Method for estimating stress-strain relationship, method for predicting rebound, and method for manufacturing press-molded article

Abstract

According to the stress-strain relation inference method, transformation parameters obtained by transforming parameters of a Giltian-Shangsen model are defined; the residual error of the experimental value and the calculated value of the stress-strain curve under the uniaxial tensile stress is calculated; the method comprises the following steps of: multiplying a residual error of an experimental value and a calculated value of a stress-strain curve under stretching-compression repeated stress and a residual error of an experimental value and a calculated value of a mechanical characteristic value of a metal material by an independent weighting coefficient respectively to obtain a weight residual sum of squares as a target function; the transformation parameters and the parameters are determined in such a manner that the objective function is minimized under limiting conditions relating to the range in which the transformation parameters and the other parameters can be taken.

Description

Technical Field

[0001] The present invention relates to a stress-strain relation inference method for inferring the relationship between stress and strain of a metal material using the Yoshida-Uemori material model representing the Bauschinger effect of a metal sheet. In addition, the present invention relates to a springback prediction method for predicting the springback of a press formed part using the relationship between stress and strain inferred by the stress-strain relation inference method. In addition, the present invention relates to a method for manufacturing a press formed part in which the springback is reduced by adjusting the press forming conditions based on the result of predicting the springback of the press formed part to manufacture a press formed part with improved dimensional accuracy. Background Art

[0002] In press forming (for example, press forming of automotive parts), defects of press forming such as shape failure caused by fracture, wrinkles and springback reduce productivity, resulting in an increase in CO2 emissions with increased production time. In addition, in recent years, due to the lightweighting of automotive bodies, the reduction of CO2 emissions from automobiles has also been promoted. In order to lightweight the automobile body, high-strength and thinning of body frame parts are necessary, but with this, the frequency of poor forming of frame parts during press forming is on the rise. Therefore, advance prediction and countermeasures for poor forming during press forming can shorten production time by reducing the incidence of poor forming, which helps to reduce CO2 emissions.

[0003] In the advance prediction of poor forming during stamping, numerical analysis (finite element analysis) based on the finite element method of the stamping process is widely used. In the finite element analysis, a material model (material model) that can reproduce the deformation properties (deformation property) of the blank (steel sheet) (blank) of the stamping product with high accuracy has been developed. As a result, the actual phenomenon in the stamping process can be numerically modeled, so that through computer-based calculations, even without implementing actual stamping, the poor forming of the stamping product can be predicted in advance.

[0004] Generally, in the stamping of higher strength materials, since the amount of springback after stamping and die release becomes larger, it is particularly important to use a material model that can accurately reproduce the springback. Moreover, as such a material model, the Yoshida-Uemori model that uses the Bauschinger effect of metal materials is increasing. The Bauschinger effect refers to the phenomenon of reyielding earlier than the absolute value of the stress before the reversal when the load direction of the stress is reversed. In the Yoshida-Uemori model, it is said to be able to reproduce this phenomenon with high accuracy.

[0005] Yoshida-Uemori model has 8 parameters, which are determined by reproducing the stress-strain relationship measured by the uniaxial tensile test and tension-compression cyclic loading test of the blank using the stamped product. On the other hand, the number of parameters of the isotropic hardening model, which is a material model widely used in the past, is two in the n-power-law hardening rule, and three in the Swift hardening rule and the Voce hardening rule. Therefore, it is relatively easy to determine the parameters of the isotropic hardening model. However, in the Yoshida-Uemori model, there are 8 parameters as mentioned above, and it is not easy to find the best combination of 8 parameters.

[0006] As an example of a method for determining multiple parameters in a material model such as the Yoshida-Uemori model, Patent Document 1 discloses a method in which a portion of the multiple parameters is first identified, and then the identification result is used to identify the parameters including the remaining parameters. In addition, Patent Document 1 also discloses a method in which, when a new parameter is added, the parameters other than the added parameter are first identified, and then the identification result is used to identify the parameters including the added parameter. Moreover, according to the method disclosed in Patent Document 1, the convergence of the parameter identification calculation can be improved compared to the case where all parameters are identified simultaneously using the initial values ​​of the pre-set parameters. Furthermore, by using the parameters identified using this method, the accuracy of the simulation of the stress-strain relationship is improved.

[0007] Patent Document 1: Japanese Patent Application Publication No. 2008-142774

[0008] In the method disclosed in Patent Document 1, since parameters are determined while gradually adding identified parameters, optimization calculations such as minimizing residuals required to determine all parameters need to be repeated multiple times. Therefore, there is a problem that the number of steps required for calculation increases compared to a method of simultaneously identifying multiple parameters of a material model. Summary of the invention

[0009] The present invention is completed to solve the above-mentioned problems, and its purpose is to provide a stress-strain relationship inference method that can appropriately determine the parameters of the Yoshida-Uemori model without requiring a large number of processes, thereby inferring the stress-strain relationship of metal materials with high accuracy. In addition, another purpose of the present invention is to provide a springback prediction method that can use the stress-strain relationship inferred by the above-mentioned method to perform press forming analysis (press forming analysis) and springback analysis (spring-back analysis), thereby predicting the springback of a stamped product with high accuracy. In addition, another purpose of the present invention is to provide a method for manufacturing a stamped product, which determines stamping conditions in a manner that suppresses the springback of the stamped product predicted by the above-mentioned method, and manufactures the stamped product under the determined stamping conditions.

[0010] The stress-strain relationship estimation method of the present invention uses the Yoshida-Uemori model representing the Bauschinger effect of metal materials to estimate the relationship between stress and strain of the above-mentioned metal material, which includes: a uniaxial tensile stress-strain curve acquisition step, in which a stress-strain curve of the above-mentioned metal material under uniaxial tensile stress is experimentally acquired by performing a uniaxial tensile test on the above-mentioned metal material as a test piece; a cyclic stress-strain curve acquisition step, in which a stress-strain curve of the above-mentioned metal material under tension-compression cyclic stress is experimentally acquired by performing a tension-compression cyclic stress test on the above-mentioned metal material as a test piece; and an experimental value calculation step of mechanical property values, in which yield stress, tensile strength, and uniform elongation are calculated as mechanical property values ​​of the above-mentioned metal material based on the stress-strain curve of the above-mentioned metal material under uniaxial tensile stress obtained by the above-mentioned uniaxial tensile test. a conversion parameter definition step, in which at least two parameters of the parameters used in the Yoshida-Uemori model are combined and the conversion parameters are converted; a constraint setting step, in which a constraint condition is set to limit the acceptable range of the conversion parameter using the experimental values ​​of the calculated mechanical characteristic values; an objective function setting step, in which the residual of the stress-strain curve under the uniaxial tensile stress obtained experimentally and the stress-strain curve under the uniaxial tensile stress calculated by the Yoshida-Uemori model, the residual of the stress-strain curve under the tension-compression repeated stress obtained experimentally and the stress-strain curve under the tension-compression repeated stress calculated by the Yoshida-Uemori model, and the residual of the experimental value of the mechanical characteristic value of the metal material and the calculated value of the mechanical characteristic value calculated by the Yoshida-Uemori model are calculated, and the weighted residual square sum (weighted residual square sum) obtained by multiplying each calculated residual by a separate weighting factor is calculated. sum) is set as the objective function;and a parameter determination step in which the transformation parameters and other parameters of the Yoshida-Uemori model are determined in such a way as to minimize the objective function under the constraints. ;

[0011] Alternatively, in the transformation parameter definition step, one or more transformation parameters given by the following equations (1) to (4) obtained by combining at least two or more parameters of the Yoshida-Uemori model are defined, and in the constraint condition setting step, the acceptable range of the transformation parameters defined in the transformation parameter definition step is limited by using equations (5) to (8) corresponding to the transformation parameters defined above.

[0012] [Formula 1]

[0013] BL=Y+a0 (1)

[0014] κ=C1 / C2 (2)

[0015] η=b / (b+R sat ) (3)

[0016] σ sat =Y+a0+b+R sat (4)

[0017] YS≤BL≤XS (5)

[0018] 1≤κ≤4 (6)

[0019] 0≤η≤1 (7)

[0020] 0.9×XS≤σ sat ≤1.1×XS (8)

[0021] in,

[0022] BL,κ,η,σ sat : Transformation parameters

[0023] Y, a0, C1, C2, b, R sat :Parameters of Yoshida-Uemori model

[0024] YS: Experimental value of yield stress

[0025] XS: Experimental value of stress in high strain region

[0026] Alternatively, in the objective function setting step, the weighted residual sum of squares may be obtained by the following equation (9).

[0027] [Formula 2]

[0028]

[0029] in,

[0030] WRSS: Weighted Residual Sum of Squares

[0031] YS exp : Experimental value of yield stress

[0032] YS cal : Calculated value of yield stress based on Yoshida-Uemori model

[0033] W YS : Weighting factor for the residual of the yield stress

[0034] TS exp : Experimental value of tensile strength

[0035] TS cal : Calculated value of tensile strength based on Yoshida-Uemori model

[0036] W TS : Weighting coefficient for the residual of tensile strength

[0037] UE exp : Experimental value of uniform elongation

[0038] UE cal : Calculated value of uniform elongation based on Yoshida-Uemori model

[0039] W uEL : Weighting coefficient for the residual error of uniform elongation

[0040] XS exp : Experimental value of stress in high strain region above uniform elongation

[0041] XS cal : Calculated value of stress in the high strain region above uniform elongation based on the Yoshida-Uemori model

[0042] W XS : Weighting coefficient for the residual stress in the high strain region above the uniform elongation

[0043] : Experimental value of stress for any strain on the stress-strain curve under uniaxial tension

[0044] : Calculated value based on the Yoshida-Uemori model for stress at an arbitrary strain on the stress-strain curve under uniaxial tension stress

[0045] W T : Weighting coefficient for the residual of stress under uniaxial tensile stress

[0046] : Experimental value of stress for any strain on the stress-strain curve under tension-compression repeated stress

[0047] : Calculated value based on the Yoshida-Uemori model for stress at an arbitrary strain on the stress-strain curve under tension-compression repeated stress

[0048] W TCk : Weighting coefficient for the residual stress under tension-compression repeated stress

[0049] The springback prediction method of the present invention uses the parameters and transformation parameters of the above-mentioned Yoshida-Uemori model determined by the stress-strain relationship inference method of the present invention to infer the stress-strain relationship of the metal material, and uses the inferred stress-strain relationship to perform stamping analysis and springback analysis of stamped products using the sheet materials of the above-mentioned metal material to predict the springback of the above-mentioned stamped products.

