Calculation method of residual stress

Abstract

The residual stress calculation method of the present invention calculates the residual stress of a metal plate subjected to plastic deformation, and includes: a strain history acquisition step (S1), in which the strain of a deformed portion of the metal plate during a deformation process in which the metal plate is plastically deformed is measured to obtain a strain history; a successive stress updating step (S3), in which the stress increment of the deformed portion during the deformation process is calculated according to a material constitutive model using an acquired strain increment calculated based on the acquired strain history and an assumed strain increment calculated by assuming a deformation state of the deformed portion using strains other than the strains in the acquired strain history, and the calculated stress increment is used to sequentially update the stress of the deformed portion from the start to the end of the deformation; and a residual stress determination step (S5), in which the stress at the end of the deformation process, among the stresses sequentially updated in the successive stress updating step (S3), is determined as the residual stress of the deformed portion.

Description

Technical Field

[0001] The present invention relates to a method for calculating residual stress, and in particular to a method for calculating residual stress generated in a metal sheet subjected to plastic deformation. Background Art

[0002] It is known that residual stress generated in press-formed parts (e.g., automotive parts) affects the fatigue life and delayed fracture properties of the parts. Therefore, understanding the residual stress generated in press-formed parts after forming is an important technology for ensuring the fatigue life of products using press-formed parts.

[0003] Conventionally, residual stress generated in press-formed parts has been measured using X-rays or ultrasonic waves, or predicted using finite element analysis.

[0004] As a technique for measuring residual stress using X-rays, for example, Patent Document 1 discloses a technique that irradiates a sample with X-rays, detects diffracted X-rays emitted from the sample, and non-destructively measures the stress within the sample based on the information from the diffracted X-rays. Furthermore, as a technique for measuring residual stress using ultrasound, for example, Patent Document 2 discloses a technique that generates ultrasound waves in a plastically deformed object to be inspected (e.g., a metal plate) and non-destructively measures the residual stress based on the measured sound velocity information from the ultrasound waves.

[0005] Furthermore, the prediction of residual stress based on finite element analysis can be performed using finite element analysis software that is generally widely used. Furthermore, in finite element analysis, the precision of material constitutive models is continuously being improved. For example, the YU model disclosed in Non-Patent Document 1 contributes to the precision of springback analysis, which is important for the prediction of residual stress.

[0006] Prior art literature

[0007] Patent Literature

[0008] Patent Document 1: Japanese Patent Application Laid-Open No. 2002-333409

[0009] Patent Document 2: Japanese Patent Application Laid-Open No. 2011-196953

[0010] Non-patent literature

[0011] Non-patent literature 1F. Yoshida and T. Uemori, International Journal of Mechanical Sciences, 45 (2003), 1687-1702. Summary of the Invention

[0012] Problems to be solved by the invention

[0013] However, the X-ray residual stress measurement disclosed in Patent Document 1 and the ultrasonic residual stress measurement disclosed in Patent Document 2 assume that the sample (metal plate, etc.) is uniform within the region where the X-rays are incident or the ultrasonic waves are generated. Accurate residual stress measurement is difficult for metal plates containing two or more phases (e.g., DP (Dual Phase) steel plates).

[0014] Furthermore, in methods for predicting residual stress in metal sheets using finite element analysis, the input values ​​(shape, material properties, deformation behavior, boundary conditions, etc.) provided to the finite element analysis software significantly influence the predicted residual stress results. Therefore, to accurately predict residual stress using finite element analysis, it is necessary to accurately account for not only the material properties of the metal sheet, but also the deformation properties of the tool that applies plastic deformation, the contact conditions between the metal sheet and the tool, and boundary conditions such as sliding properties. Furthermore, in cases of shear deformation, which is accompanied by the destruction of the metal sheet, the conditions for the destruction must be incorporated into the finite element analysis model, making it extremely difficult to accurately predict residual stress.

[0015] The present invention has been made in view of the above-mentioned problems, and an object of the present invention is to provide a residual stress calculation method capable of accurately and easily calculating the residual stress of a metal plate subjected to plastic deformation.

