Method, device, and program for calculating residual stress distribution

Abstract

This residual stress distribution calculation method calculates the distribution of residual stress occurring on a plastically deformed metal plate, and comprises: a step (S10) for acquiring a surface deformation history of a deformed portion (33) of a metal plate (31) during a deformation process in which the metal plate (31) is plastically deformed; acquiring, from the acquired surface deformation history, a strain history and a spin history generated at the deformed portion (33); a step (S20) for sequentially updating the stress in the material coordinate system of each measurement point set at the deformed portion (33) of the metal plate (31) from the beginning of deformation to the end of deformation in the deformation process; and a step (S30) for calculating the residual stress distribution by converting the stress in the material coordinate system of each measurement point at the end of the deformation into the stress in the global coordinate system.

Description

Technical Field

[0001] The present invention relates to a residual stress distribution calculation method, device and program for calculating the distribution of residual stress generated in a metal sheet subjected to plastic deformation. Background Art

[0002] It is known that the residual stress generated in a press-formed product (e.g., a press-formed product for automobiles) manufactured by press forming of a metal sheet affects the fatigue life and delayed fracture properties of the press-formed product. Therefore, understanding the residual stress generated in the press-formed product after press forming is important in ensuring the fatigue life of the product using the press-formed product.

[0003] In the past, residual stress has been measured using X-rays or supersonic waves, residual stress has been calculated by measuring strain during deformation of metal plates, and residual stress has been predicted by finite element analysis of press forming processes. As a technique for measuring residual stress using X-rays, for example, Patent Document 1 discloses a technique for detecting diffracted X-rays emitted from a sample when X-rays are irradiated to the sample, and measuring stress inside the sample in a non-destructive manner based on information from the diffracted X-rays. On the other hand, as a technique for measuring residual stress using ultrasonic waves, for example, Patent Document 2 discloses a technique for generating ultrasonic waves in a plastically deformed object to be inspected (for example, a metal plate), and measuring residual stress in a non-destructive manner based on information on the speed of sound of the ultrasonic waves.

[0004] As a technique for finding the residual stress generated in a press-formed product, for example, the following technique is disclosed in Patent Document 3: according to the strain history of the part where the residual stress in the metal plate is measured and the material constitutive law, the stress from the beginning to the end of the deformation is successively updated, and the residual stress after the deformation is completed is calculated. In addition, the prediction of the residual stress by finite element analysis of the press-forming process can be performed using the generally widely used finite element analysis software, and in this finite element analysis, the high precision of the material constitutive law is continuously promoted. For example, the material constitutive law disclosed in Non-Patent Document 1 (hereinafter referred to as the "YU model (Yoshida-Uemori model)") contributes to the high precision of the spring-back analysis (spring-back analysis) which is very important for the prediction of the residual stress of the press-formed product.

[0005] Prior art literature

[0006] Patent Literature

[0007] Patent Document 1: Japanese Patent Application Publication No. 2002-333409

[0008] Patent Document 2: Japanese Patent Application Publication No. 2011-196953

[0009] Patent Document 3: Japanese Patent No. 6981521

[0010] Non-patent literature

[0011] Non-patent document 1: F. 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 measurement of stress using X-rays disclosed in Patent Document 1 and the measurement of residual stress using ultrasound disclosed in Patent Document 2 assume that the sample (metal plate, etc.) is uniform in the region where the X-rays are incident (incidence) or the ultrasound is generated. Therefore, in these measurement techniques, it is difficult to accurately measure the residual stress of a metal plate having two or more phases (e.g., DP (Dual Phase) steel plate, etc.). Moreover, the techniques of Patent Document 1 and Patent Document 2 both measure the residual stress after deformation, and cannot measure the stress history during deformation.

[0014] According to the technology disclosed in Patent Document 3, since stress is calculated successively in the process of calculating residual stress using strain history and material constitutive law, the stress history during deformation can be obtained. However, since it is a technology for calculating local stress at a deformed part, in the case of large deformation, rigid body motion, and rigid body rotation of the metal plate itself as the measurement object, the coordinate system of stress and strain will deviate from the coordinate system before deformation. As a result, the generation direction of the stress calculated successively becomes unclear.

[0015] Furthermore, the techniques of Patent Documents 1 to 3 are all techniques for obtaining stress at a specific point, and in order to obtain the distribution of residual stress, it is necessary to repeatedly measure stress at a plurality of positions.

[0016] With respect to these technologies, according to the method of predicting residual stress by finite element analysis, the distribution of residual stress, which is one of the subjects of the technology, can be easily calculated. However, the input values ​​(shape, material properties, deformation properties, boundary conditions, etc.) provided to the finite element analysis software used in the finite element analysis have a great influence on the prediction results of residual stress. Therefore, in order to correctly predict the residual stress by finite element analysis, not only the material properties of the metal plate, but also various input values ​​such as the deformation properties of the tool that applies plastic deformation, the contact conditions between the metal plate and the tool, and the boundary conditions such as sliding properties need to be set to more correct values. Moreover, in the case of shear deformation accompanied by the fracture of the metal plate, it is necessary to incorporate the fracture conditions into the finite element analysis model, and it is very difficult to predict the residual stress with high accuracy.

[0017] The present invention has been made to solve the above-mentioned problems, and an object of the present invention is to provide a residual stress distribution calculation method, device, and program for accurately and easily calculating the distribution of residual stress generated in a metal plate subjected to plastic deformation.

[0018] Means for solving problems

[0019] The residual stress distribution calculation method of the present invention calculates the residual stress distribution generated in a metal plate subjected to plastic deformation, and includes a deformation history acquisition step, a successive stress updating step, and a residual stress distribution calculation step. The deformation history acquisition step includes: a surface deformation history acquisition step, which sets a plurality of measurement points on the surface of a deformation portion of the metal plate and measures the three-dimensional coordinates of each of the measurement points in a deformation process of plastically deforming the metal plate, thereby acquiring the surface deformation history of the deformation portion from the beginning to the end of the deformation; a strain history acquisition step, which acquires the strain history of the deformation portion in the deformation process from the acquired surface deformation history of the deformation portion; and a spin history acquisition step, which acquires the spin history of the deformation portion in the deformation process from the acquired surface deformation history of the deformation portion. The successive stress updating step includes: an acquired strain increment calculation step, which calculates an acquired strain increment based on the strain history acquired in the strain history acquisition step. strain); a hypothetical strain increment calculation step of assuming the deformation state of the deformation site and calculating a hypothetical strain increment, wherein the hypothetical strain increment is an increment of strain other than the strain for which the strain history is obtained in the strain history obtaining step; an acquired spin increment calculation step of calculating an acquired spin increment (incremental spin) based on the spin history obtained in the spin history obtaining step; a stress increment calculation step of calculating the stress increment (incremental stress) of each of the measurement points according to the material constitutive law using the acquired strain increment, the hypothetical strain increment and the acquired spin increment; and a successive stress updating step of successively updating the stress in the material coordinate system of each of the measurement points from the start of deformation to the end of deformation in the deformation process using the stress increment calculated for each of the measurement points, wherein the residual stress distribution calculation step includes a stress coordinate system transformation step of converting the stress in the material coordinate system of each of the measurement points at the end of deformation in the deformation process, which is successively updated and obtained in the successive stress updating step, into a global coordinate system (global coordinate system). The global stress value of each of the measurement points obtained by the conversion is obtained as the residual stress distribution of the deformed portion.

[0020] The residual stress distribution calculation step may further include a residual stress distribution display step of displaying the residual stress distribution of the deformed portion obtained in the stress coordinate system conversion step.

[0021] Alternatively, in the step of calculating the assumed strain increment, a deformation state is assumed according to a deformation process of the deformation portion, and the assumed strain increment is calculated based on a theory of plasticity under the assumed deformation state.

[0022] In the step of calculating the assumed strain increment, a deformation state of the deformation portion may be assumed by finite element analysis of a deformation process of the metal plate, and the assumed strain increment may be calculated based on the assumed deformation state.

[0023] The residual stress distribution calculation device of the present invention calculates the distribution of residual stress generated on a metal plate subjected to plastic deformation, and is provided with a deformation history acquisition unit, a successive stress updating unit and a residual stress distribution calculation unit, wherein the deformation history acquisition unit comprises: a surface deformation history acquisition unit, for a plurality of measurement points set at a deformation site of the metal plate, acquiring three-dimensional coordinates measured during a deformation process of plastically deforming the metal plate as a surface deformation history of the deformation site from the beginning to the end of the deformation; a strain history acquisition unit, for acquiring the strain history of the deformation site during the deformation process from the acquired surface deformation history of the deformation site; and a spin history acquisition unit, for acquiring the spin history of the deformation site during the deformation process from the acquired surface deformation history of the deformation site, wherein the successive stress updating unit comprises: an acquired strain increment calculation unit, for calculating an acquired strain increment based on the strain history acquired by the strain history acquisition unit; and an assumed strain increment calculation unit, for assuming the deformation state of the deformation site and calculating a presumed strain increment, the presumed strain increment being an increment of strain other than the strain obtained by the strain history obtained by the strain history obtaining unit; an acquired spin increment calculating unit, calculating an acquired spin increment based on the spin history obtained by the spin history obtaining unit; a stress increment calculating unit, using the acquired strain increment, the presumed strain increment and the acquired spin increment, to calculate the stress increment of each of the measuring points according to the material constitutive law; and a successive stress updating unit, using the stress increment calculated for each of the measuring points, to successively update the stress in the material coordinate system of each of the measuring points from the start of deformation to the end of deformation of the deformation process, wherein the residual stress distribution calculating unit comprises a stress coordinate system converting unit, converting the stress in the material coordinate system of each of the measuring points at the end of deformation of the deformation process, which is successively updated and obtained by the successive stress updating unit, into a global stress value in a specified direction in a global coordinate system, and obtaining the converted global stress value of each of the measuring points as the residual stress distribution of the deformation portion.

