Method for Predicting Shape Change after Springback of Sheet Metal Press Bending Formed Products

Abstract

To provide a method for estimating a shape change after the spring back of a plate press flexure molded article for estimating a shape change with a time elapse immediately after the spring back of a plate press flexure molded article produced by flexure-molding a metal plate.SOLUTION: A method for estimating a shape change after spring back of a plate press flexure molded article related to this invention is a method for calculating, on the basis of a material constitutive equation, strain and stress in a flexure curved surface 23 of a plate press flexure molded article 21 and flexure moment and curvature of the flexure curved surface 23 with respect to each process of: a process (S20) for flexure-molding a metal plate 11 into the plate press flexure molded article 21; a process (S30) for retaining the flexure molded plate press flexure molded article 21 in a metal mold 1; a process (S40) for forcing the plate press flexure molded article 21 unloaded by mold release from the metal mold 1 to spring back; and a process (S60) for leaving the plate press flexure molded article 21 after spring back on unloading.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to a method for predicting the shape change of a plate press bending formed product after springback and a shape change prediction program, and particularly to a method for predicting the shape change occurring in the bent curved surface portion of the plate press bending formed product with the passage of time from immediately after springback that occurs instantaneously when released from the mold, which is a method for predicting the shape change of a plate press bending formed product after springback.

Background Art

[0002] Press forming is a manufacturing method capable of manufacturing metal parts at low cost and in a short time, and is used in the manufacture of many automobile parts. In recent years, in order to achieve both the collision safety of automobiles and the weight reduction of vehicle bodies, higher-strength metal plates have been used in automobile parts.

[0003] One of the main problems when press forming a high-strength metal plate is a decrease in dimensional accuracy due to springback. When the metal plate is deformed by press forming, the residual stress generated in the press formed product becomes the driving force, and the phenomenon that the press formed product released from the mold instantaneously tries to return to the shape of the metal plate before press forming like a spring is called springback.

[0004] The residual stress generated during press forming becomes larger for higher-strength metal plates (for example, high-tensile steel plates), so the shape change due to springback also becomes larger. Therefore, it becomes more difficult to keep the shape of a higher-strength metal plate within the specified dimensions after springback. Thus, a technique for accurately predicting the shape change of a press formed product due to springback becomes important.

[0005] In predicting the shape change due to springback, it is common to use press forming simulation by the finite element method. As procedures in the press forming simulation, first, a press forming analysis of the process of press forming a metal sheet to the bottom dead center of forming is performed to predict the residual stress at the bottom dead center of press forming (for example, Patent Document 1). And a springback analysis of the process in which the shape of the press formed product released (removed) from the mold changes due to springback is performed to predict the shape in which the moment of force and the residual stress in the released press formed product are balanced (for example, Patent Document 2). It can be divided into a second step.

[0006] So far, by performing a press forming simulation that integrates the above-described first-step press forming analysis and second-step springback analysis, the shape of the press formed product released from the mold and springback has been predicted. However, when comparing the shape of the press formed product predicted by the press forming simulation with the shape of the actually press formed product, there are press formed products in which the shape prediction accuracy by the press forming simulation is low.

[0007] As an example, as shown in FIG. 10, a plate press bending formed product 21 obtained by press forming (bending) a metal sheet 11 using a mold 1 provided with a punch 3 and a die 5 has a different shape of the plate press bending formed product 21 immediately after being released from the mold 1 and springback and after several days have passed. The bent curved surface portion 23 of the plate press bending formed product 21 is deformed.

[0008] The time-dependent change of such a plate press bending formed product 21 seems to be similar to a phenomenon in which a structural member that continuously receives a high load from the outside gradually deforms like a creep phenomenon (for example, Patent Document 3). However, it is a shape change that occurs in a plate press bending press formed product that is not receiving a load from the outside, and an analysis method for dealing with the shape change due to the creep phenomenon cannot be applied.

[0009] On the other hand, as a method for predicting the shape change of a press-formed product over time after springback at the moment of release from the mold, by performing springback analysis of the press-formed product, the shape and residual stress of the press-formed product immediately after springback are obtained, and for a press-formed product with a set value of residual stress that is relaxed and reduced compared to the residual stress, a shape analysis is performed to obtain a shape in which the moment of force is balanced (for example, Patent Document 4).

Prior Art Documents

Patent Documents

[0010]

Patent Document 1

Patent Document 2

Patent Document 3

Patent Document 4

Summary of the Invention

Problems to be Solved by the Invention

[0011] However, in the method for predicting the shape change of a press-formed product over time after springback at the moment of release from the mold disclosed in Patent Document 4, it is necessary to set a value of residual stress that is relaxed and reduced by a predetermined ratio compared to the residual stress of the press-formed product immediately after springback, and it is necessary to adjust the ratio of relaxation and reduction of the residual stress so as to match the shape change immediately after springback of the actual press-formed product.

[0012] The present invention has been made to solve the above-described problems, and regarding a plate press bending molded product obtained by bending a metal plate, it is based on the overstress theory and the kinematic hardening rule to predict the shape change that occurs in the bent curved surface portion of the plate press bending molded product over time from immediately after springback that occurs instantaneously when it is released from the mold. The object is to propose a method for predicting the shape change after springback of a plate press bending molded product.

Means for Solving the Problems

[0013] The inventors conducted various investigations into the cause of the shape change that occurs with the passage of time from immediately after the springback of the above-described plate press bending molded product. As a result, in the plate press bending molded product after springback, it was found that the shape of the plate press bending molded product changes due to the internal residual stress gradually and non-uniformly changing (stress relaxation).

[0014] Therefore, they intensively studied a method for predicting the shape change per unit time of such a plate press bending molded product. As a result, in each process of the process of press-forming a metal plate into a plate press bending molded product by a mold, the process of holding the plate press bending molded product in the mold, the process of releasing the plate press bending molded product from the mold and causing springback of the plate press bending molded product, and the process of leaving the springback plate press bending molded product, based on the material constitutive equation considering the overstress theory and the kinematic hardening rule, by calculating the strain and stress of the plate press bending molded product by an elementary solution method, it was found that it is possible to accurately predict the shape change over time of the plate press bending molded product after springback. The present invention has been made based on such findings, and specifically, it has the following configuration.

