JP5146395B2 - Stretch flange crack estimation method considering strain gradient and stretch flange crack judgment system of press forming simulation - Google Patents

Description

  In the present invention, when designing and manufacturing automotive parts, mainly by press forming metal plates, it is possible to predict stretch flange cracks using simulation in order to pre-evaluate the part shape to avoid stretch flange cracks. It is about the technology to make.

  Work materials such as automobiles, home appliances, and building structures are often punched with a punch 2 and a die 3 as shown in FIG. As shown in FIG. 2, the punched surface is formed by a workpiece 4 (see FIG. 1) being entirely pushed by a punch 2 (see FIG. 1) 4, a punch 2 and a die 3 (see FIG. 1). Shear) formed by the work material 1 being drawn and locally stretched within the clearance (see below), where there is no particular description, and “clearance” refers to the clearance between the punch and the die) The surface 5 is constituted by a fracture surface 6 formed by breaking the workpiece 1 drawn into the clearance between the punch 2 and the die 3 and a flash 7 generated on the back surface of the workpiece 1. Punching has the advantage of lower costs compared to cutting and laser processing, but on the other hand, as shown in Non-Patent Document 1, there are other cracks during stretch flange processing where tensile deformation is applied to the punched surface. It is easier to happen than the processing method.

  As a countermeasure for such a problem, it is effective to predict the stretch flange crack of the punched surface. This is because it is possible to estimate the stretch flange forming conditions and punching conditions so that cracks do not occur in advance without trial and error in actual mold production.

  For problems such as drawing and foaming that cause cracks in the plate surface, predicting cracks using simulations such as the finite element method is routinely performed. Specifically, limit strains such as plate thickness limit lines and forming limit diagrams (also referred to as FLD) are derived experimentally or theoretically, and the limit strain state and the strain state obtained by simulation are calculated. By comparing, it has been carried out to determine the presence or absence of cracks. Therefore, for the above-described processing, a certain degree of quantification is obtained in the prediction of the crack occurrence location and the occurrence time.

  For example, Patent Literature 1 discloses a press molding system related to computer simulation that uses a molding limit diagram to prevent breakage during press molding.

  It is well known that stretch flange cracks are greatly affected by strain gradient. According to Non-Patent Document 2, in stretch flange cracks, constriction progress suppression and crack progress delay are caused by the effect of strain gradient in the vicinity of the crack. Has been pointed out. Based on the results of Non-Patent Document 2, Non-Patent Document 3 includes a finite element simulation for punching holes, and derives an instability index using local bifurcation theory for each element. In order to consider the influence of the above, there is disclosed a method for deriving the plastic strain value at the hole end where the spatial integral value of the instability index is negative as the limit strain value at which stretch flange cracking occurs.

  Furthermore, in Non-Patent Document 4, as a simple method for predicting stretch flange cracking, the fracture limit strain obtained from the results of the hole expansion test is applied to a stretch flange forming simulation in a punched ridge shape other than hole expansion. A technique for predicting whether stretch flange cracking will occur is described.

JP 2006-167766 A

"Press Drawing", Japan Metal Press Industry Association, Nikkan Kogyo Shimbun, Nakamura, Kuwahara, 91-94 Proceedings of the 45th Plastic Working Joint Lecture pp.437-440 Proceedings of the 57th Japan Plastic Working Conference pp.175-176 CP778 Volume A, Numisheet2005, edited by L.M.Smith, F.Pourboghrat, J.W.Yoon, and T.B.Stoughton, American Institute of Physics 0-7354-0265-5- / 05

  There are several problems with the method introduced above. Stretch flange cracking is a rupture phenomenon in which the edge of a thin plate is stretched to cause cracking. However, including the invention described in Patent Document 1, ball head punch overhang molding and cylindrical punch that have been used for conventional crack evaluation Since the forming limit diagram obtained by overhang forming is a theory that deals with the breaking phenomenon on the plate surface, it is impossible in principle to evaluate the stretch flange crack that causes the plate end portion to break.

  In addition, the method disclosed in Non-Patent Document 3 attempts to make predictions using local branching theory for stretch flange cracks, but since it is necessary to use a special material model, a commercially available finite number is generally available. It is difficult to apply to element codes, and the method disclosed in Non-Patent Document 4 does not consider the effect of strain gradient, and makes a considerable safety prediction when dealing with problems other than hole expansion deformation. End up.

  SUMMARY OF THE INVENTION An object of the present invention is to provide a simulation method that simply uses a commercial finite element code to preliminarily predict stretch flange cracks in a punched portion in consideration of the effect of strain gradient.

  The gist of the present invention is as follows.

