Stress-strain behavior prediction method and stress-strain behavior prediction program

Abstract

To efficiently and highly accurately predict nonlinear stress-strain behavior.SOLUTION: A stress-strain behavior prediction method includes: acquiring a stress-strain curve of a resin material at a plurality of temperatures; acquiring parameters of Formula (1) from the stress-strain curve; acquiring temperature-dependent data for each parameter on the basis of the acquired parameters; calculating stress or strain generated in a resin molded body by simulation using a model of the resin molded body; calculating parameters of the Formula (1) at a temperature set in the simulation on the basis of the temperature-dependent data; and calculating nonlinearity of the stress and strain using the stress or strain calculated by the simulation and the Formula (1) in which the calculated parameters are set. Mathematical Formula 1.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present disclosure relates to a stress-strain behavior prediction method and a stress-strain behavior prediction program. [Background technology]

[0002] Generally, strength and durability are taken into consideration when designing resin products (resin molded products). For example, if the specifications for strength and durability are not met after the design is completed, or if a problem occurs, the design is changed. In this case, the later the design change is made, the higher the countermeasure costs (man-hours, time) will be. Therefore, it is preferable to be able to determine the design direction and specifications at an early stage of the design.

[0003] Therefore, in order to shorten the time and reduce the cost of prototyping, attempts are being made to substitute numerical analysis for mechanical strength tests of various resin products in the design of various resin products. By predicting the strength of a resin product using numerical analysis, tests that involve destruction of the resin product or its prototype are no longer necessary, eliminating the need to prepare prototypes for the number of tests, and making it easy to repeat strength predictions even when the design is changed.

[0004] When predicting the strength of a resin product using numerical analysis, stress-strain data obtained from strength tests using resin molded products is used. For example, stress-strain data may be a stress-strain curve that shows the relationship between stress and strain magnitude. In order to accurately predict the strength of a resin product, the nonlinearity of the stress-strain curve may be taken into account. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] Japanese Patent Application Publication No. 2019-082985 [Patent Document 2] Japanese Patent Application Laid-Open No. 2003-194686 Summary of the Invention [Problem to be solved by the invention]

[0006] However, when predicting the strength of a resin product using a stress-strain curve, the material testing required to obtain the stress-strain curve requires time, which can prevent the design period from being shortened sufficiently. Specifically, because the stress-strain curve varies depending on the temperature of the resin material, material testing must be performed under various temperature environments in order to perform highly accurate numerical analysis. Therefore, data collection in material testing under various temperature environments becomes a time-limiting factor, which can hinder the shortening of the design period.

[0007] The technology disclosed herein has been developed in consideration of these points, and aims to provide a stress-strain behavior prediction method and a stress-strain behavior prediction program that can predict nonlinear stress and strain behavior efficiently and with high accuracy. [Means for solving the problem]

[0008] According to one aspect of the present disclosure, a stress-strain behavior prediction method includes a stress-strain curve acquisition step of acquiring stress-strain curves of a resin material at multiple temperatures, and a parameter acquisition step of determining parameters of Equation (1) that indicate nonlinearity of stress and strain from the acquired stress-strain curves;

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[0009] According to another aspect of the present disclosure, a stress-strain behavior prediction method includes a stress-strain curve acquisition step of acquiring stress-strain curves of a resin material at a plurality of temperatures, and a parameter acquisition step of calculating parameters of Equation (3) indicating nonlinearity of stress and strain from the acquired stress-strain curves.

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[0010] According to another aspect of the present disclosure, a stress-strain behavior prediction method includes a stress-strain curve acquisition step of acquiring stress-strain curves of a resin material at a plurality of temperatures, and a parameter acquisition step of calculating parameters of Equation (5) indicating nonlinearity of stress and strain from the acquired stress-strain curves.

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[0011] According to another aspect of the present disclosure, a stress-strain behavior prediction program causes a computer to execute the above-described stress-strain behavior prediction method. [Brief explanation of the drawings]