[0015] The method for predicting the shape change after springback of a sheet metal press bending formed product according to the present invention is a method for predicting the shape change that occurs in the bending curved surface portion of the sheet metal press bending formed product with the passage of time from immediately after springback that occurs instantaneously after the sheet metal press bending formed product obtained by bending a metal sheet is released from the mold, and is a method for predicting the shape change after springback of a sheet metal press bending formed product, Using a mold, the process of bending the metal sheet into the sheet metal press bending formed product, the process of holding the bent sheet metal press bending formed product at the forming bottom dead center position in the mold, the process of releasing and unloading the held sheet metal press bending formed product from the mold so that the sheet metal press bending formed product undergoes springback, and the process of leaving the sheet metal press bending formed product after unloading and springback. For each of these processes, a simple bending curved surface model is used in which three or more evaluation points are set at positions including the bending center line in the thickness direction of the plate cross-section of the bending curved surface portion. For each discretized time step of each of these processes, based on the material constitutive equations of the following formulas (1) to (6), the strain and stress at each evaluation point, and the bending moment and curvature of the bending curved surface portion are obtained. A calculation parameter setting step of setting calculation parameters including the material constants of the material constitutive equations, the time steps of each process, the curvature rate corresponding to the processing speed of the bending curved surface portion in the bending forming process, and the target curvature of the bending curved surface portion. For the bending forming process, until the simple bending curved surface model is bent at the curvature rate to reach the target curvature, for each time step of the bending forming process, based on the material constitutive equations, the strain and stress at each evaluation point of the simple bending curved surface model and the curvature of the simple bending curved surface model are calculated in the bending forming process calculation step. For the process of holding in the mold, until a predetermined holding time has elapsed, for each time step of the process of holding in the mold, based on the material constitutive equations, the strain and stress at each evaluation point of the simple bending curved surface model are calculated in the in-mold holding process calculation step. Regarding the process of demolding and unloading the plate press bending formed product, the curvature velocity of the simple model of the bent curved surface part is set in the reverse direction of the bending forming process calculation step, and until the bending moment of the simple model of the bent curved surface part becomes 0, for each time step of the unloading process, based on the material constitutive equation, the strain and stress at each evaluation point of the simple model of the bent curved surface part, and the bending moment and curvature of the bent curved surface part are calculated, which is the unloading process calculation step, Regarding the process of leaving the plate press bending formed product after unloading and springback to stand, for each time step of the standing process, based on the material constitutive equation, the strain and stress at each evaluation point of the simple model of the bent curved surface part, and the bending moment and curvature of the bent curved surface part are calculated, which is the standing process calculation step, The standing process calculation step is, at each time step, setting a temporary curvature velocity to calculate the strain and stress at the evaluation point of the simple model of the bent curved surface part, calculating the bending moment of the simple model of the bent curved surface part based on the calculated stress, and until the calculated bending moment becomes a value sufficiently close to 0, correcting the temporary curvature velocity of the simple model of the bent curved surface part so that the bending moment approaches 0, and repeating the calculation of the strain and stress at each evaluation point and the bending moment, and when it is determined that the bending moment has become a value sufficiently close to 0, updating the curvature of the simple model of the bent curved surface part and proceeding to the next time step, which is characterized by this.

Number

Advantages of the Invention

[0016] According to the present invention, it is possible to accurately predict the shape change over time after springback occurs when a plate press bending molded product having a bent curved surface portion formed by bending a metal plate (for example, a press molded product having a U-shaped or hat-shaped cross-sectional shape) is released from the mold. Further, based on the predicted shape change, it is also possible to design the shape of the mold to be used for the bending molding.

Brief Description of the Drawings

[0017]

Figure 1

Figure 2

Figure 3

Figure 4

Figure 5

Figure 6

Figure 7

Figure 8

Figure 9

Figure 10

DETAILED DESCRIPTION OF THE INVENTION

[0018] Prior to explaining the method for predicting the shape change after springback of a press-bent plate product according to an embodiment of the present invention, a material constitutive equation for predicting the shape change after springback and a discretization calculation method for the material constitutive equation will be described below.

[0019] <Material Constitutive Equation> As shown in FIG. 10 described above, the bent curved surface portion 23 of the press-bent plate product 21 obtained by bending the metal plate 11 is considered to be in a deformed state close to plane strain equal bending. Therefore, in the present invention, the metal plate 11 or the bent curved surface portion 23 during the bending process is modeled as a bent curved surface simple model 31 shown in FIG. 2, and the bent curved surface simple model 31 is used to predict the shape change after springback of the press-bent plate product 21.

[0020] First, as shown in FIG. 2, a rectangular coordinate system is defined in which the longitudinal direction of the bent curved surface simple model 31 is x, the plate thickness direction is y, and the width direction is z. The coordinate origin O of the rectangular coordinate system is on the inner surface of the bend, and the plate bending center line coincides with the central axis in the plate thickness direction. At this time, the strain and stress in the bent curved surface simple model 31 shown in FIG. 2 are represented by the following material constitutive equations (1) to (6) based on the excess stress theory and kinematic hardening assuming plane strain equal bending, a plane stress field in the plate thickness direction, and constant plate thickness.

[0021] (A) Strain Since the change in plate thickness is not considered in the bent curved surface simple model 31, the true strain ε in the x direction (longitudinal direction) of the bent curved surface simple model 31 x is represented by Equation (1).

[0022] [Number]

[0023] Here, κ is a dimensionless curvature represented by the ratio (h / ρ) of the plate thickness h and the bending radius ρ of the bending curved surface model 31, h is the plate thickness of the metal plate 11, ρ is the bending radius of the bending curved surface 23, and y is the coordinate in the plate thickness direction. Note that the strain ε in the y direction (plate thickness direction) y and the strain ε in the z direction (plate width direction) z are always 0.

[0024] (B) Strain rate The strain rate dε in the x direction (longitudinal direction) of the bending curved surface model 31 x / dt is calculated from the difference in the true strain ε at the current time step and the previous time step calculated by Equation (1) when the process of change in the shape of the bending curved surface 23 is discretized with two or more time steps as described later. x is calculated from the difference. Note that the strain rate dε in the y direction (plate thickness direction) y / dt and the strain rate dε in the z direction (plate width direction) z / dt are always 0.

[0025] (C) Plastic strain rate (plastic component of strain rate) In the bending curved surface model 31, assuming a plane stress state where the stress σ in the plate thickness direction y is 0, the plastic strain rate dε p ij / dt can be described as in Equation (2) based on the strain increment theory.

[0026] [Number]

[0027] Here, the subscripts i and j represent any one of the x direction, y direction, and z direction. Also, X is the excess stress (residual stress), s ijis the deviatoric stress, α ' ij is the back stress α ij is the deviatoric component (deviatoric back stress). Also, <x d>is the Macaulay bracket, and when X / D ≤ 0, <x d>=0, when X / D > 0 <x d>= X / D. Furthermore, Y, D, and p are material constants. Y represents the magnitude of the yield surface (elastic limit surface), and D and P are material constants of the overstress theory. D is the resistance stress, and p is the stress sensitivity index.

