Abstract:
By using, as a raw material, a thick hot-rolled steel sheet having a chemical composition containing, by mass %, C: 0.02% or more and 0.10% or less, Si: 0.05% or more and 0.30% or less, Mn: 0.80% or more and 2.00% or less, and Nb: 0.010% or more and 0.100% or less and satisfying the condition that a carbon equivalent Ceq is 0.25% or more and 0.50% or less, a microstructure including a bainitic ferrite phase and/or a bainite phase, a high strength of 52 ksi or more in terms of yield strength and a high toughness of −45° C. or lower in terms of fracture transition temperature vTrs, an electric resistance weld zone having a microstructure including a bainitic ferrite phase and/or a bainite phase and satisfying the condition that the ratio of the average crystal grain size of the coarsest-grain portion to the average crystal grain size of the finest-grain portion is 2.0 or less in every portion in the wall thickness direction is obtained.

Description:
TECHNICAL FIELD 
       [0001]    The present invention relates to a technology of performing plastic deformation on a blank, such as stretch forming, in multiple stages to form the blank into a final shape. 
       BACKGROUND ART 
       [0002]    When a blank is formed into a final shape by press forming, an improvement of yields or an improvement of formability is an important issue. 
         [0003]    Generally, to improve yields, it is preferable to adjust the forming conditions to as close as the conditions for stretch forming by minimizing the flow rate at which a material flows into a mold set during forming. However, an excessively low flow rate of the material would cause a shortage of the material in the mold set during forming, whereby the blank would be excessively thin and would have defects such as cracks. When, on the other hand, forming mainly including drawing were performed in order to prevent cracks, yields would be lowered. In order to address such problems, various measures have been taken thus far. 
         [0004]    Patent Literature 1 has disclosed a method for improving yields by reducing excess metal as a result of reserving, in the early stage of press forming, a range in which a blank is not restrained. Patent Literature 2, on the other hand, has disclosed a method for preventing forming defects by allowing a local area of a press die set to drive as an individual movable punch and performing forming using the movable punch after placing a blank in the mold set in advance. 
       CITATION LIST 
     Patent Literature 
       [0005]    PTL 1: Japanese Unexamined Patent Application Publication No. 2007-118021 
         [0006]    PTL 2: Japanese Unexamined Patent Application Publication No. 2007-326112 
       SUMMARY OF INVENTION 
     Technical Problem 
       [0007]    The method disclosed in Patent Literature 1 is capable of reducing excess metal compared to an existing method but still needs some excess metal. Moreover, the method disclosed in Patent Literature 1 is drawing and thus yields or promise of improvement is/are limited. 
         [0008]    The method disclosed in Patent Literature 2 is capable of preventing forming defects. The method, however, is drawing, so that yields are lowered. 
         [0009]    The invention focuses on the above-described points and aims to provide a method for forming a blank, the method being capable of improving both yields and formability, and a method for determining a preforming shape. 
       Solution to Problem 
       [0010]    It is generally known that the formability is improved when press forming is divided into multiple forming steps and is performed in multiple stages. This is because, in contrast to the case where a blank is formed into a final shape with one forming step, in the case where forming is performed stepwise in multiple forming steps, strain is prevented from being localized at a portion and easily dispersed throughout the blank. However, the shape of the die set used at the preforming stage preceding the final stage of press working largely depends on the experience of technical experts and the method for determining the shape has not be established. 
         [0011]    The inventors have studied to find effective preforming in order to solve both requirements of yield improvement and formability improvement. The inventors have found that, as long as a cross-sectional line length approximately the same as that of the final shape is acquired in the preforming stage, a final shape that has substantially the same strain distribution as that at the time of preforming can be acquired at the time of final forming. 