[0012] [Figure 1] FIG. 1 is a flowchart showing a stress-strain behavior prediction method according to the first embodiment. [Figure 2] FIG. 2 is a diagram showing an example of a true stress-true strain curve. [Figure 3] FIG. 3 is a diagram showing an example of curve fitting when the first mathematical formula is used. [Figure 4] FIG. 4 is a diagram showing another example of a true stress-true strain curve. [Figure 5]FIG. 5 is a diagram showing another example of curve fitting when the first mathematical formula is used. [Figure 6] FIG. 6 is a diagram showing a specific example of a finite element model. [Figure 7] FIG. 7 is a diagram showing a specific example of boundary conditions applied to a finite element model. [Figure 8] FIG. 8 is a diagram showing an example of strain distribution. [Figure 9] FIG. 9 is a diagram showing an example of the elastic modulus distribution. [Figure 10] FIG. 10 is a diagram showing an example of curve fitting when the second mathematical formula is used. [Figure 11] FIG. 11 is a diagram showing an example of curve fitting when the third mathematical formula is used. [Figure 12] FIG. 12 is a diagram showing an example of a resin molded product according to an embodiment. [Figure 13] FIG. 13 is a diagram illustrating an example of temperature-dependent data of parameters. [Figure 14] FIG. 14 is a diagram showing another example of temperature-dependent data of parameters. [Figure 15] FIG. 15 is a diagram showing another example of temperature-dependent data of parameters. [Figure 16] FIG. 16 is a diagram showing the predicted results of stress-strain behavior according to Example 1. [Figure 17] FIG. 17 is a diagram illustrating a structural analysis calculation result according to the first embodiment. [Figure 18] FIG. 18 is a diagram showing another example of temperature-dependent data of parameters. [Figure 19] FIG. 19 is a diagram showing the predicted results of stress-strain behavior according to Example 2. [Figure 20] FIG. 20 is a diagram showing the structural analysis calculation results according to the second embodiment. [Figure 21] FIG. 21 is a diagram showing another example of temperature-dependent data of parameters. [Figure 22] FIG. 22 is a diagram showing another example of temperature-dependent data of parameters. [Figure 23] FIG. 23 is a diagram showing another example of temperature-dependent data of parameters. [Figure 24] FIG. 24 is a diagram showing the predicted results of stress-strain behavior according to Example 3. [Figure 25] FIG. 25 is a diagram showing the structural analysis calculation results according to the third embodiment. [Figure 26] FIG. 26 is a diagram illustrating an example of curve fitting according to a comparative example. [Figure 27] FIG. 27 is a block diagram illustrating an example of the configuration of an information processing device. DETAILED DESCRIPTION OF THE INVENTION

[0013] Hereinafter, an embodiment according to the present disclosure will be described with reference to the accompanying drawings. The embodiment described below is an example and should not be construed as being limited by this description.

[0014] (Embodiment 1) FIG. 1 is a flow diagram showing a stress-strain behavior prediction method according to the first embodiment. This method predicts nonlinear behavior of stress and strain in a resin molded product. As shown in FIG. 1, the stress-strain behavior prediction method includes the steps of obtaining a stress-strain curve (step S101), calculating true stress and true strain (step S102), curve fitting (step S103), obtaining temperature-dependent data (step S104), creating a finite element model (step S105), setting element attributes and physical property values ​​(step S106), calculating nonlinearity (step S107), and structural analysis calculation (step S108).

[0015] [Obtaining stress-strain curve (Step S101)] Using a test piece made from a resin material whose stress-strain behavior is to be predicted, a stress-strain curve is obtained, for example, according to the method described in ISO 527 (JIS K 7161, 7162). At this time, stress-strain curves are obtained at a plurality of discrete temperatures within a predetermined range. For example, stress-strain curves are obtained at a plurality of representative temperatures within a range from -40°C to 100°C.

[0016] The resin material here includes a resin mixture containing multiple resins and a resin composition containing a resin material and a filler. The resin composition also includes a resin composition to which additives such as nucleating agents, colorants, antioxidants, stabilizers, plasticizers, lubricants, mold release agents, and flame retardants are added to impart desired properties. Examples of inorganic fillers contained in the resin composition include fibrous fillers, granular fillers, and plate-like fillers.

[0017] Examples of fibrous fillers include inorganic fibrous materials such as glass fibers, asbestos fibers, silica fibers, silica-alumina fibers, alumina fibers, zirconia fibers, boron nitride fibers, silicon nitride fibers, boron fibers, potassium titanate fibers, and metal fibers such as stainless steel, aluminum, titanium, copper, and brass.

[0018] Examples of powdery and granular fillers include silica, quartz powder, glass beads, milled glass fiber, glass balloons, glass powder, calcium silicate, aluminum silicate, kaolin, talc, clay, diatomaceous earth, silicates such as wollastonite, metal oxides such as iron oxide, titanium oxide, zinc oxide, antimony trioxide, and alumina, metal carbonates such as calcium carbonate and magnesium carbonate, metal sulfates such as calcium sulfate and barium sulfate, ferrite, silicon carbide, silicon nitride, boron nitride, and various metal powders.

[0019] Examples of the plate-like filler include mica, glass flakes, and various metal foils.

[0020] [Calculating true stress and true strain (Step S102)] The stress and strain obtained by obtaining a stress-strain curve are nominal stress and nominal strain, so true stress and true strain can be calculated from the nominal stress and nominal strain. By converting to true stress and true strain, it is possible to ensure additivity when strain increases, and the stress and strain can be used in finite element method calculations.

[0021] The nominal stress σ and nominal strain ε can be converted to true stress σ and true strain ε by the following calculations: σt=(1+ε0)σ0 εt=log(1+ε0)

[0022] By calculating the true stress and true strain, a stress-strain curve showing the relationship between true stress and true strain is obtained at each temperature. That is, from the stress-strain curve for each temperature acquired in step S101, a stress-strain curve of true stress and true strain is obtained for each temperature, as shown in Figure 2. Note that Figure 2 is an example of a stress-strain curve when DURACON (registered trademark) POM M90-44 is used as the resin material. As can be seen from this figure, the true stress and true strain are nonlinear at all temperatures.

