Method for estimating stress-strain curves

Abstract

To easily estimate a stress strain curve of a constituting structure about a metal material having a composite structure composed of two constituting structures in an estimation method of the stress strain curve.SOLUTION: A stress strain curve estimation method is configured to prepare an analysis model 6 corresponding to a structure observation image 5 of a metal material 1; define a stress strain curve of a constituting structure 3 by a prescribed approximation rule letting a material parameter of the constituting structure 3 be a design variable; execute a finite element analysis following a homogenization method with the analysis model 6 and a stress strain curve of constituting structures 3 and 4 as input data, and thereby calculate stress strain curve of a composite structure 2 of the analysis model 6; and optimize an objective function defining coincidence of the analytically calculated stress strain curve of the composite structure 2 of the analysis model 6 with the preliminarily experimentally acquired stress strain curve of the composite structure 2 of the metal material 1 by adjusting the design variable; and estimate a stress strain curve of the constituting structure 3 with the design variable optimizing the objective function as an optimal solution.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] This invention relates to a method for estimating stress-strain curves. [Background technology]

[0002] When modeling a metallic material with a composite structure composed of multiple constituent structures and performing a mechanical numerical analysis, it is sometimes necessary to obtain the stress-strain curves of the individual constituent structures rather than the overall composite structure of the metallic material. Various methods have been studied for obtaining these individual structural stress-strain curves.

[0003] Non-Patent Document 1 describes how a single-phase material having the same metallic structure as the target structure is fabricated, and the stress-strain curve of the target structure is obtained by performing a tensile test on this single-phase material. Furthermore, by performing an analysis according to the homogenization method using the obtained stress-strain curves of multiple structured materials as input data, the stress-strain curve of a composite structure composed of multiple structured materials is accurately estimated. Non-Patent Document 2 describes how the stress-strain curve of a structure is estimated from the relationship between the obtained load and the amount of indentation by performing an indentation test targeting a minute region that precisely targets the structure. [Prior art documents] [Non-patent literature]

[0004] [Non-Patent Document 1] Kurosawa, "Multiscale Strength Analysis of Dual-Phase Steel by Homogenized Elastoplastic FEM," Kobe Steel Technical Report Vol. 71 No. 1, July 2021. [Non-Patent Document 2] Sakamaki et al., "A Proposal for a Method of Estimating Stress-Strain Relationships in Individual Steel Structures Using Indentation Tests," 8th Materials WEEK Materials Symposium, 2022. [Overview of the Initiative] [Problems that the invention aims to solve]

[0005] The method described in Non-Patent Document 1 requires not only searching for heat treatment conditions to produce a single-phase material identical to the target microstructure, but also makes actual adjustment to such heat treatment conditions difficult. In Non-Patent Document 2, targeting the specific microstructure is difficult, and disturbances must be eliminated. Therefore, for metallic materials consisting of multiple microstructures, there is a need for a simpler method for estimating the stress-strain curves of the constituent microstructures.

[0006] The present invention aims to provide a method for estimating stress-strain curves, specifically for a metallic material consisting of two constituent structures, that allows for easy estimation of the stress-strain curves of the constituent structures. [Means for solving the problem]

[0007] The present invention provides a method for estimating the stress-strain curve of a metal material consisting of two constituent structures, which is performed by computer, and includes: creating an analysis model corresponding to a microstructure observation image of the metal material; defining the stress-strain curve of the constituent structure by a predetermined approximation rule with material parameters of the constituent structure as design variables; calculating the stress-strain curve of the composite structure of the analysis model by performing finite element analysis according to a homogenization method using the analysis model and the stress-strain curve of the constituent structure as input data; optimizing an objective function that defines the degree of agreement between the analytically calculated stress-strain curve of the composite structure of the analysis model and the stress-strain curve of the composite structure of the metal material obtained experimentally in advance, by adjusting the design variables; and estimating the stress-strain curve of the constituent structure as the optimal solution for optimizing the objective function.