(1) A method for predicting stretched flange cracks on a punched end face, in which a test different from the predicted shape or a tool condition is performed in advance and a test for applying tensile deformation to the punched end face is performed. One or both of shear surface ratio γ during punching, strain gradient Δεθ in the edge ridge line direction and strain gradient Δεr in the edge ridge line vertical direction, and limit equivalent plastic strain that causes cracks in the end surface in the tensile test of the punched end surface Approximating the relationship with εcr as an equation, measuring the shear plane ratio γpart of the material subjected to punching as the prediction target, and performing stretch flange forming analysis of the punched end surface of the prediction target by a finite element method, Calculate one or both of the strain gradient Δεθ in the edge ridge line direction and the strain gradient Δεr in the edge ridge line vertical direction, and either the shear plane ratio γpart and the strain gradients Δεθ or Δεr Substituting either or both into the above formula to determine the critical strain εcr part that causes cracks in the punched end face to be predicted, and then the equivalent plastic strain εp of the flange portion for each element determined by the molding analysis, A method for estimating stretch flange cracks, wherein stretch flange cracks are estimated by comparing critical strains εcr part of actual parts.
(2) A method for predicting stretched flange cracks on the punched end face, in which a test different from the predicted shape or a tool condition and a test for applying tensile deformation to the punched end face are performed in advance. One or both of shear surface ratio γ during punching, strain gradient Δεθ in the edge ridge line direction and strain gradient Δεr in the edge ridge line vertical direction, and limit equivalent plastic strain that causes cracks in the end surface in the tensile test of the punched end surface After obtaining the relationship with εcr as a mathematical expression, the shear surface ratio γpart of the stretch flange of the punched end surface of the prediction target is measured, and the stretch flange forming analysis of the punched end surface of the prediction target is performed by a finite element method. One or both of the strain gradient Δεθ in the ridge line direction and the strain gradient Δεr in the edge ridge line vertical direction is calculated, and one of the shear surface ratio γpart and the strain gradients Δεθ and Δεr. Or, by substituting both into the mathematical formula, the critical strain εcr part that causes cracks in the punched end face to be predicted is obtained, and then the uniaxial tensile strain in the theoretical molding limit diagram or experimental molding limit diagram is the actual part. After the correction of the theoretical forming limit diagram or the experimental forming limit diagram so as to match the limit strain εcr part of the flange, the equivalent plastic strain εp of the flange portion for each element obtained by the forming analysis, A method for estimating stretch flange cracks, wherein stretch flange cracks are estimated by comparing the limit strain εcr part in uniaxial tension in the theoretical forming limit diagram or the experimental forming limit diagram.
(3) A method for predicting stretched flange cracks on the punched end face, in which a test is performed in advance to perform punching according to a shape or tool condition different from the shape to be predicted and tensile deformation to the punched end face. The clearance C at the time of punching, the strain gradient Δεθ in the end ridge line direction, the strain gradient Δεr in the vertical direction of the end ridge line, or both, and the limit equivalent plastic strain εcr that causes cracks in the end face in the tensile test of the punched end face The finite element method is used to calculate the stretch flange formation analysis of the target end face to be predicted, and either the strain gradient Δεθ in the edge ridge line direction or the strain gradient Δεr in the edge ridge line vertical direction is selected. One or both are calculated, and one or both of the punching clearance Cpart and the strain gradients Δεθ and Δεr to be predicted are substituted into the formula, and the prediction is performed. The critical strain εcr part that causes cracks on the punched end face is obtained, and then the equivalent plastic strain εp of the flange portion for each element obtained by the molding analysis is compared with the critical strain εcr part of the actual part. A method for estimating an elongated flange crack, wherein the flange crack is estimated.
(4) A method for predicting stretched flange cracks on the punched end face, in which a test is performed in advance by punching with a shape or tool condition different from the shape to be predicted and applying tensile deformation to the punched end face. The clearance C at the time of punching, the strain gradient Δεθ in the end ridge line direction, the strain gradient Δεr in the vertical direction of the end ridge line, or both, and the limit equivalent plastic strain εcr that causes cracks in the end face in the tensile test of the punched end face After calculating the relationship with the equation as a mathematical expression, a stretched flange forming analysis of the punched end face to be predicted is performed by the finite element method, and either one of the strain gradient Δεθ in the end ridge line direction and the strain gradient Δεr in the end ridge line vertical direction is performed. Or both are calculated, and one or both of the punching clearance Cpart and the strain gradients Δεθ and Δεr to be predicted are substituted into the formula. The critical strain εcr part that causes cracks in the punched end surface is obtained, and then the theoretical molding is performed so that the uniaxial tensile strain in the theoretical molding limit diagram or the experimental molding limit diagram matches the critical strain εcr part of the actual part. After correcting the limit diagram or the experimental molding limit diagram, the equivalent plastic strain εp of the flange portion for each element obtained by the molding analysis, and the corrected theoretical molding limit diagram or experimental molding limit diagram A method for estimating stretch flange cracks, wherein stretch flange cracks are estimated by comparing critical strains εcr part in uniaxial tension.
(5) The test according to any one of (1) to (4), wherein the test for applying a tensile deformation to the punching and punching end surface is a punching test for a round hole and a hole expanding process for the round hole. Estimating method of stretch flange crack.
(6) The elongation according to any one of (1) to (4), wherein the test for applying tensile deformation to the punching and punching end face is a bending test for a notched specimen prepared by punching and punching. Method for estimating flange cracks.
(7) The stress gradient Δσθ in the end ridge line direction is used instead of the strain gradient Δεθ in the end ridge line direction, and the stress gradient Δσr in the end ridge line vertical direction is used instead of the strain gradient Δεr in the end ridge line vertical direction. The stretch flange crack estimation method according to any one of (1) to (6), which is characterized.
(8) It has a reading part of a press forming analysis result by a finite element method, and has a function of extracting an element of an edge part from an analysis result read into the reading part, and the elements of the edge part. 6. A stretch flange crack determination system for press forming simulation, which has a function of performing crack determination by the stretch flange crack estimation method of any one of 6.
(9) It has a reading unit for a press molding analysis result by a finite element method, and has a function of extracting an element of an edge portion from an analysis result read into the reading unit, and the element of the edge portion. A function for performing crack determination by an estimation method of any one of the flange flange cracks, a function for performing crack determination based on a forming limit line or a plate thickness reduction rate for elements other than the edge portion, and performing the crack determination A stretch flange crack determination system for press forming simulation, which has a function of simultaneously displaying elements determined to be cracks by function on a three-dimensional deformation diagram.