[0023] [Curve fitting (step S103)] Once the stress-strain curves for each temperature are obtained, curve fitting using a function is performed for the stress-strain curves at each temperature. Specifically, curve fitting for the stress-strain curves for each temperature is performed by expressing the relationship between stress F(ε) and strain ε using the first mathematical formula (1) shown below.

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[0024] In curve fitting, P in the first equation is adjusted to obtain the curve that best fits the stress-strain curve at each temperature. ij , r s , B s , m, and n are calculated. By curve fitting using the first equation, for example, the curve shown in Figure 3 is obtained for the stress-strain curve shown in Figure 2. In this way, by introducing the first equation and performing curve fitting, it is possible to express a stress-strain curve with relatively high accuracy at each temperature. In other words, the first equation can accurately express the nonlinearity of stress and strain at each temperature.

[0025] An example of a stress-strain curve when DURANEX (registered trademark) PBT 2002 (unfilled) is used as the resin material is shown in Figure 4, and the results of curve fitting using the first formula are shown in Figure 5. In this way, even if the resin material changes, the stress-strain curve for each temperature can be accurately expressed by curve fitting using the first formula.

[0026] [Acquire temperature-dependent data (step S104)] When the stress-strain curve for each temperature is fitted, temperature-dependent data for each parameter of the first equation is obtained. That is, for example, within the measured temperature range, the parameters calculated for each temperature may be interpolated by linear interpolation, spline interpolation, or the like to estimate the parameters at temperatures not actually measured. Furthermore, for example, outside the measured temperature range, the value of each parameter may be set to the same value as the parameter at the minimum or maximum temperature within the measured temperature range.

[0027] In this way, temperature-dependent data is obtained for the parameters of the first equation, which vary with temperature, and the P ij , r s , B s , m, n can be referenced.

[0028] [Creating a finite element model (step S105)] On the other hand, for a resin product to be subjected to structural analysis, a finite element model is created by dividing the shape of the resin product into minute regions. For example, the shape of the resin product is first converted into digital data using a CAD or the like, and the modeling range is set on this data. Then, element division using the finite element method or the like is performed using an element division preprocessor or the like, and an analysis model in which the resin product is divided into multiple elements is created.

[0029] The shape of the elements may be selected from, for example, tetrahedral primary elements, quadratic elements, hexahedral primary elements, quadratic elements, etc. By increasing the number of element divisions and making each element sufficiently fine, high calculation accuracy can be obtained, but as the number of element divisions increases, the calculation time becomes longer. Therefore, it is preferable to adopt an appropriate number of element divisions taking into consideration the calculation accuracy, calculation time, etc.

[0030] A specific example of a model that has been divided into finite elements using quadratic tetrahedral elements is shown in Figure 6. This finite element model has a rectangular parallelepiped shape with a width of 10 mm, a length of 64 mm, and a thickness of 4 mm.

[0031] [Element attribute and physical property value setting (Step S106)] Once a finite element model is created, the physical properties used in the calculation are set according to the attributes of the finite element model. That is, physical property values ​​are assigned to the elements of the finite element model according to the attributes of each element. Examples of such physical property values ​​include the modulus of elasticity, shear modulus of elasticity, Poisson's ratio, and coefficient of linear expansion. In addition, constraint conditions, loading conditions, calculation time step, output conditions, etc. are set as boundary conditions for simulations using the finite element model. Specifically, for example, when a bending test conforming to ISO 178 is performed, the boundary conditions are set to constrain both edges of the finite element model in the thickness and width directions and to apply a forced displacement to the center, as shown in Figure 7.

[0032] [Nonlinearity calculation (step S107)] The stress or strain is calculated by a simulation using a finite element model, and the nonlinearity of the stress and strain is calculated using a first mathematical formula that indicates the nonlinearity of the stress and strain. The simulation using the finite element method can be performed using, for example, ANSYS manufactured by Ansys Inc., Dassault Systems (registered trademark), ABAQUS (registered trademark) manufactured by SE, and ADVENTURE CLUSTER (registered trademark) manufactured by Allied Engineering Co., Ltd.

[0033] In this simulation, for example, the maximum principal strain, von Mises strain, maximum principal stress, or von Mises stress is calculated. Figure 8 shows an example of the von Mises strain distribution obtained as a result of the simulation. In this figure, the darker the color, the larger the strain. Therefore, it can be seen that the strain is larger in elements closer to the center where the forced displacement is applied, and the strain is smaller in elements at both edges.

[0034] Once the stress or strain is calculated, the parameters of the first equation at the temperature set in the simulation are calculated from the temperature-dependent data acquired in step S104. That is, P ij , r s , B s , m, and n are obtained from the temperature-dependent data for each parameter. Then, the nonlinear strain or stress is calculated from the stress or strain using a first mathematical formula to which the obtained parameters are applied. At this time, the initial elastic modulus E0 is calculated based on the other parameters P ij , r s , B s The modulus of elasticity may be determined by acquiring temperature-dependent data similar to those for m, n, and m, or may be calculated separately, taking temperature dependency into account. The strain or stress calculated using the first formula in this manner takes into account the nonlinearity of stress and strain, as well as the temperature dependency of the parameters of the first formula that express the nonlinearity. Therefore, the nonlinear stress and strain behavior of a resin product can be predicted with high accuracy.

