characteristics experimentally obtained in advance for the rubber material samples, and on at least one of the crosslink density and the component compounding amount of the rubber material to be analyzed; a prediction unit that predicts the stress-strain characteristics of the rubber material to be analyzed based on the calculated values ​​of the parameters and the eight-chain model. A device for predicting stress-strain characteristics of rubber materials, characterized by:

6. A program for predicting the stress-strain characteristics of a rubber material based on an eight-chain model by computer simulation, On the computer, a step A of calculating the parameters based on at least one of crosslink density and component compounding amount experimentally obtained in advance for a plurality of rubber material samples with different compoundings and stress-strain characteristics experimentally obtained in advance for the rubber material samples, and a correlation equation between the number of molecular chains n and the number of segments N, which are parameters of the 8-chain model, and at least one of the crosslink density and the component compounding amount, and based on at least one of the crosslink density and the component compounding amount of the rubber material to be analyzed; and a procedure B for predicting the stress-strain characteristics of the rubber material to be analyzed based on the calculated values ​​of the parameters and the eight-chain model. A program for predicting the stress-strain characteristics of rubber materials.

7. A computer-readable recording medium having recorded thereon the stress-strain characteristic prediction program for rubber materials according to claim 6.

8. A method for designing a rubber material, comprising a method for predicting stress-strain characteristics of the rubber material based on an eight-chain model by computer simulation, determining the formulation of a basic rubber material; a step of creating a correlation equation between the number of molecular chains n and the number of segments N, which are parameters of the eight-chain model, and at least one of the crosslink density and the component compounding amount, based on at least one of the crosslink density and the component compounding amount experimentally obtained in advance for a plurality of rubber material samples having a compounding amount different from that of the basic rubber material, and on stress-strain characteristics experimentally obtained in advance for the plurality of rubber material samples; determining a compounding ratio of a rubber material to be analyzed; calculating the parameters based on the correlation equation and at least one of the crosslink density and the component blending amount of the rubber material to be analyzed; a step of predicting stress-strain characteristics of the rubber material to be analyzed based on the calculated values ​​of the parameters and the eight-chain model; and a step of determining whether or not the predicted stress-strain characteristics of the rubber material to be analyzed satisfy desired requirements, in this order; When it is determined in the determining step that the desired requirements are not satisfied, the process returns to the step of determining the composition of the rubber material to be analyzed, and the steps from the step of determining the composition of the rubber material to be analyzed to the determining step are repeated until it is determined that the predicted stress-strain characteristics of the rubber material to be analyzed satisfy the desired requirements. A method for designing a rubber material.

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