[0024] The residual stress distribution calculation unit may further include a residual stress distribution display unit that displays the residual stress distribution of the deformed portion obtained by the stress coordinate system conversion unit.

[0025] The assumed strain increment calculation unit may assume a deformation state according to a deformation process of the deformation portion, and calculate the assumed strain increment based on a plastic mechanics theory under the assumed deformation state.

[0026] The assumed strain increment calculation unit may assume a deformation state of the deformation portion by finite element analysis of a deformation process of the metal plate, and calculate the assumed strain increment based on the assumed deformation state.

[0027] The residual stress distribution calculation program of the present invention calculates the distribution of residual stress generated on a metal plate subjected to plastic deformation, and enables a computer to function as a deformation history acquisition unit, a successive stress update unit, and a residual stress distribution calculation unit, wherein the deformation history acquisition unit comprises: a surface deformation history acquisition unit, which acquires, for a plurality of measurement points set at a deformation site of the metal plate, three-dimensional coordinates measured during a deformation process in which the metal plate is plastically deformed as the surface deformation history of the deformation site from the beginning to the end of the deformation; a strain history acquisition unit, which acquires the strain history of the deformation site during the deformation process from the acquired surface deformation history of the deformation site; and a spin history acquisition unit, which acquires the spin history of the deformation site during the deformation process from the acquired surface deformation history of the deformation site, wherein the successive stress update unit comprises: an acquired strain increment calculation unit, which calculates an acquired strain increment based on the strain history acquired using the strain history acquisition unit; and an assumed strain increment calculation unit, which assumes the deformation of the deformation site. state and calculate an assumed strain increment, wherein the assumed strain increment is an increment of strain other than the strain obtained by the strain history obtained by the strain history obtaining unit; an acquired spin increment calculating unit, which calculates an acquired spin increment based on the spin history obtained by the spin history obtaining unit; a stress increment calculating unit, which uses the acquired strain increment, the assumed strain increment and the acquired spin increment to calculate the stress increment of each of the measuring points according to the material constitutive law; and a successive stress updating unit, which uses the stress increment calculated for each of the measuring points to successively update the stress in the material coordinate system of each of the measuring points from the start of deformation to the end of deformation of the deformation process, wherein the residual stress distribution calculating unit has a stress coordinate system converting unit: converting the stress in the material coordinate system of each of the measuring points at the end of deformation of the deformation process, which is successively updated and obtained by the successive stress updating unit, into a global stress value in a specified direction in a global coordinate system, and obtaining the converted global stress value of each of the measuring points as the residual stress distribution of the deformation part.

[0028] The residual stress distribution calculation unit may further include a residual stress distribution display unit that displays the residual stress distribution of the deformed portion obtained by the stress coordinate system conversion unit.

[0029] The assumed strain increment calculation unit may assume a deformation state according to a deformation process of the deformation portion, and calculate the assumed strain increment based on a plastic mechanics theory under the assumed deformation state.

[0030] The assumed strain increment calculation unit may assume a deformation state of the deformation portion by finite element analysis of a deformation process of the metal plate, and calculate the assumed strain increment based on the assumed deformation state.

[0031] Effects of the Invention

[0032] According to the present invention, even when the direction of the material coordinate system of the deformed portion of the metal plate subjected to plastic deformation changes, the direction of the stress can be made consistent and the distribution of the residual stress in the deformed portion can be obtained with high accuracy. In addition, according to the present invention, the history of the stress distribution during deformation can be obtained with high accuracy. Moreover, according to the present invention, even for the shear deformation accompanied by the fracture of the metal plate, which is difficult to predict by the finite element method, the distribution of the residual stress generated in the metal plate can be accurately and easily calculated. BRIEF DESCRIPTION OF THE DRAWINGS

[0033] Figure 1 This is a flowchart showing the flow of processing in the method for calculating residual stress distribution according to the embodiment of the present invention.

[0034] Figure 2 The diagram illustrates changes in the directions of the material coordinate system and the global coordinate system before and after bending deformation of a metal plate ((a) before deformation, (b) after deformation).

[0035] Figure 3 It is a diagram for explaining the structure of a residual stress distribution calculation device according to the present embodiment.

[0036] Figure 4 This figure illustrates the surface deformation history of each measurement point obtained based on the three-dimensional coordinates of the three measurement points before and after deformation in the calculation method of the residual stress distribution in the present embodiment, and the strain and spin generated in the area formed by the three measurement points ((a) before deformation, (b) after deformation).

[0037] Figure 5 It is a figure which shows the shape of the metal plate used as a test object in Example.

[0038] Figure 6 This is a graph showing the results of calculating the distribution of residual stress in the tensile direction generated at a deformed portion of a metal plate subjected to uniaxial tensile deformation in Examples.

[0039] Figure 7 This is a distribution diagram (contour plot) showing the results of obtaining the distribution of residual stress in the tensile direction generated at a deformed portion of a metal plate subjected to uniaxial tensile deformation by the method of the present invention in the examples as invention examples.

[0040] Figure 8This is a distribution diagram showing the results of obtaining the distribution of residual stress in the tensile direction generated at the deformed portion of the metal plate subjected to uniaxial tensile deformation by finite element analysis as a comparative example in the examples.

[0041] Fig. 9 This is a graph showing the results of determining the residual stress in the tensile direction generated at the measurement points A to D of the deformed portion of the metal plate subjected to uniaxial tensile deformation in the Examples as the inventive examples and the comparative examples. DETAILED DESCRIPTION

[0042] Before describing a method, device, and program for calculating residual stress distribution according to an embodiment of the present invention, the process of arriving at the present invention will be described.

[0043] <How the Invention Was Acquired>

[0044] The method disclosed in the above-mentioned patent document 3 calculates the residual stress generated in the metal plate subjected to plastic deformation based on the coordinate system defined by each position of the metal plate. Therefore, when the direction of the coordinate system changes due to the rotational deformation of the metal plate itself during the deformation process, the direction in which the residual stress is generated becomes unclear.

[0045] As an example of the change in the direction of the material coordinate system of a metal plate subjected to plastic deformation, consider Figure 2 The bent and deformed metal plate 31 is shown. Figure 2 , (a) shows the metal plate 31 before bending deformation, and (b) shows the metal plate 31 after bending deformation. The coordinate system defined by each position of the metal plate 31 is called a material coordinate system. In contrast, the coordinate system when the deformed metal plate 31 is observed from the outside is called a global coordinate system.

[0046] In the metal plate 31 before bending deformation, as Figure 2 As shown in (a), the direction of the material coordinate system is constant and is not affected by the position in the metal plate 31, and is consistent with the direction of the global coordinate system. Figure 2 As shown in (b), the direction of the material coordinate system varies depending on the position in the metal plate 31 and deviates from the direction of the global coordinate system.

[0047] That is, the material coordinate system changes its direction according to the deformation of the metal plate 31, and the direction of the coordinate system varies according to the position in the metal plate 31. In contrast, the global coordinate system is different from the material coordinate system, and its direction does not change regardless of the deformation of the metal plate 31, and it is the same coordinate system regardless of the position in the metal plate 31.

[0048] In order to calculate the distribution of residual stress at the deformed part of the metal plate, it is necessary to calculate the residual stress at multiple positions in the metal plate. However, the residual stress calculated by the method disclosed in Patent Document 3 is subject to the material coordinate system of the position where the stress is calculated. Therefore, when calculating the residual stress at multiple positions, since the direction of the residual stress is different depending on the position, it is possible that a deviation will occur and become inconsistent.

[0049] In order to make the direction of the residual stress consistent, it is considered that the direction of the residual stress can be made consistent based on the direction of the material coordinate system at each position where the residual stress is calculated. However, in the method disclosed in Patent Document 3, only the strain history is used to successively calculate the stress during the deformation process. Therefore, it is unknown in which direction the metal plate changes during the deformation process, and it is impossible to obtain information related to the direction of the material coordinate system at each position where the stress is calculated.