       [First Means] 
       [0012]    In order to solve the problems, a method for forming a blank according to an aspect is a method for forming a blank by forming the blank into a preforming shape by plastic deformation and then by plastically deforming the blank into a final shape from the preforming shape. The method includes determining the preforming shape so that, in each of cross sections taken at a plurality of positions in the final shape, a ratio of a cross-sectional line length in one of the cross sections in the preforming shape to a cross-sectional line length in the same cross section in the final shape falls within a predetermined tolerance range. 
         [0013]    A method for determining a preforming shape according to another aspect is a method for determining a preforming shape of a blank in a case where the blank, after being formed into the preforming shape by plastic deformation, is plastically deformed into a final shape from the preforming shape. The method includes determining the preforming shape so that, in each of cross sections taken at a plurality of positions in the final shape, a ratio of a cross-sectional line length in one of the cross sections in the preforming shape to a cross-sectional line length in the same cross section in the final shape falls within a. predetermined tolerance range. of multiple cross sections are determined so as to be taken, for example, in a grid-like form or in a radial form. 
       [Second Means] 
       [0014]    In order to solve the problems, a method for forming a blank according to an aspect of the invention is a method for forming a blank including determining, when the blank, after being formed into a preforming shape by plastic deformation, is plastically deformed into a final shape from the preforming shape, the preforming shape so that a ratio of a second line length to a first line length falls within a predetermined tolerance range. An internal reference point is determined in a forming area of the final shape and a plurality of external reference points are determined on a peripheral border line of the forming area. In the final shape, a plurality of cross-sectional lines individually connecting a first internal point corresponding to the internal reference point to first external points corresponding to the external reference points are determined, division points at which the determined cross-sectional lines are divided at a predetermined set ratio are calculated, and a length of an endless annular line formed by connecting adjacent ones of the division points together is determined as the first line length. In the preforming shape, a length of an endless annular line formed by connecting together adjacent ones of division points, at which a plurality of cross sections are divided at the predetermined set ratio, are determined as the second line length, the plurality of cross sections individually connecting a second internal point corresponding to the internal reference point and second external points corresponding to the external reference points. 
         [0015]    A method for determining a preforming shape according to another aspect of the invention is a method for determining a preforming shape of a blank in a case where the blank, after being formed into the preforming shape by plastic deformation, is plastically deformed into a final shape from the preforming shape. The method includes determining the preforming shape so that a ratio of a second line length to a first line length falls within a predetermined tolerance range. An internal reference point is determined in a forming area of the final shape and a plurality of external reference points are determined on a peripheral border line of the forming area. In the final shape, a plurality of cross-sectional lines individually connecting a first internal point corresponding to the internal reference point to first external points corresponding to the external reference points are determined, division points at which the determined cross-sectional lines are divided at a predetermined set ratio are calculated, and a length of an endless annular line formed by connecting adjacent ones of the division points together is determined as the first line length. In the preforming shape, a length of an endless annular line formed by connecting together adjacent ones of division points, at which a plurality of cross sections are divided at the predetermined set ratio, are determined as the second line length, the plurality of cross sections individually connecting a second internal point corresponding to the internal reference point and second external points corresponding to the external reference points. 
       Advantageous Effects of Invention 
       [0016]    According to an aspect of the present invention, as a result of acquiring at a preforming stage a cross-sectional line length that is approximately equivalent to that of a final shape, a final shape having substantially the same strain distribution as that of the time of preforming can be acquired at the time of final forming. Thus, the aspect of the present invention can provide a method for forming a blank and a method for determining a preforming shape that can achieve both of yield improvement and formability improvement. 
         [0017]    The invention is particularly effective for stretch forming. 
         [0018]    For example, when press forming is adopted as an example of forming and the invention is applied to press forming, high yields can be achieved and stretch forming is easily performed at the time of press forming. 
