JP6669290B1 - Stress-strain relationship estimation method - Google Patents

Abstract

PROBLEM TO BE SOLVED: To provide a stress-strain relationship estimation method for accurately estimating the relationship between stress and strain in a high strain region exceeding uniform elongation of a metal material. A stress-strain relationship estimation method according to the present invention is a tensile load-strain distribution acquisition step of applying a tensile load to a tensile test piece up to a strain region beyond uniform elongation to acquire the tensile load and strain distribution. S1, a stress-strain relationship acquisition step S3 for acquiring the stress-strain relationship up to the uniform elongation of the tensile test piece, a material constant identification step S5 for identifying the material constants of the two types of hardening rules, and a uniform elongation is exceeded. Tensile load estimation step S7 of estimating the tensile load acting on the tensile test piece by using the strain distribution in the strain region and the equivalent stress obtained by the mixing rule obtained by adding the two types of hardening rules by using the weighting coefficient. And a weighting factor determining step S9 for determining the value of the weighting factor so that the estimated tensile load and the acquired tensile load match. [Selection diagram] Fig. 1

Description

  The present invention relates to a stress-strain relationship estimation method, and more particularly, to a stress-strain relationship estimation method capable of accurately estimating the relationship between stress and strain in a high strain region exceeding uniform elongation of a metal material.

2. Description of the Related Art In recent years, in order to reduce greenhouse gas emissions that cause global warming, the automobile industry has been actively working on reducing the weight of automobile bodies. On the other hand, from the viewpoint of occupant protection, the demand for collision safety of automobiles is becoming stricter year by year.
The application of high-strength steel sheets to automotive parts has been progressing in order to satisfy these conflicting demands for reducing the weight of automobile bodies and improving collision safety.Thus, the thickness of parts and the number of parts have been reduced while ensuring collision performance. Reductions have been made. In the past, the strength level of steel sheets used for automotive parts was 340 MPa class to 780 MPa class in the past, but in recent years the development of steel materials has progressed, and high-tensile steel sheets of 980 MPa class or higher with excellent press formability are applied Is starting to be.

Many automotive parts are manufactured by press molding. Press molding is a method of processing a material by pressing a mold against a material (blank) and pressing the mold to transfer the shape of the mold to the blank.
In press forming using a high-tensile steel sheet, forming defects such as cracks and wrinkles are apt to occur during the press forming process, which is a major problem. In general, as the strength of a steel sheet increases, the press formability decreases, so that the frequency of occurrence of cracks and wrinkles increases as compared with a steel sheet having a low strength. Therefore, in order to press-mold without generating cracks and wrinkles, it is necessary to perform trial and error by correcting a mold, and there is a problem that it takes a lot of cost and time.

  In response to this problem, finite element method (FEM) software has recently become widespread, and using a computer to perform press forming analysis, predicts molding defects such as cracks and wrinkles in advance, and based on the prediction results, It became possible to take measures such as modifying the shape and changing the construction method. In addition to these press forming analyses, plastic working simulation by FEM is also performed in collision analysis, springback analysis, and the like.

  In the plastic working simulation of a metal material, the stress-strain relationship of the metal material is indispensable. In particular, since the metal material undergoes large deformation in press forming, the stress-strain relationship in a high strain region has a great influence on the analysis accuracy of the plastic working simulation.

  The most common method for measuring the stress-strain relationship of a metal material is a tensile test. In the tensile test, a tensile load is applied to the tensile test piece 1 having the parallel portion 3 as shown in FIG. 9 to apply tensile deformation, and the stress-strain relationship is calculated from the elongation between the evaluation points and the tensile load in the tensile test piece 1. calculate. FIG. 10 shows an example of a stress-strain relationship obtained in a tensile test using the tensile test piece 1. When the stress of the metal material reaches the yield stress (point A in FIG. 10), plastic deformation starts, and as the strain progresses, the metal material is work-hardened and the stress increases. Then, the tensile load becomes maximum at the point B, and thereafter, the constriction occurs in the tensile test piece 1 and the tensile load decreases, leading to fracture (point C in FIG. 10). The strain at point B in FIG. 10 is referred to as uniform elongation, and is considered to be stable uniaxial tensile deformation until uniform elongation is reached. In this region (the range from point 0 (zero) to point B in FIG. The stress-strain curve at uniform strain has been used for plastic working simulation such as finite element method (FEM).