  According to the present invention, the influence of the plate end face processing conditions obtained from the preliminary evaluation test, the strain gradient Δεθ in the direction of the edge ridge line in the vicinity of the crack portion, and the edge ridge line perpendicular to the stretch flange crack prediction in the press forming of the metal plate By using one or both of the correlation equations of the strain gradient Δεr in the direction, it is possible to perform advance prediction of the stretch flange crack, which was difficult to evaluate simply by conventional crack limit prediction.

It is sectional drawing which shows a punching process typically. It is sectional drawing which shows typically the shape of the punching end surface of a workpiece. It is a figure which shows the coordinate system with respect to a punching ridgeline. It is explanatory drawing of the method of correct | amending FLD. It is explanatory drawing of the method of determining a stretch flange crack using FIG. It is sectional drawing which shows a side bend test typically. It is a block diagram which shows the structure of the crack determination system of this invention. It is a figure of the blank board which performs the stretch flange crack prediction in Examples 1-6, (a) is a perspective view, (b) is a top view. It is a perspective view which shows the metal mold | die structure for stretch flange molding which performs stretch flange crack prediction in Examples 1-6. It is a perspective view which shows typically the hole expansion test in Examples 1-4, 6, (a) is the state at the time of a hole expansion test, (b) is the state of the test piece after a hole expansion test. It is a figure which shows the relationship between the shear surface ratio (gamma) of the punching surface measured in Example 1, strain gradient (DELTA) epsilon, and limit equivalent plastic strain (epsilon) cr. It is a figure which shows measured FLD in Example 2, and FLD correct | amended according to this invention (2). It is a figure which shows the measured FLD in Example 4, and the FLD corrected according to the present invention (4). 6 is a plan view showing the shape of a test piece for side bend used in Example 5. FIG. It is a perspective view which shows the circular blank with an inner hole and the cylindrical deep drawing molded product after a process which perform crack prediction including the stretch flange crack in Example 7. FIG. It is a perspective view which shows the area | region of the edge element automatically extracted in Example 7. FIG. It is explanatory drawing which showed the example of the crack determination by the crack determination system of this invention on the distortion | strain top view. It is a perspective view which shows the example which displayed the position of the element by which the crack determination was carried out by the crack determination system of this invention.

  The inventors of the present invention have conducted and studied crack prediction using a conventional plate thickness limit and FLD using simulation, and the prediction accuracy of stretch flange cracking, which is a material fracture phenomenon at the blank edge, is low, In particular, it was confirmed that it was difficult to predict in a high-strength material having low ductility.

  Subsequently, in order to overcome this decrease in prediction accuracy, an attempt was made to apply the already disclosed stretch flange crack prediction method, but since a special material model was required, a prediction device that the present inventors can use, There were cases where it could not be implemented within the scope of the software. Therefore, as a result of trial and error, the inventors previously determined the punching shape and stretch flange molding conditions as an evaluation model, and obtained the strain gradient and stretch flange cracking obtained from the punching / stretch flange molding test, or the punching clearance and It was found that stretch flange cracks can be easily predicted by applying the correlation formula of stretch flange cracks to stamping under different conditions and stretch flange forming conditions.

  The present invention requires the following.

  In the estimation method in the present invention (1), the shear plane ratio γ and one or both of the strain gradient Δεθ in the edge ridge line direction and the strain gradient Δεr in the edge ridge line vertical direction are used for the material used for the evaluation target component. In this method, the relationship with the critical equivalent plastic strain εcr is obtained in advance by experiments, and after the functional relationship of the following equation (1) is identified, the relationship is applied to the prediction of stretch flange cracking in another stretch flange molding. .

  Here, the shear surface ratio γ is the length ts (mm) in the thickness direction of the shear surface 5 shown in FIG. 2 / the thickness t (mm) × 100%.

  The definitions of the critical equivalent plastic strain εcr and strain gradients Δεr, Δεθ will be described below.

  As shown in FIG. 3, when the vertical direction with respect to the punched portion ridgeline 8 in the plate surface of the workpiece 1 is r, the ridgeline 8 direction is θ, and the plate thickness direction (perpendicular to the paper surface) is z, the r-direction distortion is obtained. The average value of the whole plate thickness, the average value of the whole plate thickness of the θ direction strain, and the average value of the whole plate thickness of the z direction strain are respectively expressed as εr (r, θ), εθ (r, θ), εz (r, Assuming that θ), the equivalent plastic strain εp is expressed as a function of r and θ, (2). The definition of equivalent plastic strain (≈function g) is widely described in textbooks of elastoplastic mechanics.

  The critical equivalent plastic strain εcr in the equation (1) is equivalent plastic strain when stretch flange cracking occurs, and the strain equivalent plastic strain εr, εθ, εz in each direction when stretch flange cracking occurs, or It is derived by substituting these values into equation (2). Δεr and Δεθ are defined as in the following equations (3) and (4).

  In an actual evaluation test, εr, εθ, and εz are measured or calculated by simulation at several points with different coordinate values r and θ, and the value of the strain gradient is obtained by taking the difference between these values. Convenient. The unit of r may be arbitrarily set such as mm, um, m, etc., but the unit system used in the preliminary evaluation test and the prediction of the stretch flange crack must be aligned. The same applies to θ. Alternatively, the strain distribution measured in a certain range, for example, a range of about 10 mm, may be approximated by function and substituted into the equations (3) and (4). The latter calculation method has an advantage that experimental measurement errors can be reduced.

  Examples of the evaluation test for identifying the formula (1) include a punched notched material tensile test, a punched notched material bending test, a punched holed material tensile test, and a punched hole expansion test. These are easy to identify because of their simple shape. For example, in the case of a tensile test of a notched material, a tensile test is performed with test pieces having different notch radii and punching clearances. By obtaining data of the limit equivalent plastic strain εcr and strain gradients Δεr, Δεθ by measurement or calculation, the equation (1) can be identified.