         [0019]    In stretch forming performed using a punch and a die, when a blank is formed into a final shape with one step, the material is negligibly strained at a portion corresponding to the punch bottom due to the frictional resistance whereas the material becomes extremely thin at a portion corresponding to a punch shoulder or a die shoulder and may be highly likely to be cracked. On the other hand, when a strain is introduced in advance at the preforming stage at a portion corresponding to the punch bottom in the final shape, the formability at the final forming stage can be simulatively improved. 
         [0020]    Here, it is desirable that strain be uniformly introduced to the entirety. Thus, it is desirable to perform preforming with the forming method, such as hydraulic bulge forming, with which the strain resulting from is likely to be uniformly distributed. Preforming may instead be normal press working. 
     
    
     
       BRIEF DESCRIPTION OF DRAWINGS 
         [0021]      FIG. 1  is a schematic diagram illustrating a forming step according to an embodiment of the invention. 
           [0022]      FIG. 2  is a flowchart relating to a first embodiment and illustrates a method for determining a preforming shape. 
           [0023]      FIG. 3  is a diagram relating to the first embodiment and a top plan view of a first example of positions of multiple cross sections at each of which a cross-sectional line shape is acquired. 
           [0024]      FIG. 4  is a diagram relating to the first embodiment and a top plan view of a second example of positions of multiple cross sections at each of which a cross-sectional line shape is acquired. 
           [0025]      FIG. 5  is a diagram relating to the first embodiment and illustrates a final shape of Example 1. 
           [0026]      FIG. 6  is a diagram relating to the first embodiment and illustrates a preforming shape of Example 1, where  FIG. 6( a )  illustrates an example of a shape resulting from an existing method whereas  FIG. 6( b )  illustrates an example of a shape resulting from the method according to the invention. 
           [0027]      FIG. 7  is a diagram relating to the first embodiment and illustrates a final shape of Example 2. 
           [0028]      FIG. 8  is a diagram relating to the first embodiment and illustrates a preforming shape of Example 2. 
           [0029]      FIG. 9  is a flowchart relating to a second embodiment and illustrates a method for determining a preforming shape. 
           [0030]      FIG. 10  is a diagram relating to the second embodiment and a top plan view of a setting example of an internal reference point and external reference points. 
           [0031]      FIG. 11  is a diagram relating to the second embodiment and illustrates how endless annular lines (first endless annular lines) in a final shape are determined. 
           [0032]      FIG. 12  is a diagram relating to the second embodiment and illustrates the positions of endless annular lines (second endless annular line) in a preforming shape. 
           [0033]      FIG. 13  is a diagram relating to the second embodiment and illustrates a final shape of Example. 
           [0034]      FIG. 14  is a diagram relating to the second embodiment and a top plan view of endless annular lines (first endless annular lines) of a final shape of Example. 
           [0035]      FIG. 15  is a diagram relating to the second embodiment and a top plan view of endless annular lines (second endless annular lines) of a preforming shape of Example. 
       
    
    
     DESCRIPTION OF EMBODIMENTS 
       [0036]    Referring now to the drawings, embodiments of the invention are described. The invention is not limited to the embodiments described below. 
       First Embodiment 
       [0037]      FIG. 1  is a schematic diagram illustrating forming steps according to an embodiment. 
         [0038]    As illustrated in  FIG. 1 , forming according to an embodiment includes two forming steps, that is, a preforming step, in which a blank  1  is plastically deformed into a preforming shape, and a main forming step, in which the blank  1  formed into the preforming shape in the preforming step is plastically deformed into a final shape to serve as a product. Here, the preforming step itself may have multiple preforming steps. 
         [0039]    The preforming step is performed by, for example, press forming using a preforming die set for forming the blank  1  into the above-described preforming shape. The die set includes, for example, a set of a punch and a die. 
         [0040]    Similarly, the main forming step is also performed by press forming using a main-forming die set for forming the blank  1  into the above-described final shape. The die set includes, for example, a set of a punch and a die. 
         [0041]    The above-described press forming is, for example, stretch forming. 