[0050] The manufacturing method of the stamped product of the present invention adjusts the stamping conditions in a manner to reduce the springback amount to manufacture the stamped product with improved dimensional accuracy, which includes: a test piece collection step, in which test pieces for the uniaxial tensile test in the uniaxial tensile stress-strain curve acquisition step of the stress-strain relationship inference method of the present invention and the tensile-compression repeated test in the repeated stress-strain curve acquisition step are collected from the metal material used as the blank of the stamped product; a stress-strain relationship inference parameter acquisition step, in which the collected test pieces are used to obtain the above-mentioned transformation parameters and the above-mentioned other parameters of the Yoshida-Uemori model based on the stress-strain relationship inference method of the present invention; a temporary stamping condition setting step, in which the temporary stamping conditions of the stamped product are set; a springback amount prediction step, in which the stress-strain relationship inferred by the above-mentioned transformation parameters and the above-mentioned other parameters of the Yoshida-Uemori model obtained in the above-mentioned stress-strain relationship inference parameter acquisition step is used to perform stamping under the above-mentioned temporary stamping conditions of the stamped product using the blank of the metal material. Forming analysis and springback analysis, predicting the springback amount of the stamped product; a springback amount determination process, in which it is determined whether the springback amount of the stamped product predicted in the springback amount prediction process is within a predetermined range; a temporary stamping forming condition change process, in which, when it is determined in the springback amount determination process that the springback amount of the stamped product is outside the predetermined range, the temporary stamping forming conditions are changed; a repetitive process, in which the temporary stamping forming condition change process, the springback amount prediction process and the above process are repeatedly executed. The springback amount determining step is performed until the springback amount of the stamped product is determined to be within a predetermined range in the springback amount determining step; an actual stamping condition determining step is performed, in which, when the springback amount of the stamped product is determined to be within a predetermined range in the springback amount determining step, the temporary stamping condition in this case is determined to be the actual stamping condition; and an actual stamping step is performed, in which, under the determined actual stamping condition, the stamped product is stamped using the blank of the metal material.

[0051] According to the present invention, the parameters of the Yoshida-Uemori model representing the Bauschinger effect of a metal material can be easily and appropriately determined, and the stress-strain relationship of the metal material can be estimated with high accuracy.

[0052] Furthermore, according to the present invention, by performing press forming analysis and springback analysis of a press-formed product using the stress-strain relationship of the metal material estimated as described above, the springback of the press-formed product can be predicted with high accuracy.

[0053] In addition, according to the present invention, it is possible to adjust the stamping conditions in a manner that reduces the amount of springback to manufacture stamped products with improved dimensional accuracy. In particular, during mass production of actual stamped products, the actual stamping conditions can be changed according to the deviation of the metal material used as the blank, thereby also being able to suppress the large-scale generation of dimensional defects caused by the springback of the stamped products. Moreover, it is also possible to significantly shorten the cost and period of production preparation of the actual stamped products. BRIEF DESCRIPTION OF THE DRAWINGS

[0054] Figure 1 This is a flowchart showing the processing flow of the stress-strain relationship estimation method according to the first embodiment of the present invention.

[0055] Figure 2 This is a graph showing an example of the relationship between stress and strain in a metal material which is subjected to tensile deformation, the load is removed (unloading), and further subjected to compressive deformation (compressive deformation).

[0056] Figure 3 This is a schematic diagram explaining the Yoshida-Uemori model that reproduces the kinematic hardening behavior of metal materials by moving and expanding the yield surface and boundary surface.

[0057] Figure 4 is a graph schematically showing the stress-strain relationship obtained through a uniaxial tensile test of a metal material.

[0058] Figure 5 It is a graph schematically showing the stress-strain relationship obtained through tension-compression repeated tests of metal materials.

[0059] Figure 6 This is a graph schematically showing possible ranges of conversion parameters in the stress-strain relationship estimation method according to the first embodiment of the present invention.

[0060] Figure 7 The present invention is a diagram illustrating the residuals of the experimental values ​​of the stress-strain curve and the calculated values ​​based on the Yoshida-Uemori model in the first embodiment of the present invention ((a) residual of the stress-strain curve under uniaxial tensile stress, (b) residual of the stress-strain curve under tension-compression repeated stress).

[0061] Figure 8 This is a flowchart showing the processing flow of the springback prediction method according to the second embodiment.

[0062] Fig. 9This is a graph showing the transition and convergence point of the objective function used in the optimization calculation of the genetic algorithm based on the parameters of the Yoshida-Uemori model in the embodiment.

[0063] Fig.10 This is a graph showing the stress-strain relationship under uniaxial tensile stress estimated using the parameters of the Yoshida-Uemori model determined in the Examples and the stress-strain relationship under uniaxial tensile stress obtained experimentally.

[0064] Fig.11 This is a graph showing the stress-strain relationship under tension-compression repeated stress estimated using the parameters of the Yoshida-Uemori model determined in the Examples and the stress-strain relationship under tension-compression repeated stress obtained experimentally.

[0065] Fig.12 The figures ((a) are a perspective view, (b) are cross-sectional views) for explaining a stamped product that is a target of springback prediction in the embodiment, and a springback amount of a flange portion that is determined as a springback amount of the stamped product.

[0066] Fig.13 This is a flowchart of a method for manufacturing a press-formed product according to a third embodiment of the present invention.

[0067] Fig.14 This is a diagram for explaining an example of manufacturing a stamped product by stamping using a stretch bending method using a stamping die composed of a die, a punch, a gasket and a bracket in a method for manufacturing a stamped product according to Embodiment 3 of the present invention. DETAILED DESCRIPTION

[0068] Before describing the first and second embodiments of the present invention, the principle of the Yoshida-Uemori model used in the present invention and the history leading to the present invention will be described.

[0069] <Principle of the Yoshida-Uemori Model>

[0070] Figure 2 It represents the relationship between stress and strain when a metal material is subjected to further compression deformation after the load is removed after tensile deformation. In the isotropic hardening model used in the past, Figure 2 As shown by the dashed line in the middle, the deformation proceeds from the point B where the load is removed in the compression direction and yields at point B'. In contrast, in actual metal materials, Figure 2 As indicated by the circle in the middle, the re-yield occurs earlier near point C than at point B'. This phenomenon of re-yielding earlier than the absolute value of stress before the reversal when the deformation direction of a metal material is reversed is called the Bauschinger effect.

[0071] In order to accurately predict the shape change, i.e., springback, that occurs when the stamped product is removed from the die after stamping, it is necessary to reproduce the Bauschinger effect with high accuracy. However, in the isotropic hardening model, as mentioned above, the Bauschinger effect cannot be reproduced. Therefore, a kinematic hardening model that reproduces the Bauschinger effect has been proposed. Among them, the Yoshida-Uemori model, which can reproduce the Bauschinger effect with high accuracy, has begun to be widely used in stamping analysis, etc. The Yoshida-Uemori model is as follows Figure 2 The solid line in the middle shows that the Bauschinger effect of metal materials can be reproduced with high accuracy.

[0072] In addition, if Figure 3 As shown in FIG. 1 , the Yoshida-Uemori model is a two-surface model having a yield surface and a bounding surface. Moreover, in the Yoshida-Uemori model, by appropriately defining the hardening of the above-mentioned hyperboloid, the Bauschinger effect can be reproduced with high accuracy. The principle of the Yoshida-Uemori model is described below.

[0073] In finite element analysis, the relationship between the Jaumann stress rate dσJ of the Cauchy stress σ and the strain rate tensor D is expressed by equation (A1). In equation (A1), Cep is a fourth rank tensor called the elastic-plastic tangent modulus tensor.

[0074] [Formula 3]

[0075] dσ J =C ep :D...(A1)

[0076] If it is assumed that the outward normal direction of the yield surface is consistent with the direction of the incremental plastic strain, that is, assuming the associated flow rule, then in the Yoshida-Uemori model, the elastic-plastic coefficient tensor Cep is expressed by the following equation (A2).

[0077] [Formula 4]

[0078]

[0079] f is the yield function, Ce is the elastic tangent modulus tensor. In addition, a, b, C, m, α, α*, and β are defined as follows in the Yoshida-Uemori model.

[0080] The Yoshida-Uemori model is a hyperbolic model that reproduces the hardening behavior of metal materials by moving and expanding the yield surface and boundary surface. The yield surface is a kinematic hardening type in which the surface moves as the deformation progresses. On the other hand, the boundary surface is a combined hardening type that combines kinematic hardening with isotropic hardening in which hardening is reproduced by expanding the size of the surface itself.

[0081] In the schematic representation of the kinematic hardening characteristics based on the Yoshida-Uemori model Figure 3 In the equation, the yield surface is center α and radius Y, and the boundary surface is center β and radius Y+a0+R. a0 is the difference between the initial radius of the yield surface and the boundary surface, and R is the isotropic hardening amount of the boundary surface. In addition, the relative position of the center of the yield surface relative to the center of the boundary surface is expressed as α*(=(α-β)).