[0050] Therefore, the inventors conducted in-depth research to solve such a problem. As a result, they came up with the idea of ​​not only obtaining the history of strain during the deformation of the metal plate, but also obtaining the history of rotation (hereinafter referred to as "spin") of the material coordinate system at multiple positions. Then, the history of spin is obtained as information related to the direction of the material coordinate system relative to the global coordinate system, which is updated successively during the deformation process of each position of the metal plate. In addition, it was found that by converting the residual stress calculated according to the material coordinate system at each position of the metal plate into a stress of a specified direction in the global coordinate system based on the obtained spin, the directions of the residual stresses at multiple positions are made consistent and their distribution is obtained.

[0051] The present invention has been made based on the above-mentioned research results, and specifically has the following structure.

[0052] <Calculation method of residual stress distribution>

[0053] The method for calculating residual stress distribution according to an embodiment of the present invention calculates the distribution of residual stress generated in a metal plate subjected to plastic deformation. Figure 1 As shown in FIG. 1 , the residual stress distribution calculation method of the present embodiment includes a deformation history acquisition step S10, a successive stress update step S20, and a residual stress distribution calculation step S30. Figure 3 The above-described steps will be described with reference to an example of calculating the distribution of residual stress generated in a deformed portion 33 of a metal plate 31 that is bent and deformed using a punch 41 and a die 43 .

[0054] 《Deformation history acquisition process》

[0055] The deformation history acquisition step S10 is a step of acquiring the surface deformation history of the deformation portion 33 of the metal plate 31 during the deformation process of plastically deforming the metal plate 31, and acquiring the strain history and spin history generated in the deformation portion 33 from the acquired surface deformation history. Figure 1 As shown, the deformation history acquisition step S10 includes a surface deformation history acquisition step S11 , a strain history acquisition step S13 , and a spin history acquisition step S15 .

[0056] (Surface deformation history acquisition step)

[0057] First, in the surface deformation history acquisition step S11, a plurality of measurement points are set on the surface of the deformation portion 33 of the metal plate 31. Then, by measuring the three-dimensional coordinates of each measurement point in the deformation process of plastically deforming the metal plate 31, the surface deformation history from the start to the end of the deformation of the deformation portion 33 is acquired.

[0058] In this embodiment, if Figure 3 As shown, two cameras 11 and 13 are installed at positions capable of capturing images of the surface of the deformed portion 33 of the metal plate 31. Then, the three-dimensional coordinates of each measurement point are measured by digital image correlation (hereinafter referred to as "DIC").

[0059] In DIC, the surface of the deformed portion 33 of the metal plate 31 during the deformation process is photographed at predetermined time intervals using the cameras 11 and 13, and image analysis is performed on the images photographed at each time step (hereinafter referred to as "DIC images"). Thus, the three-dimensional coordinates of each measurement point at each time step from the start of deformation to the end of deformation can be measured.

[0060] (Strain history acquisition steps)

[0061] Next, in the strain history acquisition step S13 , the strain history of the deformed portion 33 during the deformation process is acquired from the surface deformation history of the deformed portion 33 acquired in the surface deformation history acquisition step S11 .

[0062] (Spin history acquisition step)

[0063] Then, in the spin history acquisition step S15 , the spin history of the deformed portion 33 during the deformation process is acquired from the surface deformation history of the deformed portion 33 acquired in the surface deformation history acquisition step S11 .

[0064] Regarding the specific processing in the deformation history acquisition step S10, Figure 4As shown in FIG. 1 , a case where three measurement points are set at the deformed portion 33 of the metal plate 31 will be described as an example.

[0065] First, if Figure 4 As shown, a plurality of measurement points are set at the deformation site 33 of the metal plate 31, and the three-dimensional coordinates of each measurement point are measured at predetermined time intervals during the deformation process.

[0066] exist Figure 4 In the deformation process, the coordinates of each measured point in a certain time step are set as the coordinates before deformation X i The coordinates of each measurement point in the time step after a predetermined time interval from this time step are set as the coordinates x after deformation i (i=0, 1, 2).

[0067] Then, when the region a1 composed of three measurement points in the time step before deformation is deformed into the region a2 in the time step after deformation, the strain and spin generated by the deformation of the region composed of three measurement points can be calculated as follows.

[0068] For each of the region a1 before deformation and the region a2 after deformation, the coordinates X 0 and x 0 Then, the coordinate X i 、x i The relative position of the measurement point (X 0 or x 0 ) are represented by dX i =X i -X 0 (i=1,2),dx i =x i -x 0 (i=1,2). At this time, dx i =FdX i F is called the deformation gradient tensor.

[0069] Generally speaking, the deformation of a region composed of a plurality of measurement points does not need to be determined from the displacements of the three measurement points described above, and can be expressed by the following equation (1).

[0070] [Mathematical formula 1]

[0071] dx=FdX …(1)

[0072] Here dX=(dX 1 dX 2 ...)、dx=(dx 1 dx 2 …)

[0073] When equation (1) is solved for the deformation gradient tensor F, equation (2) is obtained.

[0074] [Mathematical formula 2]

[0075] F = dxdX T (dXdX T ) -1 …(2)

[0076] Furthermore, using the deformation gradient tensor F, the right Cauchy-Green deformation tensor C and the right stretch tensor U are expressed by equations (3) and (4), respectively.

[0077] [Mathematical formula 3]

[0078] C=F T ·F…(3)

[0079]

[0080] Using these, the logarithmic strain tensor (Hencky strain tensor E) and the spin tensor R are defined by equation (5) and equation (6), respectively.

[0081] [Formula 4]

[0082]

[0083] R=F·U -1 …(6)

[0084] In equation (5), the Hencky strain tensor E is the strain in each time step from the start of deformation to the end of deformation. In equation (6), the spin tensor R is the spin in each time step from the start of deformation to the end of deformation.

[0085] As described above, in acquiring the deformation history using DIC, first, the surface of the deformed portion 33 of the metal plate 31 during the deformation process is imaged at predetermined time intervals. Next, the DIC images captured at each time step are analyzed to measure the three-dimensional coordinates (X, Y, and Y) of each measurement point set at the deformed portion 33. i , x i ). Next, based on the three-dimensional coordinates of each measured point, the Hencky strain tensor E and the spin tensor R at a predetermined position of the deformation site 33 are calculated (Formulas (1) to (6)).

[0086] Then, the Hencky strain tensor E calculated at each time step from the start of deformation to the end of deformation is acquired as the strain history (S13). Similarly, the spin tensor R calculated at each time step from the start of deformation to the end of deformation is acquired as the spin history (S13).

[0087] 《Sequential stress update process》

[0088] The sequential stress updating step S20 is a step of sequentially updating the stress (hereinafter also referred to as “local stress”) in the material coordinate system of each measurement point set at the deformation location 33 of the metal plate 31 from the start of the deformation process to the end of the deformation process. Figure 1 As shown, the sequential stress updating step S20 includes a strain increment calculation step S21 , a provisional strain increment calculation step S23 , a spin increment calculation step S25 , a stress increment calculation step S27 , and a sequential stress updating step S29 .

[0089] (Steps for calculating the strain increment)

[0090] First, in the acquired strain increment calculation step S21 , the acquired strain increment is calculated based on the strain history acquired in the strain history acquisition step S13 .

[0091] The acquired strain increment refers to the increment of the strain for which the strain history is acquired in the strain history acquisition step S13. When the three-dimensional coordinates of each measurement point set at the deformation site 33 during the deformation process are acquired as the surface deformation history in the surface deformation history acquisition step S11, the strain history acquired in the strain history acquisition step S13 is the strain in two directions within the plane and the shear strain within the plane. Therefore, the acquired strain increment calculated in the acquired strain increment calculation step S21 is the strain increment of each of the strain in two directions within the plane and the shear strain within the plane.

[0092] Then, the acquired strain increment is calculated for each time step of the acquired strain history. The acquired strain increment in each time step can be calculated based on the strain in the time step and the strain in the previous and next time steps, for example.

[0093] (Assuming the strain increment calculation step)

[0094] Next, the assumed strain increment is calculated in the assumed strain increment calculation step S23. The assumed strain increment refers to the strain increment of each time step of the strain other than the strain whose strain history is obtained in the strain history obtaining step S13. In addition, the deformation state can be assumed according to the deformation process of the deformation part 33, and the strain other than the strain whose strain history is obtained can be obtained based on the plastic mechanics theory under the assumed deformation state.

[0095] As described above, in the strain history acquisition step S13 , three strain components, namely, strains εx and εy in two in-plane directions (x direction and y direction) of the surface of the deformed portion 33 and shear strain εxy in the plane (xy plane), are calculated.

[0096] However, at the deformed portion 33 of the metal plate 31, not only the strain component in the in-plane direction but also six strain components (ε ) including the strain component in the out-of-plane direction (z direction) are generated. x , ε y , ε z , ε xy , ε yz , ε zx ).

[0097] Generally, since the surface of the metal plate 31 during deformation becomes a free surface, no stress is generated in the direction perpendicular to the surface of the metal plate 31. That is, the deformation state of the deformation portion 33 of the metal plate 31 can be assumed to be a plane stress state.