[0028] (D) Equivalent plastic strain rate In the overstress theory, it is considered that the overstress X serves as the driving force for plastic deformation. This is expressed by Equation (3), and the equivalent plastic strain rate dε eq / dt is described by the power law of the overstress X. Here, X is the overstress (residual stress), and D and P are material constants. D is the resistance stress, and p is the stress sensitivity index.

[0029] [Number]

[0030] (E) Stress rate In the simplified model 31 of the bending curved surface part, from the plane strain condition where the strain rate dε z / dt in the plate width direction becomes 0 and Hooke's law, the stress rate dσ x / dt in the x - direction and the stress rate dσ z / dt in the z - direction can be expressed by Equation (4).

[0031] [Number]

[0032] Here, dε x / dt 、 dε z / dt are the strain rates in the x - direction and the z - direction, and dε p x / dt, dε p z / dt are the plastic strain rates in the x - direction and the z - direction (the plastic components of the strain rates dε x / dt, dε z / dt). Also, E and ν are material constants. E is Young's modulus, and ν is Poisson's ratio.

[0033] (E) Deviation back stress velocity The work hardening of the material (metal sheet) is expressed by the development of the deviation back stress α ' ij and, for example, the non-linear hardening law given by Equation (5) can be used.

[0034] [Number]

[0035] Here, dα ’ ij / dt is the velocity of the deviation back stress, and C and a are material constants related to work hardening (kinematic hardening law parameters), where C represents the rate of convergence of kinematic hardening and a represents the magnitude of kinematic hardening.

[0036] (F) Excess stress (residual stress) In the excess stress theory, when the load increases and the stress point goes outside the yield surface (elastic limit surface), the amount of overhang (= excess stress X) is represented, and a plastic strain rate dε p ij / dt occurs and plastic deformation progresses.

[0037] [Number]

[0038] Here, s ij is the deviation stress, and α ' ij is the back stress α ij 's deviation component (deviation back stress), and Y is a material constant representing the size of the yield surface (elastic limit surface). Note that the deviation stress s ij is given by Equation (7).

[0039] [Number]

[0040] Here, δ ij is the Kronecker delta, σ m is the average vertical stress, σ m =(1 / 3)(σ x +σ y +σ z ).

[0041] For the above material constitutive equations (1) to (6), a total of seven material constants are required: Young's modulus E, Poisson's ratio ν, resistance to stress D, stress sensitivity index p, kinematic hardening rule parameters C and a, and yield stress (yield surface size) Y.

[0042] Among these material constants, it is preferable to use the measured value of Young's modulus E from a material test and a general value for Poisson's ratio ν (for example, 0.3 for a steel plate). Also, it is preferable to identify the resistance to stress D and the stress sensitivity index p, which are material constants of the overstress theory, based on data related to the rate dependence of the flow stress.

[0043] Furthermore, the kinematic hardening rule parameters C (the rate of convergence of kinematic hardening) and a (the magnitude of kinematic hardening), and the yield stress Y (the size of the yield surface on the model) are, for example, as shown in Figure 3, by applying uniaxial tensile deformation to the test piece 41 of the metal plate, holding the strain constant at a predetermined strain, measuring the changes in strain and stress over time (tensile-hold test results), and, as shown in Figure 4, after applying uniaxial tensile deformation to the test piece 41 of the metal plate and unloading, reversing the loading direction and applying compressive deformation while preventing buckling of the test piece 41, holding the strain constant at a predetermined strain, and measuring the changes in true strain and true stress over time (tensile unloading reverse compression hold test results). It is preferable to adjust them based on these results.

[0044] That is, based on the above material constitutive equations (1) to (6), the values of the material constants D, p, a, C, and Y can be adjusted so that the calculated results of the time changes in true strain and true stress of the tensile-hold test and the tensile unloading reverse compression hold test match the experimental results of each material test.

[0045] The mechanism for expressing the stress relaxation behavior and the shape change according to the above material composition formulas (1) to (6) will be described with reference to FIG. 5.

[0046] In the initial undeformed state of the metal plate, it coincides with the origin of the deviatoric stress space at the center of the yield surface. When the stress applied to the metal plate is within the yield surface, it is in an elastic deformation state following Hooke's law, and no change occurs to the yield surface.

[0047] When the load increases and the stress point goes outside the yield surface, a plastic strain rate dε p ij / dt occurs according to the amount of overshoot (= excess stress X), and plastic deformation progresses. As the plastic deformation progresses, a deviatoric back stress α ’ ij develops, and this deviatoric back stress represents the center position of the yield surface. That is, as the plastic deformation progresses, the yield surface moves without changing its size. This movement of the yield surface represents work hardening (kinematic hardening), and the deviatoric back stress α ’ ij can also be said to be a state variable representing the amount of movement of the center of the yield surface at this time. Here, the strain rate dε ij / dt is the sum of the elastic strain rate dε e ij / dt and the plastic strain rate dε p ij / dt (dε ij / dt = dε e ij / dt + dε p ij / dt).

[0048] Even if the plastic deformation is stopped halfway and the strain is kept constant (dε ij / dt = 0), at that point, since the stress point is outside the yield surface, a plastic strain rate dε p ij / dt occurs, and at the same time, an elastic strain rate dε e ij / dt of the same magnitude but opposite in sign (dε ij / dt = dε e ij / dt + dε p ij Since / dt = 0, this will occur. As a result, a stress rate will occur, causing a change in stress, that is, stress relaxation.

[0049] During stress relaxation, the plastic strain rate dε p ij Since / dt exists, the development of the deviatoric back stress α ’ ij continues, and the yield surface continues to move. However, as a result of the change in the stress value and the movement of the yield surface, the amount of stress point overshoot (excess stress X) gradually decreases, so the stress relaxation also gradually becomes gentler, and finally the stress relaxation converges when the stress point returns to the yield surface.

[0050] Furthermore, in the bent curved surface part during stress relaxation, a shape change occurs so that the moment of force and the stress are balanced. And when the stress relaxation converges, the shape change of the bent curved surface part also ends.

[0051] Note that the dimensionless curvature and dimensionless curvature rate in the above material constitutive equations (1) to (6) are obtained by dimensionlessizing the curvature and curvature rate of the bent curved surface part, respectively, but a material constitutive equation formulated without dimensionlessizing them may also be used.

[0052] <Discretization calculation method> Next, based on the above material constitutive equations (1) to (6), a discretization calculation method for predicting the shape change of a sheet metal press bending formed product over time will be described.

[0053] In the discretization calculation method, first, the bent curved surface part of the sheet metal press bending formed product is modeled as a simple model 31 of the bent curved surface part shown in Fig. 2, and three or more evaluation points 33 are set in the thickness direction including the position on the plate bending center line of the plate cross section in the simple model 31 of the bent curved surface part.