         [0042]    This embodiment includes, before performing the preforming step, a process of acquiring the shape of the preforming die set, that is, the preforming shape from the final shape. After the preforming shape is determined, the preforming die set is manufactured so as to have the determined preforming shape. 
         [0043]    In a method for determining the preforming shape, the preforming shape is determined so that, after cross sections of the blank  1  having the final shape are taken at multiple positions along the thickness direction, the ratio of the cross-sectional line length in the preforming shape to the cross-sectional line length in the final shape at the same cross section position falls within a predetermined tolerance range. Specifically, the preforming shape is determined so that, after the cross-sectional line length in the final shape and the cross-sectional line length in the preforming shape are compared with each other, the ratio of one of the cross-sectional line length to the other cross-sectional line length falls within a predetermined tolerance range. 
         [0044]    Here, the direction “parallel to the direction of the thickness of the blank  1 ” corresponds to the direction of pressing. 
         [0045]      FIG. 2  illustrates an operation example performed by the method for determining a preforming shape on the basis of the final shape. 
         [0046]    Specifically, two or more cross sections are determined in the blank  1  (step A). It is preferable to determine the cross sections at such positions that the cross sections pass characteristic portions in which the curvature of the cross-sectional shape in at least the final shape is steep. By determining the positions of cross sections at such positions, the number of cross sections that are determined can be kept small. 
         [0047]      FIG. 3  illustrates a first example method for determining multiple positions of cross sections. 
         [0048]    Specifically, the example illustrated in  FIG. 3  is an example of the case where, as multiple positions of cross sections, cross sections are determined at (n+m) positions so as to be taken in an n×m grid-like form (in a mesh-like form) when viewed in a direction parallel to the thickness direction of the blank  1  before being subjected to forming (when viewed in a plan or viewed in the stretch forming direction in the forming). The determined positions are described below. The peripheral border line of the forming area corresponds to the outline of the final shape. 
         [0049]    Subsequently, the cross-sectional line lengths at the multiple determined positions are calculated in the final shape (step B). The cross-sectional line length L 0  in the final shape is acquired by performing final-shape forming simulation using, for example, computer aided engineering (CAE). Alternatively, the cross-sectional line length LO in the final shape may be acquired by manufacturing a product having a final shape through actual press forming and measuring the cross-sectional line length L 0  by, for example, a method of optical measurement. The method for acquiring the cross-sectional line length L 0  is not limited to these and other publicly known methods may naturally be used. 
         [0050]    Thereafter, a cross-sectional line length L 1  in the preforming shape taken at each cross section is specified so that the cross-sectional line length L 1  at the position the same as the cross section position determined in the final shape is equal to the cross-sectional line length corresponding to the acquired cross-sectional line length (Step C). At this time, the cross-sectional line length L 1  at each cross section is determined so as to fall within, for example, a tolerance range, described below. 
         [0051]    The cross-sectional line length corresponding to the cross-sectional line length is a cross-sectional line length acquired when the ratio of the cross-sectional line length in the preforming shape to the cross-sectional line length in the final shape falls within a predetermined tolerance range. In this embodiment, the predetermined tolerance range is the range within which (L 1 /L 0 ) is 0.8 times or greater and 1.2 times or smaller. When this condition is satisfied, the cross-sectional line length in the final shape and the cross-sectional line length in the preforming shape in the same cross section approximate to each other. 
         [0052]    Subsequently, the preforming shape is specified (Step D) so as to satisfy all the conditions of the cross-sectional line lengths L 1  at the specified cross sections. 
         [0053]    Here, in Step A described above, the accuracy improves with increasing number of cross sections at each of which the cross-sectional line length is acquired. Although the cross sections may be taken in any manner, it is preferable to take at least two cross sections. 
         [0054]    Here, rectangular coordinates are assumed where the direction of the thickness of the blank  1  before being subjected to forming is defined as a Z axis and the directions orthogonal to the Z axis are defined as an X axis and a Y axis. The X axis and the Y axis here are directions parallel to the surface of the blank  1  before being subjected to forming. 