[0008] This configuration allows for highly accurate estimation of the stress-strain curve of the constituent structure of a metallic material using relatively simple methods such as tensile testing, acquisition of microstructure observation images, and finite element analysis according to the homogenization method. In particular, the tensile testing eliminates the need to fabricate difficult single-phase materials, allowing the direct use of metallic materials with composite structures. Furthermore, it eliminates the need for difficult indentation tests that target minute constituent structures. Microstructure observation images can be easily acquired by imaging the metallic material with a microscope. Finite element analysis according to the homogenization method is a conventionally known technique, as mentioned above, and the analysis work itself is not difficult. In addition, when creating the analysis model, two constituent structures may be recognized by image recognition, such as by binarizing the microstructure observation images. For the predetermined approximation side, for example, Swift's law, the N-th power hardening law, or Ludwick's law may be adopted. For the objective function, for example, the sum of squared residuals with a defined degree of agreement may be adopted.

[0009] In the stress-strain curve estimation method described above, one of the two structural tissue stress-strain curves is known and the other is unknown, and the design variable with the highest degree of agreement in the optimization may be used as the optimal solution to estimate the stress-strain curve of the other structural tissue.

[0010] This configuration allows for easy and highly accurate estimation of the stress-strain curve of an unknown structural element when one of the two structural elements' stress-strain curves is known and the other is unknown. In particular, the algorithm is simple because it simply estimates the one with the highest degree of agreement as the optimal solution.

[0011] The stress-strain curve estimation method may further include the following steps: assuming that both stress-strain curves of the two constituent tissues are unknown, extracting a predetermined number of candidate solutions in order of decreasing agreement during optimization, calculating the equivalent stress for any equivalent plastic strain in each of the stress-strain curves of the predetermined number of candidate solutions to create a histogram, and estimating the stress-strain curves of the two constituent tissues by selecting the candidate solution with the highest agreement among those in the mode interval of the histogram as the optimal solution.

[0012] According to this configuration, when the stress-strain curves of the two constituent structures are both unknown, the stress-strain curves of the two unknown constituent structures can be estimated easily and with high accuracy. Furthermore, when estimating the stress-strain curves of two constituent structures, there is a chance of accidentally falling into a spurious solution where the aforementioned degree of matching is extremely high. However, since the mode interval of the histogram is used, solutions other than those that are probabilistically highly likely can be eliminated. That is, the possibility of falling into such a spurious solution can be reduced, and high estimation accuracy can be ensured.

[0013] In the stress-strain curve estimation method, the plurality of histograms may be created by calculating the plurality of equivalent stresses corresponding to the plurality of equivalent plastic strains, and overlapping candidate solutions located in the mode interval in each of the plurality of histograms may be extracted, and the candidate solution having the highest degree of matching among the extracted overlapping candidate solutions may be used as the optimal solution to estimate the stress-strain curves of the two constituent structures.

[0014] According to this configuration, more of the aforementioned spurious solutions can be eliminated, so higher estimation accuracy can be ensured.

Effects of the Invention

[0015] According to the present invention, in a stress-strain curve estimation method, the stress-strain curves of the constituent structures can be easily estimated for a metal material consisting of two constituent structures.

Brief Description of Drawings

[0016] [Figure 1] A schematic configuration diagram of a control device that executes the stress-strain curve estimation method according to the first embodiment. [Figure 2] A flowchart showing the stress-strain curve estimation method according to the first embodiment. [Figure 3] An image showing a microstructure observation image of a metal material. [Figure 4] An image showing an analysis model corresponding to the microstructure observation image of Fig. 3. [Figure 5] A graph visually showing the relationship between a tensile test and analysis. [Figure 6]A graph showing the accuracy of the stress-strain curve estimation method according to the first embodiment. [Figure 7] A flowchart showing the stress-strain curve estimation method according to the second embodiment. [Figure 8] A histogram of equivalent stress when equivalent plastic strain is 0.05. [Figure 9] A histogram of equivalent stress when equivalent plastic strain is 0.1. [Figure 10] A graph showing the accuracy of the stress-strain curve estimation method according to the second embodiment.

Mode for Carrying Out the Invention

[0017] Hereinafter, embodiments of the present invention will be described with reference to the accompanying drawings.

[0018] (First Embodiment) In the stress-strain curve estimation method according to the first embodiment, for a metal material having a composite structure composed of two constituent structures, when one of the stress-strain curves of the two constituent structures is known and the other is unknown, the stress-strain curve of the other constituent structure is estimated. The estimation can be executed by a computer (control device).

