Method for predicting rubber material properties

Abstract

To reduce man-hours and prediction time required for predicting rigidity of a rubber material.SOLUTION: The rubber material characteristic prediction method includes a tensile test process S1 for acquiring a stress-strain relation by a tensile test for one representative rubber material among a plurality of rubber materials, and a representative Young modulus acquiring process S3 for acquiring Young modulus of the representative rubber material. Further, the method includes an identification process S2 for calculating the material parameters of the strain-energy-density functions of the superelastic material model by identifying the strain-energy-density functions of the superelastic material model and the stress-strain relationship, and a relational equation derivation process S4 for deriving the relational equations between the material parameters and the Young's moduli.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present disclosure relates to a method for predicting rubber material properties, and more particularly to a method for predicting material parameters in a material model used to predict rubber material properties. [Background technology]

[0002] Conventionally, a simulation method for analyzing rubber products such as tires has been a numerical analysis method using, for example, the finite element method (FEM). In order to simulate such rubber products, it is necessary to derive, or identify, the material parameters of the rubber material, i.e., the material parameters (coefficients) of a hyperelastic material model that express the rubber elasticity characteristics.

[0003] For example, Patent Document 1 discloses a method for identifying material parameters that can improve the accuracy of material parameters of rubber materials. [Prior art documents] [Patent documents]

[0004] [Patent Document 1] Japanese Patent Application Publication No. 2018-84471 Summary of the Invention [Problem to be solved by the invention]

[0005] However, the tensile test performed to calculate the rubber material properties for predicting the stiffness of the rubber material requires time and skill, which increases the man-hours and prediction time required to predict the stiffness of the rubber material using the rubber material properties. Note that even the material parameter identification method disclosed in Prior Art 1 cannot solve this problem. [Means for solving the problem]

[0006] The rubber material property prediction method according to the present disclosure includes a tensile test step of conducting a tensile test to obtain a stress-strain relationship for a representative rubber material among a plurality of rubber materials, a representative Young's modulus acquisition step of obtaining a Young's modulus for the representative rubber material, an identification step of calculating material parameters of the strain energy density function of the hyperelastic material model by identifying the strain energy density function of the hyperelastic material model and the stress-strain relationship, and a relational equation derivation step of deriving a relational equation between the material parameters and the Young's modulus. [Effects of the Invention]

[0007] According to the simulation method of the present disclosure, rubber material properties can be easily calculated, thereby reducing the man-hours and prediction time required to predict the stiffness of a rubber material using the rubber material properties. [Brief explanation of the drawings]

[0008] [Figure 1] 10 is a flowchart illustrating a process for calculating material parameters of a hyperelastic material model according to the present embodiment. [Figure 2] FIG. 1 is a diagram showing a uniaxial tensile test according to the present embodiment. [Figure 3] FIG. 1 is a diagram showing a uniaxial fixed uniaxial tensile test according to the present embodiment. [Figure 4] FIG. 1 is a diagram showing a biaxial tensile test according to the present embodiment. [Figure 5] FIG. 10 is a diagram showing the measured values ​​of the stress-strain relationship and the strain energy density function after identification according to the present embodiment. [Figure 6] FIG. 4 is a diagram showing the relationship between the stiffness coefficient and Young's modulus according to the present embodiment. DETAILED DESCRIPTION OF THE INVENTION

[0009] Hereinafter, an example of an embodiment of the rubber material property prediction method according to the present disclosure will be described in detail with reference to the drawings. The embodiment described below is merely an example, and the present disclosure is not limited to the following embodiment. Furthermore, the present disclosure also includes embodiments that are formed by selectively combining multiple embodiments and modified examples described below.

[0010] The method for predicting material parameters according to this embodiment will be described in detail with reference to Figures 1 to 6. Figure 1 is a flowchart illustrating the method for predicting material parameters of a hyperelastic material model according to this embodiment. Each step will be described in detail according to the flowchart in Figure 1.

[0011] First, a tensile test is conducted using one representative rubber material from among the multiple rubber materials (Step S1). This obtains the stress-strain relationship of the representative rubber material. The tensile test will be described in detail with reference to Figures 2 to 4. Figures 2 to 4 are diagrams illustrating the uniaxial tensile test, fixed uniaxial tensile test, and equibiaxial tensile test according to this embodiment, respectively.

[0012] In the tensile test process of step S1, a stress-strain relationship is obtained by a tensile test on one representative rubber material among a plurality of rubber materials. The tensile test is, for example, at least one of a uniaxial tensile test, a uniaxial fixed uniaxial tensile test, and an equibiaxial tensile test. Note that the tensile test process may include all of the uniaxial tensile test, the uniaxial fixed uniaxial tensile test, and the equibiaxial tensile test.

[0013] The tensile test is performed using a representative rubber material test piece 10 formed from a representative rubber material in a square sheet shape, and a gripper 11 for fixing the representative rubber material test piece 10. In the tensile test process according to this embodiment, a case where a uniaxial tensile test, a uniaxial fixed uniaxial tensile test, and an equibiaxial tensile test are all performed will be described.