[0035] Instead of calculating the strain or stress from the stress or strain while taking into account the nonlinearity, the elastic modulus used in the linear calculation in the simulation may be corrected by determining the nonlinearity from the obtained strain. Specifically, to correct the elastic modulus, the ratio of the secant elastic modulus to the initial elastic modulus is calculated, and this ratio is reflected in the elastic modulus used in the linear calculation, thereby correcting the elastic modulus to one that takes into account the nonlinearity. The ratio of the secant elastic modulus to the initial elastic modulus can be calculated using the following equation (2), which is a modification of the first equation.

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[0036] However, in equation (2), E s is the secant modulus of elasticity, and the other parameters are the same as in the first equation (1). Figure 9 shows an example of the elastic modulus distribution corrected using equation (2). As shown in this figure, it is possible to obtain the elastic modulus distribution taking into account the nonlinearity of stress and strain.

[0037] [Structural analysis calculation (Step S108)] Structural analysis calculations for a resin product are performed using the stress, strain, or elastic modulus obtained by taking nonlinearity into consideration. That is, for example, the elastic force distribution obtained by taking nonlinearity of stress and strain into consideration is set in a finite element model, and stress and strain are calculated under boundary conditions similar to those described above.

[0038] As described above, according to this embodiment, the temperature-dependent data of the parameters in the first formula expressing the nonlinearity of stress and strain are acquired, and the stress and strain that take the nonlinearity into consideration are calculated using a simulation using a model of the resin product to be analyzed and the first formula in which parameters determined based on the temperature-dependent data are set. As a result, the behavior of nonlinear stress and strain can be predicted efficiently and with high accuracy.

[0039] (Embodiment 2) The feature of the second embodiment is that curve fitting of the stress-strain curve is performed using a second mathematical expression that has fewer temperature-dependent parameters than the first mathematical expression. The stress-strain behavior prediction method according to the second embodiment is the same as that of the first embodiment (FIG. 1) except for the use of the second mathematical expression, and therefore a description thereof will be omitted.

[0040] [Curve fitting (step S103)] Once the stress-strain curves for each temperature are obtained, curve fitting using a function is performed for the stress-strain curves at each temperature. Specifically, curve fitting for the stress-strain curves for each temperature is performed by expressing the relationship between stress F(ε) and strain ε using the second mathematical formula (3) shown below.

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[0041] In curve fitting, a and b in the second formula are calculated so as to obtain a curve that best fits the stress-strain curve at each temperature. By curve fitting using the second formula, the curve shown in Figure 10, for example, is obtained for the stress-strain curve shown in Figure 2. In this way, by introducing the second formula and performing curve fitting, it is possible to express a stress-strain curve with relatively high accuracy at each temperature. In other words, the second formula can accurately express the nonlinearity of stress and strain at each temperature.

[0042] [Acquire temperature-dependent data (step S104)] After curve fitting of the stress-strain curve for each temperature is performed, temperature-dependent data of each parameter of the second equation is obtained. That is, for example, within the measured temperature range, the parameters calculated for each temperature may be interpolated by linear interpolation, spline interpolation, or the like to calculate parameters at temperatures not actually measured. Furthermore, for example, outside the measured temperature range, the value of each parameter may be set to the same value as the parameter at the minimum or maximum temperature within the measured temperature range.

[0043] In this way, temperature-dependent data is obtained for the parameters of the second formula that vary depending on the temperature, and a and b at any temperature can be referenced.

[0044] [Nonlinearity calculation (step S107)] The stress or strain is calculated by a simulation using a finite element model, and the nonlinearity of the stress and strain is calculated using a second mathematical formula that indicates the nonlinearity of the stress and strain. In this simulation, for example, the maximum principal strain, von Mises strain, maximum principal stress, or von Mises stress is calculated.

[0045] Once the stress or strain is calculated, the parameters of the second formula at the temperature set in the simulation are calculated from the temperature-dependent data acquired in step S104. That is, a and b at the desired temperature are acquired from the temperature-dependent data for each parameter. Then, the nonlinear strain or stress is calculated from the stress or strain using the second formula to which the acquired parameters are applied. In this case, the initial elastic modulus E0 may be obtained by acquiring temperature-dependent data similar to that for the other parameters a and b, or a separate elastic modulus taking temperature dependence into account may be calculated. In this way, the strain or stress calculated using the second formula takes into account the nonlinearity of the stress and strain, as well as the temperature dependence of the parameters of the second formula that express the nonlinearity. Therefore, the nonlinear stress and strain behavior of a resin product can be accurately predicted.