[0082] In the Yoshida-Uemori model, the moving rate dα* of the relative position α* of the center of the yield surface relative to the center of the boundary surface is defined by equation (A3), and the moving rate dβ of the center of the boundary surface β is defined by equation (A4). C is a coefficient related to the kinematic hardening rate of the yield surface, a is the difference between the radius of the yield surface and the boundary surface, m is a coefficient representing the rate of kinematic hardening and isotropic hardening of the boundary surface, and b is the maximum value of the kinematic hardening amount of the boundary surface.

[0083] [Formula 5]

[0084]

[0085] Here, a=a0+R,

[0086]

[0087] In addition, by taking different values for the coefficient C related to the kinematic hardening rate of the yield surface in Equation (A3) in the initial stage of deformation and thereafter, the Yoshida-Uemori model can accurately reproduce characteristics such as the yield stage behavior in the initial stage of deformation. Generally, C is determined by the equivalent plastic strain εpeq as shown in the following Equation (A5).

[0088] [Equation 6]

[0089]

[0090] Through the above Equations (A3) to (A5), the kinematic hardening of the yield surface and the bounding surface is reproduced. On the other hand, the isotropic hardening amount R of the bounding surface is defined by Equation (A6). Rsat is the maximum value of the isotropic hardening amount of the bounding surface, and m is a coefficient representing the kinematic hardening and isotropic hardening rates of the bounding surface.

[0091] [Equation 7]

[0092] dR = m(R sat - R)dλ ··· (A6)

[0093] In this way, in the Yoshida-Uemori model, the hardening behavior of metallic materials is reproduced through the kinematic hardening of the yield surface (Equations (A3) and (A5)), the kinematic hardening of the bounding surface (Equation (A4)), and the isotropic hardening of the bounding surface (Equation (A6)). Moreover, accurately determining the parameters (Y, a0, C1, C2, b, m, Rsat) in Equations (A3) to (A6) is required to accurately reproduce the Bauschinger effect.

[0094] In addition, in the Yoshida-Uemori model, in order to represent the work hardening stagnation region after stress reversal, the anisotropic hardening region (center q, radius r) is defined by the following Equations (A7) to (A9). Moreover, while the center β of the bounding surface exists within the anisotropic hardening region (satisfying f(β - q) < r), the bounding surface does not undergo isotropic hardening (R = 0). h is a parameter representing the ratio of the expansion amount to the movement amount of the anisotropic hardening region.

[0095] [Equation 8]

[0096]

[0097] As described above, the stress-strain relationship of the metal material is modeled in the Yoshida-Uemori model. The parameters of the Yoshida-Uemori model are summarized in Table 1.

[0098] [Table 1]

[0099] parameter Meaning of parameters Y Radius of the yield surface <![CDATA[a0]]> The initial radius difference between the yield surface and the boundary surface <![CDATA[C1]]> Coefficient related to the kinematic hardening rate of the yield surface (initial deformation) <![CDATA[C2]]> Coefficient related to the kinematic hardening rate of the yield surface (after the initial deformation) b The maximum value of kinematic hardening of the boundary surface m Coefficients representing the kinematic and isotropic hardening rates of boundary surfaces <![CDATA[R sat ]]> Maximum value of isotropic hardening at the boundary surface h Ratio of the expansion and movement of the non-isotropic hardening area

[0100] <History of the Present Invention>

[0101] In general isotropic hardening models, as shown in the following equations (A10) to (A14), there are Swift hardening rule, Ludwik hardening rule, Gosh hardening rule, Voce hardening rule, Hockett-Sheby hardening rule, and the like.

[0102] [Formula 9]

[0103] Swift hardening rules:

[0104] Ludwik hardening law:

[0105] Gosh Hardening Law:

[0106] Voce hardening law:

[0107] Hockett-Sherby Hardening Law:

[0108] The ci (i=1 to 4) used in the above hardening laws are parameters, and the maximum number of parameters used in the above hardening laws is 4. These parameters are determined so that the stress-strain curve under uniaxial tensile stress obtained by uniaxial tensile test (hereinafter referred to as "tensile SS curve (tensile stress-strain curve)", see Figure 4 a2) and the residual of the tensile SS curve calculated by the isotropic hardening model are minimized (fitting). At this time, the number of parameters of the isotropic hardening model is less than that of the Yoshida-Uemori model, and in order to determine these parameters, it is only necessary to fit the tensile SS curve, so the parameters of the isotropic hardening model can be easily determined.

[0109] In contrast, the Yoshida-Uemori model has eight parameters as shown in Table 1, and there is no specific range for each parameter. Therefore, when determining the parameters of the Yoshida-Uemori model, the parameters need to be adjusted within a very wide range, and there is a problem that it is difficult to find the optimal values ​​for all parameters at the same time.

[0110] In order to reproduce the Bauschinger effect with high accuracy using the Yoshida-Uemori model, it is also necessary to analyze the stress-strain curve under compression-tension stress obtained by the tension-compression repeated test (hereinafter referred to as the "cyclic stress-strain curve"; see Figure 5 ) is fitted. Therefore, in order to determine the parameters of the Yoshida-Uemori model, more complicated calculations are required compared to the case of determining the parameters of the isotropic hardening model (c1 to c4 in equations (A10) to (A14)).

[0111] In addition, when determining the parameters of the Yoshida-Uemori model, it is necessary to be able to reproduce the mechanical properties such as yield stress (YS), tensile strength (TS), uniform elongation (uEL), etc., which are the basic characteristic values ​​of the material. Moreover, by reproducing these mechanical properties, high-precision predictions based on finite element analysis such as stamping analysis and springback analysis of stamped products can be performed.

[0112] For example, under uniaxial tensile stress, if further deformation is applied to the tensile strength (TS) and uniform elongation (uEL), necking will occur, and the deformation will be concentrated at the necking part, resulting in fracture. Therefore, in high-precision stamping analysis, it is necessary to accurately reproduce the timing of the occurrence of this necking.

[0113] As described above, it is particularly important to be able to reproduce the mechanical property values ​​that are the basic characteristic quantities of the material using a material model. However, there is a problem that it is difficult to determine whether the mechanical property values ​​can be reproduced based only on the tensile SS curve.

[0114] Therefore, the inventors have studied methods for solving the above-mentioned problems. In this study, the inventors focused on the correlation between the parameters of the Yoshida-Uemori model and the stretched SS curve. As a result, it was found that a new parameter obtained by combining and transforming at least two of the parameters used in the Yoshida-Uemori model and the characteristic values ​​(YS, TS, etc.) of the stretched SS curve can obtain a strong correlation. In addition, the parameters obtained by such a transformation can determine their desirable ranges according to the stretched SS curve, thus obtaining a view that the parameters can be determined more appropriately and easily compared to the existing method of determining the parameters.

[0115] The present invention has been accomplished based on the above findings, and its specific structure is as follows.

[0116] [Implementation Method 1]

[0117] <Stress-strain relationship estimation method>

[0118] The stress-strain relationship estimation method of the first embodiment of the present invention estimates the stress-strain relationship of the metal material using the Yoshida-Uemori model representing the Bauschinger effect of the metal material. Figure 1 As shown, the stress-strain relationship inference method of this embodiment includes: a uniaxial tensile stress-strain curve acquisition step S1, a repeated stress-strain curve acquisition step S3, an experimental value calculation step S5 of a mechanical property value, and a transformation parameter definition step S7. Figure 1 As shown, the stress-strain relationship estimation method of the first embodiment includes a constraint setting step S9, an objective function setting step S11, a parameter determination step S13, and a stress-strain relationship estimation step S15. Each of the above steps will be described below.

[0119] 《Uniaxial Tensile Stress-Strain Curve Acquisition Process》

[0120] The uniaxial tensile stress-strain curve acquisition step S1 is a step of experimentally acquiring a stress-strain curve of the metal material under uniaxial tensile stress by performing a uniaxial tensile test on the metal material as a test piece.

[0121] 《Repeated stress-strain curve acquisition process》

[0122] The repeated stress-strain curve acquisition step S3 is a step of experimentally acquiring a stress-strain curve of the metal material under repeated tension-compression stress by performing a repeated tension-compression test on the metal material as a test piece.

[0123] 《Mechanical property value experimental value calculation process》

[0124] The mechanical property value experimental value calculation step S5 is a step of calculating the experimental value of the mechanical property value of the metal material based on the stress-strain curve under the uniaxial tensile stress of the metal material obtained through the uniaxial tensile test experiment. In this embodiment, the mechanical property value experimental value calculation step S5 obtains the yield stress YS, tensile strength TS, uniform elongation uEL, and stress XS in the high strain region above the uniform elongation as the experimental value of the mechanical property value.

[0125] 《Transformation Parameter Definition Process》

[0126] The transformation parameter definition step S7 is a step of defining transformation parameters obtained by combining and transforming at least two or more parameters among the parameters used in the Yoshida-Uemori model.

[0127] In the first embodiment, conversion parameters BL, κ, η, and σsat are defined by the following equations (1) to (4).

[0128] [Formula 10]

[0129] BL=Y+a0 (1)

[0130] κ=C1 / C2 (2)

[0131] η=b / (b+R sat ) (3)

[0132] σ sat =Y+a0+b+R sat (4)

[0133] The transformation parameter BL defined by equation (1) is a parameter obtained by combining the parameters a0 and Y of the Yoshida-Uemori model and transforming the parameter a0. The transformation parameter κ defined by equation (2) is a parameter obtained by combining the parameters C1 and C2 of the Yoshida-Uemori model and transforming the parameter C1. The transformation parameter η defined by equation (3) is a parameter obtained by combining the parameters b and Rsat of the Yoshida-Uemori model and transforming the parameter b. The transformation parameter σsat defined by equation (4) is a parameter obtained by combining the parameters Y, a0, b and Rsat of the Yoshida-Uemori model and transforming the parameter Rsat.