[0054] Then, in the present invention, as an example, as shown in FIG. 10, in the process of bending a metal plate 11 into a plate press bending formed product 21 using a mold 1 having a punch 3 and a die 5, the process of holding the plate press bending formed product 21 in the mold 1, the process in which the plate press bending formed product 21 unloaded and released from the mold 1 springs back, and the process of leaving the plate press bending formed product 21 after unloading and springing back are each divided (discretized) into two or more time intervals from the start to the end.

[0055] Then, for each process, the values of strain, equivalent plastic strain, stress, and deviatoric stress at each evaluation point 33 of the bending curved surface simple model 31 are calculated for each time interval using the values at the previous time interval. Further, from the calculated stress, the deviatoric stress and the excess stress at each evaluation point 33 and the bending moment of the bending curved surface simple model 31 are calculated.

[0056] In such a discretization calculation method, by representing history variables such as the strain and stress of the bent curved surface formed by bending the metal plate, the influence of the non-linear hardening behavior in plastic deformation can be accurately calculated. Furthermore, by numerically integrating the stress at each evaluation point 33 in the plate thickness direction, it becomes possible to calculate in detail the history of the bending moment in the bending curved surface simple model 31.

[0057] <Method for Predicting Shape Change after Springback of Plate Press Bending Formed Product> The method for predicting the shape change after springback of a plate press bending formed product according to an embodiment of the present invention predicts the shape change that occurs over time in the bending curved surface portion 23 of the plate press bending formed product 21 from immediately after springback that occurs instantaneously after the release of the plate press bending formed product 21 formed by bending the metal plate 11 using the mold 1, as shown in FIG. 10. Then, as shown in FIG. 10 as an example, the process of bending the metal plate 11 into the plate press bending formed product 21 (FIGS. 10(a)-(b)), the process of holding the bent plate press bending formed product 21 at the forming bottom dead center position in the mold 1 (FIG. 10(b)), the process of releasing and unloading the held plate press bending formed product 21 from the mold 1 and the plate press bending formed product 21 springing back (FIG. 10(c)), and the process of leaving the plate press bending formed product 21 after unloading and springing back (FIG. 10(d)), for each of these processes, as shown in FIG. 2, using the simple bending curved surface model 31 in which three or more evaluation points 33 are set at positions including the plate bending center line in the plate thickness direction of the cross section of the bending curved surface portion 23, for each discretized time step of each process, based on the material constitutive equations of the above equations (1)-(6), the strain and stress at each evaluation point 33, and the bending moment and curvature of the simple bending curved surface model 31 of the bending curved surface portion are obtained. As shown in FIG. 1, it includes a calculation parameter setting step S10, a bending forming process calculation step S20, a holding process calculation step S30 in the mold, a unloading process calculation step S40, and a leaving process calculation step S60. Hereinafter, each of these steps will be described.

[0058] ≪Calculation Parameter Setting Step≫ The calculation parameter setting step S10 is a step of setting calculation parameters including the material constants of the material constitutive equations (1)-(6), the time step of each process, the curvature rate corresponding to the processing speed of the bending curved surface portion 23 in the bending forming process, and the target curvature of the bending curved surface portion 23.

[0059] In the present embodiment, in the calculation parameter setting step S10, (i) setting of the material constants of the material constitutive equation (S11), (ii) setting of the calculation conditions (S13), (iii) setting of the time step (S15), (iv) setting of the target dimensionless curvature and dimensionless curvature rate of the simple bending curved surface model 31 of the bending curved surface portion (S17), are performed.

[0060] (i) Setting of the material constants of the material constitutive equation First, the material constants of the material constitutive equations of equations (1)-(6) are set (S11). As described above, the material constants to be set are a total of seven, namely Young's modulus E, Poisson's ratio ν, back stress D, stress sensitivity index p, kinematic hardening rule parameters C and a, and yield stress (yield surface size) Y.

[0061] As described above, for example, Young's modulus E can be obtained from the slope of the linear part in the stress-strain relationship measured by a material test in which a tensile load or a compressive load is applied to a test piece 41 cut out from a metal plate 11 as shown in Fig. 3(a). Poisson's ratio ν may be set according to the metal plate to be subjected to press forming. For example, in the case of a steel plate, a general value (=0.3) may be set.

[0062] The size Y of the yield surface (elastic limit surface), back stress D, stress sensitivity index p in Eqs. (1) and (2), and kinematic hardening rule parameters C and a in Eq. (4) can be determined by a tension-hold test (Fig. 3), which is a uniaxial tensile test, and a tension-unloading-reverse compression-hold test (Fig. 4).

[0063] Specifically, Y, D, p, a, and C in the theoretical formula (8) of the flow stress in plastic deformation during the tension-hold test, which is derived from the unified visco-elasto-plastic constitutive equation based on the overstress theory and the kinematic hardening rule in the uniaxial stress state, can be determined by adjusting based on the results of the tension-hold test (Figs. 3(b) and (c)) and the results of the tension-unloading-reverse compression-hold test (Figs. 4(b) and (c)).

[0064]

Number

[0065] Table 1 shows an example of the material constants of the material constitutive equations (1) to (6) obtained by the above method for a 1180 MPa grade ultra-high tensile steel plate.

[0066]

Table 1

[0067] Note that each material constant in the material constitutive equations (1) to (6) may be set to a value obtained in advance by a tension-holding test and a tension-unloading-reverse compression-holding test.

[0068] (ii) Setting of calculation conditions Next, the calculation conditions are set (S13). As the calculation conditions, the plate thickness (= h) and the bending curvature (K = 1 / ρ) of the simplified model 31 of the bent curved surface part are set.

[0069] (iii) Setting of time step Subsequently, the time step is set (S15). The time step is used in the discretization calculation method of the material constitutive equations (1) to (6), and for each of the bending process, the holding process, the unloading process, and the standing process, time steps discretized into two or more with a predetermined time step width are set. Furthermore, the bending forming time in the bending process, the holding time in the holding process, the unloading (springback) time in the unloading process, and the standing time in the standing process are divided by the time step width in each process, and the time step lengths in each step of the bending process calculation step S20, the in-die holding process calculation step S30, the unloading process calculation step S40, and the standing process calculation step S60 are set.

[0070] The time step width is preferably set to approximately 1 / 10 to 1 / 1000 seconds. While setting it shorter can be expected to improve the calculation accuracy, the calculation time becomes longer, so it is set according to the purpose. However, in the standing process calculation step, since the process takes a long time and its deformation speed slows down with the passage of time, it is preferable to increase the time step width with the passage of time, and it is also effective to set a time step width of 1 second or more.