[0016] Means for solving problems

[0017] The residual stress calculation method of the present invention calculates the residual stress of a metal plate subjected to plastic deformation, wherein the residual stress calculation method includes: a strain history acquisition step, in which the strain of a deformed portion of the metal plate during a deformation process in which the metal plate is plastically deformed is measured, and a strain history of the measured strain is acquired; and a sequential stress updating process, in which an acquired strain increment calculated based on the strain history and an assumed strain increment calculated by assuming a deformation state of the deformed portion using strains other than the strains acquired from the strain history are used. strain increment), calculating the stress increment of the deformed portion during the deformation process according to a material constitutive model, and successively updating the stress of the deformed portion from the beginning to the end of the deformation using the calculated stress increment; and a residual stress determining step, in which the stress of the deformed portion at the end of the deformation process, among the stresses successively updated in the successive stress updating step, is determined as the residual stress of the deformed portion.

[0018] The strain history acquisition step may measure the strain history of the strain in two directions in the plane and the shear stress in the plane at the deformed portion by a digital image correlation method to acquire these strain histories.

[0019] The successive stress updating step may assume a deformation state of the deformation portion according to a deformation process of the deformation portion, and calculate the assumed strain increment based on plasticity theory under the assumed deformation state.

[0020] The successive stress updating step may assume a deformation state of the deformed portion through finite element analysis of the deformation process of the metal plate, and calculate the assumed strain increment based on the assumed deformation state.

[0021] Effects of the Invention

[0022] According to the residual stress calculation method of the present invention, even for a metal plate with non-uniform composition or a metal plate subjected to deformation accompanied by fracture such as cracking or shearing, which is difficult to predict in finite element analysis, the residual stress generated in the metal plate subjected to plastic deformation can be accurately and easily calculated. BRIEF DESCRIPTION OF THE DRAWINGS

[0023] Figure 1 This is a flowchart showing the flow of processing in the residual stress calculation method according to the embodiment of the present invention.

[0024] Figure 2 It is a diagram illustrating a roller bending test (roller bending test) for plastically deforming a metal plate in Examples.

[0025] Figure 3 This is a diagram showing the positions of evaluation points for calculating residual stress by obtaining the strain history of the end surface at the deformed portion of the metal plate in the Examples.

[0026] Figure 4 This is a graph showing the relationship between the strain and the calculated stress during deformation and the results of the residual stress at the end of deformation in Examples. DETAILED DESCRIPTION

[0027] The residual stress calculation method of the embodiment of the present invention is a method for calculating the residual stress of a metal plate subjected to plastic deformation, such as Figure 1 As shown in FIG, the process includes a strain history acquisition step S1, a successive stress update step S3, and a residual stress determination step S5. Figure 1 Each of these steps will be described.

[0028] <Strain History Acquisition Process>

[0029] The strain history acquisition step S1 is a step of measuring the strain of a deformed portion of a metal plate during a deformation process in which the metal plate is plastically deformed, and acquiring a strain history of the measured strain.

[0030] Here, the deformed portion of the metal plate refers to the portion that has undergone plastic deformation during the deformation process of the metal plate. Furthermore, in this embodiment, two cameras are positioned at positions capable of capturing images of the surface of the deformed portion of the metal plate, and digital image correlation (DIC) is used to obtain a strain history of the surface of the deformed portion during the deformation process.

[0031] To acquire strain histories using DIC, the surface of the deformed portion of the metal plate is imaged at predetermined intervals during the deformation process. Image analysis is performed on the images captured at each time step to measure the in-plane strain in both directions and the in-plane shear strain at predetermined locations on the surface of the deformed portion. This allows for the acquisition of strain histories for both in-plane strain in both directions and the in-plane shear strain from the start to the end of the deformation process.

[0032] It should be noted that the acquisition of strain history in the strain history acquisition step is not limited to DIC. A strain gauge may be attached to the surface of the deformed portion of the metal plate to acquire the strain history of the surface of the deformed portion during the deformation process.