  Next, the punched end face of the stretch flange crack prediction target portion in the punched blank of the evaluation target part is observed before forming, and the shear surface ratio γpart of this portion is obtained.

Subsequently, a stretch flange forming simulation (not including punching) of the evaluation target part is performed by the finite element method, and a strain gradient Δεθ in the end ridge line direction and a strain gradient Δεr in the end ridge line vertical direction are calculated from the simulation result. By substituting one or both of these and γpart obtained above into the equation (1), the critical strain εcr part of the stretch flange crack prediction target part is obtained. Next, the equivalent plastic strain εp of the prediction target part obtained from the analysis result is compared with the limit strain εcr part,
If εp <εcr part, no stretch flange cracks occur,
If εp = εcr part or εp> εcr part, stretch flange cracking occurs,
Thus, stretch flange cracks are estimated.

  Usually, the strain value for each element is often evaluated, but when a plurality of integration points are arranged in each element of the finite element method, the equivalent plastic strain εp of the flange portion and the above-mentioned each integration point The stretch flange crack determination may be performed by comparing the limit strain εcr part of the actual part.

  The estimation method in the present invention (2) is the same as that in the present invention (1) until the identification of the functional relationship of the expression (1) in the target material and the procedure for identifying the critical strain εcr part using it.

  In the present invention (2), a theoretical FLD or an experimental FLD that has been conventionally used is used, and as shown in FIG. 4, the experimental FLD is made so that the intersection of the FLD line and the (εθ = −2εr) axis coincides with εcr part. Alternatively, the theoretical FLD is corrected. By doing this, even if the ratio of εr and εθ of the evaluation test for deriving equation (1) and the stretch flange crack evaluation target material is significantly different, stretch flange cracks can be predicted more accurately. It becomes. At the time of this correction, it is desirable to multiply the original FLD by a constant rate α for each distortion ratio. That is, (α × εr, α × εθ) is used as a new point on the FLD with respect to the point (εr, εθ) on the FLD before correction. Here, α = εcr part / {εθ at the intersection of the FLD line and the (εθ = −2εr) axis}. According to this method, the correction of the FLD according to the present invention can be easily performed on commercial software having an FLD display function.

  After deriving the FLD corrected as described above, if the εr and εθ of each element calculated in the molding simulation are outside the corrected FLD line as shown in FIG. Presumed to happen.

  In the estimation method in the present invention (3), instead of the equation (1), the relationship between the clearance at the time of punching and the limit equivalent plastic strain εcr is obtained from the equation (5), and the punching clearance of the member to be evaluated for stretch flange cracking is obtained. This is a method for obtaining a critical equivalent plastic strain εcr part from Cpart. Since the clearance C at the time of punching is a design matter and is usually known, no particular work such as measurement is required. If the amount of clearance is unknown, for example, it may be measured by pouring clay into the clearance to take a mold and measuring the size of the mold. The test level for identifying the formula (5) is the same as the formula (1) except for the necessity of measuring the shape of the end face.

  If the FLD is corrected in the same manner as in the present invention (2) using the εcr part derived by performing the same work as in the present invention (1), as in the present invention (2), Even when the ratio of Δεr and Δεθ of the evaluation flange test member and the stretch flange crack evaluation target member are greatly different, it is possible to predict stretch flange crack with higher accuracy (the present invention (4)).

  In the above method, when a hole expansion test is performed using a round hole test piece created by punching with different clearances and hole diameters, the identification of formula (1) or (5) is simple and highly accurate. The stretch flange crack can be predicted (the present invention (5)). In the hole expansion test, the deformation state of the end face is close to that of the normal stretch flange processing, and εcr can be obtained from equation (6) from the hole expansion rate λ%, so equations (1) and (5) Data processing for identifying can be performed simply (may be obtained by measuring a scribed circle or grid). If the hole diameter in the hole expansion test is changed, a plurality of combinations of εcr and Δεr can be obtained. Since the combination of εcr and Δεr is different between the conical hole expansion test and the cylindrical hole expansion test, it is possible to identify the expression (1) or (5) with higher accuracy by using these tests together. However, in the hole expansion test, it should be noted that Δεθ = 0 because the strain distribution is uniform in the ridgeline direction (circumferential direction) of the punched hole. Equation (1) or (5) cannot have a Δεθ term, and if the error in stretch flange crack prediction is large, Δεθ will not be zero. It is necessary to perform a flange-up test with a model mold that reproduces the same and a side bend test described later.

  As an evaluation test method capable of reproducing the influence of Δεθ, a bending test as shown in FIG. 6 for a punched-out notched material can be cited in addition to the hole expansion test (the present invention (6)). Hereinafter, this test is referred to as a side bend test. In the side bend test, the punched portion ridgeline 8 of the test piece 9 is often semicircular, and the values of Δεθ and Δεr can be changed by changing the diameter of the semicircle. Since the stretch flange deformation and the punched surface deformation state are close, it is possible to identify the expression (1) or (5) with higher accuracy.

  Further, if the stress gradient value is used instead of the strain gradient value, the stretch flange crack can be predicted with higher accuracy (the present invention (7)). Since the value of the equivalent plastic strain εp varies depending on the deformation history, the deformation history is greatly different between the test for identifying the equation (1) or (5) and the subject of the stretch flange crack evaluation target. Large errors can occur. On the other hand, since the equivalent stress σp is not affected by the deformation history, such a problem does not occur.