[0071] (iv) Setting of target dimensionless curvature and dimensionless curvature speed Subsequently, the target dimensionless curvature and dimensionless curvature speed of the simplified model 31 of the bent curved surface part are set (S17). The target dimensionless curvature κ is obtained by making dimensionless the curvature of the bent curved surface portion 23 at the bottom dead center of forming of the plate press bending formed product 21, and the curvature K of the plate bending center line indicated by the dashed line in the cross section in the plate thickness direction of the simplified model 31 of the bent curved surface portion shown in Fig. 2 is made dimensionless using the plate thickness h as shown in the following formula (9).

[0072]

Equation

[0073] Since the relationship between the bending radius ρ and the curvature K of the simplified model 31 of the bent curved surface portion is expressed as K = 1 / ρ, when the bending angle of the bent curved surface portion 23 at the bottom dead center of forming is 90°, the target dimensionless curvature may be calculated and set by κ = h / ρ.

[0074] Furthermore, the dimensionless curvature speed corresponds to the processing speed of the bent curved surface portion in the bending forming process, and is the amount of change per unit time (per unit time step width) of the dimensionless curvature of the simplified model 31 of the bent curved surface portion. Therefore, the value calculated by dividing the target dimensionless curvature by the time step length of the bending forming process calculation step S20 is set as the dimensionless curvature speed.

[0075] ≪Bending Forming Process Calculation Step≫ In the bending forming process calculation step S20, for the process of bending forming, until the simplified model 31 of the bent curved surface portion is bent formed at the curvature speed and reaches the target curvature, for each time step of the bending forming process, based on the material constitutive equations (1) to (6), the strain and stress at each evaluation point 33 of the simplified model 31 of the bent curved surface portion and the curvature of the simplified model 31 of the bent curved surface portion are calculated.

[0076] In the present embodiment, the dimensionless curvature at the current time step is calculated (S21). The dimensionless curvature at the current time step is calculated by adding the value obtained by multiplying the dimensionless curvature speed by the time step width to the dimensionless curvature at the previous time step. Here, as the dimensionless curvature at the start of the bending forming process calculation step S20, for example, the dimensionless curvature of the metal plate 11 (=0) may be given.

[0077] Next, in the stress relaxation reflection strain / stress calculation step S23, strains (true strain, plastic strain, equivalent plastic strain) and stresses (stress, deviatoric stress, back stress, excess stress) at each evaluation point 33 of the metal plate 11 are calculated based on the material constitutive equations (1) to (6) (S23).

[0078] In the present embodiment, strains and stresses at the current time step (this time step) are calculated based on the strains (strain, plastic strain, equivalent plastic strain) and stresses (stress, deviatoric stress, back stress, excess stress) at the previous time step (the previous time step). As shown in FIG. 6, it includes a true strain calculation step S23a, a strain rate calculation step S23b, an equivalent plastic strain rate / plastic strain rate calculation step S23c, a stress rate calculation step S23d, a back stress rate calculation step S23e, an equivalent plastic strain / plastic strain / stress / back stress calculation (update) step S23f, and an excess stress calculation (update) step S23g.

[0079] (True Strain Calculation Step) In the true strain calculation step S23a, based on Equation (1), from the dimensionless curvature κ at the current time step and the plate thickness h of the metal plate, the true strain ε in the longitudinal direction (x direction in the bending curved surface part simple model 31) at the current time step x is calculated.

[0080] (Strain Rate Calculation Step) In the strain rate calculation step S23b, the strain rate in the x direction (longitudinal direction) at the previous time step is calculated by dividing the change amount of the true strain ε x from the previous time step to the current time step by the time step width.

[0081] (Equivalent Plastic Strain Rate / Plastic Strain Rate Calculation Step) In the equivalent plastic strain rate / plastic strain rate calculation step S23c, using the excess stress X at the previous time step, from Equation (3), the equivalent plastic strain rate dε eq / dt at the previous time step is calculated, and the excess stress X and the deviatoric stress s at the previous time step ij and the deviatoric back stress α ’ ij Using these and Equation (2), the plastic strain rate dε p ij / dt at the previous time step is calculated.

[0082] (Stress rate calculation step) In the stress rate calculation step S23d, the strain rate dε x / dt at the previous time step calculated in the strain rate calculation step S23b and the plastic strain rate dε p ij / dt at the previous time step calculated in the equivalent plastic strain rate and plastic strain rate calculation step S23c are used to calculate the stress rate dσ x / dt and dσ z / dt at the previous time step from Equation (4).

[0083] (Deviatoric back stress rate calculation step) In the deviatoric back stress rate calculation step S23e, the equivalent plastic strain rate and plastic strain rate and the deviatoric back stress at the previous time step calculated in the equivalent plastic strain rate and plastic strain rate calculation step S23c are used to calculate the deviatoric back stress rate dα ’ ij / dt at the previous time step from Equation (5).

[0084] (Equivalent plastic strain, plastic strain, stress, and deviatoric back stress calculation (update) step) In the equivalent plastic strain, plastic strain, stress, and deviatoric back stress calculation (update) step S23f, the equivalent plastic strain, plastic strain, true stress, and deviatoric back stress at the current time step are calculated using the equivalent plastic strain, plastic strain, true stress, and deviatoric back stress at the previous time step.

[0085] The equivalent plastic strain ε eq at the current time step is obtained by multiplying the equivalent plastic strain rate (previous dε eq / dt) calculated in the equivalent plastic strain rate and plastic strain rate calculation step S23c at the previous time step by the time step width (=Δt), and adding this to the equivalent plastic strain (previous ε eq ) is added to, and the equivalent plastic strain (this time ε eq ) at the current time step is calculated (updated). (This time ε eq = previous time ε eq + previous time dε eq / dt·Δt)

[0086] The plastic strain ε p ij at the current time step is obtained by multiplying the plastic strain rate (previous time dε p ij / dt) calculated in the equivalent plastic strain rate - plastic strain rate calculation step S23c by the time step width Δt, and adding this to the plastic strain (previous time ε p ij ) at the previous time step to calculate the plastic strain (this time ε p ij ). (This time ε p ij = previous time ε p ij + previous time dε p ij / dt·Δt)

[0087] The true stress σ x , σ z at the current time step is obtained by multiplying the stress rate (previous time dσ x / dt and previous time dσ z / dt) calculated in the stress rate calculation step S23d by the time step width Δt, and adding this to the true stress (previous time σ x and previous time σ z ) at the previous time step to calculate the true stress (this time σ x and this time σ z ). (This time σ x = previous time σ x + previous time dσ x / dt·Δt, this time σ z = previous time σ z + previous time dσ z / dt·Δt)