[0033] <Sequential Stress Update Process>

[0034] The sequential stress updating step S3 is a step that uses the acquired strain increments calculated from the strain history acquired in the strain history acquisition step S1 and the assumed strain increments calculated based on strains other than those acquired in the strain history and assuming the deformation state of the deformed portion to calculate the stress increments at the deformed portion during the deformation process according to the material constitutive model. The calculated stress increments are then used to sequentially update the stress at the deformed portion from the start to the end of deformation. The specific processing in the sequential stress updating step S3 is described below.

[0035] Calculation of strain increments

[0036] First, the strain increment is calculated based on the strain history acquired in the strain history acquisition step S1 ( S3 a ).

[0037] The acquired strain increments are, for example, strain increments of the strains in two directions in the plane and the shear strain in the plane when the strain history is acquired by DIC in the strain history acquisition step S1 .

[0038] Then, the strain increment is calculated in each time step of the deformation process. The strain increment in each time step can be calculated based on the strains in the time step and the previous and next time steps, for example.

[0039] Calculation of Assumed Strain Increment

[0040] Next, the assumed strain increment is calculated (S3b). The assumed strain increment is the strain increment in addition to the strain for which the strain history was obtained in the strain history obtaining step. Furthermore, the deformation state of the deformed portion is assumed based on the deformation process of the deformed portion, and the strain in addition to the strain for which the strain history was obtained is calculated based on the theory of plasticity under the assumed deformation state.

[0041] As described above, when the strain history of the surface of the deformed portion of the metal plate is obtained by DIC in the strain history acquisition step S1, the strain ε in each of the two in-plane directions (x direction and y direction) of the metal plate surface is measured at each time step during the deformation process. x and ε y , and the in-plane (xy plane) shear strain ε xy However, at the deformed part of the metal plate, not only in-plane strain is generated, but also six components of strain (ε x , ε y , ε z , ε xy , ε yz , ε zx ).

[0042] Generally, the surface of a metal plate during deformation becomes a free surface, so no stress is generated in the direction perpendicular to the metal plate surface. In other words, the deformation state of the deformed portion of the metal plate can be assumed to be a plane stress state.

[0043] Then, based on the plasticity theory under the assumed deformation state, the strain (ε x , ε y and ε xy ) and the unknown strains including the out-of-plane direction (ε z , ε yz , ε zx ) gives the formula for the stress increment in the out-of-plane direction.

[0044] Here, if the deformation state of the deformed part is assumed to be a plane stress state, the stress increment in the out-of-plane direction is 0. Therefore, the strain in the out-of-plane direction (ε) can be uniquely calculated using the strain and stress increment formula based on the plasticity theory. z ).

[0045] That is, the deformation state of the deformed portion of the metal plate is assumed based on the deformation process of the metal plate, and strains other than the strains whose strain history is acquired in the strain history acquisition step S1 can be obtained based on the plasticity theory under the assumed deformation state.

[0046] In this way, strains other than those for which strain history was obtained are calculated at each time step during the deformation process. Then, similar to the strain increments described above, an assumed strain increment is calculated based on the strains calculated at each time step during the deformation process. The assumed strain increment at each time step can be calculated, for example, based on the strains calculated at that time step and the previous time step.

[0047] Note that the calculation of the assumed strain increment ( S3 b ) is not limited to the calculation based on the strain obtained from the assumed deformation state as described above, and also includes the case where the value of the assumed strain increment is given based on other assumed deformation states.

[0048] Stress Increment Calculation

[0049] Next, the obtained strain increment and the assumed strain increment are used to calculate the stress increment (S3c) at the deformed portion during the deformation process. The stress increment can be calculated using a material constitutive model based on elasto-plastic mechanics. The strain increment (obtained strain increment and assumed strain increment) and the stress increment are expressed by the relationship shown in Equation (1).

[0050] [Mathematical formula 1]

[0051]

[0052] Here, stress increment tensor

[0053] C ep : elasto-plastic coefficient tensor

[0054] D: strain increment tensor

[0055] The elastic-plastic coefficient tensor C in formula (1) ep It can be given by formula (2).