  Since the equivalent stress σp cannot be measured, when it is obtained by actual measurement, it can be obtained from the equivalent plastic strain value as shown in equation (7).

  Here, the function p is called a work hardening rule. The stress gradient value is defined as the following equations (8) and (9).

  Equations (1) and (5), in which the strain gradient value is replaced with the stress gradient value, are as shown in equations (10) and (11).

  Here, the expression (10) ′ and the expression (11) ′ may be used by using the expression (12).

  For the present inventions (2) and (4), a stress gradient can be used instead of the strain gradient. In this case, a stress FLD in which the strain value ε in FIG. 4 is replaced with the stress value σ is used.

  In addition, the strain state of the edge portion where stretch flange cracking occurs is a uniaxial tensile state, and it goes without saying that the equivalent plastic strain in the uniaxial tensile deformation is synonymous with the strain in the uniaxial tensile direction or the maximum principal strain. Yes. That is, the equivalent plastic strain used for the limit equivalent plastic strain εcr, the limit strain εcr part, the equivalent plastic strain εp of the prediction target portion, etc. described here can be rephrased as the strain in the uniaxial tensile direction or the maximum principal strain.

  Furthermore, in the crack determination system according to the present invention, it is possible to automatically determine the part where the stretch flange crack is generated by a computer using the press molding simulation result by the finite element method.

  FIG. 7 shows the configuration of a crack determination system according to the present invention. With reference to FIG. 7, the flow of processing of the crack determination system will be described. The crack determination system of the present invention has a reading section 31 for forming analysis results by the finite element method, and the reading section 31 can take in the results analyzed by general-purpose software for the finite element method. And it has the automatic extraction function 32 which extracts the element of an edge part automatically from all the taken in elements. The automatic extraction of the elements of the edge part can be determined from the sharing situation of the node numbers constituting each element. For example, in the case of a quadrilateral element, a node shared by only two elements can be recognized as a node on the outer periphery, so that the element possessed by the node can be identified as an edge element. Alternatively, there is a method of judging from the sharing situation of the sides constituting each element. Since the sides of the elements other than the edge portions are always shared with other elements, elements having sides that are not shared with other elements can be recognized as edge elements.

  By having the crack judging function 33 based on the method for estimating the stretch flange crack described above for each element of the extracted edge portion, the stretch flange crack can be automatically judged by a computer. For elements other than the edge portion, there is a crack determination function 34 for performing normal crack determination, that is, crack determination based on a forming limit diagram and a plate thickness reduction rate. The judgment based on the forming limit diagram here refers to determining whether the strain value of each element exceeds the limit line by reading the forming limit line by experiment or theory on the strain plan. is there. Further, instead of strain, a stress limit line on the stress plan view may be used to compare with the stress value of each element. In addition, crack judgment based on the plate thickness reduction rate is to determine whether the plate thickness reduction rate of each element exceeds the limit value by preliminarily determining the limit plate thickness strain of the workpiece by experiment and theory. It is. By determining cracks simultaneously with these methods, it is possible to evaluate whether cracks of stretch flange cracks or normal cracks occur earlier. Furthermore, it has a display function 35 for simultaneously displaying on the three-dimensional deformation diagram the result of determining the edge flange crack of the edge element and the result of determining the normal crack of the elements other than the edge, so that the crack risk position corresponding to each crack form can be visualized. Can grasp.

  In this way, if it becomes possible to accurately predict not only normal cracks but also stretch flange cracks in computer-based press molding simulations, measures can be taken in advance, and trial and error during mold manufacturing or mold correction Can be reduced and man-hours can be reduced.

  As Example 1 of the present invention, a blank plate 11 having the shape shown in FIG. 8 is formed by punching, and the flange plate is cracked when the blank plate 11 is formed with the mold 17 for forming an extended flange shown in FIG. The prediction was carried out.

  The shape of the stretch flange portion of the blank plate 11 by the stretch flange molding die 17 is composed of the corner curvature radius R of the blank plate 11 and the straight portion opening angle θ. In this embodiment, the blank plate 11 has a shape of R = 60 mm and θ = 120 °. Further, the die 22 and the punch 21 corresponding to the punched shape were used for the stretch flange molding. The blank plate 11 was a cold-rolled steel plate having a plate thickness of 1.6 mm and a tensile strength of 780 MPa. The width W of the blank plate 11 was constant at 140 mm. Moreover, the pad 23 (plate reverse pressing) was used for punching, and punching was performed under the condition of a pad back pressure of 5 tons. The clearance at the time of punching is 11% with respect to the plate thickness. The flange height test was conducted by setting the flange height H to five levels of 10, 15, 20, 25, and 30 mm. The flange height H is a distance (Htotal-Hflat) obtained by subtracting the central height Hflat of the flat portion of the blank plate 11 sandwiched between the punch 21 and the pad 23 from the total length Htotal of the central portion of the blank plate 11 shown in FIG. is there. Note that Lp in FIG. 8 indicates the shape of the edge of the punch 21. As a result of the molding test, molding feasibility for each flange height is as shown in Table 1, and stretch flange cracking occurred when the flange height H was 25 mm.