         [0055]    In the first setting example method illustrated in FIG.  3 , n cross sections are determined so as to be taken parallel to the XZ plane at predetermined intervals and m cross sections are determined so as to be taken parallel to the YZ plane at predetermined intervals. Here, n and m are one or greater. 
         [0056]    When n and m are determined to be two or greater, the cross sections are determined so as to be taken in a grid-like form (meshed form) when viewed in the direction of the thickness of the blank  1  before being subjected to forming. Here, the grid-like form is not limited to an orthogonal grid-like form. The cross sections only have to be determined so as to be taken in at least two directions crossing each other when viewed in a plan and so as to include multiple cross-sectional shapes for each direction. when the direction of the thickness of the blank  1  before being subjected to forming and the direction of pressing are not parallel to each other, it is preferable that the direction of each section be parallel to the direction of pressing, not parallel to the Z axis. 
         [0057]    As described above, it is preferable to select a cross section that passes a large number of portions at which the curvature in the final shape steeply changes to a predetermined extent or higher. The line for specifying the cross section is not limited to a straight line but is simpler when determined, to be a straight line. 
         [0058]    When the preforming shape is determined with cross sections taken in the two directions, the final shape of the preforming shape is determined by, for example, temporarily determining the preforming shape on the basis of the cross-sectional line shape in the direction in which the extent to which the curvature changes is smaller and then correcting the preforming shape on the basis of the cross-sectional line shape in the other direction. 
         [0059]    It is preferable that the ratio of the cross-sectional line length in the preforming shape to the cross-sectional line length in the final shape fall within the above-described range of 0.8 times to 1.2 times and more preferable that the ratio fall within the range of 0.9 times to 1.1 times. It has been confirmed that, adjusting the ratio so as to fall within the range of 0.8 times to 1.2 times enables significant reduction of occurrences of cracks or wrinkles on the product surface. As it has been confirmed that high yields are securely acquired when the ratio is adjusted so as to fall within at least this range, these values are defined. 
         [0060]    Here, the example illustrated in  FIG. 3  is an example in which multiple cross sections are determined so as to be in a grid-like form. Multiple cross sections may be determined so as to be in other forms besides this form. 
         [0061]    Subsequently,  FIG. 4  illustrates a second setting example method for determining multiple positions of cross sections. 
         [0062]    This is an example where the multiple positions of cross sections are determined so as to be in a radial form. Specifically, when viewed in the direction parallel to the direction of pressing (in the direction parallel to the direction of the thickness of the blank before being subjected to forming), an internal set point P 0  is determined within the forming area of the final shape, multiple lines CA 1  to CA 8  that pass the internal set point P 0  and extend in directions different from one another are determined, and the multiple cross sections are determined at the positions of the determined multiple lines. 
         [0063]    Although  FIG. 4  illustrates the case where multiple lines are eight lines, the multiple lines may be other than eight lines. However, it is preferable that the number of cross sections be eight or greater. If the same level of accuracy is required, the number of cross sections can be kept smaller in the case. of radially taking the, cross sections than in the case of taking the cross sections in a grid-like form. 
         [0064]    The radially extending lines do not have to be evenly spaced apart from one another. It is preferable that the radially extending lines be determined so as to pass portions at which the curvature changes to a large extent in the final shape. 
         [0065]      FIG. 4  exemplarily illustrates the case of using, as a single line, a straight line that passes through the internal set point P 0  and has both ends arriving at the peripheral border line of the forming area of the final shape. However, as illustrated in  FIG. 7 , described below, each line may be determined so as to connect the internal set point PO to a single point on the peripheral border line of the forming area of the final shape. In this case, the lines in the example of  FIG. 4  are regarded as 16 lines. Here, the “forming area” expresses an area of a pressed product subjected to preforming or main forming over which plastic deformation has been actively provided, the area including the product surface and excess metal. The area, however, does not include a portion formed with a bead. 