[0056] [Mathematical formula 2]

[0057]

[0058] Here, C e : elastic coefficient tensor

[0059] f: yield function

[0060] r: plastic flow direction tensor

[0061] q: internal variable tensor (equivalent plastic strain or back stress tensor, etc.)

[0062] h: function representing the increment of the internal variable tensor

[0063] Plastic multiplier

[0064] In this embodiment, as an example of a material constitutive model, the stress increment is calculated from the strain increment based on the material constitutive model (YU model) disclosed in Non-Patent Document 1, which can reproduce the Bauschinger effect with high accuracy. The Y-U model can be classified as a two-surface model in which the yield surface moves within the bounding surface. The progression of the bounding surface (center β, radius R) and the yield surface (center α, radius Y) is defined by the following equation (3) based on the strain increment.

[0065] [Mathematical formula 3]

[0066]

[0067] Here, Y, α0, C, b, m, and Rsat are material constants.

[0068] At this time, equation (2) is expressed by equation (4).

[0069] [Formula 4]

[0070]

[0071] In this way, if the strain increment is clear, the stress increment can be obtained according to the material constitutive model. It should be noted that in the Y-U model, the stress-strain relationship is defined by the velocity system. Therefore, in the case of non-linear deformation, if the strain increment is not sufficiently reduced, the stress increment will produce errors. Therefore, the strain increment is preferably 10 -6 the following.

[0072] In addition, the material constitutive model is not limited to the above-mentioned YU model, and the elastic-plastic coefficient tensor can be calculated according to any material constitutive model. For example, when a material constitutive model assuming isotropic hardening is used instead of the YU model, the elastic-plastic coefficient tensor C ep It is expressed by formula (5).

[0073] [Formula 5]

[0074]

[0075] Here, H is the equivalent stress in the uniaxial tensile test. and equivalent plastic strain The function of the relationship

[0076] In addition, in the case of giving the elastic-plastic coefficient tensor C ep As the yield function f, not only the isotropic von Mises yield function but also any yield function such as Hill'48 and Yld2000-2d that can express the anisotropy of the material (metal plate) with high accuracy can be used.

[0077] Stress Update

[0078] After calculating the stress increment for each time step during the deformation process (S3c), the stress of the deformed portion in each time step is successively updated (S3d). It is then determined whether the deformation of the deformed portion has been completed, that is, whether there is a next time step before the deformation of the deformed portion is completed (S3e). If it is determined that the deformation has not been completed and there is a next time step, the assumption of the deformation state (S3a), calculation of the strain increment (S3b), calculation of the stress increment (S3c), and successive updates of the stress (S3d) are repeated until it is determined that there is no next time step.

[0079] <Residual Stress Determination Process>

[0080] The residual stress determination step S5 is a step of obtaining the stress at the end of the deformation process among the stresses sequentially updated in the sequential stress updating step S3 as the residual stress of the deformed portion.

[0081] As described above, according to the residual stress calculation method of the present embodiment, the residual stress of the plastically deformed metal plate can be accurately calculated by obtaining the strain history of the deformed portion during the deformation process of the metal plate.

[0082] Moreover, the residual stress calculation method of this embodiment calculates the residual stress by obtaining the strain history of the surface of the metal plate. Therefore, even for an inhomogeneous metal plate having two or more phases, which is a problem in the measurement of residual stress using X-rays or ultrasound as in the prior art, the residual stress can be accurately calculated.

[0083] Furthermore, as described above, in finite element analysis, in order to predict residual stress with high accuracy, a large amount of calculation time is required, or analysis is difficult in the case of fracture accompanied by cracks or shearing, but in the residual stress calculation method of this embodiment, the residual stress can be easily calculated by obtaining the strain history of the metal plate that is actually subjected to plastic deformation during the deformation process.