[0098] Then, based on the plasticity theory under the assumed deformation state, the strain (ε x , ε y and ε xy ), and the unknown out-of-plane strain (ε z , ε yz , ε zx ) gives a formula that provides the stress increment in the out-of-plane direction.

[0099] When the deformation state of the deformation portion 33 is assumed to be a plane stress state, since the stress increment in the out-of-plane direction becomes 0, the strain in the out-of-plane direction (ε z ).

[0100] That is, the deformation state of the deformation portion 33 can be assumed according to the deformation process of the metal plate 31 , and strains other than the strains whose strain history is acquired in the strain history acquisition step S13 can be obtained based on the plasticity theory under the assumed deformation state.

[0101] Thus, in the assumed strain increment calculation step S23, the deformation state of the deformation part is assumed and other strains are calculated except for the strains for which the strain history is obtained in each time step of the deformation process. Then, similarly to the above-mentioned strain increment, the assumed strain increment is calculated based on the strain (assumed strain) calculated by assuming the deformation state of the deformation part in each time step of the deformation process. Similar to the above-mentioned strain increment, the assumed strain increment in each time step can be calculated based on the strains obtained in the time step and the time steps before and after it.

[0102] The assumed strain increment calculation step S23 is not limited to the calculation of the strain obtained based on the assumed deformation state as described above, and includes a case where the value of the assumed strain increment is provided based on other assumed deformation states.

[0103] (Steps to calculate the spin increment)

[0104] Next, in the acquired spin increment calculation step S25, the acquired spin increment is calculated based on the spin history acquired in the spin history acquisition step S15. The acquired spin increment refers to the increment of the spin of each time step of the deformation part 33 acquired at a predetermined time interval. The acquired spin increment in each time step can be calculated based on the spin in the time step and the spin in the time step before and after it, for example.

[0105] (Stress increment calculation steps)

[0106] Next, in the stress increment calculation step S27 , the stress increment of the deformation portion 33 during the deformation process is calculated using the acquired strain increment and the assumed strain increment and the acquired spin increment.

[0107] The material constitutive law based on elastic-plastic mechanics can be used to calculate the stress increment. At this time, the stress increment in the material coordinate system is expressed by the relationship shown in equation (7) using the strain increment (acquired strain increment and assumed strain increment) and the spin increment.

[0108] [Mathematical formula 5]

[0109]

[0110] Here, σ: stress tensor

[0111] Incremental stress tensor

[0112] C ep :elastic-plastic tangent modulus tensor

[0113] D: Incremental strain tensor

[0114] W: Incremental spin tensor

[0115] In equation (7), the strain increment tensor D is the increase of the strain tensor E in one time step, and the spin increment tensor W is the increase of the spin tensor R in one time step.

[0116] Moreover, the elastic-plastic coefficient tensor C in equation (7) is ep It can be provided by formula (8).

[0117] [Mathematical formula 6]

[0118]

[0119] Here, Ce: elastic tangent modulus tensor

[0120] f: yield function

[0121] rIncremental plastic strain tensor

[0122] q: internal variable tensor

[0123] (equivalent plastic strain

[0124] or back stress tensor, etc.)

[0125] h: function representing the increment of internal variable tensor

[0126] Plastic tangent modulus

[0127] In this embodiment, as an example of a material constitutive law, a stress increment is calculated from a strain increment (acquired strain increment, assumed strain increment) based on the YU model disclosed in Non-Patent Document 1 that can reproduce the Bauschinger effect with high accuracy.

[0128] The YU model can be classified as a two-surface model in which the yield surface moves within the bounding surface. The development of the bounding surface (center β, radius R) and the yield surface (center α, radius Y) is defined by the following equation (9) through the strain increment.

[0129] [Formula 7]

[0130]

[0131] Here, Y,a 0 ,C,b,m,R sat is the material constant

[0132] At this time, equation (8) is expressed as equation (10).

[0133] [Mathematical formula 8]

[0134]

[0135] In this way, if the strain increment and the spin increment become clear, the stress increment can be obtained according to the material constitutive law.

[0136] The material constitutive law is not limited to the above-mentioned YU model, and the elastic-plastic coefficient tensor can also be calculated according to any material constitutive law. For example, when a material constitutive law assuming isotropic hardening is used instead of the YU model, the elastic-plastic coefficient tensor C ep It is expressed as formula (11).

[0137] [Mathematical formula 9]

[0138]

[0139] Here, H is the equivalent stress in the uniaxial tensile test. Equivalent plastic strain The function of the relationship

[0140] In addition, in order to provide the elastic-plastic coefficient tensor C ep The yield function f used can be 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.

[0141] (Successive stress update steps)

[0142] Next, in the successive stress updating step S29 , the stress in the material coordinate system of each measurement point is successively updated from the start of deformation to the end of deformation in the deformation process using the stress increment calculated for each measurement point.

[0143] In the sequential stress updating step S29, first, in a certain time step of the deformation process, the local stress is updated using the stress increment calculated for each measurement point (S29a), and then it is determined whether the local stress has been updated for all measurement points (S29b).

[0144] When it is determined that the local stresses have not been updated for all the measuring points (S29b), Figure 1 As shown, the above-mentioned processes of S21, S23, S25 and S27 are executed for the measurement point, and the local stress is updated (S29a).

[0145] When it is determined that the local stresses have been updated for all the measurement points ( S29b ), it is determined whether the deformation of the metal plate is completed, that is, whether there is a next time step until the deformation of the metal plate is completed ( S29c ).

[0146] If it is determined that the deformation is not completed, the next time step of the deformation process is entered. Then, the calculation of the strain increment (S21), the calculation of the assumed strain increment (S23), the calculation of the spin increment (S25), the calculation of the stress increment (S27), the update of the local stress (S29a), and the determination of the stress update (S29b) are performed for all the measurement points. In this way, in the successive stress update step S29, the local stress of all the measurement points from the start of deformation to the end of deformation is successively updated by performing the processing of S29a to S29c.

[0147] 《Residual stress distribution calculation process》

[0148] The residual stress distribution calculation step S30 is a step of converting the local stress of each measurement point at the end of deformation into a global stress value in the global coordinate system and calculating the residual stress distribution. In this embodiment, the residual stress distribution calculation step S30 includes a stress coordinate system conversion step S31 and a residual stress distribution display step S33.

[0149] (Stress coordinate system conversion steps)

[0150] First, in the stress coordinate system conversion step S31, the local stress at the end of deformation among the local stresses of each measuring point successively updated from the start of deformation to the end of deformation in the successive stress updating step S20 is converted into a value of stress in a predetermined direction in the global coordinate system (global stress value). Then, in the stress coordinate system conversion step S31, the converted global stress value of each measuring point is obtained as the residual stress distribution of the deformation part.

[0151] When the local stress obtained at each measurement point is σ and the predetermined direction in the global coordinate system is vector n, the global stress value σ in the global coordinate system g It can be calculated using formula (12).

[0152] [Formula 10]

[0153] σ g =n T σn…(12)

[0154] Here, σ: local stress in the material coordinate system

[0155] n: specified direction in the global coordinate system

[0156] The predetermined direction in the global coordinate system may be a direction expressed in the global coordinate system, is not particularly limited, and may be appropriately set to a direction calculated so that the direction of stress is consistent.

[0157] (Residual stress distribution display steps)

[0158] Next, in the residual stress distribution display step S33 , the residual stress distribution of the deformed portion obtained in the stress coordinate system conversion step S31 is displayed.

[0159] In order to display the residual stress distribution, for example, the coordinates of each measurement point obtained by calculating the global stress value may be converted into coordinates on the DIC image of the deformed portion.

[0160] In order to convert the coordinates of the deformed part 33 on the DIC image, the coordinates (X, Y, Z) of each measurement point in the global coordinate system can be converted into coordinates (u, v) in a two-dimensional plane on the DIC image using equation (13).

[0161] [Mathematical formula 11]

[0162]

[0163] Here, f x , f y :Focal length

[0164] cx , c y : Optical center (image center)

[0165] r ij : rotation matrix component

[0166] t i : Translation matrix component

[0167] A: intrinsic parameter matrix

[0168] (R|t): extrinsic parameter matrix

[0169] In the present embodiment, the residual stress distribution calculation step S30 is performed after the completion of the successive stress updating step S20. Of course, in order to display the strain distribution of the deformed portion 33 during the deformation process, the residual stress distribution calculation step S30 can be performed in time steps after the completion of all stress updates measured in the successive stress updating step S29 in time steps (S29b).

[0170] As described above, in the calculation method of the residual stress distribution of the present embodiment, the strain history and spin history of the deformation portion 33 in the deformation process of the metal plate 31 being plastically deformed are obtained, and the stress of the material coordinate system is updated and calculated for the plurality of measurement points set at the deformation portion 33. Then, the stress of the material coordinate system of each measurement point at the end of the deformation is converted into a global stress value of a predetermined direction in the global coordinate system. Thus, even if the direction of the material coordinate system of the deformation portion 33 of the metal plate 31 subjected to plastic deformation changes, the direction of the stress can be made consistent and the distribution of the residual stress in the deformation portion 33 can be calculated.