[0014] Known methods can be used to determine the actual measured values ​​of the stress-strain relationship in uniaxial tensile tests, uniaxial fixed uniaxial tensile tests, and equibiaxial tensile tests. Here, strain refers to the amount of deformation per unit dimension that occurs when an object is subjected to stress, and indicates the ratio of the amount of displacement in the tensile direction that occurs when stress is applied to the rubber material to the length in the tensile direction when no stress is applied to the target rubber material.

[0015] In a uniaxial tensile test, a representative rubber material is pulled in one direction without being fixed in two of three mutually perpendicular axial directions, and the stress-strain relationship is obtained. For example, as shown in Figure 2, a square sheet-shaped representative rubber material test piece 10 is used, and the test is performed by fixing one end in the left-right direction and pulling the other end, without fixing the other end in the up-down direction.

[0016] A uniaxial fixed uniaxial tensile test (pure shear test) is a test in which a representative rubber material is fixed in one axial direction and pulled in the other axial direction, and the stress-strain relationship is obtained. For example, as shown in Figure 3, a square sheet-shaped representative rubber material test piece 10 is used, and while it is fixed with gripping tools 11 so that the strain in the up-down direction is 0%, one end in the left-right direction is fixed with gripping tools 11 and the other end is pulled.

[0017] In an equibiaxial tensile test, a representative rubber material is pulled in two axial directions at the same speed, and the stress-strain relationship is obtained. For example, as shown in Figure 4, a square sheet-shaped representative rubber material test piece 10 is used, and one end in the left-right direction and one end in the up-down direction are fixed with grippers 11, and the other end of each is pulled at the same speed.

[0018] Next, the measured values ​​of the stress-strain relationship obtained in the tensile test process and the strain energy density function of the hyperelastic material model, which indicates the elastic properties of the rubber material, are identified (step S2). The identification of the stress-strain relationship and the strain energy density function will be described in detail with reference to Fig. 5. Fig. 5 is a diagram showing the results of identifying the measured values ​​of the stress-strain relationship and the strain energy density function according to this embodiment.

[0019] In the identification process of step S2, the material parameters of the hyperelastic material model are calculated by identification using a hyperelastic material model for each of the measured values ​​obtained above. That is, the material parameters of the strain energy density function in the hyperelastic material model are identified based on the measured values. The identification of the material parameters can be performed using a computer. As an example of an embodiment, the material parameter identification device has a measured value acquisition unit that acquires the measured values ​​and a material parameter identification unit that identifies the material parameters of the hyperelastic material model based on the measured values, and these can be realized by causing a processor installed in the computer to execute a program.

[0020] The hyperelastic material model may be a known hyperelastic material model, such as the Arruda-Boyce model. Identification of material parameters of the strain energy density function in the Arruda-Boyce model will be described in detail below.

[0021] The strain energy density function of the Arruda-Boyce model is expressed by the following formula (1).

[0022]

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[0023] Here, W is the amount of strain energy per unit volume. Also, μ and λ m is a material parameter in the strain energy density function of the Arruda-Boyce model. μ is a stiffness coefficient, which is a material constant related to stiffness, and λ m is an exponential coefficient, which is a material constant related to the maximum elongation ratio. Furthermore, I1 is the first invariant of strain related to the amount of change in length. I1 is expressed by the following formula (2). Here, λ1, λ2, and λ3 in formula (2) represent the principal elongation ratios in the respective axial directions. The principal elongation ratios are the rate of change in length in the principal axial directions when an object is deformed.

[0024]

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[0025] The method for identifying the stress-strain relationship and the strain energy density function is not particularly limited, and can be performed using a known method, for example, the least squares method. That is, the material parameters μ and λ in the strain energy density function of the Arruda-Boyce model can be m can be calculated by approximating the strain energy density function of the hyperelastic material model using the least squares method to the actual values ​​measured in the tensile test process. The solid line in Figure 5 shows the results of identifying the strain energy density function of the hyperelastic material model. Meanwhile, the dotted line is a line showing the stress-strain relationship of the actual values ​​measured in the tensile test. In addition, in the identification process, identification is performed on the stress-strain relationship of each of the uniaxial tensile test, uniaxial fixed uniaxial tensile test, and equibiaxial tensile test obtained in the tensile test process.

[0026] Furthermore, the Arruda-Boyce model has better reproducibility of measured results in the low strain region of the stress-strain relationship (for example, tensile strain of 50% or less) than other models, and therefore can reduce errors relative to the measured values ​​when predicting the static spring constant (rigidity), which is greatly affected by the low strain region.

[0027] Next, the Young's modulus of the representative rubber material is obtained (step S3). The representative Young's modulus obtaining step of step S3 is a step of obtaining the Young's modulus of the representative rubber material by testing. The representative Young's modulus obtaining step may be performed in parallel with the tensile test step and the identification step. In the representative Young's modulus obtaining step, the Young's modulus may be calculated using a Mooney tester. By placing a part of the representative rubber material in the Mooney tester and performing a test, the Young's modulus is calculated from the stress in the torsional direction, etc. In this case, by measuring the Young's modulus under two or more different conditions, two or more different Young's moduli are calculated.