[0046] In the second embodiment, instead of calculating the strain or stress from the stress or strain while taking into account the nonlinearity, the elastic modulus used in the linear calculation in the simulation may be corrected by taking into account the nonlinearity. Specifically, to correct the elastic modulus, the ratio between the secant elastic modulus and the initial elastic modulus is calculated, and this ratio is reflected in the elastic modulus used in the linear calculation, thereby correcting the elastic modulus to one that takes into account the nonlinearity. The ratio between the secant elastic modulus and the initial elastic modulus can be calculated using the following formula (4), which is a modification of the second formula.

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[0047] However, in equation (4), E s is the secant modulus of elasticity, and the other parameters are the same as in the second equation (3).

[0048] As described above, according to this embodiment, the temperature-dependent data of the parameters in the second equation expressing the nonlinearity of stress and strain are acquired, and the stress and strain taking the nonlinearity into account are calculated using a simulation using a model of the resin product to be analyzed and the second equation in which parameters determined based on the temperature-dependent data are set. Therefore, the behavior of nonlinear stress and strain can be predicted efficiently and accurately. Furthermore, the number of temperature-dependent parameters is small, which reduces the amount of calculation.

[0049] (Embodiment 3) The feature of the third embodiment is that curve fitting of the stress-strain curve is performed using a third mathematical formula that has fewer temperature-dependent parameters than the first mathematical formula. The stress-strain behavior prediction method according to the third embodiment is the same as that of the first embodiment (FIG. 1) except for the use of the third mathematical formula, and therefore a description thereof will be omitted.

[0050] [Curve fitting (step S103)] Once the stress-strain curves for each temperature are obtained, curve fitting using a function is performed for the stress-strain curves at each temperature. Specifically, curve fitting for the stress-strain curves for each temperature is performed by expressing the relationship between stress F(ε) and strain ε using the third equation (5) shown below.

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[0051] In curve fitting, C1, C2, and τ in the third formula are calculated so as to obtain a curve that best fits the stress-strain curve at each temperature. By curve fitting using the third formula, the curve shown in Figure 11, for example, is obtained for the stress-strain curve shown in Figure 2. Thus, by introducing the third formula and performing curve fitting, it is possible to express a stress-strain curve with relatively high accuracy at each temperature. In other words, the third formula can accurately express the nonlinearity of stress and strain at each temperature.

[0052] [Acquire temperature-dependent data (step S104)] After curve fitting of the stress-strain curve for each temperature is performed, temperature-dependent data of each parameter of the third equation is obtained. That is, for example, within the measured temperature range, the parameters calculated for each temperature may be interpolated by linear interpolation, spline interpolation, or the like to estimate the parameters at temperatures not actually measured. Furthermore, for example, outside the measured temperature range, the value of each parameter may be set to the same value as the parameter at the minimum or maximum temperature within the measured temperature range.

[0053] In this way, temperature-dependent data is obtained for the parameters of the third formula that vary depending on the temperature, and C1, C2, and τ at any temperature can be referenced.

[0054] [Nonlinearity calculation (step S107)] The stress or strain is calculated by a simulation using a finite element model, and the nonlinearity of the stress and strain is calculated using a third mathematical formula that indicates the nonlinearity of the stress and strain. In this simulation, for example, the maximum principal strain, von Mises strain, maximum principal stress, or von Mises stress is calculated.

[0055] Once the stress or strain is calculated, the parameters of the third formula at the temperature set in the simulation are calculated from the temperature-dependent data acquired in step S104. That is, C1, C2, and τ at the desired temperature are acquired from the temperature-dependent data for each parameter. Then, the nonlinear strain or stress is calculated from the stress or strain using the third formula to which the acquired parameters are applied. In this case, the initial elastic modulus E0 may be obtained by acquiring temperature-dependent data similar to that for the other parameters C1, C2, and τ, or a separate elastic modulus taking temperature dependence into account may be calculated. The strain or stress calculated using the third formula in this way takes into account the nonlinearity of the stress and strain, as well as the temperature dependence of the parameters of the third formula that express the nonlinearity. Therefore, the nonlinear stress and strain behavior of a resin product can be accurately predicted.

[0056] In the third embodiment, instead of calculating the strain or stress from the stress or strain while taking into account the nonlinearity, the elastic modulus used in the linear calculation in the simulation may be corrected by determining the nonlinearity from the obtained strain. Specifically, to correct the elastic modulus, the ratio of the secant elastic modulus to the initial elastic modulus is calculated, and this ratio is reflected in the elastic modulus used in the linear calculation, thereby correcting the elastic modulus to one that takes into account the nonlinearity. The ratio of the secant elastic modulus to the initial elastic modulus can be calculated using the following equation (6), which is a modification of the third equation.

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[0057] However, in equation (6), E s is the secant modulus of elasticity, and the other parameters are the same as in the third equation (5).

[0058] As described above, according to this embodiment, the temperature-dependent data of the parameters in the third equation expressing the nonlinearity of stress and strain are acquired, and stress and strain taking nonlinearity into account are calculated using a simulation using a model of the resin product to be analyzed and the third equation in which parameters determined based on the temperature-dependent data are set. Therefore, it is possible to predict the behavior of nonlinear stress and strain efficiently and with high accuracy. Furthermore, since the number of temperature-dependent parameters is small, the amount of calculation can be reduced.