The uniform elongation obtained by the tensile test is 0.20 to 0.3 for general work steel and 0.15 to 0.25 for aluminum alloy. On the other hand, in recent years, ductility of high-strength steel sheets, which have been increasingly applied to frame parts of automobiles, decreases as the material strength increases, and is about 0.14 to 0.17 for 590 MPa grade steel sheets and about 0.07 to 0.1 for 980 MPa grade steel sheets.
However, the strain applied to the metal material in actual press forming exceeds the range of uniform strain obtained in the above-described tensile test. Particularly, in crack prediction in press forming analysis, since a metal material receives a large strain immediately before cracking, the stress-strain relationship (hardening property) in a strain region exceeding uniform elongation has a great influence on the prediction accuracy of crack generation.
In press molding analysis by FEM, a method is generally used in which the stress-strain relationship in a high strain region exceeding uniform elongation is extrapolated by a hardening law (a mathematical model that defines the hardening behavior of a material). However, this is not based on actually measured values, and there is a problem that the relationship between stress and strain can greatly change depending on the type of hardening rule and material constant.

  For this reason, various methods have been proposed in the past as material tests for obtaining a stress-strain relationship in a high strain region exceeding uniform elongation. For example, there are a shear test (Patent Document 1), a hydraulic bulge test (Non-Patent Document 1), and a compression test (Non-Patent Document 2). According to these tests, deformation larger than normal uniaxial tensile deformation can be given to the test piece.

Japanese Patent No. 5910803

Gerhard Gutscher, Hsien-Chih Wu, Gracious Ngaile, Taylan Altan, Determination of flow stress for sheet metal forming using the viscous pressure bulge (VPB) test, Journal of Materials Processing Technology, 146 (2004), 1-7. Kozo Kosaka, Mitsunobu Shiraishi, Shigeji Muraki, Masayasu Tokuoka: Deformation Resistance Measurement Method by Ring Compression Test, Transactions of the Japan Society of Mechanical Engineers (C), Vol. 55, No. 516 (1989), 2213-2220.

  The results obtained by the methods disclosed in the above-mentioned prior art documents are as follows: a stress-strain relationship in a shearing state in Patent Document 1; ), And in Non-Patent Document 2, the stress-strain relationship in a compressed state. Therefore, in order to use the stress-strain relationship obtained by these methods in press-forming analysis by FEM, it is necessary to convert it into a stress-strain relationship in a uniaxial tensile state. However, errors may occur during this conversion, and the stress-strain relationship obtained by the conversion was not sufficiently accurate. Further, the above method requires a special test machine, which is not practical in terms of versatility.

  The present invention has been made to solve such problems, without using a special tester, it is possible to highly accurately estimate the stress-strain relationship in a high strain region beyond the uniform elongation of the metal material. It is an object of the present invention to provide a method for estimating a stress-strain relationship.

(1) The method for estimating a stress-strain relationship according to the present invention is for estimating the relationship between stress and strain of a metal material. A tensile load from the start of action to a strain range exceeding uniform elongation and a tensile load-strain distribution obtaining step of obtaining a strain distribution in the tensile test piece, and the tensile test based on the obtained tensile load and strain distribution. A stress-strain relationship acquisition step of acquiring the relationship between stress and strain up to uniform elongation of the piece, and selecting two types of hardening rules giving the relationship between stress and strain, and material constants of each of the two types of hardening rules, A material constant identification step for identifying based on a stress-strain relationship acquired in the stress-strain relationship acquisition step, and a uniform elongation acquired in the tensile load-strain distribution acquisition step. Estimate the tensile load acting on the tensile test piece using the strain distribution in the exceeded strain range and the equivalent stress determined by the mixing rule obtained by adding the two types of hardening rules using a temporary weighting coefficient. A tensile load estimating step, and a weighting factor for determining a value of the weighting factor of the mixing rule so that the tensile load estimated in the tensile load estimating step matches the tensile load obtained in the tensile load-strain distribution obtaining step. Determination step, wherein the tensile load estimating step specifies a constriction generating portion in which constriction has occurred at an end of the tensile test piece in a direction perpendicular to the tensile direction, and along a tensile normal direction at a predetermined position of the constriction generating portion. The tensile test piece is divided into a plurality of microscopic regions, and each of the fine The strain in the tensile direction and the direction perpendicular to the tensile direction is set in the region, and the tensile direction in each minute region is set using the strain in the tensile direction and the tensile perpendicular direction set in each minute region and the equivalent stress obtained by the mixing rule. Is calculated, based on the strain in the tensile direction and the direction perpendicular to the tension set in each of the micro regions, calculates the plate thickness of each of the micro regions, and calculates the stress in the tensile direction calculated for each of the micro regions. Calculating the tensile load acting on each of the micro regions from the sheet thickness and adding the calculated tensile loads acting on each of the micro regions to act on the tensile test piece in a strain region exceeding the uniform elongation. And estimating a tensile load to be applied.