[0019] Referring to FIG. 1, the control device 10 includes an arithmetic circuit 11, a storage device 12, and an input / output interface device 13.

[0020] The arithmetic circuit 11 is a control unit that executes processing in the control device 10. The arithmetic circuit 11 includes a general-purpose processor such as a CPU or MPU that realizes predetermined functions by executing a program. The arithmetic circuit 11 is configured to communicate with the storage device 12 and realizes various processing in the control device 10 by calling and executing arithmetic programs etc. stored in the storage device 12. The processing in the control device 10 will be described later. The arithmetic circuit 11 may be a configuration in which hardware resources and software cooperate to realize predetermined functions, or it may be a hardware circuit specifically designed to realize predetermined functions. That is, the arithmetic circuit 11 can be realized with various processors other than CPUs and MPUs, such as GPUs, FPGAs, DSPs, ASICs, etc. Such an arithmetic circuit 11 may be composed of, for example, a signal processing circuit which is a semiconductor integrated circuit.

[0021] The storage device 12 is a storage medium capable of storing various types of information. The storage device 12 can be implemented as, for example, memory such as DRAM, SRAM, or flash memory, an HDD, an SSD, or other storage devices, or a combination thereof as appropriate. The storage device 12 stores programs for implementing the various processes performed by the arithmetic circuit 11 as described above. The storage device 12 can also store various types of data, which will be described later, as well as analysis models and information acquired or calculated by the control device 10.

[0022] The input / output interface device 13 functions as an input device for receiving information from the user and as an output device for outputting information to the user. The input / output interface device 13 is equipped with one or more human-machine interfaces. The human-machine interface includes, for example, input devices such as a keyboard, pointing device (mouse, trackball, etc.), and touchpad, and output devices such as a display and speaker. The human-machine interface also includes input / output devices such as an in-cell touch panel display (e.g., a liquid crystal panel or an organic EL panel).

[0023] Referring to Figure 2, in the stress-strain curve estimation method according to this embodiment, first, a microstructure observation image of the target metal material is obtained (step S1-1). Microstructure observation images can be easily obtained by imaging a small area of ​​the metal material with a microscope.

[0024] Referring to Figure 3, in this embodiment, as a metallic material 1 having a composite structure 2 composed of two constituent structures 3 and 4, a steel material 1 having a composite structure 2 composed of a ferrite phase 3 and a W-ferrite phase 4 is given as an example. In the illustrated microstructure observation image 5, a microscale region is displayed. In this embodiment, the stress-strain curve of the ferrite phase 3 is known, and the stress-strain curve of the W-ferrite phase 4 is unknown. That is, in this embodiment, the stress-strain curve of the W-ferrite phase 4 is estimated. However, this is an example, and the target of estimation could be the stress-strain curve of the constituent structure of any metallic material.

[0025] Referring again to Figure 2, the next step is to create an analysis model corresponding to the tissue observation image 5 (Step S1-2). For example, this analysis model is a three-dimensional finite element model in which the shape corresponding to the tissue observation image 5 is meshed and one layer is provided in the depth direction.

[0026] Referring to Figure 4, an example of an analysis model 6 corresponding to the tissue observation image 5 is shown. When creating this analysis model 6, the tissue observation image 5 may be binarized and the boundaries of the ferrite phase 3 and W-ferrite phase 4 may be clarified. In the illustrated analysis model 6, ferrite phase 3 and W-ferrite phase 4 are created with approximately the same position, shape, and size as in the tissue observation image 5 (Figure 3). The creation of such an analysis model 6 from the tissue observation image 5 may be performed automatically by the calculation circuit 11.

[0027] Referring again to Figure 2, the stress-strain curve of the constituent structure is then defined by a predetermined approximation rule using the material parameters of W ferrite phase 4 as design variables (step S1-3). In this embodiment, Swift's law is adopted as the predetermined approximation rule. In Swift's law, the stress-strain curve is expressed by the following equation (1): where σ is the equivalent stress, σ0 is the yield stress, and ε p σ0 represents the equivalent plastic strain, and α and N are both coefficients. Hereafter, the material parameters σ0, α, and N will also be referred to as design variables. Therefore, Swift's law allows us to define the stress-strain curve by determining these design variables.