  Subsequently, in order to identify the equation (1), a hole expansion test using a conical punch 15 having a vertical angle of 60 degrees as shown in FIG. The shape of the test piece 12 was a rectangle of 120 mm × 120 mm, and a hole was formed in the center by punching. Experiments with a total of 9 levels were performed 5 times each, with the initial hole diameter d0 of the test piece 12 being 3 levels of 5 mm, 10 mm, and 15 mm, and the punching clearance being 3 levels of 5%, 10%, and 15%. The shearing surface ratio γ of the punched surface was obtained by taking a punched sample as shown in FIG. 10B for end face observation at each level and observing with an optical microscope. Further, as the critical tensile strain at the hole edge, a value converted into a logarithmic strain from a hole expansion ratio based on the hole diameter d1 after the hole expansion test was used. The result of averaging the five experimental results is shown in FIG. From the results of the shear plane ratio γ, strain gradient Δεr, and critical equivalent plastic strain εcr obtained from this experiment, it is assumed that each parameter and εcr are in a linear relationship and the least square method is used ( Equation (1) was derived as Equation (13).

  The strain gradient was measured by transferring a 2 mm grid scribe pattern by etching and measuring the strain distribution in the clearance direction at the time when the crack occurred. After approximating this strain distribution with a fifth-order polynomial, the derivative was determined to determine the strain gradient of the hole edge. This corresponds to the strain gradient Δεr in the direction perpendicular to the end ridge line.

  Subsequently, the above-described stretch flange forming test was simulated by the finite element method. ABAQUS / Standard, a commercially available FEM code, was used as the finite element method solver. For the flange height H, five levels of H = 10, 15, 20, 25, and 30 mm, which are the same as the actual molded product, were implemented, and the reduced strain shell element in the ABAQUS / Standard element library was used as the element type. The initial element size was 2 mm.

  The shear surface ratio γpart of the punched surface measured in the stretch flange molding test, which is a value necessary for the expression (13), was 28%. Δεr was calculated by obtaining a derivative after approximating the strain distribution at the center of each element with a fifth-order polynomial in the simulation. Using these values, it was determined that stretch flange cracking occurred when an element satisfying equation (14) was present after the end of the molding simulation.

  As a result, an analysis result is obtained in which the strain concentrates on the corner central portion 10 shown in the blank plate 11 of FIG. 8, and the actual crack position and the place coincide with each other. Cracks occurred at 30 mm, and the other flange height simulations resulted in no cracks.

  Although this result is a large estimate, the predicted value of the critical flange height is close to the molding test result shown in Table 1, confirming the effect of the present invention.

  After performing the same test as in Example 1, an overhang test called the Nakajima method was performed on the same material as in Example 1 to obtain an FLD (molding limit diagram) shown in FIG. The FLD shown in FIG. 12 is a graph showing a strain state in which a fracture of the plate material occurs such that a crack occurs when the strain state is plotted outside the limit line across the origin.

  Εcr part is calculated from γpart obtained by end face measurement and Δεr obtained from stretch flange forming simulation, and FLD is further corrected as shown in FIG. 12 using this value. When stretched flange cracks were determined from the corrected FLD in FIG. 12, cracks occurred when the flange height was 30 mm, and cracks did not occur below that. Although it is larger than the actual stretch flange cracking results shown in Table 1, the predicted values according to the present invention are generally consistent with the experimental results, and the effects of the present invention were confirmed.

  The same test as in Example 1 was performed, and the relational expression (15) that approximated the relation between the clearance C, the strain gradient Δεr, and the limit equivalent plastic strain εcr by a quadratic polynomial was obtained from the hole expansion test result.

  Subsequently, the same stretch flange forming test as in Example 1 was simulated. Since the clearance in the stretch flange test is 11% with respect to the plate thickness, C / t = 11. Therefore, the conditional expression for crack determination is the expression (16), and the element satisfying the expression (16) is If it exists, it is determined that a stretch flange crack has occurred.

  As a result, an analysis result in which the strain concentrates on the corner central portion 10 shown in the blank plate 11 of FIG. 8 is obtained, and the actual cracking position and the location coincide with each other, and whether or not the stretch flange crack is possible is determined using the equation (16). As a result, cracking occurred at 20 mm, and the simulation of the flange height below that resulted in no cracking.

  Although this result is a smaller estimate than the actual stretch flange cracking result shown in Table 1, the predicted value of the limit flange height is close to the molding test result of Table 1, confirming the effect of the present invention. It was done.

  The same test as in Example 2 was performed, and εcr part obtained by substituting Δεr obtained from the clearance Cpart and stretch flange forming simulation into the equation (15) for the obtained FLD as shown in FIG. When the FLD was corrected and the stretched flange crack was judged from the corrected FLD of FIG. 13, a crack was generated when the flange height was 20 mm, and no crack was generated below that. Although it is lower than the actual stretch flange cracking results shown in Table 1, the predicted values according to the present invention are generally consistent with the experimental results, confirming the effects of the present invention.

  The same test as in Example 1 was performed except that a side bend test was performed for identification of the formula (1).

  For the side bend test, a test piece 9 shown in FIG. 14 was used. The test piece 9 shown in FIG. 14 is provided with a semicircular cutout 16 by punching. A total of 18 experiments were performed 5 times each, with the notch 16 having a diameter d2 of 6 levels of 5 mm, 10 mm, 15 mm, 20 mm, 25 mm and 30 mm and a punching clearance of 3 levels of 5%, 10% and 15%. . The punching surface shear surface ratio γ was obtained by taking a punched sample for end face observation at each level and observing with an optical microscope. Table 2 shows the results of averaging the five experimental results. From the result values of the shear plane ratio γ, strain gradient Δεr, and critical equivalent plastic strain εcr of the punched surface obtained by this experiment, when the least square method is used in consideration of terms up to the second order of each parameter, (1 ) Was identified as (17).

  The measurement of strain and strain gradient was performed in the same manner as in Example 1.

  Subsequently, the same stretch flange forming test as in Example 1 was simulated by the finite element method. Since γpart = 28%, the conditional expression for crack determination is expression (18), and it is determined that an elongated flange crack has occurred when an element satisfying expression (18) exists after the end of the molding simulation.