[0088] The deviatoric back stress α ’ ij is the deviatoric stress rate (previous dα ’ ij / dt) calculated in the deviatoric stress rate calculation step S23e at the previous time increment, multiplied by the time increment width Δt, and added to the deviatoric stress (previous α ’ ij ) at the previous time increment to calculate (update) the deviatoric stress (current α ’ ij ) at the current time increment. (Current α ’ ij = Previous α ’ ij + Previous dα ’ ij / dt·Δt)

[0089] (Excess stress calculation (update) step) In the excess stress calculation (update) step S23g, the deviatoric stress s x and σ z at the current time increment calculated (updated) in the equivalent plastic strain·plastic strain·stress·deviatoric stress calculation (update) step S23f are used to calculate the deviatoric stress s ij from Equation (7), and the deviatoric stress α ' ij at the current time increment calculated (updated) in the equivalent plastic strain·plastic strain·stress·deviatoric stress calculation (update) step S23f and the deviatoric stress s ij are used to calculate (update) the excess stress X at the current time increment from Equation (6).

[0090] Thus, once the strain and stress at the current time increment are calculated, it is determined whether the dimensionless curvature at the current time increment is greater than or equal to the target dimensionless curvature (S25). If it is determined that the dimensionless curvature at the current time increment is not greater than or equal to the target dimensionless curvature, the next time increment is advanced (S27), and the calculation of the dimensionless curvature (S21) and the stress relaxation reflected strain·stress calculation step (S23) are repeated. And if it is determined that the dimensionless curvature at the current time increment is greater than or equal to the target dimensionless curvature, the process proceeds to the next mold holding process calculation step S30.

[0091] <<Mold internal holding process calculation step>> The mold internal holding process calculation step S30 is a step of calculating the strain and stress at each evaluation point 33 of the bending curved surface part simple model 31 based on the material constitutive equations (1) to (6) at each time increment of the process of holding in the mold 1 until a predetermined holding time elapses for the process of holding in the mold 1.

[0092] In the present embodiment, first, for the bending curved surface part simple model 31 at the time when the target dimensionless curvature is reached in the bending forming process calculation step S20, the values of strain (true strain, equivalent plastic strain, plastic strain) and stress (true stress, deviatoric stress, deviatoric back stress, excess stress) remain as they are, and the value of the dimensionless curvature rate is set to 0 (S31).

[0093] Next, in the stress relaxation reflected strain / stress calculation step S33, similar to the stress relaxation reflected strain / stress calculation step S23 in the bending forming process calculation step S20, based on the material constitutive equations (1) to (6), the strain (true strain, equivalent plastic strain, plastic strain) and stress (true stress, deviatoric stress, deviatoric back stress, excess stress) that reflect the stress relaxation at each evaluation point 33 of the bending curved surface part simple model 31 are calculated.

[0094] Next, it is determined whether the current time increment is greater than or equal to the holding time in the mold 1 (S35). If it is determined that the current time increment is less than the holding time, the process proceeds to the next time increment (S37), and the setting of the dimensionless curvature (S31) and the calculation of strain and stress (S35) are repeated. And if it is determined that the current time increment is greater than or equal to the holding time, the process proceeds to the next unloading process calculation step S40. Note that the larger the time increment length in the mold internal holding process calculation step S30, the more the stress relaxation progresses while the bending curved surface part is held in a state where the dimensionless curvature is constant, so the bending moment changes more compared to the bending curved surface part simple model 31 immediately after the bending forming process calculation step S20.

[0095] <UNK> <<Unloading process calculation step>> In the unloading process calculation step S40, for the process of releasing and unloading the sheet metal press bending formed product 21, the curvature speed of the simple model 31 of the bent curved surface part is set in the reverse direction to that in the bending forming process calculation step S20. Until the bending moment of the simple model 31 of the bent curved surface part becomes 0, for each time increment in the unloading process, based on the material constitutive equations (1) to (6), the strain and stress at each evaluation point 33 of the simple model 31 of the bent curved surface part, and the bending moment and curvature of the simple model 31 of the bent curved surface part are calculated.

[0096] Springback occurs during the process of bending a metal sheet. After stress relaxation during holding in the mold, the residual stress remaining in the sheet metal press bending formed product becomes the driving force, and the released and unloaded sheet metal press bending formed product 21 tries to return to the shape of the original metal sheet 11 like a spring until the balance between the moment of force and the residual stress is achieved.

[0097] Therefore, in the unloading process calculation step S40, until the balance between the moment of force and the residual stress is achieved in the simple model 31 of the bent curved surface part, that is, until the bending moment of the simple model 31 of the bent curved surface part becomes 0, for each time increment, the strain (true strain, equivalent plastic strain, plastic strain) and stress (true stress, deviatoric stress, deviatoric back stress, excess stress) at each evaluation point 33 of the simple model 31 of the bent curved surface part and the bending moment of the simple model 31 of the bent curved surface part are calculated.

[0098] First, set the dimensionless curvature speed in the unloading direction (S41). For the dimensionless curvature speed in the unloading direction, for example, a value with the opposite sign and the same absolute value as the dimensionless curvature speed in the bending forming process can be set.

[0099] The dimensionless curvature rate in the unloading process calculation step S40 may be appropriately set to the dimensionless curvature rate in the unloading direction during springback. For example, in advance, based on the relationship between the amount of change in the curvature of the bent curved surface portion 23 due to springback and the time when springback occurs through springback analysis of the sheet metal press bending formed product 21 by FEM analysis or the like, the dimensionless curvature rate in the unloading direction during springback may be set.

[0100] Next, the springback is performed by an amount obtained by multiplying the dimensionless curvature rate by the elapsed time increment length from immediately after the sheet metal press bending formed product 21 is demolded and unloaded, and the dimensionless curvature at the current time increment is calculated (S43).

[0101] Subsequently, in the stress relaxation reflected strain and stress calculation step S45, similar to the stress relaxation reflected strain and stress calculation step S23 in the bending forming process calculation step S20, using formulas (1) to (6), the strains (true strain, equivalent plastic strain, plastic strain) and stresses (true stress, deviator stress, deviator back stress, excess stress) reflecting the stress relaxation at each evaluation point 33 are calculated (S45).

[0102] Furthermore, using the calculated stresses at each evaluation point 33, the bending moment M of the plate cross-section around the plate thickness center is calculated by formula (10) (S47).