[0084] In particular, since plastically deformed metal sheets often begin to break at their edge faces, accurately determining the residual stress at these edges is crucial for understanding fatigue life and delayed fracture characteristics. The method of the present invention makes it possible to easily measure the strain history of the edge faces during the plastic deformation process, enabling accurate calculation of the residual stress at these edges.

[0085] While the above description assumes the deformation state of a metal plate based on the deformation process of a deformed portion, the present invention also allows for finite element analysis of the metal plate's plastic deformation process to be performed, and the deformation state of the deformed portion (e.g., strain ratio) to be estimated based on the results. In this case, the entire metal plate, including the deformed portion, need not be analyzed for finite element analysis; only the deformed portion and its vicinity, where residual stress is to be calculated, can be modeled and analyzed.

[0086] Therefore, according to the present invention, since it is not necessary to perform finite element analysis of the entire metal plate including the deformed portion, the residual stress of the deformed portion can be calculated in a shorter time than when the residual stress is predicted by finite element analysis of the entire metal plate.

[0087] In particular, finite element analysis using solid elements that can calculate stress in the thickness direction with high accuracy is rarely used in press forming analysis of general stamped parts because the calculation time is greatly increased. However, if a part of the metal plate including the deformed part is taken as the analysis object, the deformation state of the deformed part can be predicted in a short time and with high accuracy even if solid elements are used. Therefore, in the present invention, by assuming the deformation state predicted by the finite element analysis based on the solid element and combining it with the acquisition of the strain history during the deformation process, it is possible to calculate the residual stress with higher accuracy.

[0088] It should be noted that in the successive stress updating step following the strain history acquisition step, in order to calculate the strain increment and stress increment using the acquired strain history, as described above, the strain increment value is preferably small (10 -6Therefore, in the strain history acquisition step, the shorter the time interval for acquiring the strain history, the better.

[0089] When using a standard camera in DIC to image a deformed area and acquire strain history, the imaging interval can be approximately one second. In this case, since strain values ​​measured at consecutive time steps can be interpolated and calculated, strain values ​​between consecutive time steps can be obtained, and thus strain history can be acquired at predetermined time intervals.

[0090] Furthermore, the strain history acquired in the strain history acquisition step can be considered to include measurement noise. Therefore, if the small strain increments (acquired strain increments) calculated from the strain history are used to calculate the stress increment in the successive stress update step, the strain history measurement noise significantly impacts the stress increment, potentially reducing the accuracy of the calculated residual stress. In such cases, smoothing the strain history using a low-pass filter or the like to remove the noise is preferred, as this allows for highly accurate residual stress calculation.

[0091] [Example]

[0092] The effects of the residual stress calculation method of the present invention were verified and will be described below.

[0093] In the embodiment, the residual stress and its error calculated by the method of the present invention are calculated based on the residual stress calculated by the finite element method which can be obtained with high accuracy. Figure 2 As shown, the metal plate 1 is plastically deformed by a roller bending test, and the residual stress of the end surface 3 a at the deformed portion 3 of the metal plate 1 is calculated.

[0094] First, a pair of left and right rollers 11 with a diameter (D) of 20 mm are set with a center-to-center distance (L) of 35 mm, and a metal plate 1 is placed on the upper surfaces of the rollers 11. The rollers 11 are provided with a mechanism that rotates smoothly following the deformation of the metal plate 1.

[0095] Next, a punch 13 with a top radius (R) of 3 mm is used to press the punch 13 in 10 mm at a speed of 10 mm / min, and then the punch 13 is unloaded until it separates from the metal plate 1. Bending deformation is applied to the deformed portion 3 of the metal plate 1 to obtain the strain history of the end face 3a of the deformed portion 3 during the deformation process of plastically deforming the metal plate 1.

[0096] In this embodiment, the end surface 3a of the deformed portion 3 of the metal plate 1 is obtained by DIC in two directions ( Figure 2The strain in the x-direction and y-direction) and the in-plane ( Figure 2 Strain history of shear strain in the xy plane (in the image).