[0028]

number

[0029] Furthermore, the N-th power hardening rule can also be adopted as a predetermined approximation rule. In the N-th power hardening rule, the stress-strain curve is expressed by the following equation (2). Here, σ is the equivalent stress, ε is the equivalent strain, and K and n are both coefficients. Therefore, in the N-th power hardening rule, the stress-strain curve can be defined by determining the material parameters K and n as design variables.

[0030]

number

[0031] Furthermore, Ludwick's law can also be adopted as a predetermined approximation law. In Ludwick's law, the stress-strain curve is expressed by the following equation (3): where σ is the equivalent stress, σ0 is the yield stress, and ε p σ₀ represents the equivalent plastic strain, and K and n are both coefficients. Therefore, Ludwick's law allows us to define the stress-strain curve by determining the material parameters σ₀, K, and n as design variables.

[0032]

number

[0033] Next, the stress-strain curve of the composite structure of the analysis model 6 is calculated by performing finite element analysis according to the homogenization method using the analysis model 6, the stress-strain curve of the ferrite phase 3, and the stress-strain curve of the W-ferrite phase 4 as input data (step S1-4). Since the finite element analysis according to the homogenization method is a known method, detailed description thereof is omitted. Briefly, this calculates the stress-strain curve of a homogeneously integrated composite structure from the stress-strain curves of two constituent structures.

[0034] Next, an objective function that defines the degree of matching between the analytically calculated stress-strain curve of the composite structure of the analysis model 6 and the experimentally obtained stress-strain curve of the composite structure of the steel material 1 in advance is optimized by adjusting the design variables described above (step S1-5). In the present embodiment, a residual sum of squares represented by the following formula (4) is adopted as the objective function RSS. Here, σ1 εp=0.005 represents the true stress obtained as a result of a tensile test (experiment) when the equivalent plastic strain ε p is 0.005, and σ2 εp=0.005 represents the equivalent stress in finite element analysis according to the homogenization method when the equivalent plastic strain ε p is 0.005. Therefore, the objective function RSS of formula (4) represents the residual sum of squares of these stresses for each 0.005 increment of the equivalent plastic strain ε p . However, the step size of the equivalent plastic strain ε p is not particularly limited.

[0035] [Math.]]

[0036] The optimization of the objective function RSS is repeatedly performed until the adjustment of design variables within a predetermined range is completed (step S1-6). In the present embodiment, as design variables within such a predetermined range, σ0 is set to 400 to 1000 [MPa], α is set to 1.0×10 -4 to 5.0×10 -4 , and N is set to 0.1 to 1.0. Design variables within such a predetermined range may vary depending on the constituent structure of the target metal material.

[0037] Methods for optimizing the objective function RSS described above include differential evolution, conjugate gradient method, quasi-Newton method, or genetic algorithms. In this embodiment, differential evolution was used to perform the optimization calculation.

[0038] Since the objective function RSS is the sum of squared residuals, a smaller value indicates a higher degree of agreement. Therefore, in this optimization calculation, we extract the design variables that minimize the objective function RSS. Once the design variables that minimize the objective function RSS are extracted through optimization, we select them as the optimal solution (step S1-7).

[0039] Once the optimal design variables (in this embodiment, material parameters σ0, α, N) are obtained, the stress-strain curve can be obtained by substituting them into equation (1) above. In this way, the stress-strain curve of the W ferrite phase 4 can be estimated.

[0040] Each of the above processes is executed by the arithmetic circuit 11, and the data required for each process is stored in the storage device 12. Additionally, the necessary data and settings may be input via the input / output interface device 13.

[0041] Referring to Figure 5, the stress-strain curve estimation method according to this embodiment will be visually explained using a graph to facilitate understanding.

[0042] In Figure 5, the horizontal axis represents the equivalent plastic strain ε, and the vertical axis represents the equivalent stress σ. Curves C1 to C4 are shown on the graph as various stress-strain curves. Curve C1, shown as a dashed line, represents the stress-strain curve of W-ferrite phase 4. Curve C2, also shown as a dashed line, represents the stress-strain curve of ferrite phase 3. Curve C1 is the target of estimation. Curve C2 is known data. Curve C3, shown as a series of black circles, represents the stress-strain curve of the composite structure. Curve C3 is obtained by finite element analysis according to the homogenization method. Curve C4, shown as a solid line, represents the stress-strain curve obtained by actually performing a tensile test on steel material 1. Curve C4 is known data.