[0171] In the above description, the residual stress distribution calculating step S30 includes the residual stress distribution displaying step S33 of displaying the global stress value of the global coordinate system, but the present invention is not limited to including the residual stress distribution displaying step S33.

[0172] In addition, in the calculation method of the residual stress distribution of the present embodiment, the assumed strain increment calculation step S23 assumes the deformation state of the deformation part in the metal plate according to the deformation process, and calculates the assumed strain increment based on the plastic mechanics theory under the assumed deformation state. Of course, in the present invention, the assumed strain increment calculation step may also perform finite element analysis of the process of plastic deformation of the metal plate, and assume the deformation state (e.g., strain ratio) of the deformation part based on the result.

[0173] When the deformation state of the deformation part is assumed and the assumed strain increment is calculated by finite element analysis of the deformation process of the metal plate, it is not necessary to analyze the entire metal plate, and only the deformation part and its vicinity are modeled to perform finite element analysis. As a result, the deformation state of the deformation part can be assumed in a shorter time than finite element analysis that uses the entire metal plate as the analysis object.

[0174] In particular, the finite element analysis using solid elements that can calculate the stress in the plate thickness direction with high accuracy has a significantly increased calculation time, and is therefore rarely used in press forming analysis of general press forming products. However, as long as a portion of the metal plate including the deformed portion is taken as the analysis object, the deformation state of the deformed portion can be predicted in a short time and with high accuracy even if the finite element analysis is performed using solid elements. Therefore, in the present invention, by assuming the deformation state predicted by the finite element analysis based on solid elements and combining the acquisition of the strain history and the spin history during the deformation process, it is possible to calculate the residual stress distribution with higher accuracy.

[0175] <Residual stress distribution calculation device>

[0176] The residual stress distribution calculation device according to the embodiment of the present invention (hereinafter referred to as "residual stress distribution calculation device") calculates the distribution of residual stress generated in a metal plate subjected to plastic deformation. Figure 3 As shown in FIG. 1 , each structure of the residual stress distribution calculation device 1 will be described for calculating the distribution of residual stress generated in the metal plate 31 plastically deformed by using the punch 41 and the die 43 .

[0177] As an example, Figure 3As shown, the residual stress distribution calculation device 1 includes a display device 3, an input device 5, a main data storage device 7, an auxiliary data storage device 9, cameras 11 and 13, and a measurement control and arithmetic processing unit 15.

[0178] In the residual stress distribution calculation device 1, the display device 3, the input device 5, the main storage device 7, the auxiliary storage device 9, and the measurement control and operation processing unit 15 can be a device composed of a PC (personal computer) or the like. In this case, the display device 3, the input device 5, the main storage device 7, the auxiliary storage device 9, the camera 11, and the camera 13 are connected to the measurement control and operation processing unit 15, and perform their respective functions according to the instructions from the measurement control and operation processing unit 15.

[0179] The display device 3 is used to display the image of the deformed portion 33 captured by the camera 11 and the camera 13 , the calculated residual stress distribution, etc., and is composed of a liquid crystal monitor (LCD monitor) or the like.

[0180] The input device 5 is used for displaying an image of the deformed portion 33 , displaying residual stress distribution, inputting conditions by an operator, and the like, and is composed of a keyboard, a mouse, and the like.

[0181] The main storage device 7 is used to store various files such as images of the deformed portion 33 of the metal plate 31 captured by the cameras 11 and 13 and programs for calculating residual stress distribution, and is composed of a hard disk or the like.

[0182] The auxiliary storage device 9 is used for temporary storage and calculation of data used in the measurement control and calculation processing unit 15, and is composed of a RAM (Random Access Memory) and the like.

[0183] The cameras 11 and 13 perform stereo photography of the surface of the deformed portion 33 of the metal plate 31 during the deformation process.

[0184] The measurement control and calculation processing unit 15 includes a measurement control unit 17 that controls the measurement of the surface deformation history of the deformation site 33 and a calculation processing unit 19 that performs calculation processing for calculating the residual stress distribution based on the measured surface deformation history.

[0185] The measurement control unit 17 includes an image capturing unit 21 and a three-dimensional coordinate calculating unit 23. The image capturing unit 21 controls the capturing of the surface of the deformed portion 33 of the metal plate 31 during the deformation process at a predetermined time interval using the two cameras 11 and the camera 13. The three-dimensional coordinate calculating unit 23 calculates the three-dimensional coordinates of a plurality of measurement points set at the deformed portion 33 during the deformation process by performing image analysis on the captured images.

[0186] In this embodiment, the three-dimensional coordinate calculation unit 23 performs image processing on the images of the deformed portion 33 of the metal plate 31 obtained by stereoscopically photographing the cameras 11 and 13 using DIC, and calculates the three-dimensional coordinates of a plurality of measurement points set at the deformed portion 33 .

[0187] In DIC, the surface of the deformed part is photographed at a predetermined time interval during the deformation process of the metal plate 31, and the image captured at each time step (hereinafter referred to as "DIC image") is analyzed. In this way, the three-dimensional coordinates of each measurement point in each time step from the start of deformation to the end of deformation can be measured.

[0188] The calculation processing unit 19 includes a deformation history acquisition unit 25 , a successive stress update unit 27 , and a residual stress distribution calculation unit 29 .

[0189] "Transformation History Acquisition Unit"

[0190] The deformation history acquisition unit 25 acquires the surface deformation history of the deformation portion 33 of the metal plate 31 during the deformation process of plastically deforming the metal plate 31, and acquires the strain history and spin history generated in the deformation portion 33 from the acquired surface deformation history. Figure 3 As shown, the deformation history acquisition unit 25 includes a surface deformation history acquisition unit 25 a , a strain history acquisition unit 25 b , and a spin history acquisition unit 25 c .

[0191] The surface deformation history acquisition unit 25 a acquires three-dimensional coordinates measured during the deformation process of plastically deforming the metal plate 31 for a plurality of measurement points set at the deformation site 33 of the metal plate 31 as the surface deformation history from the start to the end of deformation of the deformation site 33 .

[0192] The strain history acquisition unit 25 b acquires the strain history of the deformation portion 33 during the deformation process from the surface deformation history of the deformation portion 33 acquired by the surface deformation history acquisition unit 25 a .

[0193] The spin history acquisition unit 25 c acquires the spin history of the deformation portion 33 during the deformation process from the surface deformation history of the deformation portion 33 acquired by the surface deformation history acquisition unit 25 a .

[0194] Successive Stress Update Unit

[0195] The successive stress updating unit 27 successively updates and obtains the stress in the material coordinate system of each measurement point set at the deformation location 33 of the metal plate 31 from the start of the deformation process to the end of the deformation process. Figure 3 As shown, the successive stress updating means 27 includes an acquired strain increment calculating section 27a, a provisional strain increment calculating section 27b, an acquired spin increment calculating section 27c, a stress increment calculating section 27d, and a successive stress updating section 27e.

[0196] (Getting the strain increment calculation part)

[0197] The acquired strain increment calculation unit 27a calculates the acquired strain increment based on the strain history acquired by the strain history acquisition unit 25b. The acquired strain increment is the increment of the strain whose strain history is acquired by the strain history acquisition unit 25b.

[0198] For example, when the three-dimensional coordinates of each measurement point set on the surface of the deformation part 33 during the deformation process are obtained as the surface deformation history by the surface deformation history acquisition unit 25a, the strain history obtained by the strain history acquisition unit 25b is the strain in two directions in the plane and the shear strain in the plane. In this case, the acquired strain increment calculated by the acquired strain increment calculation unit 27a is the strain increment of each of the strain in two directions in the plane and the shear strain in the plane.

[0199] Then, the acquired strain increment is calculated for each time step of the acquired strain history during the deformation process. The acquired strain increment in each time step can be calculated, for example, from the strain in the time step and the strain in the previous and next time steps.

[0200] (Assumed strain increment calculation section)

[0201] The assumed strain increment calculation unit 27b calculates the assumed strain increment. The assumed strain increment refers to the strain increment of other strains other than the strain whose strain history is obtained by the strain history acquisition unit 25b. In addition, the deformation state can be assumed according to the deformation process of the deformation part 33, and other strains other than the strain whose strain history is obtained can be calculated based on the plastic mechanics theory under the assumed deformation state.

[0202] The calculation of the provisional strain increment by the provisional strain increment calculation unit 27 b may be performed by the same procedure as the provisional strain increment calculation step S23 of the residual stress distribution calculation method of the present embodiment described above.

[0203] That is, first, the deformation state of the deformation portion 33 of the metal plate 31 is assumed to be a plane stress state. Then, based on the plastic mechanics theory under the assumed deformation state, the strains in the two directions in the plane and the shear strain in the plane and the strain in the unknown out-of-plane direction obtained in the strain history acquisition unit 25b are used to obtain a formula that provides a stress increment in the out-of-plane direction.