[0059] Next, a description will be given of examples of calculating stress and strain using the stress-strain behavior prediction methods according to the above-described embodiments 1 to 3. Note that the technology of the present disclosure is not limited to these examples.

[0060] In the following examples, stress-strain curves are obtained at multiple temperatures using a test specimen made from DURACON POM M90-44, a resin material. This test specimen has the shape shown in FIG. 12, for example, and conforms to ISO 527. Data that can be obtained from this test specimen are nominal stress and nominal strain at multiple temperatures. In this example, stress-strain curves are obtained at six different temperatures, for example, -40°C, 0°C, 23°C, 40°C, 60°C, and 100°C.

[0061] Example 1 Example 1 corresponds to the above-described first embodiment, and uses the first mathematical formula for curve fitting. The results of curve fitting using the first mathematical formula are shown in Fig. 3. However, since the stress-strain curve at 80°C was not actually measured, the stress-strain curve at 80°C was not curve-fitted.

[0062] By fitting the curve at each temperature, the parameters in the first equation when fitting the stress-strain curve at these temperatures are obtained. Then, by interpolating these parameters, the temperature dependence data of each parameter is obtained. Figures 13 to 15 show the P ij , r s , B s By acquiring these temperature-dependent data, it is possible to calculate the parameters of the first equation at, for example, 80°C, which is not actually measured from the test specimen.

[0063] Specifically, when each parameter is calculated from the temperature-dependent data at, for example, 80°C, P ij =-0.0328, r s =4.72×10 -4 , B s = -0.1304. Furthermore, m = -19.07 and n = -2.80. Figure 16 shows the stress-strain curve at 80°C when these parameter values ​​are applied to the first mathematical formula. In Figure 16, the solid line is the stress-strain curve obtained by the first mathematical formula, and the plot of black dots is the true stress and true strain values ​​actually measured from the test piece at 80°C.

[0064] As can be seen from this figure, by using the first equation to which parameters determined from the temperature-dependent data are applied, a stress-strain curve that closely matches the measured values ​​can be obtained.

[0065] In addition, a bending test was conducted at 23°C using a resin product made of DURACON POM M90-44 with the shape shown in Figure 6, and the measured values ​​were compared with the calculated values. Specifically, for nodes to which forced displacements were applied on the resin product or the finite element model, the bending stress was calculated from the sum of the repulsive forces corresponding to each forced displacement. The resulting measured and calculated values ​​are shown in Figure 17. In Figure 17, the solid line indicates the measured values, and the dashed line indicates the calculated values. The dashed line indicates the calculated values ​​when linear calculations are performed without considering the nonlinearity of stress and strain.

[0066] As can be seen from this figure, the calculated values ​​taking nonlinearity into account using the first formula reproduce the tendency of the measured values. Therefore, it is clear that the use of the first formula makes it possible to predict nonlinear stress and strain behavior efficiently and with high accuracy.

[0067] Example 2 Example 2 corresponds to the above-mentioned second embodiment, and uses the second mathematical formula for curve fitting. The result of curve fitting using the second mathematical formula is as shown in Fig. 10. However, in this example, the stress-strain curve at 80°C was not actually measured, so the stress-strain curve at 80°C was not curve-fitted.

[0068] By fitting the curve at each temperature, the parameters in the second equation when fitting the stress-strain curve at these temperatures are obtained. Then, by interpolating these parameters, temperature-dependent data for each parameter is obtained. Figure 18 shows the temperature-dependent data for a and b in the second equation. In Figure 18, the solid line represents the temperature-dependent data for parameter a, and the dashed line represents the temperature-dependent data for parameter b. By obtaining this temperature-dependent data, it is possible to calculate the parameters of the second equation at, for example, 80°C, which are not actually measured on the test specimen.

[0069] Specifically, when the parameters at, for example, 80°C were calculated from the temperature-dependent data, the results were a = 10.52 and b = -18.06. Fig. 19 shows the stress-strain curve at 80°C when these parameter values ​​are applied to the second formula. In Fig. 19, the solid line is the stress-strain curve obtained by the second formula, and the plot of black dots is the true stress and true strain values ​​actually measured from the test piece at 80°C.

[0070] As can be seen from this figure, by using the second equation to which parameters derived from temperature-dependent data are applied, a highly accurate stress-strain curve can be obtained with a deviation from the actual measured values ​​of approximately 10% or less.

[0071] In addition, a bending test was conducted at 23°C using a resin product made of DURACON POM M90-44 with the shape shown in Figure 6, and the measured values ​​were compared with the calculated values. Specifically, for nodes to which forced displacements were applied on the resin product or the finite element model, the bending stress was calculated from the sum of the repulsive forces corresponding to each forced displacement. The resulting measured and calculated values ​​are shown in Figure 20. In Figure 20, the solid line indicates the measured values, and the dashed line indicates the calculated values. The dashed line indicates the calculated values ​​when linear calculations are performed without considering the nonlinearity of stress and strain.