[0134] 《Restriction Setting Process》

[0135] The constraint condition setting step S9 is a step of setting a constraint condition for limiting the possible range of the conversion parameter defined in the conversion parameter definition step S7 using the experimental values ​​of the mechanical characteristic values ​​calculated in the mechanical characteristic value experimental value calculation step S5 .

[0136] In the first embodiment, the possible range of the transformation parameter defined in the transformation parameter definition step S7 is set by the following formula (5) to (8) corresponding to the defined transformation parameter. That is, the possible range of the transformation parameter BL is defined by the formula (5), the possible range of the transformation parameter κ is defined by the formula (6), the possible range of the transformation parameter η is defined by the formula (7), and the possible range of the transformation parameter σsat is defined by the formula (8).

[0137] [Formula 11]

[0138] YS≤BL≤XS (5)

[0139] 1≤κ≤4 (6)

[0140] 0≤η≤1 (7)

[0141] 0.9×XS≤σ sat ≤1.1×XS (8)

[0142] Table 2 collectively shows possible ranges of conversion parameters set as constraint conditions in the first embodiment and possible ranges of other parameters of the Yoshida-Uemori model.

[0143] [Table 2]

[0144]

[0145] The reasons for the possible ranges of the transformation parameters BL, κ, η, and σsat are as follows.

[0146] (a) Transformation parameter BL

[0147] The transformation parameter BL represents the initial radius of the boundary surface, and as shown in the above formula (1), it is represented by the sum of the radius Y of the yield surface and the radius difference a0 between the yield surface and the boundary surface. In the Yoshida-Uemori model, the yield surface moves inside the boundary surface and does not exceed the boundary surface. That is, it is clear that the initial radius BL of the boundary surface is the maximum value of the radius Y of the yield surface, that is, YS (yield stress) or more (YS ≤ BL).

[0148] As described in the principle of the Yoshida-Uemori model, the movement of the yield surface is defined by the relative position from the boundary surface. When the yield surface approaches the center of the boundary surface, the hardening rate increases, and when the yield surface approaches the boundary surface, the hardening rate decreases.

[0149] That is, if uniaxial tensile deformation is considered, the material yields (plastic deformation begins) under stress Y, and the yield surface is close to the center of the boundary surface just after yielding, so work hardening is greatly performed. However, the yield surface gradually approaches the boundary surface, and if the stress value is close to the size of the initial radius BL of the boundary surface, the work hardening becomes smaller, and the slope of the stress-strain curve becomes smaller, gradually approaching the experimental value XS of the stress in the high strain region. In this way, according to the principle of the Yoshida-Uemori model, the initial radius BL of the boundary surface becomes the convergence value of work hardening, that is, below the experimental value XS of the stress in the high strain region above the uniform elongation. Based on the above reasons, in the present embodiment 1, the acceptable range of BL is limited to YS≤BL≤XS ( Figure 6 The range of the arrow of BL).

[0150] (b) Transformation parameter κ

[0151] As shown in the above formula (2), the transformation parameter κ is the ratio of the parameters C1 and C2 of the Yoshida-Uemori model. Moreover, the parameters C1 and C2 are coefficients related to the kinematic hardening rate of the yield surface, and are parameters that determine the movement speed of the relative position α* of the center of the yield surface relative to the center of the boundary surface.

[0152] The difference between C1 and C2 is that C1 is used at the initial stage of deformation, and C2 is switched to use thereafter. When switching from C1 to C2 at a certain strain (usually equivalent plastic strain 0.005), if there is a large difference between the two, a discontinuous portion is generated in the stress-strain curve. Such discontinuity of the stress-strain curve is appropriate for materials that reproduce the yield stage phenomenon, but in other cases, there is no need to distinguish between C1 and C2. Therefore, when C1 and C2 are equal (κ=1), the transformation parameter κ becomes the minimum value.

[0153] In addition, in order to reproduce the degree of the Bauschinger effect in the Yoshida-Uemori model, the parameters C1 and C2 have a greater influence.

[0154] When stress is reversed, the difference between the yield surface and the boundary surface becomes larger for the reverse loading direction, so the hardening speed of the yield surface is larger. At this time, the larger the values ​​of parameters C1 and C2, the faster the yield surface moves and gradually approaches the boundary surface. On the contrary, if the values ​​of parameters C1 and C2 are small, the time until gradually approaching the boundary surface becomes longer, the stress changes smoothly, and the Bauschinger effect can be more expressed.

[0155] In the case of low tensile strength such as 270MPa-grade steel sheets, the parameters C1 and C2 are mostly around 500 to 1000, and the higher the tensile strength, the smaller the values ​​of C1 and C2. In addition, in high-strength materials above 980MPa-grade steel sheets, the parameters C1 and C2 are mostly around 100 to 200.

[0156] On the other hand, in order to reproduce the above-mentioned yield stage phenomenon, it is necessary to set C1>C2, but if C1 and C2 are values ​​exceeding 1000, the difference in the stress-strain curve becomes small. Therefore, the value of the conversion parameter κ representing the ratio of C1 to C2 hardly exceeds 4. Based on the above reasons, in the present embodiment 1, the range of κ is limited to 1≤κ≤4.

[0157] (c) Transformation parameter η

[0158] The transformation parameter η represents the ratio of the kinematic hardening of the boundary surface to the isotropic hardening of the boundary surface. Moreover, as shown in the above formula (3), the transformation parameter η is the ratio of the maximum value b of the kinematic hardening of the boundary surface to the maximum value of the composite hardening combining the kinematic hardening and isotropic hardening of the boundary surface. The maximum value of the composite hardening is given by the sum of the maximum value b of the kinematic hardening of the boundary surface and the maximum value Rsat of the isotropic hardening of the boundary surface.

[0159] In proportional deformation (proportional deformation) in which the load direction is constant, such as in uniaxial tensile tests, there is no difference between kinematic hardening and isotropic hardening, and the shape of the stress-strain curve depends only on the maximum value of the hardening amount and the hardening rate of the boundary surface. On the other hand, when the load direction changes in tension-compression repeated tests, the difference caused by the kinematic hardening and isotropic hardening of the boundary surface occurs on the stress-strain curve. When the transformation parameter η is the lower limit value (η=0), the boundary surface becomes isotropically hardened, and the Bauschinger effect becomes smaller. On the other hand, when the transformation parameter η is the upper limit value (η=1), the boundary surface becomes kinematic hardening, and the Bauschinger effect becomes larger. That is, the parameter η represents the degree of the Bauschinger effect. Based on the above reasons, in this embodiment 1, the acceptable range of the transformation parameter η is limited to 0≤η≤1.

[0160] (d) Transformation parameter σsat

[0161] The transformation parameter σsat represents the maximum value (convergence stress) of stress convergence in uniaxial tensile deformation. According to the principle of the Yoshida-Uemori model, the maximum value σsat of stress in uniaxial tensile deformation is expressed as the sum of the initial radius Y+a0 (= transformation parameter BL) of the boundary surface, the maximum value b of the kinematic hardening amount of the boundary surface, and the maximum value Rsat of the isotropic hardening amount of the boundary surface as shown in the above formula (4). That is, the transformation parameter σsat can be obtained by σsat=Y+a0+b+Rsat.

[0162] On the other hand, the stress-strain curve in a uniaxial tensile test usually shows a continuous increase in stress as the strain increases (cf. Figure 4 ). Therefore, the stress XS at any strain εXS in the high strain region above the uniform elongation uEL (experimental value of stress in the high strain region, Figure 4 a6) in the figure is used as the reference to determine the range of σsat.

[0163] The method for determining any strain εXS in the high strain region above the uniform elongation is preferably determined based on the deformation of the metal material to which the Yoshida-Uemori model is applied, but the Yoshida-Uemori model has stress convergence in the high strain region as described above. Therefore, for example, εXS=1 may be sufficient.

[0164] However, usually in uniaxial tensile tests, the strain exceeds the uniform elongation uEL, and it is difficult to determine the exact stress after necking occurs ( Figure 4 Therefore, the stress in the high strain region above the uniform elongation uEL cannot be measured until the strain εxs. Therefore, after necking occurs, that is, after the uniform elongation uEL, the stress-strain curve ( Figure 4 a3) in can be deduced using any hardening law.

[0165] As a hardening law, for example, the Swift hardening law (Formula (A10), σeq=c1(c2+εpeq)c3) widely used in finite element analysis software can be applied. The following is an example of using the Swift hardening law to infer the stress-strain curve after the uniform elongation uEL and determine the acceptable range of σsat. First, based on the tensile SS curve ( Figure 4 The parameters c1 to c3 of the Swift hardening law are determined by fitting. Next, the stress-strain curve ( Figure 4 Then, in the stress-strain curve after the estimated uniform elongation uEL, the range of σsat is determined based on the stress XS at any strain εXS in the high strain region above the uniform elongation uEL. The acceptable range of σsat can be set to, for example, ±10% of XS. Based on the above reasons, in the first embodiment, the acceptable range of σsat is limited to 0.9×XS≤σsat≤1.1×XS( Figure 6 The range of the arrow of σsat).

[0166] The constraint condition setting step S9 is not limited to the constraint conditions on the transformation parameters, and may further set constraint conditions that limit the acceptable ranges of other parameters of the Yoshida-Uemori model. In the first embodiment, as shown in the above-mentioned Table 2, the acceptable ranges of other parameters Y, C2, m, and h are limited. The basis for the acceptable ranges of these parameters is as follows.