[0103]

Equation

[0104] Then, it is determined whether the calculated bending moment M is equal to 0 (S49). When it is determined that the bending moment M is not equal to 0 (for example, the absolute value of the bending moment M is equal to or greater than a predetermined value that is sufficiently small), the process proceeds to the next time increment (S51), and the calculation of the dimensionless curvature (S43), the calculation of the stress, strain, and excess stress (S45), the calculation of the bending moment (S47), are repeated, and again, the determination of the bending moment (S49) is performed. When it is determined that the bending moment M is 0 (less than a predetermined value where the absolute value of the bending moment is sufficiently small) (S49), the process proceeds to the next relaxation process calculation step S60.

[0105] ≪Relaxation Process Calculation Step≫ In the relaxation process calculation step S60, for the process of leaving the sheet metal press bending formed product 21 after unloading and springback, at each time interval of the leaving process, based on the material constitutive equation, the strain and stress at each evaluation point 33 of the bending curved surface simple model 31, and the bending moment M and curvature (dimensionless curvature) of the bending curved surface simple model 31 are calculated.

[0106] Immediately after the springback ends, the moment of force and the residual stress are in balance, that is, the bending moment M of the plate cross-section is 0. However, in the subsequent process of leaving the sheet metal press bending formed product 21, as the stress relaxes over time, a shape change occurs in the bending curved surface part 23 so as to offset the change in the bending moment M of the plate cross-section, and it is presumed that the state where the bending moment M is 0 is maintained.

[0107] Therefore, in the relaxation process calculation step S60, first, a temporary dimensionless curvature rate in the relaxation process of the bending curved surface simple model 31 is set (S61), and a temporary dimensionless curvature after a unit time interval is calculated (S63).

[0108] As will be described later, the dimensionless curvature rate in the relaxation process calculation step S60 is used to obtain the dimensionless curvature at each time interval by convergence calculation so that the state where the bending moment M of the bending curved surface simple model 31 becomes 0. Therefore, a temporary value may be appropriately set as the dimensionless curvature rate, and a temporary dimensionless curvature may be calculated as the initial value of the convergence calculation.

[0109] Next, under the dimensionless curvature after each unit time step calculated in (S63), in the stress relaxation reflected strain and stress calculation step S65, similar to the stress relaxation reflected strain and stress calculation step S23 in the bending forming process calculation step S20, using the material constitutive equations of Equations (1) to (6), strains (true strain, equivalent plastic strain, plastic strain) and stresses (true stress, deviatoric stress, deviatoric back stress, excess stress) that reflect stress relaxation at each evaluation point 33 of the bending curved surface part simple model 31 are calculated (S65).

[0110] Subsequently, using the stresses at each evaluation point 33 of the bending curved surface part simple model 31 calculated in the stress relaxation reflected strain and stress calculation step S65, the bending moment M of the bending curved surface part simple model 31 is calculated (S67) by the aforementioned Equation (10).

[0111] Then, it is determined whether the calculated bending moment M is 0 (S69). If it is determined that the bending moment M is not equal to 0 (the absolute value of the bending moment M is equal to or greater than a predetermined value that is sufficiently small), until the bending moment M becomes a value sufficiently close to 0, the correction of the dimensionless curvature after each unit time step (S71) to make the bending moment M approach 0, the calculation of the strains and stresses at each evaluation point 33 in the stress relaxation reflected strain and stress calculation step (S65), and the calculation of the bending moment of the bending curved surface part simple model 31 (S67) are repeated, and again, the determination of the bending moment M (S69) is performed. And if it is determined that the bending moment M is 0 (the absolute value of the bending moment is less than a predetermined value that is sufficiently small), the dimensionless curvature of the bending curved surface part simple model after each unit time step is determined (S73). Then, it is determined whether the time after each unit time step (the current time) has reached the target time for leaving the sheet metal press bending formed product 21 (S75). If the current time has not reached the target time, the process proceeds to the next time step (S77). In this way, at each time step until the target time in the process of leaving, the curvature (dimensionless curvature) of the bending curved surface part that is bent so that the bending moment M becomes 0 is updated.

[0112] Finally, after the idle process calculation step S60 ends, the calculation result is output (S80), and the calculation ends.

[0113] As described above, according to the method for predicting the shape change after springback of the plate press bending formed product according to the present embodiment, after the bent plate press bending formed product is held in the mold and then released, and when it is left without applying an external force after springback, it is possible to predict the phenomenon that the strain stress distribution and curvature in the thickness direction of the bent curved surface portion of the plate press bending formed product change with time while maintaining the state that satisfies the condition of the bending moment 0 from the outside.

[0114] Further, in the present embodiment, by representing history variables such as strain and stress at three or more evaluation points set in the thickness direction of the plate cross section including the plate bending center line in the bent curved surface portion simple model 31, and calculating the bending moment of the bent curved surface portion simple model 31 by numerical integration using the stress at each evaluation point, it becomes possible to calculate in detail the history of strain or stress, excess stress, and bending moment at each position in the thickness direction of the bent cross section.

[0115] Furthermore, for each process of the bending process, the holding process in the mold, the unloading process, and the idle process, by using a discretization calculation method that divides each process into two or more time steps and calculates the strain and stress at each time step, it is possible to accurately calculate the influence of the non-linear hardening behavior in the plastic deformation of the metal plate.

[0116] Note that the method for predicting the shape change after springback of the plate press bending formed product according to the present invention is not particularly limited by the type of metal plate, the type and shape of the plate press bending formed product, but it is more effective when using a high-strength metal plate and when the thickness is thin relative to the curvature of the bent curved surface portion formed by bending. Specifically, it is preferable to target a metal plate having a tensile strength of 270 MPa or more and a thickness of 0.3 mm or more and 3.6 mm or less. In addition, as types of sheet metal press bending formed products, it is preferable to target outer panel parts such as doors, roofs, and hoods with relatively low rigidity as automotive parts, and skeleton parts such as A-pillars, B-pillars, roof rails, side rails, front side members, rear side members, and cross members that are bent and formed using high-strength metal sheets.

Example

[0117] The function and effect of the method for predicting the shape change after springback of the sheet metal press bending formed product of the present invention will be described based on specific examples. In this example, the L-bending test was targeted for the bending forming by press working of the metal sheet, the shape change after springback was predicted, and it was compared and verified with the experimental results of the shape change after springback by the actual L-bending test.

[0118] In the L-bending test in this example, as the metal sheet 11, it was rectangular with a width of 100 mm, a length of 250 mm, and a thickness of 1.2 mm, and a super high-tensile steel sheet with a tensile strength of 1180 MPa, which has a large shape change after springback, was used.