(2) The method according to (1), wherein the stress in the tensile direction of each of the micro regions in the tensile load estimating step is calculated according to the following procedures (a) to (c). It is.
(A) Calculating the ratio of the strain increment in the tensile direction and the strain perpendicular direction and the ratio of the strain increment in the tensile perpendicular direction and the strain thickness direction, respectively, from the strains in the tensile direction and the tensile perpendicular direction set in each of the micro regions. .
(B) Calculating the stress ratio in the tensile direction and the tensile perpendicular direction in each of the micro regions from the ratio of the calculated two strain increments.
(C) calculating the stress in the tensile direction of each of the minute regions based on the calculated stress ratio, the equivalent strain calculated from the strain set in each of the minute regions, and the equivalent stress determined by the mixing rule. I do.

  According to the present invention, it is possible to accurately estimate the relationship between stress and strain in a high strain region exceeding the uniform elongation of the metal material.

It is a flowchart which shows the flow of a process in the stress-strain relationship estimation method which concerns on embodiment of this invention. FIG. 3 is a diagram illustrating a distribution of strain in a direction perpendicular to the tensile direction when a tensile load is applied to a tensile test piece exceeding uniform elongation in the present embodiment. FIG. 7 is a flowchart showing a flow of a procedure for estimating a tensile load from a strain distribution acquired in a strain region exceeding a uniform elongation of a tensile test piece in the present embodiment. FIG. 4 is a diagram showing (a) a constriction generated in a tensile test piece, (b) a micro area set in the tensile test piece, and (c) a stress and a plate thickness in the micro area in the present embodiment. 5 is a graph showing the results of tensile loads obtained using tensile test pieces and their estimated values in Examples (metallic material: 590 MPa class steel plate). 4 is a graph showing an estimation result of a stress-strain relationship in Examples (metallic material: 590 MPa class steel plate). 4 is a graph showing the results of tensile loads obtained using tensile test pieces and their estimated values in Examples (metallic material: 1180 MPa grade steel plate). 4 is a graph showing an estimation result of a stress-strain relationship in Examples (metallic material: 1180 MPa grade steel plate). It is a figure which shows an example of the shape of the tensile test piece used for a normal tensile test. It is a figure which shows an example of the stress-strain relationship acquired by a normal tensile test.

  The method for estimating a stress-strain relationship according to the embodiment of the present invention estimates a relationship between stress and strain of a metal material. As shown in FIG. -Strain relation acquisition step S3, material constant identification step S5, tensile load estimation step S7, and weight coefficient determination step S9. Hereinafter, each of the above steps will be described.

<Tension load-strain distribution acquisition step>
The tensile load-strain distribution obtaining step S1 is to apply a tensile load to the strip-shaped tensile test piece 1 having the parallel portion 3 parallel to the tensile direction as shown in FIG. This is a step of acquiring a tensile load up to a strain region exceeding the range and a strain distribution of the tensile test piece 1.

  In the present embodiment, the uniform elongation of the tensile test piece 1 is such that when the tensile load applied to the tensile test piece 1 reaches a maximum value, or at the end of the tensile test piece 1 in the direction perpendicular to the tensile direction. Can be time. Then, it is preferable to acquire the tensile load and the strain distribution in a strain region beyond the uniform elongation of the tensile test piece 1 until a break occurs.

  Since the distribution of the tensile load and strain applied to the tensile test piece 1 changes every moment during the tensile deformation, the tensile load-strain distribution acquisition step S1 is performed from the start of the tensile load to beyond the uniform elongation to breakage. In a predetermined time step during tensile deformation, a tensile load and a strain distribution are acquired.

  The strain distribution obtained in the tensile load-strain distribution obtaining step S1 is the distribution of strain in the tensile direction and the direction perpendicular to the tensile direction on the surface of the tensile test piece 1, and may be measured using DIC (digital image correlation method). In the measurement of the strain distribution by the DIC, the surface of the tensile test piece 1 during tensile deformation is imaged at predetermined time intervals, and the strain distribution in the tensile direction and the direction perpendicular to the tensile direction can be obtained from the captured image.

  As the tensile test piece 1 having the parallel portion 3, for example, a standardized test piece such as JIS5 can be used.

<Step of acquiring stress-strain relationship>
The stress-strain relationship obtaining step S3 is a step of obtaining the stress-strain relationship of the tensile test specimen 1 up to uniform elongation based on the tensile load-strain distribution measured in the tensile load-strain distribution obtaining step S1.

<Material constant identification step>
In the material constant identification step S5, two kinds of hardening rules that give a relationship between stress and strain are selected, and the material constant of each of the two hardening rules is determined by the stress up to the uniform elongation obtained in the stress-strain relationship obtaining step S3. The step of identifying based on the strain relationship.

  As the hardening rule, the following linear hardening rule (Equation (1)), n-th power hardening rule (Equation (2)), Ludwik rule (Equation (3)), Swift rule (Equation (4)), and Voce rule ( Equation (5)) is known, and any two of these curing rules may be selected.