[0028] Next, a relational expression showing the relationship between the material parameters calculated in the above-mentioned identification step and the Young's modulus calculated in the above-mentioned Young's modulus calculation step is derived (step S4). The derivation of the relational expression between the material parameters and the Young's modulus will be described in detail with reference to Fig. 6. Fig. 6 is a diagram showing the relationship between the Young's modulus and the stiffness coefficient according to this embodiment.

[0029] In the relational equation deriving step S4, the relationship between the stiffness coefficient and Young's modulus is plotted as shown by the black dots in FIG. 6 based on the material parameters (stiffness coefficient) calculated in the identification step and the Young's modulus calculated in the Young's modulus calculation step. In the plot, the correspondence between the stiffness coefficient and Young's modulus is determined by a conventionally known method. Furthermore, an approximation line is drawn from the plotted relationship between the stiffness coefficient and Young's modulus to derive the relational equation. The relational equation may express the relationship between the stiffness coefficient and Young's modulus as a linear function of Young's modulus. The relational equation between the stiffness coefficient μ and Young's modulus E is expressed, for example, as in the following equation (3).

[0030]

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[0031] Hereinafter, the rigidity prediction of rubber materials other than the representative rubber material among the plurality of rubber materials will be described in detail.

[0032] Material parameters corresponding to the rubber material other than the representative rubber material may be calculated based on the Young's modulus of the rubber material other than the representative rubber material among the multiple rubber materials and the relational expression derived in the relational expression derivation step. As will be described in detail later, this allows the rigidity of the rubber material to be predicted by inputting the material parameters. Here, if the Young's modulus of the rubber material other than the representative rubber material among the multiple rubber materials is known, the material parameter (stiffness coefficient) corresponding to the rubber material can be calculated simply by substituting it into the relational expression. On the other hand, the exponent coefficient has a strong influence mainly in the high strain region (e.g., tensile strain of 50% or more) and little influence in the low strain region, and therefore has little influence on the prediction of the rigidity of the rubber material. Therefore, when predicting the rigidity of a rubber material, the exponent coefficient may be a constant value. In this case, the exponent coefficient for the representative rubber material calculated in the identification step may be input.

[0033] The material parameters of the rubber material obtained in the above manner can be used in a simulation to analyze a rubber product that includes the rubber material. That is, the material parameters can be used to perform a simulation of a rubber product that is modeled using elements that can be numerically analyzed.

[0034] Specifically, the stiffness of a rubber material other than the representative rubber material may be predicted based on material parameters corresponding to the rubber material other than the representative rubber material. More specifically, the material parameters for the rubber material calculated based on the above-mentioned relational expression are input into an analysis device equipped with an analysis solver, and a static spring constant is calculated from the relationship between displacement and load. Conventionally, when no relational expression exists, a tensile test must be performed on the rubber material whose stiffness is to be predicted and a hyperelastic material model must be identified. However, by using the relational expression, these steps can be eliminated and the stiffness of the rubber material can be easily predicted. Abaqus or Marc is used as the analysis solver. The analysis device may also be integrated with the above-mentioned identification device.

[0035] As described above, the rubber material property prediction method having the above configuration allows for easy calculation of material parameters of the strain energy density function of a hyperelastic material model for a specified rubber material using the Young's modulus of the specified rubber material. This eliminates the need for a tensile test and an identification process for the specified rubber material, thereby shortening the time required to predict the stiffness of the rubber material. Furthermore, by using the Arruda-Boyce model as the hyperelastic material model, the accuracy of identifying the low strain region in the stress-strain relationship can be improved. This in turn improves the accuracy of stiffness prediction. [Explanation of symbols]

[0036] 10 rubber material test piece, 11 gripping tool

Claims

1. a tensile test step of obtaining a stress-strain relationship for one representative rubber material among the plurality of rubber materials by a tensile test; a representative Young's modulus acquisition step of acquiring the Young's modulus of the representative rubber material; an identification step of calculating material parameters of the strain energy density function of the hyperelastic material model by identifying the strain energy density function of the hyperelastic material model and the stress-strain relationship; a relational expression deriving step of deriving a relational expression between the material parameters and the Young's modulus; A rubber material property prediction method comprising:

2. The rubber material property prediction method according to claim 1 , wherein the tensile test is at least one of a uniaxial tensile test, a fixed uniaxial tensile test, and an equibiaxial tensile test.

3. The rubber material characteristic prediction method according to claim 1 , wherein the relational expression is a linear function of the Young's modulus that indicates the relationship between the material parameter and the Young's modulus.

4. a material parameter calculation step of calculating material parameters corresponding to the rubber materials other than the representative rubber material based on the Young's modulus of the rubber materials other than the representative rubber material among the plurality of rubber materials and the relational expression.

5. 5. The rubber material property prediction method according to claim 4, further comprising a stiffness prediction step of predicting stiffness of a rubber material other than the representative rubber material based on material parameters corresponding to the rubber material other than the representative rubber material.

6. The rubber material property prediction method according to any one of claims 1 to 5, wherein the hyperelastic material model is an Arruda-Boyce model.

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