         [0066]    It is preferable to determine the internal set point PO at the centroid position of the forming area when the forming area is viewed from the direction parallel to the direction of pressing. 
         [0067]    Here, the above description has been given taking a case, as an example, where a blank is formed into the final shape with two forming steps including a preforming step and a main forming step. The preforming step may include two or more provisional forming steps. 
         [0068]    In this case, it is preferable that, in each of the multiple cross sections in the final shape, a ratio of the cross-sectional line length in the process shape acquired after being subjected to each provisional forming step with respect to the cross-sectional line length in the final shape in the same cross section be determined for each provisional forming step so as to fall within the above-described tolerance range. However, it suffices if the preforming shape acquired in the step preceding the forming into the final shape satisfies the above-described conditions. 
         [0069]    This invention is applicable to all the different types of press forming of the blank  1  not only automobile parts. The material subjected to press forming is not limited to steel. This invention is also applicable to iron alloys such as stainless steel, nonferrous materials, or nonmetal materials. 
         [0070]    The invention is also particularly applicable to other materials such as a high-tensile steel material, which has been difficult to be process. 
       Second Embodiment 
       [0071]      FIG. 1  (the same as  FIG. 1  used for illustrating the first embodiment) is a schematic diagram illustrating the forming step according to this embodiment. 
         [0072]    As illustrated in  FIG. 1 , forming according to this embodiment includes two forming steps, that is, a preforming step, in which a blank  1  is plastically deformed into a preforming shape, and a main forming step, in which the blank  1  formed into the preforming shape in the preforming step is plastically deformed into a final shape to serve as a product. Here, the preforming step itself may have multiple preforming steps. 
         [0073]    The preforming step is performed by, for example, press forming using a preforming die set for forming the blank  1  into the above-described preforming shape. The die set includes, for example, a set of a punch and a die. 
         [0074]    Similarly, the main forming step is also performed by press forming using a main-forming die set for forming the blank  1  into the above-described final shape. The die set includes, for example, a set of a punch and a die. 
         [0075]    The above-described press forming is, for example, stretch forming. includes, before performing the preforming step, a process of acquiring the shape of the preforming die set, that is, the preforming shape from the final shape. After the preforming shape is determined, the preforming die set is manufactured so as to have the determined preforming shape. 
         [0076]    A method for determining the preforming shape includes determining the preforming shape so that a ratio of a second line length to a first line length falls within a predetermined tolerance range. An internal reference point is determined in a forming area of the final shape and a plurality of external reference points are determined on a peripheral border line of the forming area. In the final shape, a plurality of cross-sectional lines individually connecting a first internal point corresponding to the internal reference point to first external points corresponding to the external reference points are determined, division points at which the determined cross-sectional lines are divided at a predetermined set ratio are calculated, and a length of an endless annular line formed by connecting adjacent ones of the division points together is determined as the first line length. In the preforming shape, a length of an endless annular line formed by connecting together adjacent ones of division points, at which a plurality of cross sections are divided at the predetermined set ratio, are determined as the second line length, the plurality of cross sections individually connecting a second internal point corresponding to the internal reference point and second external points corresponding to the external reference points. Now, the method for determining external points in the preforming shape is described. The internal reference point determined in the final shape is defined as an original point and the direction of pressing is defined as the Z direction. Three-dimensional coordinates are determined in which the directions that are orthogonal to the Z direction and in which two straight lines, which pass the original point and are orthogonal to each other, are directed are defined as an X direction and a Y direction. Thus, each external reference point is allowed to be expressed using the X, Y, and Z coordinates. Subsequently, the X, Y, and Z coordinates are similarly defined in the space in which the preforming shape is designed and the coordinates of each external reference point acquired in the above-described manner are referred. Thus, each external reference point in the space in which the preforming shape is designed can be acquired. 