In selecting a hardening rule, the following points are considered.
First, a mixing rule in which two types of hardening rules are added using a weight coefficient α as shown in the following equation (6) is considered.

In equation (6), σ _{eq, HR} is the equivalent stress given by the mixing rule, and σ _{eq, A} and σ _{eq, B} are the equivalent stresses represented by the two types of hardening rules, respectively. The weighting coefficient α is an arbitrary constant. When α is 1, σ _{eq, HR} = σ _{eq, A} , and when α is 0, σ _{eq, HR} = σ _{eq, B.}

In the two types of hardening rules selected in the material constant identification step S5, it is desirable that the value of the equivalent stress σ _{eq, HR} greatly changes depending on the value of the weight coefficient α. For this purpose, it is preferable to select two types of hardening rules having greatly different stress behaviors with respect to strain. For example, it is preferable to select the Swift rule (Equation (4)) and the Voce rule (Equation (5)). When the Swift's rule and the Voce's rule are selected, the material constants C, ε ₀ , and n in the above equation (4) and Y, Q, and b in the equation (5) are converted into a material constant identification step. Each is identified in S5.

<Tension load estimation step>
The tensile load estimating step S7 is based on a mixing rule obtained by adding the strain distribution in the strain region exceeding the uniform elongation obtained in the tensile load-strain distribution obtaining step S1 and the two types of hardening rules selected in the material constant identification step S5. This is a step of estimating the tensile load acting on the tensile test specimen 1 in the strain region exceeding the uniform elongation, using the equivalent stress calculated by giving the value of the temporary weight coefficient.

When a uniaxial tensile load is applied to the tensile test piece 1, the tensile test piece 1 in the strain region exceeding the uniform elongation which is the maximum load point (the region of points B to C in FIG. 10) is perpendicular to the tensile direction. Constriction occurs at the end, resulting in uneven deformation in the tensile direction and the direction perpendicular to the tensile direction. FIG. 2 shows an example of the distribution of strain ε _x in the tensile direction at the center in the tensile direction of the constriction generating portion 5 generated in the tensile test piece 1 in the direction perpendicular to the tensile direction. The strain ε _x in the tensile direction becomes the largest at the center in the direction perpendicular to the tensile direction (y = 0 in the graph of FIG. 2), and the end (y = −W / 2) of the width W of the constriction generating portion in the tensile test piece 1. , W / 2).

  Therefore, in the tensile load estimation step S7, the tensile load acting on the tensile test piece 1 is estimated in consideration of the strain distribution in the direction perpendicular to the tensile direction in the constriction generating portion 5. FIG. 3 shows a flow of a specific procedure for estimating the tensile load (S11 to S25).

  Note that, in the present embodiment, an example will be described in which the constriction generating unit 5 evaluates the strain and stress of the tensile test piece 1 having a line-symmetric shape with respect to a straight line in the direction perpendicular to the tension at the most constricted position of the constriction generating unit 5. I do. The strain and stress applied to the cross section of the necking portion 5 are determined in the tensile direction (x direction) and the direction perpendicular to the tensile direction (y direction), and the strain in the thickness direction (z direction) is determined from the constant volume condition. In the estimation of the tensile load, the shear component (xy component) is not considered.

≫Division of minute area≫
First, as shown in FIG. 4, the constriction generating part 5 in which constriction has occurred at the end of the tensile test piece 1 in the direction perpendicular to the tension is specified, and along the direction perpendicular to the tension at the most restrictive position of the constriction generating part 5 The tensile test piece 1 is divided into a plurality of minute regions 11 (S11).

Although the number of divisions of the minute region 11 depends on the measurement resolution of the strain distribution in the tensile load-strain distribution acquisition step S1, it is desirable to set the division width dy of the minute region 11 (see FIG. 4B) small.
Note that the position at which the tensile test piece 1 is divided into the minute regions 11 in the direction perpendicular to the tension is not limited to the most constricted position in the constriction generating part 5, and may be a predetermined position in the tensile direction if the constriction generating part 5. .

ひ ず み Setting of strain for each minute area≫
Next, based on the strain distribution at the predetermined time step acquired in the tensile load-strain distribution acquiring step S1, a strain ε _{x in the} tensile direction and a strain ε _{y in the} perpendicular direction to the tensile direction are set in each of the micro regions 11 (S13). .
Strain epsilon _x and epsilon _y is set to the minute region 11 and total strain (logarithmic strain), as shown in the following equation (7), the sum of the elastic strain epsilon _i ^e and plastic strain epsilon _i ^p.