[0043] To implement the stress-strain curve estimation method according to this embodiment, data for curves C2 and C4 are prepared in advance. Next, curve C1 is defined using a predetermined approximation rule such as equation (1) above. Then, finite element analysis is performed according to the homogenization method using curve C1 and the known curve C2 as input data, and curve C3 is calculated as output data. Then, optimization processing is performed to optimize the degree of agreement (objective function) between curve C3 and curve C4. In this optimization processing, various curves C1 are defined by changing the design variables (material parameters σ0, K, n), and various curves C3 are calculated accordingly, and the degree of agreement with curve C4 is checked. In this way, the optimal curve C1 is searched for.

[0044] In this embodiment, the curve C1 that shows the highest degree of agreement between curve C3 and curve C4 is output as the stress-strain curve of the W ferrite phase 4 to be estimated. The output result at this time may be output to the user for confirmation by the input / output interface device 13. In this embodiment, the analysis results and test results are matched in the state of the composite structure, and the stress-strain curve of the constituent structure is estimated.

[0045] Referring to Figure 6, the effectiveness of the stress-strain curve estimation method according to this embodiment will be explained.

[0046] In Figure 6, the horizontal axis represents the equivalent plastic strain ε, and the vertical axis represents the equivalent stress σ. The curve c1, shown by a series of black circles, shows the stress-strain curve of the W ferrite phase 4 estimated by the stress-strain curve estimation method according to this embodiment. The curve c2, shown by a solid line, shows the stress-strain curve of the W ferrite phase 4 obtained separately experimentally, i.e., it shows correct data.

[0047] As shown in the figure, curves c1 and c2 are in good agreement, confirming that the stress-strain curve estimation method according to this embodiment is effective.

[0048] The stress-strain curve estimation method according to this embodiment provides the following effects.

[0049] The stress-strain curve of the constituent structure can be estimated with high accuracy using relatively simple methods such as tensile testing of steel material 1, acquisition of microstructure observation images, and finite element analysis according to the homogenization method. In particular, for tensile testing, it is unnecessary to manufacture difficult single-phase materials (materials consisting only of W ferrite phase 4), and steel material 1 with composite structure 2 can be used as is. Furthermore, it is unnecessary to perform difficult indentation tests that target minute W ferrite phase 4. Microstructure observation images 5 can be easily obtained by imaging steel material 1 with a microscope. Finite element analysis according to the homogenization method is a conventionally known method as described above, and the analysis work is not difficult.

[0050] Furthermore, when one of the two constituent structures (ferrite phase 3 and W-ferrite phase 4) has a known stress-strain curve (ferrite phase 3) and the other (W-ferrite phase 4) is unknown, the stress-strain curve of the unknown constituent structure (W-ferrite phase 4) can be easily and accurately estimated. In particular, the algorithm is simple because it simply estimates the one with the highest degree of agreement as the optimal solution. Note that even when the stress-strain curve of ferrite phase 3 is unknown and the stress-strain curve of W-ferrite phase 4 is known, the stress-strain curve of ferrite phase 3 can also be estimated.

[0051] (Second Embodiment) The stress-strain curve estimation method of the second embodiment shown in Figure 7 differs from the first embodiment in that both stress-strain curves of the two constituent structures are unknown. Aside from this aspect, it is substantially the same as the first embodiment. Therefore, explanations of the parts shown in the first embodiment may be omitted.

[0052] In the stress-strain curve estimation method according to this embodiment, the stress-strain curves of two unknown constituent tissues are estimated. This estimation is performed by a computer (control device 10).

[0053] In this embodiment, similar to the first embodiment, the target is a steel material 1 having a composite structure 2 composed of a ferrite phase 3 and a W-ferrite phase 4, as a metallic material having a composite structure composed of two constituent structures. In this embodiment, both the stress-strain curve of the ferrite phase 3 and the stress-strain curve of the W-ferrite phase 4 are unknown, and both stress-strain curves are estimated.