[0072] As can be seen from this figure, the calculated values ​​taking nonlinearity into account using the second formula reproduce the tendency of the measured values. Therefore, it is clear that the use of the second formula makes it possible to predict nonlinear stress and strain behavior efficiently and with high accuracy.

[0073] Example 3 Example 3 corresponds to the third embodiment, and uses the third mathematical formula for curve fitting. The results of curve fitting using the third mathematical formula are shown in Fig. 11. However, since the stress-strain curve at 80°C was not actually measured, the stress-strain curve at 80°C was not curve-fitted.

[0074] By fitting the curves at each temperature, the parameters in the third equation when fitting the stress-strain curves at those temperatures are obtained. Then, by interpolating these parameters, temperature-dependent data of each parameter is obtained. Figures 21 to 23 show the temperature-dependent data of C1, C2, and τ in the third equation, respectively. By obtaining this temperature-dependent data, it is possible to calculate the parameters of the third equation at, for example, 80°C, which are not actually measured on the test specimen.

[0075] Specifically, when the parameters at, for example, 80°C were calculated from the temperature-dependent data, the results were C1 = -0.7088, C2 = 0.08434, and τ = 0.0898. The stress-strain curve at 80°C obtained by applying these parameter values ​​to the third formula is shown in Figure 24. In Figure 24, the solid line is the stress-strain curve obtained by the third formula, and the plot of black dots is the true stress and true strain values ​​actually measured from the test specimen at 80°C.

[0076] As can be seen from this figure, by using the third equation to which parameters determined from the temperature-dependent data are applied, a stress-strain curve that closely matches the measured values ​​can be obtained.

[0077] In addition, a bending test was conducted at 23°C using a resin product made of DURACON POM M90-44 with the shape shown in Figure 6, and the measured values ​​were compared with the calculated values. Specifically, for nodes to which forced displacements were applied on the resin product or the finite element model, the bending stress was calculated from the sum of the repulsive forces corresponding to each forced displacement. The resulting measured and calculated values ​​are shown in Figure 25. In Figure 25, the solid line indicates the measured values, and the dashed line indicates the calculated values. The dashed line indicates the calculated values ​​when linear calculations are performed without considering the nonlinearity of stress and strain.

[0078] As can be seen from this figure, the calculated values ​​taking nonlinearity into account using the third formula reproduce the tendency of the measured values. Therefore, it is clear that the use of the third formula makes it possible to predict nonlinear stress and strain behavior efficiently and with high accuracy.

[0079] (Comparative Example) So far, we have explained examples of predicting stress and strain behavior using the first, second, and third formulas, but it is also possible to use other formulas to fit the stress-strain curve. For example, the following formula (7) is commonly known to describe the relationship between stress σ(x) and intermolecular distance x.

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[0080] In the above equation (7), λ is half the intermolecular distance that is the maximum value when the differential equation of the potential energy is approximated by a sine curve, and σ f is the maximum value of the bonding force. From this equation (7), the following equation (8) is obtained for the stress σ(ε) and strain ε.

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[0081] The results of curve fitting of the stress-strain curve shown in Figure 2 using the above equation (8) instead of the first, second, and third equations are shown in Figure 26. As shown in this figure, the curve obtained using equation (8) deviates significantly from the stress-strain curve shown in Figure 2 when the strain is 5% or more.

[0082] The stress-strain behavior prediction method according to the present disclosure can be executed by an information processing device. Fig. 27 is a block diagram showing an example of the hardware configuration of an information processing device 100 that executes the stress-strain behavior prediction method. As shown in Fig. 27, the information processing device 100 includes a processor 101, a main memory device 102, an auxiliary memory device 103, an I / O (Input / Output) interface 104, and a network interface (hereinafter abbreviated as "NW interface") 105.

[0083] The processor 101 includes, for example, a central processing unit (CPU), a field programmable gate array (FPGA), or a digital signal processor (DSP), and controls the entire information processing device 100 and executes various types of arithmetic processing.

[0084] The main storage device 102 includes, for example, a random access memory (RAM) or a read only memory (ROM), and stores information used in the arithmetic processing executed by the processor 101.

[0085] The auxiliary storage device 103 includes, for example, a hard disk drive (HDD) or a solid state drive (SSD), and stores various programs and data.

[0086] The I / O interface 104 is an interface through which a user inputs information and outputs information to a user, and may include, for example, a keyboard, a display, a touch panel, a microphone, or a speaker.

[0087] The NW interface 105 is an interface for connecting to a network via wire or wirelessly.

[0088] The information processing device 100 acquires data such as stress-strain curves measured using test pieces and shape data of resin products via the I / O interface 104 and the NW interface 105. The processor 101 then executes programs stored in the auxiliary storage device 103 while utilizing the main storage device 102, thereby performing various processes such as curve fitting, temperature-dependent data acquisition, finite element model creation, and nonlinearity calculation. Furthermore, the processor 101 performs structural analysis calculations based on the stresses and strains calculated taking nonlinearity into consideration.