≫Calculation of strain increment ratio≫
Subsequently, based on the strain ε _x in the tensile direction and the strain ε _{y in the} perpendicular direction to the tension set in each of the micro regions 11, the ratio of the increment in the strain in the tensile direction and the strain in the perpendicular direction to the strain and the strain in the perpendicular direction and the thickness direction respectively The ratio of the increment is calculated (S15).
Regarding the ratio of the strain increment in the tensile direction and the strain perpendicular direction, first, as shown in the following equation (8), the strain increment dε _i (i = x, Find y).

  In the equation (8), n is a time step for estimating a tensile load, n + c and n−c are time steps before and after, and c is a parameter (an integer of 1 or more) for setting an interval between time steps for obtaining a strain increment.

  When the ratio of the strain increment in the tensile direction and the strain increment in the perpendicular direction to the tensile direction is a, it can be expressed as the following equation (9).

_{Dε i (i = x, y} ) in equation (9) is the total incremental strain, because if you are large deformation negligible component of elastic strain becomes relatively small, ε _i ≒ ε _i ^p becomes , Can be approximated as in the following equation (10).

Here, regarding the plastic strain increments dε _x ^p and dε _y ^p approximated in the equation (10), the relevant flow law (Reference: Sojin Yoshida, Basics of Elasto-Plastic Deformation, pp. 164-165, Kyoritsu Shuppan, 1997 ).
The related flow law is a relational expression expressing the relationship between the plastic strain increment and the stress state. In the elasto-plastic finite element analysis or the like, the stress-strain calculation is performed according to this assumption.
Related If flow law assuming a tensile direction (x direction) and the tensile direction perpendicular (y direction) of the respective plastic strain increment d? _X ^p and d? _Y ^p can be expressed as follows.

Here, f is an anisotropic yield function, which is a function including stresses σ _x and σ _{y in the x} and y directions and an anisotropic parameter. Dλ is an equivalent plastic strain increment.

  In the present embodiment, in order to estimate the cross-sectional change of the tensile test piece 1 during the tensile deformation, in particular, the change in the sheet width and the sheet thickness, the anisotropy parameter is determined by the r value (the increase in the sheet thickness direction strain and the sheet width). Directional strain increment). Therefore, it is desirable that the anisotropy parameter included in the anisotropic yield function f be identified using the r value in the tensile direction.

R value of the tensile direction, as shown in the following equation (13), expressed as the ratio of the tensile direction perpendicular (y-direction) and thickness direction (z-direction) each strain increment, the pulling direction of the strain increment d? _X It can be determined using the strain increment dε _{y in the} direction perpendicular to the tensile direction.

  Since the r value changes during tensile deformation, the identification of the anisotropic parameter in the present embodiment uses the r value calculated from the strain distribution obtained at each time step until uniform elongation is reached. In the strain range exceeding the uniform elongation, the r value calculated from the strain distribution at the uniform elongation shall be used.

As the anisotropic yield function f, Hill'48 anisotropic yield function can be used.
Hill'48's anisotropic yield function f is given by the following equation (14) using the r value in the tensile direction.

Here, σ _eq is an equivalent stress obtained from the hardening rule shown in the equations (1) to (5).
Accordingly, the strain increments in the tensile direction (x direction) and the direction perpendicular to the tensile direction (y direction) can be expressed by the following equations (15) and (16), respectively.

  Therefore, the ratio a of the strain increment in the tensile direction and the strain perpendicular direction is expressed by the following equation (17).

  Although the above description is based on the use of the Hill'48 anisotropic yield function as the anisotropic yield function, other anisotropic yield functions such as Yld2000-2d yield function and Yoshida yield function In the present invention, any anisotropic yield function considering the r value may be used.

≫Calculation of stress ratio≫
The stress ratio between the stress σ _x in the tensile direction and the stress σ _{y in} the direction perpendicular to the tensile direction in each minute region 11 is calculated from the calculated ratio a of the increment of strain (S17). Specifically, it is calculated as follows.
First, the stress ratio b is expressed by the following equation (18).

  When the Hill'48 yield function is used as the anisotropic yield function f, the following equation (19) is obtained from the equations (17) and (18).

  Therefore, the stress ratio b is given by the following equation (20).

  Then, from the measured values of the strains, the ratio a of the strain increment in each of the tensile direction and the tensile perpendicular direction and the r value which is the ratio of the strain increment in each of the tensile perpendicular direction and the plate thickness direction are calculated. ) To calculate the stress ratio b.

≫Calculation of tensile stress≪
Subsequently, a stress σ _x in the tensile direction in each of the micro regions 11 is calculated based on the stress ratio b calculated for each of the micro regions 11 and the equivalent stress σ _{eq, HR} determined by the mixing rule (S19).