[0054] Steps S2-1 to S2-6 of the stress-strain curve estimation method according to this embodiment are substantially the same as those of the first embodiment. However, in this embodiment, both the material parameters of ferrite phase 3 and W-ferrite phase 4 are used as design variables.

[0055] In the design variable setting process (step S2-3), the material parameters σ0, α, and N shown in equation (1) are set for ferrite phase 3 and W-ferrite phase 4 respectively, and these are estimated by optimization processing. In this embodiment, the predetermined range of the design variables to be optimized is set as follows: For ferrite phase 3, σ0 is 20 to 150 [MPa] and α is 1.0 × 10 -4 ~1.0×10 -3 N was set to 0.2-0.35. For W ferrite phase 4, σ0 was 500-1000 [MPa] and α was 1.0 × 10 -4 ~1.0×10 -3 N was set to 0.1 to 0.2.

[0056] In this embodiment, once the optimization calculation is completed within a predetermined range of the design variables as in the first embodiment (N: step S2-6), a predetermined number (e.g., 50) of candidate solutions are extracted for each of the ferrite phase 3 and W ferrite phase 4 in order of the degree of agreement in the optimization (step S2-7).

[0057] Referring to Figures 8 and 9, in the stress-strain curves according to the design variables extracted as a predetermined number (e.g., 50) of candidate solutions, an arbitrary equivalent plastic strain ε p The equivalent stress for is calculated and a histogram is created. Here, the equivalent plastic strain ε pTwo histograms were created, illustrating the cases where the value is 0.05 (Figure 8) and 0.1 (Figure 9).

[0058] In the histogram, the horizontal axis represents the equivalent stress σ, and in the example shown, the distribution is divided into intervals of 50 [MPa]. The vertical axis represents the frequency Z of the equivalent stress σ within that interval. Distributions D81 and D91 on the left represent ferrite phase 3, while distributions D82 and D92 on the right represent W ferrite phase 4.

[0059] Next, the mode intervals are determined in the histograms (step S2-8). In distribution D81, the frequency Z is most numerous with 16 occurrences in the 300-350 [MPa] interval. In distribution D82, the frequency Z is most numerous with 13 occurrences in the 950-1000 [MPa] interval. In distribution D91, the frequency Z is most numerous with 16 occurrences in the 350-400 [MPa] interval. In distribution D92, the frequency Z is most numerous with 12 occurrences in the 1050-1100 [MPa] interval. Therefore, these intervals are determined as the mode intervals.

[0060] In this embodiment, overlapping candidate solutions in the mode interval of each of the two histograms are extracted, and the one with the highest degree of agreement is selected as the optimal solution to estimate the stress-strain curves of the two constituent structures (step S2-9). Specifically, for ferrite phase 3, overlapping solutions are first extracted from the 16 candidate solutions in the mode interval of 300-350 [MPa] in distribution D81 and the 16 candidate solutions in the mode interval of 350-400 [MPa] in distribution D91. Next, for example, if 10 candidate solutions overlap, the one with the highest degree of agreement (smallest objective function value) is selected as the optimal solution for ferrite phase 3. Similarly, for W-ferrite phase 4, overlapping solutions are first extracted from the 13 candidate solutions in the mode interval of 950-1000 [MPa] in distribution D82 and the 12 candidate solutions in the mode interval of 1050-1100 [MPa] in distribution D92. Next, if, for example, eight candidate solutions overlap, the one with the highest degree of agreement (smallest objective function value) is selected as the optimal solution for W-ferrite phase 4.

[0061] In the example above, we illustrated and explained the case where there are two equivalent plastic strains for which a histogram is created, but there may be one equivalent plastic strain or three or more. In particular, when there is only one equivalent plastic strain for which a histogram is created, there is no need to consider the duplication of candidate solutions, and the one with the highest degree of agreement in the mode interval (the one with the smallest objective function value in this embodiment) is extracted as the optimal solution.

[0062] Referring to Figure 10, the effectiveness of the stress-strain curve estimation method according to this embodiment will be explained.