[0167] (e) Parameter Y

[0168] As explained in the principle of the Yoshida-Uemori model, the parameter Y represents the radius of the yield surface (see Figure 3 ), if the stress exceeds Y, the material yields, i.e., begins to deform plastically. On the other hand, the characteristic quantity obtained from the stress-strain curve based on the uniaxial tensile test, i.e., the yield stress YS (refer to Figure 6 ) 0.2% yield strength (stress value of 0.2% of plastic strain) is usually used. This is because it is very difficult to strictly determine the yield point from the stress-strain curve obtained by experiment. Above, it is considered that the parameter Y is roughly equal to the yield stress YS or smaller than YS.

[0169] In order to reproduce the Bauschinger effect more, Y is preferably smaller. For example, in a tension-compression repeated test, when a certain stress σa is reached after tensile deformation, the load direction is reversed and compressive deformation is applied. In this case, the stress at which plastic deformation starts again in the Yoshida-Uemori model, i.e., the re-yielding stress σb, becomes σb=σa-2Y.

[0170] When the Bauschinger effect is greater, the re-yield stress becomes higher. That is, it can be seen that there is a tendency that the smaller Y is, the greater the Bauschinger effect is, but the positive constant according to the definition of parameter Y is clear. As described above, in this embodiment 1, the range of parameter Y is preferably limited to 0<Y<YS( Figure 6 range of the Y arrow).

[0171] (f) Parameter C2

[0172] As described above, parameter C2 is a parameter indicating the hardening rate (a parameter that determines the moving speed of the relative position α* of the center of the yield surface relative to the center of the boundary surface). For a steel plate having a tensile strength of about 270 MPa to 1470 MPa, the value of C2 is basically about 100 to 600. As for materials that are not suitable for this, as described above, for materials having a yielding stage, C1 is about 1000 to 2000. Therefore, in the first embodiment, it is preferred that the range of C2 is limited to 10≤C2≤2000.

[0173] (g) Parameter m

[0174] Parameter m is a parameter that determines the moving speed of the center β of the boundary surface (kinematic hardening) and the expansion speed of the boundary surface (isotropic hardening). Parameter m governs the hardening speed of the boundary surface based on the combination of kinematic hardening (formula (A4)) and isotropic hardening (formula (A6)) of the boundary surface, and therefore has a greater impact on the stress-strain curve. Under uniaxial tensile stress, the convergence value of stress (convergence stress) is σsat=Y+a0+b+Rsat (transformation parameter σsat, formula (4)), but parameter m affects the time until gradually approaching the stress. The smaller m is, the slower the hardening speed, and it takes time to gradually approach the convergence stress, so that the stress-strain curve becomes a hardening curve like continuous hardening.

[0175] For steel plates with a tensile strength of about 270 MPa to 1470 MPa, the value of m is mostly 0.01 to 20. As with parameters C1 and C2, parameter m represents speed, so if m>20, the influence on the stress-strain curve becomes less, and m is rarely greater than 50. For the above reasons, in the first embodiment, the range of the parameter m is preferably limited to 0.01≤m≤50.

[0176] (h) Parameter h

[0177] The parameter h is the ratio of the expansion amount to the movement amount of the non-isotropic hardening area. The non-isotropic hardening area only moves when h=0 and only expands when h=1, and can take values ​​in between (0≤h≤1). When h=0, the non-isotropic hardening area does not expand, that is, there is no non-isotropic hardening area, and isotropic hardening of the boundary surface occurs immediately when the stress is reversed. When h>0, the non-isotropic hardening area expands, so when the center of the boundary surface exists in this area, isotropic hardening of the boundary surface will not occur, and the hardening after stress reversal becomes smaller.

[0178] 《Objective Function Setting Process》

[0179] The objective function setting step S11 is a step of setting an objective function for determining conversion parameters and other parameters. The objective function is set as follows.

[0180] First, the residual between the stress-strain curve obtained experimentally under uniaxial tensile stress and the stress-strain curve under uniaxial tensile stress calculated by the Yoshida-Uemori model is calculated.

[0181] Next, the residual between the stress-strain curve obtained experimentally under tension-compression repeated stress and the stress-strain curve under tension-compression repeated stress calculated by the Yoshida-Uemori model is calculated.

[0182] In addition, the residuals between the experimental values ​​of the mechanical property values ​​of the metal material and the calculated values ​​of the mechanical property values ​​calculated by the Yoshida-Uemori model are calculated.

[0183] The stress-strain curve under uniaxial tensile stress, the stress-strain curve under tension-compression repeated stress, and the calculation of the mechanical properties of metal materials based on the Yoshida-Uemori model use transformation parameters (Equations (1) to (4)) and other parameters (see Table 1).

[0184] Then, the weighted residual sum of squares obtained by multiplying each calculated residual by an individual weighting coefficient is set as the objective function.

[0185] In the first embodiment, the weighted residual sum of squares (WRSS) is calculated by the following equation (9).

[0186] [Formula 12]

[0187]

[0188] in,

[0189] WRSS: Weighted Residual Sum of Squares

[0190] YS exp : Experimental value of yield stress

[0191] YS cal : Calculated value of yield stress based on Yoshida-Uemori model

[0192] W YS : Weighting factor for the residual of the yield stress

[0193] TS exp : Experimental value of tensile strength

[0194] TS cal : Calculated value of tensile strength based on Yoshida-Uemori model

[0195] w TS : Weighting coefficient for the residual of tensile strength

[0196] UE exp : Experimental value of uniform elongation

[0197] UE cal : Calculated value of uniform elongation based on Yoshida-Uemori model

[0198] W uEL : Weighting coefficient for the residual error of uniform elongation

[0199] XS exp : Experimental value of stress in high strain region above uniform elongation

[0200] XS cal : Calculated value of stress in the high strain region above uniform elongation based on the Yoshida-Uemori model

[0201] W XS : Weighting coefficient for the residual stress in the high strain region above the uniform elongation

[0202] : Experimental value of stress for any strain on the stress-strain curve under uniaxial tension

[0203] : Calculated value based on the Yoshida-Uemori model for stress at an arbitrary strain on the stress-strain curve under uniaxial tension stress

[0204] W T : Weighting coefficient for the residual of stress under uniaxial tensile stress

[0205] : Experimental value of stress for any strain on the stress-strain curve under tension-compression repeated stress

[0206] : Calculated value based on the Yoshida-Uemori model for stress at an arbitrary strain on the stress-strain curve under tension-compression repeated stress

[0207] W TCk : Weighting coefficient for the residual stress under tension-compression repeated stress

[0208] The fifth term of formula (9) represents the residual of the stretched SS curve (refer to Figure 7 (a)), the sixth term represents the residual of the repeated SS curve (refer to Figure 7 (b)). p in equation (9) is the reversal count of the tension-compression repeated test. The reversal count must be set to p≥1 because the magnitude of the Bauschinger effect can only be determined if the reversal is at least once. Figure 7 (b) is an example of a graph schematically showing the stress-strain relationship under tension-compression repeated stress in the case of p=2.

[0209] The amount of strain at the start of reversal is arbitrary, but if necking or buckling occurs in the material, accurate stress cannot be calculated, so it is preferable to set the amount of strain below uniform deformation as the reversal start strain.

[0210] In addition, nn and mm in formula (9) are the division numbers of the strain direction of the tensile SS curve and the repeated SS curve, respectively. In order to reproduce the characteristics of work hardening and Bauschinger effect, it is preferred to increase the division number nn and mm of each SS curve. In addition, since work hardening and Bauschinger effect show a large hardening behavior in the initial stage of deformation of the first tensile and shortly after the start of reversal, there is no need to increase the division number of such a range, etc., and divide it at equal intervals from the beginning to the end of deformation. In addition, WYS, WTS, WuEL, WXS, WT and WTCk in formula (9) are weighting coefficients, and individual weights can also be specified for each item.

[0211] In the objective function setting step S11, the yield stress YS, tensile strength TS, and uniform elongation uEL, which are important deformation characteristics of metal materials, can be given a larger weight. In particular, the Yoshida-Uemori model used directly without changing the parameters has a tendency to deviate more from the tensile SS curve extrapolated by the Swift hardening law, etc., because the stress converges in the high strain region. In such a case, in the objective function setting step S11, by increasing the weighting coefficient for the residual of the stress XS in the high strain region as needed, it can be adjusted to converge to a larger stress value.

[0212] 《Parameters determine the process》

[0213] The parameter determination step S13 is a step of determining the conversion parameters and other parameters of the Yoshida-Uemori model so as to minimize the objective function under the constraint conditions set in the constraint condition setting step S9 .

[0214] The transformation parameters and other parameters can be determined by minimization techniques, and any method can be used as the minimization technique, for example, evolutionary calculation based on a genetic algorithm can be applied.

[0215] Thus, the transformation parameters and other parameters can be easily identified by using an optimization method, etc. In addition, it is clear that the transformation parameters can be easily transformed into the parameters of the existing Yoshida-Uemori model by the definition of the transformation parameters (Equations (1) to (4)).

[0216] 《Stress-strain relationship inference process》

[0217] The stress-strain relationship estimation step S15 is a step of estimating the stress-strain relationship of the metal material using the conversion parameters determined in the parameter determination step S13 and other parameters of the Yoshida-Uemori model.

[0218] In order to infer the stress-strain relationship through the Yoshida-Uemori model using the determined transformation parameters and other parameters, it is sufficient to inversely transform the definition formula of the transformation parameters shown in equations (1) to (4) into the original parameters. However, in the stress-strain relationship inference step S15, the Yoshida-Uemori model can also be formulated using the transformation parameters defined by equations (1) to (4). In addition, the stress-strain relationship can also be inferred by assigning the transformation parameters and other parameters determined in the parameter determination step S13.