As described above, in the calculation of the stress ratio b of each minute region 11, the strains ε _x and ε _y in the tensile direction and the direction perpendicular to the tension set in each minute region 11 are used. Therefore, in the present embodiment, the stress σ _{eq, HR} in the tensile direction and the direction perpendicular to the tension set in each micro region 11 and the equivalent stress σ _{eq, HR} determined by the mixing rule are used to determine the stress σ in the tensile direction of each micro region 11. _x is calculated.

The equivalent stress σ _{eq, HR} calculated by the mixing rule is, as shown in the above equation (6), the equivalent stress σ _eq, given by each of the two types of hardening rules whose material constants were identified in the material constant identification step S5 _{. It} is assumed that _A and σ _{eq, B} are added using the weight coefficient α.

The equivalent stresses σ _{eq, A} and σ _{eq, B} given by the two types of hardening rules in equation (6) are all functions of the equivalent plastic strain ε _eq . Then, the equivalent plastic strain epsilon _eq is tensile with plastic strain epsilon _x ^p and epsilon _y ^p direction (x direction) and the tensile direction perpendicular (y-direction), expressed by the following equation (21).

The equivalent stresses σ _{eq, A} and σ _{eq, B} are obtained by substituting the equivalent strain ε _eq obtained from equation (21) into each hardening rule. Then, by giving the value of the weighting coefficient α, the equivalent stress σ _{eq, HR} of the mixing rule is obtained by the equation (6).

On the other hand, the equivalent stress σ _eq can be obtained by using the yield function (for example, equation (14)). Here, the equivalent stress obtained from the yield function is σ _{eq, YF} . Then, by substituting the relationship of σ _y = bσ _x (see equation (18)) into the equation that gives the yield function, σ _{eq, YF} becomes the function of the stress σ _{x in the} tensile direction and the equivalent stress σ _{eq, YF} Become. Since the equivalent stress σ _{eq, HR} determined from the mixing rule and the equivalent stress σ _{eq, YF} determined from the yield function are equal, the stress σ _x in the tensile direction is calculated so that σ _{eq, HR} = σ _{eq, YF} I do.

≫Calculation of plate thickness≫
As shown in FIG. 2 described above, the tensile test piece 1 differs in the amount of deformation in the direction perpendicular to the tensile direction in the strain region exceeding the uniform elongation, so it is necessary to consider the plate thickness t of each minute region 11. The thickness t is obtained from the initial thickness t ₀ and the strain ε _{z in} the thickness direction. The strain ε _{z in} the thickness direction is a strain ε _{x in} two directions (tensile direction and perpendicular direction to the tensile direction) in a plane under a constant volume condition. and it can be calculated from ε _y. Therefore, as shown in the following equation (22), the plate thickness t of each minute area 11 is calculated based on the strain set in each minute area 11 in the tensile direction and the direction perpendicular to the tensile direction (S21).

≫Calculation of micro area tensile load 領域
Using the stress σ _x in the tensile direction and the plate thickness t calculated for each minute region 11, a tensile load acting on each minute region 11 is obtained as shown in the following equation (23) (S 23).

  In Expression (23), ΔT is a minute region tensile load, and dy is a division width of the minute region (see FIG. 4B).

≪Estimation of tensile load≫
As shown in the following equation (24), the tensile load T acting on the entire cross section of the tensile test piece 1 in the direction perpendicular to the tensile direction is calculated by adding the microscopic area tensile loads ΔT obtained for the respective microscopic areas 11 (S25).

  Thus, in the tensile load estimating step S7, the tensile load T can be estimated by the procedures of S11 to S25.

<Weight coefficient determination step>
The weight coefficient determining step S9 determines the value of the weight coefficient α of the mixing rule so that the tensile load estimated in the tensile load estimating step S7 and the tensile load obtained in the tensile load-strain distribution obtaining step S1 match. Step.

  As a specific procedure for determining the value of the weight coefficient α, in a tensile load estimation step S7, a temporary weight coefficient α is given to estimate the tensile load, and the value of the weight coefficient α is changed based on the estimated tensile load. Then, S19 to S25 shown in FIG. 3 are repeatedly executed until the tensile load estimated in the tensile load estimation step S7 matches the tensile load obtained in the tensile load-strain distribution obtaining step S1. Thereby, the value of the weighting coefficient α of the mixing rule shown in Expression (6) is determined.

  As described above, according to the stress-strain relationship estimation method according to the embodiment of the present invention, it is possible to accurately estimate the relationship between stress and strain in a high strain region exceeding uniform elongation that cannot be obtained by a conventional tensile test. . Furthermore, by applying the stress-strain relationship estimation method according to the present invention to the press forming analysis of a thin metal plate, it is possible to accurately predict a forming defect such as a crack, a wrinkle, or a springback caused by the press forming. Then, high-quality press-formed products can be manufactured by die design and component design based on the prediction results of the press-forming analysis.