[0204] When the deformation state of the deformation portion 33 is assumed to be a plane stress state, the stress increment in the out-of-plane direction becomes 0. Therefore, the strain in the out-of-plane direction can be uniquely calculated by using a formula of strain and stress increment based on the theory of plasticity.

[0205] In this way, the assumed strain increment calculation unit 27b assumes the deformation state of the deformation part 33 and calculates the strain other than the strain for which the strain history is obtained in each time step of the deformation process. Then, similarly to the above-mentioned strain increment, the assumed strain increment is calculated based on the strain calculated by assuming the deformation state of the deformation part in each time step of the deformation process. Similar to the above-mentioned strain increment, the assumed strain increment in each time step can be calculated based on the strain obtained in the time step and the time steps before and after it.

[0206] The assumed strain increment calculation unit 27 b is not limited to calculating the strain obtained based on the assumed deformation state as described above, and may provide a value of the assumed strain increment based on other assumed deformation states.

[0207] (Acquisition of spin increment calculation unit)

[0208] The acquired spin increment calculation unit 27c calculates the acquired spin increment based on the spin history acquired by the spin history acquisition unit 25c. The acquired spin increment refers to the increment of the spin of the deformation part obtained at a predetermined time interval. The acquired spin increment in each time step can be calculated based on the spin in the time step and the spin in the time step before and after it, for example.

[0209] (Stress increment calculation section)

[0210] The stress increment calculation unit 27d uses the acquired strain increment and the assumed strain increment and the acquired spin increment to calculate the stress increment of the deformation portion 33 during the deformation process. The calculation of the stress increment by the stress increment calculation unit 27d can be performed in the same steps as the stress increment calculation step S27 of the residual stress distribution calculation method of the present embodiment described above.

[0211] In the calculation of the stress increment by the stress increment calculation unit 27d, as the material constitutive law, the YU model (non-patent document 1) that can reproduce the Bauschinger effect with high accuracy can be preferably applied as described above. Of course, the stress increment calculation unit 27d is not limited to applying the YU model as the material constitutive law, and any material constitutive law can be applied. In addition, as a method for providing the elastic-plastic coefficient tensor C using the material constitutive law, ep The yield function f used is not limited to the isotropic von Mises yield function, and any yield function such as Hill'48 and Yld2000-2d that can express the anisotropy of the material (metal plate) with high accuracy may be used.

[0212] (Sequential stress update section)

[0213] The sequential stress updating unit 27e uses the stress increment calculated for each measurement point to sequentially update the stress (local stress) in the material coordinate system of each measurement point from the start to the end of the deformation process.

[0214] The sequential stress updating unit 27e first updates the local stress using the stress increment calculated for each measurement point in a certain time step of the deformation process.

[0215] Next, the sequential stress updating unit 27e determines whether the updating of the local stresses has been completed for all the measurement points. If it is determined that the updating of the local stresses has not been completed for all the measurement points, the measurement points for which the local stresses have not been updated are processed by the acquired strain increment calculating unit 27a, the assumed strain increment calculating unit 27b, the acquired spin increment calculating unit 27c, and the stress increment calculating unit 27d. Then, the sequential stress updating unit 27e updates the local stresses of the measurement points for which the local stresses have not been updated.

[0216] When it is determined that the local stresses have been updated for all the measurement points, the sequential stress updating unit 27 e determines whether the deformation of the metal plate 31 is completed, that is, whether there is a next time step until the deformation of the metal plate 31 is completed.

[0217] If it is determined that the deformation is not completed, the next time step of the deformation process is entered, and the processing by the acquired strain increment calculation unit 27a, the assumed strain increment calculation unit 27b, the acquired spin increment calculation unit 27c, and the stress increment calculation unit 27d is performed on all the measurement points. Then, the local stress is updated for all the measurement points. If it is determined that the deformation is completed, the processing by the sequential stress update unit 27e is completed.

[0218] In this way, the successive stress updating unit 27 successively updates the stress of the material coordinate system of all the measurement points from the start to the end of deformation.

[0219] 《Residual stress distribution calculation unit》

[0220] The residual stress distribution calculation unit 29 converts the stress of the material coordinate system at each measurement point at the end of deformation into the stress in the global coordinate system and calculates the residual stress distribution. In this embodiment, the residual stress distribution calculation unit 29 includes a stress coordinate system conversion unit 29a and a residual stress distribution display unit 29b.

[0221] (Stress Coordinate System Conversion Section)

[0222] The stress coordinate system conversion unit 29a converts the stress at the end of deformation among the stresses of the material coordinate system of each measurement point that are successively updated from the start of deformation to the end of deformation by the successive stress updating unit 27 into a value of stress in a predetermined direction in the global coordinate system (global stress value). Then, the stress coordinate system conversion unit 29a obtains the converted global stress values ​​of each measurement point as the residual stress distribution of the deformed portion 33.

[0223] When the local stress in the material coordinate system obtained for each measurement point is σ and the predetermined direction in the global coordinate system is vector n, the global stress value σ in the global coordinate system can be calculated using the above formula (12): g .

[0224] (Residual stress distribution display)

[0225] The residual stress distribution display unit 29b displays the residual stress distribution of the deformed part 33 obtained by the stress coordinate system conversion unit 29a. In order to display the residual stress distribution by the residual stress distribution display unit 29b, the coordinates of each measurement point obtained by obtaining the global stress value can be converted into coordinates on the DIC image of the deformed part 33 in the same manner as the above-mentioned residual stress distribution display step S33. In order to convert into coordinates on the DIC image of the deformed part 33, the coordinates (X, Y, Z) of each measurement point in the global coordinate system can be converted into coordinates (u, v) in the two-dimensional plane on the DIC image using the above-mentioned formula (13).

[0226] Thus, according to the residual stress distribution calculation device 1 of the present embodiment, by converting all the measured points of the deformation part 33 at the end of deformation into stress values ​​of the global coordinate system and displaying the stress values, the stress generation direction can be made consistent and the distribution of the residual stress with high accuracy can be displayed. In addition, by using the present invention, the history of the stress distribution during deformation with high accuracy can be obtained. Moreover, for the shear deformation accompanied by the fracture of the metal plate, which is difficult to predict by the finite element method, the distribution of the residual stress generated on the metal plate can also be accurately and easily calculated.

[0227] <Calculation procedure for residual stress distribution>

[0228] An embodiment of the present invention can be configured as a calculation program for residual stress distribution that enables a computer to function as each part of the above-mentioned residual stress distribution calculation device 1.

[0229] That is, the calculation program for residual stress distribution according to the present embodiment calculates the distribution of residual stress generated on a metal plate that has undergone plastic deformation. Moreover, the calculation program for residual stress distribution according to the present embodiment enables a computer to function as the deformation history acquisition unit 25, the successive stress update unit 27, and the residual stress distribution calculation unit 29 of the residual stress distribution calculation device 1.

[0230] The calculation program for residual stress distribution enables the deformation history acquisition unit 25 to function as the surface deformation history acquisition unit 25a, the strain history acquisition unit 25b, and the spin history acquisition unit 25c. In addition, the calculation program for residual stress distribution enables the successive stress update unit 27 to function as the acquired strain increment calculation unit 27a, the assumed strain increment calculation unit 27b, the acquired spin increment calculation unit 27c, the stress increment calculation unit 27d, and the successive stress update unit 27e.

[0231] Moreover, the calculation program for residual stress distribution enables the residual stress distribution calculation unit 29 to function as the stress coordinate system conversion unit 29a and the residual stress distribution display unit 29b.

[0232] As described above, in the residual stress distribution calculation device and program of the present embodiment, the strain history and spin history of the deformed part 33 during the deformation process that causes the metal plate 31 to undergo plastic deformation are acquired, and the stress in the material coordinate system is successively updated and calculated for a plurality of measurement points set in the deformed part 33. Then, the stress coordinates in the material coordinate system at the end of deformation are converted into the stress values in a specified direction in the global coordinate system. Thus, even when the direction of the material coordinate system in the deformed part of the metal plate that has undergone plastic deformation changes, the direction of the stress can be made consistent and the distribution of high-precision residual stress in the deformed part can be obtained. In addition, by using the present invention, the history of high-precision stress distribution during deformation can be acquired. Moreover, for shear deformation accompanied by fracture of the metal plate, which is difficult to predict by the finite element method, the distribution of residual stress generated on the metal plate can be correctly and easily calculated.

[0233] In the above description, the residual stress distribution calculation unit 29 has a residual stress distribution display unit 29b, and the residual stress distribution display unit 29b displays the global stress values obtained by converting the local stress in the material coordinate system of each measurement point into the stress values in a specified direction in the global coordinate system. Of course, the present invention is not limited to having the residual stress distribution display unit 29b.