[0219] As described above, in the stress-strain relationship inference method of the first embodiment, parameters obtained by transforming a part of the parameters of the Yoshida-Uemori model representing the Bauschinger effect of the metal material are defined. Then, the range of the transformation parameters is limited by the correlation with the mechanical property values ​​of the metal material calculated based on the stress-strain relationship obtained under uniaxial tensile stress. In addition, the objective function is defined by including not only the residual with the experimental value of the stress-strain curve, but also the residual with the mechanical property values ​​such as tensile strength and uniform elongation as the basic characteristic values ​​of the metal material, so as to obtain the transformation parameters and the original parameters in a way that minimizes the objective function.

[0220] As described above, according to the stress-strain estimation method of the first embodiment, the parameters of the Yoshida-Uemori model representing the Bauschinger effect of the metal material can be easily and appropriately determined while ensuring the reproducibility of the basic deformation characteristics of the metal material. As a result, the stress-strain relationship of the metal material can be estimated with high accuracy.

[0221] In the first embodiment, four transformation parameters defined by equations (1) to (4) are defined. However, the present invention may define at least one transformation parameter among the transformation parameters defined by equations (1) to (4).

[0222] [Implementation Method 2]

[0223] <Rebound prediction method>

[0224] The springback prediction method of the second embodiment determines the parameters and transformation parameters of the Yoshida-Uemori model by using the stress-strain relationship estimation method of the first embodiment described above. Figure 1 Then, the springback of the stamped product is predicted using the stress-strain relationship of the metal material estimated using the determined parameters and the transformation parameters.

[0225] In this embodiment 2, if Figure 8 As shown, the prediction of springback of the stamped product is performed by S1 to S13, stamping analysis step S21 and springback analysis step S23. Each step of S1 to S13 is the same as the above-mentioned embodiment 1, so the stamping analysis step S21 and springback analysis step S23 are described below.

[0226] 《Analysis process of stamping forming》

[0227] The press forming analysis step S21 is a step of performing finite element analysis of a process of press forming a blank of a metal material into a press formed product.

[0228] In the finite element analysis in the press forming analysis step S21 , commercially available finite element analysis software can be used. In addition, in this finite element analysis, the stress-strain relationship estimated by the stress-strain estimation method of the first embodiment is applied.

[0229] 《Springback Analysis Process》

[0230] The springback analysis step S23 is a step of performing finite element analysis on the springback behavior of the press-formed product obtained by the finite element analysis in the press-forming analysis step S21 .

[0231] The finite element analysis in the springback analysis step S23 can be performed using commercially available finite element analysis software. In addition, the stress-strain relationship estimated by the stress-strain estimation method of the first embodiment is applied to the finite element analysis.

[0232] As described above, in the springback prediction method of the second embodiment, the stress-strain relationship is estimated using the parameters and transformation parameters of the Yoshida-Uemori model determined by the stress-strain relationship estimation method of the first embodiment. Furthermore, the springback of the stamped product is predicted using the estimated stress-strain relationship, so the springback amount and the shape after the springback of the stamped product can be obtained with high accuracy.

[0233] [Implementation method 3]

[0234] <Manufacturing method of press-formed products>

[0235] The method for manufacturing a stamped product according to the third embodiment of the present invention adjusts the stamping conditions in such a way that the springback amount is reduced to manufacture a stamped product with improved dimensional accuracy. Fig.13 As shown, the manufacturing method of the stamped product of the present embodiment 3 includes a test piece collection step S31, a stress-strain relationship inference parameter acquisition step S33, and a temporary stamping forming condition setting step S35. In addition, the manufacturing method of the stamped product of the present embodiment 3 includes: a springback amount prediction step S37, a springback amount determination step S39, a temporary stamping forming condition change step S41, and a repetitive step S43. In addition, the manufacturing method of the stamped product of the present embodiment 3 includes an actual stamping forming condition determination step S45 and an actual stamping forming step S47.

[0236] In the present embodiment 3, as a press-formed product, a press-formed product is formed (manufactured) by press forming. Fig.12 The case of a stamped product 1 having a hat-shaped cross section shown in (a) of FIG. 1 is an object. Fig.14 As shown, the press-formed product 1 is press-formed by a draw-bending method using a press forming die 10 composed of a die 11 , a punch 13 , a pressure pad 15 , and a blank holder 17 .

[0237] 《Test piece collection process》

[0238] The test piece collection step S31 is a step of collecting test pieces for uniaxial tensile testing and tension-compression repeated testing from a metal material used as a blank for a stamped product. The uniaxial tensile test and tension-compression repeated testing are respectively implemented in the uniaxial tensile stress-strain curve acquisition step S1 and the repeated stress-strain curve acquisition step S3 of the stress-strain relationship inference method of the first embodiment described above.

[0239] 《Stress-strain relationship inference parameter acquisition process》

[0240] The stress-strain relationship estimation parameter acquisition step S33 is a step of obtaining transformation parameters and other parameters of the Yoshida-Uemori model based on the stress-strain relationship estimation method of the first embodiment described above, using the test piece collected in the test piece collection step S31 .

[0241] In this embodiment 3, if Fig.13 As shown, the stress-strain relationship estimation parameter acquisition step S33 obtains the transformation parameters and other parameters of the Yoshida-Uemori model by executing each of the steps S1 to S13 of the stress-strain relationship estimation method of the first embodiment.

[0242] 《Temporary stamping forming condition setting process》

[0243] The temporary press forming condition setting step S35 is a step of setting temporary press forming conditions for the press-formed product.

[0244] As the temporary stamping forming conditions set in the temporary stamping forming condition setting step S35, there can be cited conditions related to the shape of the stamping forming die and conditions set in the control panel of the press forming machine. Fig.14 In the stamping die 10 shown in the figure, the punch shoulder radius of the punch 13, the longitudinal wall portion 5 (see Fig.12 ) of the die 11 and the punch 13 relative to the press forming direction. In addition, as conditions set in the control panel of the press forming machine, the gap (clearance) between the die 11 and the punch 13 sandwiching the longitudinal wall portion 5 at the forming bottom dead center (see Fig.14). In addition, the blank holding pressure (blank holder force) of the die 11 and the bracket 17 sandwiching the flange portion 7 can also be cited (see Fig.14 ).

[0245] 《Springback prediction process》

[0246] The springback amount prediction step S37 uses the transformation parameters and other parameters of the Yoshida-Uemori model obtained in the stress-strain relationship inference parameter acquisition step S33 to perform stamping analysis and springback analysis under temporary stamping conditions of the stamped product. Then, based on the results of the stamping analysis and springback analysis, the springback amount of the stamped product is predicted.

[0247] In the springback amount prediction step S37, for the case where the metal material of the test piece collected in the test piece collection step S31 is used as the blank, stamping analysis and springback analysis are performed. Moreover, in the stamping analysis and springback analysis, finite element analysis of the process of stamping the stamped product 1 and finite element analysis of the springback behavior of the stamped product 1 obtained by the finite element analysis can be performed.

[0248] As the springback amount predicted in the springback amount prediction step S37, for example, the springback amount of the flange portion 7 caused by the warping of the vertical wall portion 5 in the stamped product 1 after springback can be cited (see Fig.12 (b)).

[0249] 《Springback determination process》

[0250] The springback amount determination step S39 is a step of determining whether the springback amount of the press-formed product predicted in the springback amount prediction step S37 is within a predetermined range determined in advance.

[0251] The predetermined range for the springback amount may be appropriately set based on, for example, the dimensional accuracy allowed when the press-formed product is actually assembled.

[0252] 《Temporary stamping forming condition change process》

[0253] The temporary stamping condition changing step S41 is a step of changing the temporary stamping condition when it is determined in the springback amount determining step S29 that the springback amount of the stamped product is not within a predetermined range.

[0254] For example, Fig.12As shown in (b), when the amount of floating of the flange portion 7 caused by the warping after the rebound of the longitudinal wall portion 5 is greater than a predetermined specified range, the shape of the stamping die 10 is changed in a manner that the warping (curl) of the longitudinal wall portion 5 after the rebound becomes smaller. The amount of floating of the flange portion 7 refers to the displacement in the forming height direction, which is defined as the amount of springback. Moreover, with regard to the change in the shape of the stamping die 10, specifically, the punch shoulder radius of the punch 13 can be reduced, or the inclination angle of the die 11 and the punch 13 clamping the longitudinal wall portion 5 relative to the stamping direction can be changed in the direction of pressing down the longitudinal wall portion 5 opposite to the warping. In addition, in the temporary stamping condition change step S41, the plate pressing force of the die 11 and the bracket 17 can be increased, and the setting conditions changed in the control panel of the stamping machine can be changed to the boundary conditions (boundary conditions) of the stamping analysis. In this manner, in the temporary press forming condition changing step S41 , the temporary press forming conditions are changed (adjusted) so that the springback amount is reduced.

[0255] Repeated process

[0256] The repetitive step S43 is a step of repeatedly executing the springback amount prediction step S37 and the springback amount determination step S39 under the temporary stamping forming conditions changed in the temporary stamping forming condition changing step S41. This repetition is performed until the springback amount of the stamped product is determined to be within a predetermined range in the springback amount determination step S39. Therefore, in the case where the stamped product is not determined to be within the range of the specified dimensional accuracy by only changing the temporary stamping forming conditions once, the temporary stamping forming condition changing step S41 is also repeated.