  Further, according to the present invention, since it can be realized with a general uniaxial tensile tester without using a special tester, it is excellent in practicality in terms of versatility.

  In the above description, the anisotropic yield function f and the stress ratio b in the tensile load estimating step S7 are calculated using the value of the strain distribution obtained in the tensile load-strain distribution obtaining step S1 (expression (formula ( Although 13)) was used, the present invention is not limited to this. For example, an r value obtained in a tensile test performed separately from the tensile load-strain distribution obtaining step S1 may be used.

  Verification for confirming the operation and effect of the stress-strain relationship estimation method according to the present invention has been performed, and will be described below.

  In Example 1, first, a stress-strain relationship of a 590 MPa class steel sheet having a thickness of 1.2 mm as a metal material was estimated.

  First, a uniaxial tensile test was performed using a tensile test piece 1 (JIS No. 5) having the shape shown in FIG. 9, and a predetermined time from the start of the application of a tensile load to the time when the tensile test piece 1 broke beyond uniform elongation. In the step, the tensile load and the strain distribution on the surface of the tensile test piece 1 were obtained. Here, for the tensile load, a value measured by a load cell was obtained, and for the strain distribution, the strain in the tensile direction and the direction perpendicular to the tensile direction obtained by DIC (image correlation method) was obtained.

  Next, a stress-strain relationship up to uniform elongation was obtained from the obtained tensile load and strain distribution. Then, the Swift rule and the Voce rule are selected as two types of hardening rules, and based on the stress-strain relationship up to uniform elongation, the material constants of the Swift rule and the Voce rule (see equations (4) and (5)) Was identified. Table 1 shows the identified material constants.

The equivalent stress σ _eq in the strain region exceeding the uniform elongation is represented by a mixed law of the equivalent stress σ _{eq, Swift} of _{the Swift} rule and the equivalent stress σ _{eq, Voce} of the Voce rule, as shown in the following equation (25).

  In the first embodiment, 11 time steps are provided in the process from the start of the application of the tensile load to the maximum strain in the central portion in the direction perpendicular to the tensile direction at the position where the most constriction of the constriction generating portion 5 occurs reaches 0.53. According to procedures S11 to S25 shown in FIG. 3, the tensile load acting on the tensile test piece 1 at each time step was estimated.

FIG. 5 shows an example of the tensile load obtained by the uniaxial tensile test and the tensile load estimated by using the strain distribution obtained by the uniaxial tensile test.
The horizontal axis is the maximum strain at the central portion in the direction perpendicular to the tensile direction, the vertical axis is the value of the tensile load at each maximum strain, the solid line is the tensile load (measured value) obtained in the uniaxial tensile test, and the plot is Swift This is a tensile load calculated by assuming that the value of the weight coefficient of the rule, the Voce rule, and the mixing rule (Equation (25)) is α = 0.85.

  The tensile load estimated with the weighting factor α = 1 in the Swift rule, that is, the mixing rule, is larger than the measured value of the tensile load, and the Voce rule, that is, the tensile load estimated with the weighting factor α = 0 in the mixing rule, is measured. It became smaller than the value.

  On the other hand, the tensile load estimated by the mixing rule giving the weighting coefficient α = 0.85 resulted in a result that coincided with the measured value of the tensile load regardless of the strain value.

  From this result, the weighting factor of the mixing rule was determined to be α = 0.85, and as shown in FIG. 6, it was shown that the stress-strain relationship in a strain region exceeding the uniform elongation could be accurately estimated by the mixing rule.

  Subsequently, a stress-strain relationship was also estimated for a 1180 MPa class steel sheet having a thickness of 1.2 mm as a metal material in the same manner as described above.

  First, a uniaxial tensile test was performed using the tensile test piece 1 of JIS No. 5 having the shape shown in FIG. 7, and a predetermined time step from the start of the application of the tensile load to the breakage of the tensile test piece 1 beyond the uniform elongation. In, the tensile load and strain distribution on the surface of the tensile test piece 1 were obtained. The acquisition of the tensile load and the strain distribution was performed in the same manner as in the case of the above-mentioned 590 MPa class steel sheet.

  Then, a stress-strain relationship up to uniform elongation is obtained from the obtained tensile load and strain distribution, and based on the stress-strain relationship, each of the Swift law (Equation (4)) and the Voce law (Equation (5)) The material constant of was identified. Table 2 shows the values of the identified material constants.

The equivalent stress σ _{eq in} the strain region exceeding the uniform elongation is represented by a mixed rule of the equivalent stress σ _{eq, Swift} of _{the Swift} rule and the equivalent stress σ _{eq, Voce} of the Voce rule, as shown in the above equation (25).