         [0077]    Specifically, the preforming shape is determined so that, after a contour-line-like (annual-ring-like) endless annular line is determined around the first internal point in the final shape and the first line length of the endless annular line is acquired, the ratio of a second line length of an endless annular line in the final shape corresponding to the endless annular line in the preforming shape to the first line length falls within a predetermined tolerance range. It is preferable that a cross-sectional line in each shape be adopted as an endless annular line. 
         [0078]      FIG. 9  illustrates an operation example of a method for determining the preforming shape based on the final shape. 
         [0079]    Firstly in Step S 10 , as illustrated in  FIG. 10 , an internal reference point A is determined within a forming area of a blank  1  before being subjected to forming that is to form the final shape. At the same time, multiple external reference points B 1  to B 8  are determined on the peripheral border line of the forming area. 
         [0080]    The internal reference point A is determined at, for example, the position of the centroid of the forming area of the blank  1  before being subjected to forming that is to form the final shape or the position of the centroid of the blank  1  formed into the final shape when the blank  1  in the final shape is viewed from the direction parallel to the direction of pressing. 
         [0081]    The multiple external reference points B 1  to B 8  are determined on the peripheral border line of the forming area along the peripheral border line of the forming area. The multiple external reference points B 1  to B 8  do not have to be evenly spaced apart from one another. 
         [0082]    This embodiment exemplarily illustrates a case where the positions of the multiple external reference points B 1  to B 8  are determined on the blank  1  before being subjected to forming. However, it is preferable to determine the positions of the multiple external reference points B 1  to B 8  on the peripheral border line (outline) of the forming area of the blank  1  subjected to final forming and to determine the positions corresponding to the positions of the multiple external reference points B 1  to B 8  on the blank  1  before being subjected to forming. 
         [0083]    By determining the positions of the multiple external reference points B 1  to B 8  on the peripheral border line (outline) of the forming area of the blank  1  subjected to final forming, the external reference points B 1  to B 8  can be determined at more appropriate positions. Specifically, by determining the external reference points B 1  to B 8  at such positions that cross sections pass portions at which the curvature changes to a large extent (for example, steep positions), the accuracy can be improved while the number of the external reference points B 1  to B 8  is kept low. 
         [0084]    The accuracy improves with increasing number of external reference points. It is preferable that the number of external reference points be four or greater. 
         [0085]    Subsequently, as illustrated in  FIG. 11( a ) , which is a schematic top plan view, a first internal point AF corresponding to the internal reference point A and first external points BF 1  to BF 8  corresponding to the external reference points B 1  to B 8  are determined in the final shape (Step S 20 ) and the positions of the cross-sectional lines D 1  to D 7  in the final shape that connect the first internal point AF to the respective first external points BF 1  to BF 8  are determined (Step S 30 ). 
         [0086]    Subsequently, in Step S 40 , as illustrated in  FIG. 11 , in the cross-sectional lines D 1  to D 7 , division points B 11  to B 82  at which the actual lengths of the cross-sectional lines are divided at set ratios are determined. In this example, two ratios have been determined. Thus, two of division points B 1  to B 82  are determined at each of the cross-sectional lines D 1  to D 7 . The accuracy improves with increasing number of set ratios. However, increasing set ratios increases the costs for calculation and time taken for design. A preferable number of set ratios is four. 
         [0087]    Subsequently, the cross-sectional lines in the final shape that pass all the division points B 11  to B 82  corresponding to the set ratios are determined as first endless annular lines C 1  and C 2 . At this time, for example, a line whose distance between adjacent two of the division points B 11  to B 82  is shortest is adopted. Alternatively, instead of the cross-sectional lines, the first endless annular lines C 1  and C 2  may be endless annular lines formed by connecting adjacent two of the division points B 11  to B 82  with straight lines. Nevertheless, the accuracy is higher in the case of adopting the cross-sectional lines. 