[0257] 《Actual stamping forming conditions determine the process》

[0258] The actual stamping forming condition determination step S45 is a step for determining the temporary stamping forming conditions as actual stamping forming conditions when the springback amount of the stamped product is determined to be within a predetermined range in the springback amount determination step S39. The actual stamping forming conditions refer to the conditions under which the stamped product is actually stamped.

[0259] In the actual stamping condition determination step S45 , the actual stamping condition can be determined as follows based on the provisional stamping condition when the springback amount is determined to be within a predetermined range in the springback amount determination step S39 .

[0260] For example, in the case where the shape of the stamping die is changed as a temporary stamping forming condition, the shape data of the stamping die (model) used for stamping analysis is input into a CAD / CAM program that cooperates with an NC machine tool (numerically-controlled machine), and converted into NC data (numerical control data) (NC program) for NC machining (NC machining). The NC machine tool machines a casting die model made of expanded polystyrene or a steel die by a full mold casting method (evaporative pattern casting method). Then, the NC data (NC program) is used to manufacture a casting die model made of expanded polystyrene or a steel die by an NC machine tool. Thus, as an actual stamping forming condition, the shape of the stamping die used for actual stamping can be determined. In addition, as a temporary stamping forming condition, it is possible to Fig.14 In the case of a gap (clearance) between the die 11 and the punch 13 of the press forming mold 10 shown in the figure at the bottom dead point of forming, the height of the distance block is determined according to the gap.

[0261] In addition, when the setting of the control panel of the stamping machine is changed as a temporary stamping condition, the changed setting of the control panel of the stamping machine is determined as the actual stamping condition. For example, when the plate pressing force of the die 11 and the bracket 17 is changed, the setting value of the air pressure or hydraulic pressure control panel of the air pressure or hydraulic die cushion (auxiliary pressure device) of the stamping machine can be determined as the actual stamping condition in such a way that it becomes the changed plate pressing force.

[0262] 《Actual stamping process》

[0263] The actual stamping step S47 is a step of stamping a stamped product using a blank of a metal material under the actual stamping conditions determined in the actual stamping condition determination step S45. The metal material used as the blank in the actual stamping step S47 is a metal material for which a test piece is collected in the test piece collection step S31 and for which the transformation parameters and other parameters of the Yoshida-Uemori model are obtained in the stress-strain relationship inference parameter acquisition step S33.

[0264] As such, in the manufacturing method of the stamped product of the present embodiment 3, a test piece is collected from the metal material used as the blank of the stamped product, and the parameters and transformation parameters of the Yoshida-Uemori model are obtained by the stress-strain relationship inference method of the embodiment 1. Then, the stamping analysis and springback analysis of the stamped product are performed using the obtained parameters and transformation parameters of the Yoshida-Uemori model to predict the springback amount. In addition, the actual stamping conditions are determined in such a way that the predicted springback amount of the stamped product converges within a specified range. By stamping the stamped product under the actual stamping conditions determined in this way, a stamped product with improved dimensional accuracy can be manufactured.

[0265] In particular, the actual stamping conditions can be determined based on the deviation of the metal material used as the blank (for example, when the metal material is a steel plate, the change in the metal structure caused by the deviation of the manufacturing conditions such as the hot-rolling condition and the annealing condition). As a result, the large-scale generation of dimensional defects caused by the springback of the stamped products actually produced can also be suppressed. In addition, the manufacturing method of the stamped products of the present embodiment 3 can adjust the actual stamping conditions in a manner that reduces the amount of springback even when it is necessary to adjust the actual stamping conditions before the start of mass production of the actual stamped products.

[0266] According to the manufacturing method of the stamped product of the third embodiment, even if the stamped product is stamped under the actual stamping conditions adjusted in a manner to reduce the springback amount, there is a case where the dimensional accuracy allowed by the springback amount is not satisfied. In this case, sometimes further adjustments to the stamping conditions such as the shape of the stamping die are repeatedly performed based on the springback amount of the stamped product stamped under the actual stamping conditions that have been determined.

[0267] However, in the method of the third embodiment, the actual stamping forming conditions are changed (adjusted) in such a way that the springback amount is reduced. Therefore, even if the shape of the stamping die is not repeatedly changed as the actual stamping forming conditions, the dimensional accuracy allowed for the stamped product can be satisfied. Therefore, according to the manufacturing method of the stamped product of the third embodiment, the cost and period of the production preparation of the stamped product can be greatly shortened.

[0268] Verification was performed to confirm the effects of the stress-strain relationship estimation method and the springback prediction method of the present invention, and therefore, these will be described below.

[0269] <Estimation of stress-strain relationship>

[0270] Using various steel plates A to E having tensile strengths of 270 MPa to 1470 MPa as shown in Table 3 as metal materials, the parameters of the Yoshida-Uemori model were determined by the method of the first embodiment of the present invention described above.

[0271] [Table 3]

[0272] YP / MPa TS / MPa uEL / % Steel Plate A 154 294 27 Steel Plate B 412 640 16 Steel Plate C 665 757 9 Steel Plate D 633 978 11 Steel Plate E 1360 1521 3

[0273] The following describes the procedure for determining the parameters of the Yoshida-Ueda model in the embodiment.

[0274] First, for each steel plate as a target, the relationship between stress and strain under tensile stress up to uniform elongation was obtained by uniaxial tensile test ( Figure 1 Then, the relationship between stress and strain in the high strain region after uniform elongation is extrapolated according to the Swift hardening law to obtain ( Figure 1 Then, the relationship between stress and strain obtained by uniaxial tensile test and the relationship between stress and strain obtained by extrapolation based on Swift hardening law are obtained as a tensile SS curve.

[0275] Next, for each steel plate as the object, the relationship between stress and strain under tension-compression repeated stress was obtained through repeated tension-compression tests. In this embodiment, the number of reversals (p) from tension to compression is set to 2 times. First, a tensile load (tensile load) is applied (first tension), and then a compressive load (compressive load) is applied (first compression). Then, a tensile load (second tension) is further reversed (see Figure 2 ). Then, the relationship between stress and strain during the first stretching, the first compression and the second stretching is obtained as a repeated SS curve.

[0276] In this embodiment, for steel sheets A and B, they are stretched to a true strain of 5% in the first stretching process, compressed to a true strain of -5% in the next first compression process, and further stretched to a true strain of 5% in the second stretching process from compression to stretching. In contrast, for steel sheets C, D, and E, the strains at the start of the reversal in the stretching process (first stretching, second stretching) and the compression process (first compression) are set to 3% and -3%, respectively.

[0277] Then, the tensile SS curve and the repeated SS curve were equally divided in the strain direction. The number of divisions nn of the tensile SS curve and the number of divisions mm of the repeated SS curve were both set to 100.

[0278] Next, the objective function is calculated. In this embodiment, the weighted residual sum of squares WRSS calculated by equation (9) shown in the above-mentioned embodiment 1 is used as the objective function. In addition, each weighting coefficient in equation (9) is a value shown in Table 4.

[0279] [Table 4]

[0280] Weighting coefficient value <![CDATA[W YS ]]> 0.3 <![CDATA[W TS ]]> 1.2 <![CDATA[W μEL ]]> 1 <![CDATA[W XS ]]> 0.2 <![CDATA[W TS ]]> 1.3 <![CDATA[W TC1 ]]> 1 <![CDATA[W TC2 ]]> 2.2 <![CDATA[W TC3 ]]> 0.3

[0281] Then, each parameter was determined so that the objective function would be minimized. A genetic algorithm was applied to minimize the objective function, and evolutionary calculations were performed up to 100 generations.

[0282] In this embodiment, similarly to the above-mentioned embodiment 1, the transformation parameters given by equations (1) to (4) among the parameters defining the Yoshida-Uemori model are used as an example of determining the transformation parameters and other parameters together as an invention example. In the invention example, the possible range of the transformation parameters is limited as shown in the above-mentioned equations (5) to (8). In addition, the possible range of the original Y is also limited to 0 as shown in the above-mentioned Table 2. <Y<YS(=1350)。

[0283] In addition, as a comparison object, an example in which the original parameters were directly determined by a genetic algorithm without converting the parameters of the Yoshida-Uemori model was used as a comparative example, and a comparative study was conducted with the invention example.

[0284] In Table 5, the convergence value and convergence generation of the objective function are shown in the invention examples and the comparative examples. Fig. 9 middle.

[0285] [Table 5]

[0286]

[0287] In the judgment of convergence, it is judged that the generation with a value of the objective function of the 100th generation of +1% or less has converged. It can be said that the smaller the value of the objective function, the higher the accuracy. On the other hand, it can be said that the smaller the convergence generation, the more efficient it is. In the invention example, as shown in Table 5 and Fig. 9 As shown, it can be seen that in any steel plate, the value of the objective function is smaller than that of the comparative example, and convergence is achieved at an earlier generation.

[0288] Table 6 shows the residuals of the experimental values ​​and the calculated values ​​of the mechanical properties of the metal materials in the invention examples and the comparative examples. In Table 6, the YS residual is the residual of the yield stress YS, the TS residual is the residual of the tensile strength TS, and the uEL residual is the residual of the uniform elongation.

[0289] [Table 6]

[0290]

[0291] As shown in Table 6, it can be seen that in the inventive examples, the residuals are smaller than those in the comparative examples regarding any mechanical property values.

[0292] In addition, for Steel Plate E, the results of estimating the tensile SS curve and the repeated SS curve are shown in FIG. Fig.10 and Fig.11 In. Fig.10 In the comparative example, a deviation from the measured value was observed in the high strain region under uniaxial tensile stress, but in the present invention, the stress-strain relationship can be inferred with high accuracy even in the high strain region. Fig.11 It can be seen that, in the present invention, the stress-strain relationship after stress reversal of a metal material under tension-compression repeated stress can be estimated with high accuracy.