[0097] Next, the stress increment of the deformation portion 3 during the deformation process is calculated using the acquired strain increment calculated from the acquired strain history and the assumed strain increment calculated by assuming the deformation state of the deformation portion.

[0098] Next, the calculated stress increment is used to sequentially update the stress of the deformed portion, and the stress of the deformed portion 3 at the end of deformation is determined as the residual stress.

[0099] In the calculation of the stress increment of the deformed portion 3 during the deformation process, in this embodiment, a plane stress state, a uniaxial stress state, or a constant strain ratio is assumed as the deformation state of the deformed portion 3 .

[0100] The plane stress state is the out-of-plane direction ( Figure 2 The stress in the z direction (in the z direction) is set to 0, and the stress increment is calculated using the equations (1) and (4) shown in the above embodiment.

[0101] The uniaxial stress state is a state in which stress is loaded in one direction (x direction) within the plane, and the stresses in the in-plane direction (y direction) and out-of-plane direction (z direction) are both set to 0. The stress increment is calculated according to equations (1) and (4).

[0102] In the “constant strain ratio”, it is assumed that the ratio (ε z / ε x ) is constant, and the stress increment is calculated according to equations (1) and (4).

[0103] When calculating the stress increment from the strain increment using equations (1) and (4), the isotropic von Mises yield function is assigned to the yield function f in equation (4).

[0104] In this example, as shown in Table 1, the residual stress generated by the roller bending test was calculated for Conditions 1 to 7 in which the material of the metal plate, the position of the residual stress evaluation point, and the assumed deformation state were changed.

[0105] [Table 1]

[0106]

[0107] Hot rolled: hot rolled steel plate, cold rolled: cold rolled steel plate

[0108] In Table 1, the material is a material with changed material strength and thickness of the metal plate. 980 is a hot-rolled steel sheet with a tensile strength of 980 MPa (thickness 2.9 mm), 590 is a hot-rolled steel sheet with a tensile strength of 590 MPa (thickness 1.6 mm), and 1470 is a cold-rolled steel sheet with a tensile strength of 1470 MPa (thickness 1.2 mm). In addition, the evaluation point positions in Table 1 are Figure 3 The positions of P, Q, and R on the end surface 3a of the metal plate 1 are shown. Evaluation point P is located outside the bend (0.1×t0 from the outermost surface of the bend), evaluation point Q is located in the center of the bend (0.5×t0 from the outermost surface of the bend), and evaluation point R is located inside the bend (0.9×t0 from the outermost surface of the bend). The assumed deformation states in Table 1 are those of the deformed portions used in the calculation of residual stress.

[0109] As an example, for condition 1 shown in Table 1, Figure 4 Indicates that it has passed the roller bending test ( Figure 2 ) The relationship between the strain and the calculated stress at the deformation site 3 of the bent metal plate 1 during the deformation process and the result of the residual stress at the end of the deformation (solid line).

[0110] In addition, as a comparison, the relationship between strain and stress during deformation of the metal plate 1 and the residual stress at the end of deformation, obtained by finite element analysis of a roller bending test of the metal plate 1, are shown together (dashed line). Figure 4 In the finite element analysis, in order to accurately reproduce the deformation process of the metal plate 1 based on the roller bending test, sufficiently small solid elements (element size: about 0.15 mm) are used.

[0111] Depend on Figure 4 It can be seen that the relationship between strain and stress and the residual stress calculated by the present invention are substantially consistent with the results obtained by finite element analysis.

[0112] Table 1 shows the results of calculating the residual stress at the end surface 3a of the deformed portion 3 for conditions 1 to 7, which vary the material of the metal plate 1, the location of the residual stress evaluation point, and the assumed deformation state. Table 1 also shows the results of calculating the residual stress using finite element analysis for each of the conditions in Table 1.

[0113] The results of conditions 1 to 3 in which the material of the metal plate 1 was changed show that the present invention can accurately calculate the residual stress regardless of the material strength and plate thickness of the metal plate.