[0119] And, as shown in FIG. 10, (a) the metal sheet 11 was placed on the die 5 having the die shoulder 5a with a predetermined die shoulder radius (12 mm), and (b) by pushing down the punch 3 by 100 mm, the metal sheet 11 was bent and formed into a 90° sheet metal press bending formed product 21 along the die shoulder 5a. (c) After the bending forming, when the punch 3 was raised to unload (release the mold), springback occurred in the bent curved surface portion 23 of the sheet metal press bending formed product 21, and (d) then it was left in that state for 100 seconds. In addition, the clearance at the forming bottom dead center of the punch 3 and the die 5 in (b) in the L-bending test was set to 1.5 mm.

[0120] In addition, the material constants in the material constitutive equations (1) to (6) were set as the Young's modulus (208 GPa) and Poisson's ratio (= 0.3) measured for the metal sheet used in the L-bending test. For the other material constants, they were identified as shown in Table 1 above by means of a tensile-holding test (see Fig. 3) and a tensile-unloading-reverse compression-holding test (see Fig. 4) in advance.

[0121] Fig. 7 shows a comparison between the experimental results of the true stress-true strain relationship obtained by the tensile-holding test and the calculation results using the theoretical formula (8) of the flow stress in the plastic deformation during the tensile-holding test derived from the unified visco-elastoplastic constitutive equation based on the overstress theory and the kinematic hardening rule in the uniaxial stress state.

[0122] It can be seen that the calculation results of the true stress-true strain relationship well capture the tendency of the experimental results. Also, the calculated value of the true stress during the holding process had an error of about 10 MPa compared with the experimental value, which was good.

[0123] Fig. 8 shows a comparison between the experimental results of the true stress-true strain relationship obtained by the tensile-unloading-reverse compression-holding test and the calculation results using Eq. (8).

[0124] Similar to the case of the tensile-holding test shown in Fig. 7, it can be seen that the calculation results of the true stress-true strain relationship well capture the tendency of the experimental results, and the Bauschinger effect after stress reversal is well reproduced. Also, the calculated value of the true stress during the holding process had an error of about 10 MPa or less compared with the experimental value, which was good.

[0125] Fig. 9 shows a comparison between the calculation results and the experimental results of the change over time of the bending angle after springback of the bent curved surface portion bent by the L-bending test using the material constants of the material constitutive equations (1) to (6) obtained in this way. From Fig. 9, although the calculation results of the present invention predict the change in the bending angle to be slightly larger than the experimental results, they well capture the tendency of the shape change over time.

[0126] As described above, according to the method for predicting the shape change of a sheet metal press-bent product after springback according to the present invention, it has been shown that the shape change of the sheet metal press-bent product after springback over time can be predicted well.

Explanation of reference numerals

[0127] 1 Mold 3 Punch 5 Die 5a Die shoulder 11 Metal plate 21 Sheet metal press-bent product 23 Bent curved surface portion 31 Simplified model of bent curved surface portion 33 Evaluation point 41 Specimen< / x> < / x> < / x>

Claims

【Claim 1】 A method for predicting the shape change of a plate press bending formed product after springback, which predicts the shape change that occurs in the bent curved surface portion of the plate press bending formed product over time from immediately after springback that occurs instantaneously after the release of the plate press bending formed product formed by bending a metal plate, comprising: Using a simple model of the bent curved surface portion in which three or more evaluation points are set at positions including the plate bending center line in the plate thickness direction of the plate cross section of the bent curved surface portion for each of the processes of bending the metal plate into the plate press bending formed product using a mold, holding the bent plate press bending formed product at the forming bottom dead center position in the mold, releasing and unloading the held plate press bending formed product from the mold so that the plate press bending formed product springs back, and leaving the plate press bending formed product after unloading and springback. For each time step of each process, based on the material constitutive equations of the following formulas (1) to (6), the strain and stress at each evaluation point, and the bending moment and curvature of the bent curved surface portion are obtained. A calculation parameter setting step of setting calculation parameters including the material constants of the material constitutive equation, the time steps of each process, the curvature rate corresponding to the processing speed of the bent curved surface portion in the bending process, and the target curvature of the bent curved surface portion; For the bending process, until the simple model of the bent curved surface portion is bent at the curvature rate to reach the target curvature, for each time step of the bending process, based on the material constitutive equation, the strain and stress at each evaluation point of the simple model of the bent curved surface portion and the curvature of the simple model of the bent curved surface portion are calculated in a bending process calculation step; For the process of holding in the mold, until a predetermined holding time has elapsed, for each time step of the process of holding in the mold, the strain and stress at each evaluation point of the simple model of the bent curved surface portion are calculated in a holding process calculation step in the mold based on the material constitutive equation; Regarding the process of demolding and unloading the plate press bending formed product, the curvature speed of the simple model of the bent curved surface part is set in the reverse direction of the above-mentioned bending forming process calculation step. Until the bending moment of the simple model of the bent curved surface part becomes 0, at each time step of the unloading process, based on the material constitutive equation, the strain and stress at each evaluation point of the simple model of the bent curved surface part, and the bending moment and curvature of the bent curved surface part are calculated. The unloading process calculation step, Regarding the process of leaving the plate press bending formed product after unloading and springback, at each time step of the leaving process, based on the material constitutive equation, the strain and stress at each evaluation point of the simple model of the bent curved surface part, and the bending moment and curvature of the bent curved surface part are calculated. The leaving process calculation step, including, The leaving process calculation step is to set a temporary curvature speed at each time step to calculate the strain and stress at the evaluation point of the simple model of the bent curved surface part, calculate the bending moment of the simple model of the bent curved surface part based on the calculated stress, and until the calculated bending moment becomes a value sufficiently close to 0, correct the temporary curvature speed of the simple model of the bent curved surface part so that the bending moment approaches 0, and repeat the calculation of the strain and stress at each evaluation point and the bending moment. When it is determined that the bending moment has become a value sufficiently close to 0, update the curvature of the simple model of the bent curved surface part and proceed to the next time step. A method for predicting the shape change after springback of a plate press bending formed product, characterized in that. 【Number 1】 However, each symbol shown in formulas (1) to (6) is as follows. ε x 、 ε y 、 ε z : True strains in the x-direction (longitudinal direction), y-direction (plate thickness direction), and z-direction (plate width direction) κ: Non-dimensional curvature of the bent curved surface part y: Coordinate in the plate thickness direction h: Plate thickness dε p ij / dt: Plastic strain rate s ij : Deviation stress α ’ ij : Deviation back stress X: Excess stress Y, D, p: Material constants <> : Macaulay brackets dε eq / dt: equivalent plastic strain rate dσ x / dt, dσ z / dt: Stress rates in the x- and z-directions E, ν: Material constants dε x / dt, dε z / dt: Strain rates in the x- and z-directions dε p x / dt, dε p z / dt: Plastic strain rate in the x - direction and z - direction dα ’ ij / dt: Deviation response stress rate C, a: Material constants Subscript i, j: x direction, y direction, z direction

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