[0293] Table 7 shows, with respect to Steel Plate E, some of the constraints set in the Inventive Examples, the ranges thereof, and the values ​​of the parameters determined in the Inventive Examples and the Comparative Examples.

[0294] [Table 7]

[0295]

[0296] In the invention example, the parameters of the Yoshida-Uemori model and the values ​​of the transformation parameters are determined within the range specified by the constraint conditions, so the determined parameters satisfy the constraint conditions. On the other hand, in the comparative example, the value of σsat calculated based on the determined parameters deviates from the constraint conditions of the invention example. In the comparative example, the value of σsat representing the characteristics of the stretched SS curve is inappropriate, so it is considered that the calculation result of the stretched SS curve deviates. On the other hand, in the invention example, the constraint conditions are set in a manner that can express the characteristics of the stretched SS curve, so it can be confirmed that the calculation result of the stretched SS curve is well consistent with the experimental result.

[0297] According to the stress-strain relationship estimation method of the present invention, the parameters of the Yoshida-Uemori model can be appropriately and easily determined, and the stress-strain relationship can be estimated with high accuracy.

[0298] <Prediction of springback amount>

[0299] Next, the springback amount of the stamped product was predicted using the parameters determined in the above-mentioned invention example and comparative example. Fig.12 The stamped product 1 having a hat-shaped cross-section with a top plate portion 3, a vertical wall portion 5, and a flange portion 7 was analyzed as an object of analysis, and finite element analysis was performed on the stamping process and the springback process after demolding after stamping. Fig.12As shown in FIG. 1 , the springback amount (displacement amount in the forming height direction) of the flange portion 7 of the press-formed product 1 after springback was determined as the springback amount.

[0300] Table 8 shows the results of determining the amount of springback of the flange portion due to springback of the press-formed product for each of the steel sheets A to E.

[0301] [Table 8]

[0302]

[0303] As shown in Table 8, it can be seen that the springback amount closer to the experimental result can be predicted in the inventive example. This shows that the springback amount prediction method of a press-formed product according to the present invention can predict the springback amount with high accuracy.

[0304] Industrial Applicability

[0305] According to the present invention, it is possible to provide a stress-strain relationship inference method that can appropriately determine the parameters of the Yoshida-Uemori model without requiring a large number of processes, and can infer the stress-strain relationship of a metal material with high accuracy. In addition, according to the present invention, it is possible to provide a springback prediction method that can use the stress-strain relationship inferred by the above method to perform stamping analysis and springback analysis, and can predict the springback of a stamped product with high accuracy. In addition, according to the present invention, it is possible to provide a stamping product manufacturing method that determines stamping conditions in a manner that suppresses the springback of the stamped product predicted by the above method, and manufactures the stamped product under the determined stamping conditions.

[0306] Description of Reference Numerals

[0307] 1 ... stamping product; 3 ... top plate portion; 5 ... vertical wall portion; 7 ... flange portion; 10 ... stamping die; 11 ... die; 13 ... punch; 15 ... gasket; 17 ... bracket.

Claims

1. A stress-strain relationship inference method, which uses the Yoshida-Uemori model representing the Bauschinger effect of a metal material to infer the relationship between stress and strain of the metal material, The stress-strain relationship inference method is characterized by comprising: a uniaxial tensile stress-strain curve acquisition step, in which a stress-strain curve of the metal material under uniaxial tensile stress is experimentally acquired by subjecting the metal material to a uniaxial tensile test as a test piece; a repeated stress-strain curve acquisition step, in which a stress-strain curve of the metal material under repeated tension-compression stress is experimentally acquired by performing repeated tension-compression tests on the metal material as a test piece; a mechanical property value experimental value calculation step, in which experimental values ​​of yield stress, tensile strength, uniform elongation, and stress in a high strain region above uniform elongation as mechanical property values ​​of the metal material are calculated based on a stress-strain curve under the uniaxial tensile stress of the metal material obtained through the uniaxial tensile test experiment; a transformation parameter definition step of defining transformation parameters obtained by combining at least two parameters used in the Yoshida-Uemori model and transforming the parameters; a constraint condition setting step of setting a constraint condition for limiting a possible range of the conversion parameter using the experimental value of the calculated mechanical characteristic value; an objective function setting step, in which the residuals of the stress-strain curve under the uniaxial tensile stress obtained by the experiment and the stress-strain curve under the uniaxial tensile stress calculated by the Yoshida-Uemori model, the residuals of the stress-strain curve under the tensile-compression repeated stress obtained by the experiment and the stress-strain curve under the tensile-compression repeated stress calculated by the Yoshida-Uemori model, and the residuals of the experimental values ​​of the mechanical properties of the metal material and the calculated values ​​of the mechanical properties calculated by the Yoshida-Uemori model are calculated, and the sum of squares of the weighted residuals obtained by multiplying the calculated residuals by separate weighting coefficients is set as the objective function; as well as A parameter determination step of determining the transformation parameter and other parameters of the Yoshida-Uemori model so as to minimize the objective function under the constraint conditions.

2. The stress-strain relationship inference method according to claim 1, characterized in that: In the transformation parameter definition step, one or more transformation parameters given by the following equations (1) to (4) obtained by combining at least two or more parameters of the Yoshida-Uemori model are defined. In the constraint condition setting step, the acceptable range of the transformation parameter defined in the transformation parameter definition step is limited by the following formulas (5) to (8) corresponding to the defined transformation parameter. [Formula 1] BL=Y+a0 (1) κ=C1 / C2 (2) n=b / (b+R sat ) (3) s sat =Y+a0+b+R sat (4) YS≤BL≤XS (5) 1≤κ≤4 (6) 0≤η≤1 (7) 0.9×XS≤σ sat ≤1.1×XS (8) in, BL,κ,η,σ sat : Transformation parameters Y,a0,C1,C2,b,R sat : Parameters of the Yoshida-Uemori model YS: Experimental value of yield stress XS: experimental value of stress in the high strain region.

3. The stress-strain relationship inference method according to claim 2, characterized in that: In the objective function setting step, the weighted residual sum of squares is calculated by the following formula (9): [Formula 2] WRSS: Weighted Residual Sum of Squares YS exp : Experimental value of yield stress YS cal : Calculated value of yield stress based on Yoshida-Uemori model W YS : Weighting factor for the residual of the yield stress TS exp : Experimental value of tensile strength TS cal : Calculated value of tensile strength based on Yoshida-Uemori model W TS : Weighting coefficient for the residual of tensile strength UE exp : Experimental value of uniform elongation UE cal : Calculated value of uniform elongation based on Yoshida-Uemori model W uEL : Weighting coefficient for the residual error of uniform elongation XS exp : Experimental value of stress in the high strain region above uniform elongation XS cal : Calculated value of stress in the high strain region above uniform elongation based on the Yoshida-Uemori model W XS : Weighting factor for the residual stress in the high strain region above uniform elongation Experimental value of stress for any strain on the stress-strain curve under uniaxial tension Calculated value of stress based on Yoshida-Uemori model for arbitrary strain on stress-strain curve under uniaxial tension stress W T : Weighting coefficient for the residual of stress under uniaxial tensile stress Experimental value of stress for any strain on the stress-strain curve under tension-compression cyclic stress Calculated value of stress based on Yoshida-Uemori model for any strain on the stress-strain curve under tension-compression repeated stress W TCk : Weighting coefficient for the residual of stress under tension-compression repeated stress.

4. A rebound prediction method, characterized in that: The stress-strain relationship of the metal material is estimated using the parameters and transformation parameters of the Yoshida-Uemori model determined by the stress-strain relationship estimation method according to any one of claims 1 to 3, Using the estimated stress-strain relationship, press forming analysis and springback analysis of a press-formed product using a plate material of the metal material are performed to predict the springback of the press-formed product.

5. A method for manufacturing a stamped product, wherein the stamping conditions are adjusted in such a way as to reduce the springback amount to manufacture a stamped product with improved dimensional accuracy, The method for manufacturing the stamped product is characterized by comprising: A test piece collection step, in which test pieces for use in the uniaxial tension test in the uniaxial tension stress-strain curve acquisition step and the tension-compression repeated test in the repeated stress-strain curve acquisition step of the stress-strain relationship inference method according to any one of claims 1 to 3 are collected from a metal material used as a blank of the stamped product; A stress-strain relationship inference parameter acquisition step, in which the acquired test piece is used to obtain the transformation parameters and other parameters of the Yoshida-Uemori model based on the stress-strain relationship inference method described in any one of claims 1 to 3; a temporary stamping forming condition setting step, in which temporary stamping forming conditions of the stamped product are set; A springback amount prediction step, in which a stamping analysis and a springback analysis are performed on the stamped product using the blank of the metal material under the temporary stamping conditions using the stress-strain relationship inferred by the transformation parameters of the Yoshida-Uemori model and the other parameters obtained in the stress-strain relationship inference parameter acquisition step, to predict the springback amount of the stamped product; a springback amount determination step, in which it is determined whether the springback amount of the stamped product predicted in the springback amount prediction step is within a predetermined range; a temporary stamping forming condition changing step, in which, when it is determined in the springback amount determining step that the springback amount of the stamped product is outside a predetermined specified range, the temporary stamping forming condition is changed; a repetitive step, in which the temporary stamping condition changing step, the springback amount prediction step and the springback amount determination step are repeatedly performed until the springback amount of the stamped product is determined to be within a predetermined range in the springback amount determination step; an actual stamping forming condition determination step, in which, when it is determined in the springback amount determination step that the springback amount of the stamped product is within a predetermined range, the temporary stamping forming condition in this case is determined as the actual stamping forming condition; as well as The actual stamping step is a step in which the stamped product is stamped using the blank of the metal material under the determined actual stamping conditions.

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