  Subsequently, in the second embodiment, six time steps are performed in the process from the start of the application of the tensile load to the maximum strain in the central portion in the direction perpendicular to the tension at the position where the most constriction of the constriction generating portion 5 occurs reaches 0.25. The tensile load acting on the tensile test piece 1 at each time step was estimated according to the steps S11 to S25 shown in FIG.

FIG. 7 shows an example of the tensile load obtained by the tensile test and the tensile load estimated using the value of the strain distribution obtained by the tensile test.
The horizontal axis is the maximum strain at the central part in the direction perpendicular to the tensile direction, the vertical axis is the tensile load at each maximum strain, the solid line is the tensile load (measured value) obtained in the tensile test, and the plots are Swift's law, Voce's law , And the tensile load estimated by setting the value of the weighting coefficient of the mixing rule (Equation (6)) to α = 0.8.

  The tensile load estimated by the Swift rule, that is, the weighting factor α = 1 in the mixing rule, becomes larger than the measured value of the tensile load, and the Voce rule, that is, the tensile load estimated by the weighting factor α = 0 in the mixing rule, is a tensile load. It became smaller than the measured value of the load.

  On the other hand, the tensile load estimated by the mixing rule giving the weight coefficient α = 0.8 resulted in a result that was consistent with the measured value of the tensile load regardless of the strain.

  From this result, the weighting factor of the mixing rule was determined to be α = 0.8, and as shown in FIG. 8, it was shown that the stress-strain relationship in the strain region beyond the uniform elongation could be estimated by the mixing rule.

DESCRIPTION OF SYMBOLS 1 Tensile test piece 3 Parallel part 5 Constriction generation part 11 Micro area

Claims (2)

A stress-strain relationship estimation method for estimating the relationship between stress and strain of a metal material,
A tensile load is applied to a tensile test piece having a parallel portion to obtain a tensile load from the start of the application of the tensile load to a strain region beyond uniform elongation and a strain distribution in the tensile test piece. Steps and
Based on the obtained tensile load and strain distribution, a stress-strain relationship obtaining step of obtaining a relationship between stress and strain up to uniform elongation of the tensile test piece,
A material constant for selecting two types of hardening rules giving a relationship between stress and strain, and identifying a material constant of each of the two types of hardening rules based on the relationship between stress and strain obtained in the stress-strain relationship obtaining step. An identification step;
Using the tensile load-strain distribution in the strain region exceeding the uniform elongation obtained in the strain distribution obtaining step and the equivalent stress determined by a mixing rule obtained by adding the two types of hardening rules using a temporary weighting coefficient. A tensile load estimating step of estimating a tensile load acting on the tensile test piece,
A weighting factor determining step of determining a value of the weighting factor of the mixing rule so that the tensile load estimated in the tensile load estimating step matches the tensile load obtained in the tensile load-strain distribution obtaining step. ,
The tensile load estimating step,
Identify the constriction occurrence part where constriction has occurred at the end in the direction perpendicular to the tensile direction of the tensile test piece,
The tensile test piece is divided into a plurality of minute regions along a direction perpendicular to the tension at a predetermined position of the constriction generating portion,
Based on the strain distribution in the strain region beyond the obtained uniform elongation, set the strain in the tensile direction and the tensile perpendicular direction to each of the micro regions,
Calculate the stress in the tensile direction of each micro-region using the strain in the tensile direction and the direction perpendicular to the tension set in each of the micro-regions and the equivalent stress determined by the mixing rule,
Based on the strain in the tensile direction and the direction perpendicular to the tension set in each of the micro regions, calculate the thickness of each of the micro regions,
Calculate the tensile load acting on each of the minute regions from the stress in the tensile direction and the plate thickness calculated for each of the minute regions,
A method for estimating a stress-strain relationship, comprising: estimating a tensile load acting on the tensile test piece in a strain region exceeding uniform elongation by adding the calculated tensile loads acting on each of the micro regions. The stress-strain relationship estimating method according to claim 1, wherein the stress in the tensile direction of each of the micro regions in the tensile load estimating step is calculated according to the following procedures (a) to (c).
(A) Calculating the ratio of the strain increment in the tensile direction and the strain perpendicular direction and the ratio of the strain increment in the tensile perpendicular direction and the strain thickness direction, respectively, from the strains in the tensile direction and the tensile perpendicular direction set in each of the micro regions. .
(B) Calculating the stress ratio in the tensile direction and the tensile perpendicular direction in each of the micro regions from the ratio of the calculated two strain increments.
(C) calculating the stress in the tensile direction of each of the minute regions based on the calculated stress ratio, the equivalent strain calculated from the strain set in each of the minute regions, and the equivalent stress determined by the mixing rule. I do.