[0063] In Figure 10, the horizontal axis represents the equivalent plastic strain ε, and the vertical axis represents the equivalent stress σ. Curve c3, shown by a series of black circles, shows the stress-strain curve of W ferrite phase 4 estimated by the stress-strain curve estimation method according to this embodiment. Curve c4, shown by a solid line, shows the stress-strain curve of W ferrite phase 4 obtained experimentally separately, i.e., it shows correct data. Curve c5, shown by a series of black circles, shows the stress-strain curve of ferrite phase 3 estimated by the stress-strain curve estimation method according to this embodiment. Curve c6, shown by a solid line, shows the stress-strain curve of ferrite phase 3 obtained experimentally separately, i.e., it shows correct data.

[0064] As shown in the figure, curves c3 and c4 agree well, and curves c5 and c6 also agree well, confirming that the stress-strain curve estimation method according to this embodiment is effective.

[0065] According to the stress-strain curve estimation method of this embodiment, when the stress-strain curves of both unknown constituent structures (ferrite phase 3 and W-ferrite phase 4) are unknown, the stress-strain curves of the two unknown constituent structures (ferrite phase 3 and W-ferrite phase 4) can be easily and accurately estimated. Furthermore, when estimating the stress-strain curves of the two constituent structures (ferrite phase 3 and W-ferrite phase 4), it is possible to accidentally fall into a false solution with a very high degree of agreement. However, by utilizing the mode interval of the histogram, solutions other than those with a high probability can be excluded. In other words, the possibility of falling into such a false solution can be reduced, and high estimation accuracy can be ensured.

[0066] Furthermore, by setting multiple equivalent plastic strains (two in this embodiment) for creating the histogram, more of the above-mentioned false solutions can be eliminated, thereby ensuring higher estimation accuracy.

[0067] Although specific embodiments and variations of the present invention have been described above, the present invention is not limited to the above embodiments and can be implemented with various modifications within the scope of this invention. For example, a combination of the contents of individual embodiments may be considered as one embodiment of this invention.

[0068] 1 Steel materials (metal materials) 2 Composite organization 3. Ferrite phase (constituent structure) 4. W-ferrite phase (constituent structure) 5. Tissue observation images 6. Analysis Model 10. Control device (computer) 11 Arithmetic circuit 12 Storage device 13 Input / Output Interface Device

Claims

1. A method for estimating the stress-strain curves of the constituent structures of a metallic material consisting of two constituent structures, performed by a computer, An analysis model corresponding to the microstructure observation image of the aforementioned metallic material is created, The stress-strain curve of the constituent tissue is defined by a predetermined approximation rule that uses the material parameters of the constituent tissue as design variables. The stress-strain curve of the composite structure of the analysis model is calculated by performing a finite element analysis according to the homogenization method using the aforementioned analysis model and the stress-strain curve of the constituent structure as input data. The objective function, which defines the degree of agreement between the stress-strain curve of the composite structure of the analytical model calculated analytically and the stress-strain curve of the composite structure of the metal material obtained experimentally in advance, is optimized by adjusting the design variables. The stress-strain curve of the constituent structure is estimated using the design variables that optimize the objective function as the optimal solution. A method for estimating stress-strain curves, including the following.

2. One of the stress-strain curves of the two constituent structures is known, and the other is unknown. A method for estimating a stress-strain curve according to claim 1, wherein in the optimization described above, the design variable with the highest degree of agreement is used as the optimal solution to estimate the stress-strain curve of the other constituent structure.

3. The stress-strain curves for both of the aforementioned constituent structures are unknown. In the optimization described above, a predetermined number of candidate solutions are extracted in order of the degree of agreement, For each of the stress-strain curves of the predetermined number of candidate solutions, the equivalent stress for any equivalent plastic strain is calculated and a histogram is created. In the histogram, the candidate solution with the highest degree of agreement among those in the mode interval is selected as the optimal solution to estimate the stress-strain curves of the two constituent tissues. A method for estimating a stress-strain curve according to claim 1 or 2, further comprising the following:

4. Multiple histograms are created by calculating multiple equivalent stresses for multiple equivalent plastic strains. A method for estimating stress-strain curves according to claim 3, comprising extracting overlapping candidate solutions in the mode interval of each of the plurality of histograms, and estimating the stress-strain curves of the two constituent tissues by selecting the one with the highest degree of agreement from among them as the optimal solution.

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