  As a result, an analysis result in which the strain concentrates on the central portion 10 of the corner shown in the blank plate 11 of FIG. 8 is obtained, and the actual crack position and the location coincide with each other, and whether or not the stretch flange crack is determined using the formula (18). As a result, cracks occurred at a flange height level of 25 mm, and the other flange height simulations showed no cracks. The predicted value of the critical flange height is consistent with the molding test results shown in Table 1, confirming the effects of the present invention.

  The stretch flange crack prediction test, which is the same as in Example 1, except that the stress value is used instead of the strain value, was performed.

  The stress value was measured by transferring a scribe pattern of a 2 mm grid by etching, measuring the strain value in the clearance direction at the time of crack occurrence, and substituting it into the work hardening function p. After the obtained stress value distribution was approximated by a fifth-order polynomial, the derivative was obtained to obtain the stress gradient of the hole edge. This corresponds to the stress gradient Δσr in the direction perpendicular to the end ridge line.

  The work hardening function was measured by performing a JIS No. 5 tensile test, and the equation (19) was obtained.

  By the above method, the equation (20) is identified, and the determination condition of the stretched flange crack from γpart = 28% is the equation (21). Δσr is calculated by obtaining a derivative after approximating the equivalent stress distribution at the center of each element with a fifth-order polynomial in the simulation.

  As a result, an analysis result is obtained in which the strain concentrates on the corner central portion 10 shown in the blank plate 11 of FIG. 8, and the actual crack position and the place coincide with each other, and whether or not stretch flange cracks can be determined using the formula (21). As a result, cracking occurred at the flange height of 30 mm, and no cracking occurred in the simulation of the flange height below that. The predicted value of the critical flange height is consistent with the molding test results shown in Table 1, confirming the effects of the present invention.

  As Example 7 of the present invention, a circular blank 24 is formed by punching an inner hole 24a having a diameter of 10 mm at the center of a disk-shaped plate having a diameter of 110 mm shown in the upper left of FIG. Stretch flange crack prediction was performed when processing into a cylindrical deep-drawn molded product 25 as shown in the lower right of FIG. 15 with a drawing punch. As the material properties, data on general steel plate SPCC was input, and the press forming analysis was performed by the finite element method software LS-DYNA with a wrinkle holding force of 2 ton and a friction coefficient of 0.15.

  The molding analysis result at the molding height of 18 mm was taken into the crack determination system of the present invention, and the edge elements were automatically extracted. Here, edge elements are extracted from shared information of edges constituting the elements. The result is shown in FIG. Only elements in contact with the outer periphery of the circular blank 24 and the inner hole 24a were extracted as edge elements. Other elements were identified as non-edge elements. An example of crack determination by the crack determination system of the present invention is shown in FIG. FIG. 17 is a plot of the strain state of each element on a strain plan view. Here, the triangular mark indicates the strain state of the edge element, and the white mark is an element that is not determined to be cracked. A black mark indicates an element that is determined to be cracked. As the strain limit εcr part for crack determination, the material used here was determined from the hole expansion limit under the same conditions as in Example 1. Further, the circle mark indicates the strain state of the elements other than the edge, and the white mark is an element that is not determined as a crack. A black mark indicates an element that is determined to be cracked. The forming limit line for crack determination was measured by the forming limit strain measurement method by the Nakajima method using a ball head overhanging tool. FIG. 18 shows the positions of the elements determined to be cracks on a three-dimensional deformation diagram. Elements that are determined to be elongated flange cracks at the end of the inner hole, and elements that are determined to be normal cracks are shown near the punch shoulder, so that a portion having a high risk of fracture can be easily displayed. When a cylindrical deep drawing test was actually performed under the same conditions, cracks occurred at the hole edge when the molding height was 18 mm. It was also found that necking occurred near the punch shoulder and the position of the crack could be predicted with sufficient accuracy.

  The present invention can be applied to the prediction of stretch flange cracks in plate materials.

DESCRIPTION OF SYMBOLS 1 Work material 2 Punch 3 Die 4 Droop 5 Shear surface 6 Fracture surface 7 Burr 8 Punching part ridge 9 Test piece 10 Corner center part 11 Blank plate 12 Test piece 15 Punch 16 Notch 17 Mold 21 for stretch flange 21 Punch 22 Die 23 Pad 24 Circular blank 24a Inner hole 25 Cylindrical deep-drawn product 31 Reading section 32 Automatic extraction function 33, 34 Crack determination function 35 Display function
Lp Punch edge shape curve

Claims (9)