[0114] The results of conditions 1, 4, and 5, which varied the evaluation point positions at the deformed portion 3, show that the residual stresses at the outer and central sides of the bend at the end face 3a of the deformed portion 3 can be calculated with high accuracy. Since fatigue failure is more likely to occur at the outer sides of the bend where tensile stress remains, the method of the present invention is proven to be effective.

[0115] When comparing the assumed conditions 1, 6, and 7 in which the deformation state is changed, differences are found in the calculated residual stress values.

[0116] Condition 1 assumes a plane stress state as the deformation state of the deformation portion 3, and is a condition for obtaining strain histories for both the strain in the two in-plane directions and the in-plane shear strain. In contrast, Condition 6 assumes a uniaxial stress state as the deformation state of the deformation portion 3, and is a condition for obtaining strain histories only in one in-plane direction (the x-direction).

[0117] The results of the present invention under condition 6, which assumes a uniaxial stress state, are less accurate than the results of the present invention under condition 1, which assumes a plane stress state. It should be noted that when the assumption of a uniaxial stress state is established based on the deformation process of the deformation portion 3, it is also possible to obtain a strain history of only the strain in one direction in the plane using a general uniaxial strain gauge, rather than obtaining the strain history of the strain in both directions in the plane and the in-plane shear strain using DIC.

[0118] Furthermore, condition 7 assumes that the strain ratio during the deformation process of the deformation portion 3 is constant. When the strain ratio is assumed to be constant, a finite element analysis of a roller bending test of the metal plate 1 is performed, and it is found that the ratio of the strain in the in-plane direction (x direction) to the strain in the out-of-plane direction (z direction) on the end face 3a of the deformation portion 3 is approximately ε z / ε x =-0.5. Then, based on this result, the deformation state of the deformation portion 3 is assumed to be constant (ε z / ε x =-0.5).

[0119] According to Table 1, the residual stress calculated under Condition 7 has a smaller difference from the result of finite element analysis than the residual stress calculated under Condition 1 assuming a plane stress state, and the residual stress can be calculated with higher accuracy.

[0120] As is apparent from the above, according to the present invention, the residual stress of a metal plate subjected to plastic deformation can be calculated easily and with high accuracy in a short time.

[0121] Industrial Applicability

[0122] According to the present invention, it is possible to provide a residual stress calculation method for accurately and easily calculating the residual stress of a metal plate that has undergone plastic deformation.

[0123] Description of Reference Numerals

[0124] 1 metal plate

[0125] 3 Deformation parts

[0126] 3a end face

[0127] 11 rollers

[0128] 13 punch

Claims

1. A method for calculating residual stress of a metal plate subjected to plastic deformation, wherein: The calculation method of the residual stress includes: a strain history acquisition step of measuring the strain of a deformed portion of the metal plate during a deformation process in which the metal plate is plastically deformed, and acquiring a strain history of the measured strain; a successive stress updating step of calculating a stress increment at the deformed portion during the deformation process according to a material constitutive model using an acquired strain increment calculated based on the strain history and an assumed strain increment calculated by assuming a deformation state of the deformed portion based on strains other than the strains acquired in the strain history, and successively updating the stress at the deformed portion from the start to the end of the deformation using the calculated stress increment; and A residual stress determining step is performed in which the stress at the deformed portion at the end of the deformation process is determined as the residual stress at the deformed portion, from among the stresses successively updated in the successive stress updating step.

2. The method for calculating residual stress according to claim 1, wherein: The strain history acquisition step measures the strain history of strains in two directions in the plane and the in-plane shear strain at the deformed portion by digital image correlation to acquire these strain histories.

3. The method for calculating residual stress according to claim 1 or 2, wherein: In the successive stress updating step, a deformation state of the deformation portion is assumed according to the deformation process of the deformation portion, and the assumed strain increment is calculated based on the plastic mechanics theory under the assumed deformation state.

4. The method for calculating residual stress according to claim 1 or 2, wherein: In the successive stress updating step, a deformation state of the deformation portion is assumed by finite element analysis of the deformation process of the metal plate, and the assumed strain increment is calculated based on the assumed deformation state.

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