[0089] The processes executed by the information processing device 100 can also be written as a computer-executable program. In this case, the program can be stored on a computer-readable, non-transitory recording medium and installed on the computer. Examples of such recording media include portable recording media such as CD-ROMs, DVD discs, and USB memory, as well as semiconductor memories such as flash memories. [Explanation of symbols]

[0090] 101 processors 102 Main storage 103 Auxiliary storage device 104 I / O Interface 105 Network Interface

Claims

1. a stress-strain curve acquisition step of acquiring stress-strain curves of the resin material at a plurality of temperatures; a parameter acquisition step of determining parameters of equation (1) that indicate the nonlinearity of stress and strain from the acquired stress-strain curve; [Equation 1] E 0 : initial elastic modulus P ij : Parameter that represents the magnitude of the potential r s : Parameter representing the intermolecular distance when strain is 0 B s : Parameter representing residual stress when strain is 0 m: Parameter related to the intermolecular distance dependence of the repulsive term n: Parameter related to the intermolecular distance dependence of the attractive term ε: strain F(ε): Stress a temperature-dependent data acquisition step of acquiring temperature-dependent data indicating the temperature dependence of each parameter based on the acquired parameters; a simulation step of calculating stress or strain generated in the resin molded body by simulation using a model of the resin molded body made of the resin material; a parameter calculation step of calculating parameters of the formula (1) at a temperature set during the simulation based on the temperature-dependent data; a nonlinearity calculation step of calculating the nonlinearity of the stress and strain using the stress or strain calculated in the simulation step and the formula (1) in which the parameters calculated in the parameter calculation step are set; A stress-strain behavior prediction method having the above.

2. The nonlinearity calculation step A correction step of correcting the elastic modulus used in the linear calculation in the simulation step using equation (2) obtained by modifying equation (1) [Equation 2] E s : secant modulus of elasticity The stress-strain behavior prediction method according to claim 1 .

3. The temperature-dependent data acquisition step includes: The temperature-dependent data is obtained by linearly interpolating the parameters obtained in the parameter obtaining step. The stress-strain behavior prediction method according to claim 1 .

4. a stress-strain curve acquisition step of acquiring stress-strain curves of the resin material at a plurality of temperatures; a parameter acquisition step of determining parameters of equation (3) that indicate the nonlinearity of stress and strain from the acquired stress-strain curve; [Equation 3] E 0 : initial elastic modulus a, b: parameters ε: strain F(ε): Stress a temperature-dependent data acquisition step of acquiring temperature-dependent data indicating the temperature dependence of each parameter based on the acquired parameters; a simulation step of calculating stress or strain generated in the resin molded body by simulation using a model of the resin molded body made of the resin material; a parameter calculation step of calculating parameters of the equation (3) at a temperature set during the simulation based on the temperature-dependent data; a nonlinearity calculation step of calculating the nonlinearity of the stress and strain using the stress or strain calculated in the simulation step and the equation (3) in which the parameters calculated in the parameter calculation step are set; A stress-strain behavior prediction method having the above.

5. The nonlinearity calculation step A correction step of correcting the elastic modulus used in the linear calculation in the simulation step using equation (4) obtained by modifying equation (3) [Equation 4] E s : secant modulus of elasticity The stress-strain behavior prediction method according to claim 4 .

6. The temperature-dependent data acquisition step includes: The temperature-dependent data is obtained by linearly interpolating the parameters obtained in the parameter obtaining step. The stress-strain behavior prediction method according to claim 4 .

7. a stress-strain curve acquisition step of acquiring stress-strain curves of the resin material at a plurality of temperatures; a parameter acquisition step of determining parameters of equation (5) indicating nonlinearity of stress and strain from the acquired stress-strain curve; [Equation 5] E 0 : initial elastic modulus C 1 , C 2 , τ: parameter ε: strain F(ε): Stress a temperature-dependent data acquisition step of acquiring temperature-dependent data indicating the temperature dependence of each parameter based on the acquired parameters; a simulation step of calculating stress or strain generated in the resin molded body by simulation using a model of the resin molded body made of the resin material; a parameter calculation step of calculating parameters of the equation (5) at a temperature set during the simulation based on the temperature-dependent data; a nonlinearity calculation step of calculating the nonlinearity of the stress and strain using the stress or strain calculated in the simulation step and the formula (5) in which the parameters calculated in the parameter calculation step are set; A stress-strain behavior prediction method having the above.

8. The nonlinearity calculation step A correction step of correcting the elastic modulus used in the linear calculation in the simulation step using equation (6) obtained by modifying equation (5) [Equation 6] E s : secant modulus of elasticity The stress-strain behavior prediction method according to claim 7 .

9. The temperature-dependent data acquisition step includes: The temperature-dependent data is obtained by linearly interpolating the parameters obtained in the parameter obtaining step. The stress-strain behavior prediction method according to claim 7 .

10. A stress-strain behavior prediction program that causes a computer to execute the stress-strain behavior prediction method according to any one of claims 1, 4 and 7.

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