A method of predicting stretch flange cracks on the punched end face,
Preliminary tests are performed in which a shape different from the shape to be predicted or a tool condition is punched and a tensile deformation is applied to the punched end surface. At that time, the shear surface ratio γ during material punching and the strain gradient in the edge ridgeline direction Approximating the relationship between one or both of Δεθ and the strain gradient Δεr in the direction perpendicular to the edge ridge line and the limit equivalent plastic strain εcr at which the end face in the tensile test of the punched end face is approximated as an equation, In addition to measuring the shear surface ratio γpart of the punched material, the elongation flange forming analysis of the punched end face to be predicted is performed by the finite element method, and the strain gradient Δεθ in the end ridge line direction and the strain in the vertical direction of the end ridge line are analyzed. Either one or both of the gradient Δεr is calculated, and one or both of the shear surface ratio γpart and the strain gradients Δεθ and Δεr are substituted into the mathematical formula, and the punching target as the prediction target is calculated. Obtain the critical strain εcr part that causes cracks on the surface, and then compare the equivalent plastic strain εp of the flange part for each element obtained in the molding analysis with the critical strain εcr part of the actual part to estimate the stretch flange crack A method for estimating a stretch flange crack in consideration of a strain gradient. A method of predicting stretch flange cracks on the punched end face,
In advance, a test is performed in which a shape different from the shape to be predicted or a tool condition is punched and a tensile deformation is applied to the punched end surface, and the shear surface ratio γ at the time of punching the material and the strain gradient Δεθ in the edge ridge line direction. And the edge end ridge line perpendicular strain gradient Δεr or both and the limit equivalent plastic strain εcr at which the end face in the tensile test of the punched end face cracks as a mathematical formula, In addition to measuring the shear surface ratio γpart of the stretch flange of the above, and performing the stretch flange forming analysis of the punched end surface to be predicted by the finite element method, the strain gradient Δεθ in the end ridge line direction and the strain gradient Δεr in the end ridge line vertical direction Either one or both are calculated, and either one or both of the shear surface ratio γpart and the strain gradient Δεθ and Δεr are substituted into the formula, and the punched end surface is the prediction target The critical strain εcr part at which cracking occurs is obtained, and then the theoretical molding limit diagram or the theoretical molding limit diagram or the experimental molding limit diagram so that the uniaxial tensile strain matches the critical strain εcr part of the actual part. After correcting the experimental forming limit diagram, the equivalent plastic strain εp of the flange portion for each element obtained by the forming analysis and the corrected theoretical forming limit diagram or the experimental forming limit diagram by uniaxial tension A method for estimating stretch flange cracks considering a strain gradient, characterized in that stretch flange cracks are estimated by comparing the critical strains εcr part of the two. A method of predicting stretch flange cracks on the punched end face,
Preliminary tests for punching with a shape or tool condition different from the shape to be predicted and applying a tensile deformation to the punched end face, clearance C at the time of punching the material, strain gradient Δεθ in the edge ridge line direction and end Approximate the relationship between one or both of the strain gradient Δεr in the vertical direction of the ridge line and the limit equivalent plastic strain εcr at which the end face is cracked in the tensile test of the punched end face, and calculate it using the finite element method. Is subjected to stretch flange forming analysis of the punched end face, and one or both of the strain gradient Δεθ in the end ridge line direction and the strain gradient Δεr in the vertical direction of the end ridge line are calculated, and the punching clearance Cpart to be predicted and the Substituting either or both of the strain gradients Δεθ and Δεr into the mathematical formula to obtain a critical strain εcr part at which the punched end face to be predicted is cracked, and then By comparing the equivalent plastic strain εp of the flange portion for each element obtained by the forming analysis and the limit strain εcr part of the actual part to estimate the stretch flange crack, the stretch flange crack considering the strain gradient is characterized. Estimation method. A method of predicting stretch flange cracks on the punched end face,
Preliminary tests for punching with a shape or tool condition different from the shape to be predicted and applying a tensile deformation to the punched end face, clearance C at the time of punching the material, strain gradient Δεθ in the edge ridge line direction and end After determining the relationship between one or both of the strain gradient Δεr in the vertical direction of the ridge line and the limit equivalent plastic strain εcr at which the end face in the tensile test of the punched end face is cracked, the finite element method Stretch flange forming analysis of the punched end face is performed, and one or both of the strain gradient Δεθ in the end ridge line direction and the strain gradient Δεr in the end ridge line vertical direction are calculated, and the punching clearance Cpart and the strain to be predicted are calculated. By substituting one or both of the gradients Δεθ and Δεr into the above formula, a critical strain εcr part at which the punched end surface to be predicted is cracked is obtained, and then After correcting the theoretical molding limit diagram or the experimental molding limit diagram so that the uniaxial tensile strain of the molding limit diagram or the experimental molding limit diagram matches the critical strain εcr part of the actual part, the molding Estimate the stretch flange crack by comparing the equivalent plastic strain εp of the flange part for each element found in the analysis with the limit strain εcr part in the uniaxial tension of the theoretical forming limit diagram or the experimental forming limit diagram after the correction. A method for estimating a stretch flange crack in consideration of a strain gradient.   5. The strain gradient according to claim 1, wherein the punching and the test for applying tensile deformation to the punched end face are a punching process of a round hole and a hole expanding process test for the round hole. Estimating method of stretch flange crack.   The strain test according to any one of claims 1 to 4, wherein the test for applying tensile deformation to the punching and punching end face is a bending test for a notch specimen prepared by punching and punching. Method for estimating stretch flange cracks.   The stress gradient Δσθ in the edge ridge line direction is used instead of the strain gradient Δεθ in the edge ridge line direction, and the stress gradient Δσr in the edge ridge line vertical direction is used in place of the strain gradient Δεr in the edge ridge line vertical direction. The estimation method of the stretch flange crack which considered the strain gradient of any one of Claims 1-6.   It has a reading part of the press molding analysis result by a finite element method, The function which extracts the element of an edge part from the analysis result read into the reading part, and any of Claims 1-6 to the element of the edge part A stretch flange crack determination system for press forming simulation, which has a function of performing crack determination by an estimation method of the stretch flange crack.   It has a reading part of the press molding analysis result by a finite element method, The function which extracts the element of an edge part from the analysis result read into the reading part, and any of Claims 1-6 to the element of the edge part The crack is determined by the function of performing crack determination by the method of estimating the stretch flange crack, the function of performing crack determination by the forming limit line or the plate thickness reduction rate for the elements other than the edge part, and the function of performing the crack determination. A stretch molding crack determination system for press forming simulation, which has a function of simultaneously displaying the elements determined to be on a three-dimensional deformation diagram.