[0234] In addition, in the residual stress distribution calculation device and program of the present embodiment, the assumed strain increment calculation unit 27b calculates the assumed strain increment based on the plastic mechanics theory under the deformation state assumed according to the deformation process of the deformation portion 33 in the metal plate 31. Of course, in the present invention, the assumed strain increment calculation unit may also perform finite element analysis of the process of plastic deformation of the metal plate and assume the deformation state (e.g., strain ratio) of the deformation portion based on the result.

[0235] When the deformation state of the deformation part is assumed and the assumed strain increment is calculated by finite element analysis of the deformation process of the metal plate, as described above, it is not necessary to take the entire metal plate as the analysis object, and only the deformation part and its vicinity are modeled to perform finite element analysis. As a result, compared with finite element analysis that takes the entire metal plate as the analysis object, the deformation state of the deformation part can be assumed in a shorter time. In addition, it is also possible to use solid elements that can calculate the stress in the plate thickness direction with high accuracy in finite element analysis, and the residual stress distribution can be calculated with higher accuracy.

[0236] The residual stress distribution calculation device and program of the present invention are not limited to measuring the three-dimensional coordinates of each measurement point by DIC, and the three-dimensional coordinates of each measurement point can be measured at a predetermined time interval from the beginning of deformation to the end of deformation. In addition, the surface deformation history acquisition unit of the residual stress distribution calculation device and program of the present invention can acquire the three-dimensional coordinates of each measurement point measured at a predetermined time interval from the beginning of deformation to the end of deformation as the surface deformation history.

[0237] As described above, the present invention calculates the residual stress distribution by obtaining the strain history and the spin history based on the surface deformation history of the deformed part in the metal plate. Therefore, the residual stress distribution can be accurately calculated even for an inhomogeneous metal plate having two or more phases, which is problematic in the measurement of residual stress using X-rays or ultrasonic waves as in the prior art.

[0238] In addition, as described above, in order to accurately predict the residual stress distribution in the finite element analysis, a long calculation time is required, or in the case of cracking, shearing, etc. accompanied by fracture, the analysis is difficult. In particular, a metal plate subjected to plastic deformation often breaks from the end face of the metal plate, so in order to understand the fatigue life and delayed failure characteristics, it is important to accurately calculate the residual stress distribution of the end face of the metal plate. In contrast, according to the present invention, since the strain history and spin history of the deformation part (end face, etc.) of the metal plate in the deformation process of plastic deformation of the metal plate can be easily measured, the residual stress distribution of the end face of the metal plate can be accurately calculated.

[0239] The above description is about the case of calculating the stress increment using the Y-U model. Since in the Y-U model, the stress-strain relation is defined in the velocity system, in the case of nonlinear deformation, if the strain increment is not sufficiently reduced, an error will occur in the stress increment. Therefore, when calculating the stress increment using the Y-U model, it is preferable that the strain increment becomes 10 -6 The following method is used to adjust the time interval for obtaining the three-dimensional coordinates of each measurement point as the surface deformation history.

[0240] In addition, it can be considered that the surface deformation history obtained in the present invention includes measurement noise, and there is a concern that the strain history and the spin history obtained from such a surface deformation history including measurement noise also include noise.

[0241] Therefore, when calculating the stress increment using a small strain increment (obtaining the strain increment) calculated based on the strain history, sometimes the influence of the noise in the strain history on the stress increment becomes large, and the accuracy of the stress calculated successively becomes low. In such a case, it is preferable to smooth the strain history by using a low-pass filter or the like for noise reduction, so that a high-precision residual stress distribution can be calculated.

[0242] Moreover, according to the present invention, not only can the residual stress after the deformation is completed be known as in the prior art, but also the stress during the deformation can be known. Therefore, the maximum stress generated on the deformed body and the stress released due to springback during the compression molding can be calculated.

[0243] Examples

[0244] Since the effects of the method for calculating the residual stress distribution of the present invention have been verified, the following description will be given thereof.

[0245] In the examples, the method of the present invention is used to calculate by Figure 5The tensile test of the metal plate 51 shown in the figure is to plastically deform the metal plate 51 and give a predetermined tensile deformation (tensile deformation) to the deformation portion 53 in the metal plate 51, thereby generating a distribution of residual stress (inventive example). In addition, as a comparative example, a finite element analysis of the process of giving tensile deformation to the metal plate 51 is performed to obtain the distribution of residual stress generated in the deformation portion 53, and calculate the error from the residual stress distribution obtained as the inventive example. In the inventive example and the comparative example, the metal plate 51 is a steel sheet with a tensile strength of 780, 980, and 1470 MPa grades.

[0246] In the invention example, first, the deformation portion 53 is photographed at predetermined time intervals by DIC during the deformation process of imparting tensile deformation to the metal plate 51, and the surface deformation history is obtained by measuring the three-dimensional coordinates of each measurement point set on the deformation portion 53. Then, the strain history and spin history of the deformation portion 53 during the deformation process are obtained from the obtained surface deformation history.

[0247] Next, the stress increment of the deformation portion 53 during the deformation process is calculated using the acquired strain increment and the acquired spin increment calculated from the acquired strain history and spin history, and the assumed strain increment calculated by assuming the deformation state of the deformation portion 53. In calculating the stress increment of the deformation portion 53 during the deformation process, in this embodiment, a plane stress state is assumed as the deformation state of the deformation portion 53.

[0248] Next, the stress of the deformed portion 53 is updated sequentially using the calculated stress increment, and the stress in the material coordinate system of the deformed portion 53 in each time step from the start of deformation to the end of deformation in the deformation process is calculated. Then, the stress in the material coordinate system at the end of deformation is converted into the stress in the tensile direction in the global coordinate system.

[0249] Furthermore, as a comparative example, a finite element analysis of a uniaxial tension test of the metal plate 51 was performed, and the stress distribution of the deformed portion 53 of the metal plate 51 during the deformation process was calculated and compared with the residual stress distribution obtained as the invention example.

[0250] Table 1 shows the average value and the root mean square error (RMSE) of the residual stress in the range of ±25 mm from the center in the longitudinal direction of the metal plate 51 at the end of deformation, which were obtained as the inventive examples and the comparative examples.

[0251] [Table 1]

[0252] (Table 1)

[0253] Tensile strength(MPa) Types of Metal Sheets Invention Example (MPa) Comparative Example (MPa) RMS Deviation Level 780 Hot rolled steel plate 827 826 18.6 Level 980 Cold rolled steel sheet 1002 1010 44.9 Level 1470 Cold rolled steel sheet 1499 1492 46.4

[0254] As can be seen from Table 1, the inventive example is not affected by the tensile strength of the steel plate used for the metal plate 51 and is in good agreement with the comparative example.

[0255] exist Figure 6 In the figure, for the case where a 780 grade steel plate is used as the metal plate 51, the residual stress distribution in the tensile direction on the center line in the width direction of the metal plate 51 is shown. Figure 6 It was confirmed that the calculated values ​​of residual stress by the inventive example and the comparative example were well consistent except for the range of ±6 mm from the center of the metal plate 51, and the distribution of residual stress can be accurately calculated by the present invention.

[0256] Moreover, from Figure 6 It can be confirmed from the graph that necking occurs in the central portion of the metal plate 51 and deformation begins to concentrate in the plate thickness direction, resulting in stress concentration.

[0257] On the other hand, there is a difference in the residual stress values ​​between the invention example and the comparative example near the center of the metal plate 51. This difference is considered as follows.

[0258] It is known that in finite element analysis, the size of the analysis element affects the reproducibility of local deformation such as the necking deformation part. The smaller the analysis element size, the more concentrated the deformation is to only a part of the analysis element, and it is easy for local deformation to occur in a narrower range, so it is easy to generate higher stress locally. However, the size of the analysis element is often determined by the plate thickness of the material, etc., and the deformation state of the necking part calculated by finite element analysis is not necessarily consistent with the actual deformation state of the material. In contrast, in the method of the present invention, since the deformation of the necking part generated on the metal plate is actually measured, it can be considered that the present invention, which calculates the residual stress based on the actual deformation, has higher accuracy.

[0259] Furthermore, as an example showing the residual stress distribution on the surface of the metal plate 51, Figure 7 The results according to the invention example are shown in Figure 8 The results according to the comparative example are shown in FIG.

[0260] like Figure 7 As shown in FIG. 1 , it can be seen that the location where the residual stress is concentrated can be accurately predicted in the example of the invention. Fig. 9 Shown in Figure 7 The results of the residual stress in the tensile direction at the positions A, B, C, and D in the deformed portion 53 of the metal plate 51 are shown for the inventive example and the comparative example.

[0261] like Fig. 9As shown, it can be seen that at position A, the residual stress values ​​diverge between the invention example and the comparative example, but at positions B, C, and D, the residual stress values ​​in the invention example and the comparative example are well consistent.

[0262] The above results show that according to the method of the present invention, the distribution of residual stress generated in the deformed portion of the metal plate subjected to plastic deformation can be calculated with high accuracy.

[0263] Industrial Applicability

[0264] According to the present invention, it is possible to provide a residual stress distribution calculation method, device, and program for accurately and easily calculating the distribution of residual stress generated in a metal plate subjected to plastic deformation.

[0265] Description of Reference Numerals

[0266] 1 Residual stress distribution calculation device

[0267] 3 Display device

[0268] 5 Input Devices

[0269] 7 Main storage device

[0270] 9 Auxiliary storage device

[0271] 11. Camera

[0272] 13 Camera

[0273] 15 Measurement control and calculation processing unit

[0274] 17 Measurement control unit

[0275] 19. Calculation Processing Unit

[0276] 21 Image capture unit

[0277] 23 Three-dimensional coordinate calculation component

[0278] 25 Deformation history acquisition unit

[0279] 25a Surface deformation history acquisition unit

[0280] 25b Strain history acquisition unit

[0281] 25c Spin history acquisition unit

[0282] 27 Successive stress update unit

[0283] 27a Obtaining the strain increment calculation section

[0284] 27b Assuming that the strain increment is calculated

[0285] 27c Obtaining the spin increment calculation unit

[0286] 27d Stress increment calculation section

[0287] 27e Successive stress update section

[0288] 29 Residual stress distribution calculation unit

[0289] 29a Stress coordinate system conversion section

[0290] 29b Residual stress distribution display

[0291] 31 Metal Plate

[0292] 33 Deformation area

[0293] 41 Punch

[0294] 43 Die

[0295] 51 Metal Plate

[0296] 53 Deformation

Claims

1. Calculation method of residual stress distribution, calculate the distribution of residual stress generated on the metal plate subjected to plastic deformation, in, The residual stress distribution calculation method includes a deformation history acquisition step, a successive stress update step and a residual stress distribution calculation step. The deformation history acquisition step includes: a surface deformation history acquisition step, wherein a plurality of measurement points are set on the surface of the deformed portion of the metal plate, and the three-dimensional coordinates of each of the measurement points during the deformation process of plastically deforming the metal plate are measured, thereby acquiring the surface deformation history of the deformed portion from the beginning to the end of the deformation; a strain history acquisition step of acquiring the strain history of the deformed portion during the deformation process from the acquired surface deformation history of the deformed portion; and a spin history acquisition step of acquiring the spin history of the deformation portion during the deformation process from the acquired surface deformation history of the deformation portion, The successive stress updating process comprises: an acquired strain increment calculation step of calculating an acquired strain increment based on the strain history acquired in the strain history acquisition step; a hypothetical strain increment calculation step of assuming a deformation state of the deformation portion and calculating a hypothetical strain increment, the hypothetical strain increment being an increment of strain other than the strain whose strain history is acquired in the strain history acquisition step; a spin increment calculation step of calculating the spin increment based on the spin history obtained in the spin history acquisition step; A stress increment calculation step, using the obtained strain increment, the assumed strain increment and the obtained spin increment, to calculate the stress increment of each of the measurement points according to the material constitutive law; and a step of successively updating stresses, using the stress increments calculated for the respective measuring points, to successively update the stresses in the material coordinate system of the respective measuring points from the start of the deformation to the end of the deformation process; The residual stress distribution calculation step includes: The stress coordinate system conversion step converts the stress in the material coordinate system of each of the measuring points at the end of the deformation process, which is successively updated and calculated in the successive stress updating step, into a global stress value in a specified direction in the global coordinate system, and calculates the global stress value of each of the measuring points obtained by the conversion as the residual stress distribution of the deformed part.

2. The method for calculating residual stress distribution according to claim 1, in, The residual stress distribution calculation step further includes a residual stress distribution display step of displaying the residual stress distribution of the deformed portion obtained in the stress coordinate system conversion step.

3. The method for calculating residual stress distribution according to claim 1 or 2, in, In the step of calculating the assumed strain increment, a deformation state 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 distribution according to claim 1 or 2, in, In the step of calculating the assumed strain increment, 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.

5. A residual stress distribution calculation device calculates the distribution of residual stress generated on the metal plate subjected to plastic deformation. in, The residual stress distribution calculation device comprises a deformation history acquisition unit, a successive stress update unit and a residual stress distribution calculation unit. The deformation history acquisition unit comprises: a surface deformation history acquisition unit that acquires, for a plurality of measurement points set at a deformation site of the metal plate, three-dimensional coordinates measured during a deformation process of plastically deforming the metal plate as a surface deformation history of the deformation site from the start of deformation to the end of deformation; a strain history acquisition unit that acquires a strain history of the deformation portion during the deformation process from the acquired surface deformation history of the deformation portion; and The spin history acquisition unit acquires the spin history of the deformation portion during the deformation process from the acquired surface deformation history of the deformation portion. The successive stress updating unit comprises: an acquired strain increment calculation unit that calculates an acquired strain increment based on the strain history acquired by the strain history acquisition unit; an assumed strain increment calculation unit that assumes a deformation state of the deformation portion and calculates an assumed strain increment, the assumed strain increment being an increment of strain other than the strain for which the strain history is acquired by the strain history acquisition unit; an acquired spin increment calculation unit that calculates an acquired spin increment based on the spin history acquired by the spin history acquisition unit; a stress increment calculation unit that calculates the stress increment at each of the measurement points according to a material constitutive law using the acquired strain increment, the assumed strain increment, and the acquired spin increment; and A successive stress updating unit sequentially updates the stress in the material coordinate system of each of the measurement points from the start of deformation to the end of deformation in the deformation process using the stress increment calculated for each of the measurement points, The residual stress distribution calculation unit has: The stress coordinate system conversion unit converts the stress in the material coordinate system of each of the measuring points at the end of the deformation process, which is successively updated and obtained by the successive stress updating unit, into a global stress value in a specified direction in the global coordinate system, and obtains the converted global stress value of each of the measuring points as the residual stress distribution of the deformed part.

6. The residual stress distribution calculation device according to claim 5, in, The residual stress distribution calculation unit further includes a residual stress distribution display unit that displays the residual stress distribution of the deformed portion obtained by the stress coordinate system conversion unit.

7. The residual stress distribution calculation device according to claim 5 or 6, in, The assumed strain increment calculation unit assumes a deformation state according to a deformation process of the deformation portion, and calculates the assumed strain increment based on a plastic mechanics theory under the assumed deformation state.

8. The residual stress distribution calculation device according to claim 5 or 6, in, The assumed strain increment calculation unit assumes a deformation state of the deformation portion by finite element analysis of a deformation process of the metal plate, and calculates the assumed strain increment based on the assumed deformation state.

9. Residual stress distribution calculation program calculates the distribution of residual stress generated on the metal plate subjected to plastic deformation. in, The computer is used as a deformation history acquisition unit, a successive stress update unit, and a residual stress distribution calculation unit. The deformation history acquisition unit comprises: a surface deformation history acquisition unit that acquires, for a plurality of measurement points set at a deformation site of the metal plate, three-dimensional coordinates measured during a deformation process of plastically deforming the metal plate as a surface deformation history of the deformation site from the start of deformation to the end of deformation; a strain history acquisition unit that acquires a strain history of the deformation portion during the deformation process from the acquired surface deformation history of the deformation portion; and The spin history acquisition unit acquires the spin history of the deformation portion during the deformation process from the acquired surface deformation history of the deformation portion. The successive stress updating unit comprises: an acquired strain increment calculation unit that calculates an acquired strain increment based on the strain history acquired by the strain history acquisition unit; an assumed strain increment calculation unit that assumes a deformation state of the deformation portion and calculates an assumed strain increment, the assumed strain increment being an increment of strain other than the strain for which the strain history is acquired by the strain history acquisition unit; an acquired spin increment calculation unit that calculates an acquired spin increment based on the spin history acquired by the spin history acquisition unit; a stress increment calculation unit that calculates the stress increment at each of the measurement points according to a material constitutive law using the acquired strain increment, the assumed strain increment, and the acquired spin increment; and A successive stress updating unit sequentially updates the stress in the material coordinate system of each of the measurement points from the start of deformation to the end of deformation in the deformation process using the stress increment calculated for each of the measurement points, The residual stress distribution calculation unit has: The stress coordinate system conversion unit converts the stress in the material coordinate system of each of the measuring points at the end of the deformation process, which is successively updated and obtained by the successive stress updating unit, into a global stress value in a specified direction in the global coordinate system, and obtains the converted global stress value of each of the measuring points as the residual stress distribution of the deformed part.

10. The residual stress distribution calculation program according to claim 9, in, The residual stress distribution calculation unit further includes a residual stress distribution display unit that displays the residual stress distribution of the deformed portion obtained by the stress coordinate system conversion unit.

11. The residual stress distribution calculation program according to claim 9 or 10, in, The assumed strain increment calculation unit assumes a deformation state according to a deformation process of the deformation portion, and calculates the assumed strain increment based on a plastic mechanics theory under the assumed deformation state.

12. The residual stress distribution calculation program according to claim 9 or 10, in, The assumed strain increment calculation unit assumes a deformation state of the deformation portion by finite element analysis of a deformation process of the metal plate, and calculates the assumed strain increment based on the assumed deformation state.

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