         [0088]    Subsequently, in Step S 50 , first line lengths of each first endless annular line for the respective ratios set in Step S 40  are calculated. In this example, two first line lengths are acquired. 
         [0089]    The first line lengths in the final shape are acquired by performing final-shape forming simulation using, for example, CAE. Alternatively, for example, the first line lengths may be measured with an optical measurement as a result of manufacturing a product having a final shape through actual press forming. 
         [0090]    Subsequently in Step S 60 , as illustrated in  FIG. 12 , straight lines that connect the internal reference point A (corresponding to the second internal point) to the respective external reference points B 1  to. B 8  in the blank  1  before being subjected to forming are determined as the positions of the cross-sectional lines D 1  to D 7  in the preforming shape and the division points B 11  to B 82  are determined by dividing the straight lines at the set ratios used in the final shape. Then, the position of the endless annular line that connects adjacent ones of the division points B 11  to B 82  for each set ratio with a straight line is specified as the position of the second endless annular line in the preforming shape. 
         [0091]    In Step S 70 , the second line length for each set ratio is acquired from the first line length for the corresponding set ratio acquired in Step S 50 . Specifically, the second line length for each set ratio is determined within the range of 0.8 times to 1.2 times as long as the first line length. 
         [0092]    Subsequently, in Step S 80 , the shape in which the portion serving as the second endless annular line in the preforming shape determined in Step S 60  has a length equal to the second line length determined in Step S 70  is determined as a preforming shape. 
         [0093]    When the lengths of the portions of multiple second endless annular lines are to be determined, a final preforming shape is determined by, for example, temporarily determining the preforming shape on the basis of a portion including a portion in which the curvature changes to a larger extent in the final shape and then correcting the length of the portions of other second endless annular lines. 
         [0094]    Here, it is preferable that the ratio of the second line length to the first line length be 0.6 times to 1.4 times and, as described above, more preferable that the ratio be within the range of 0.8 times to 1.2 times. It is most preferable that the ratio be within the range of 0.9 times to 1.1 times. If the ratio falls below 0.6 times, the line length may be insufficient at final forming, whereby cracks or yields reduction may occur. If, on the other hand, the ratio exceeds 1.4 times, the line length may be excessive at final forming, whereby wrinkles may occur on the product surface. In contrast, it has been confirmed that adjusting the ratio to the range of 0.8 times to 1.2 times enables significant reduction of cracks or wrinkles on the product surface. Specifically, the boundary values of the range of 0.8 times to 1.2 times are not critical values. Since it has been confirmed that high yields are securely acquired at least in the case where the ratio falls within this range, these values are determined. 
         [0095]    In the above description, the case where a blank is formed into a final shape with two forming steps including a preforming step and a main forming step has been described as an example. Here, the preforming step may include two or more provisional forming steps. 
         [0096]    In this case, it is preferable that the process shape acquired after being subjected to each provisional forming step be determined for each provisional forming step so that the first endless annular lines C 1  and C 2  in the final shape and the second endless annular line in the process shape after being subjected to the forming step fall within the above-described tolerance range. However, it suffices if the preforming shape acquired in the step preceding the forming into the final shape satisfies the above-described conditions. 
         [0097]    This invention is applicable to all the different types of press forming of the blank  1  not only automobile parts. The material subjected to press forming is not limited to steel. This invention is also applicable to iron alloys such as stainless steel, nonferrous materials, or nonmetal materials. 
         [0098]    The invention is also particularly applicable to other materials such as a high-tensile steel material, which has been difficult to be process. 
       EXAMPLE 
     Example According to First Embodiment 
     Example 1 
       [0099]    Example 1 described below is an example in which cross sections at each of which the cross-sectional line length is adjusted are determined to be taken in a grid-like form. 
         [0100]    The final shape designed after an automobile wheelhouse part illustrated in  FIG. 5  was fabricated with multiple steps in the press forming process. 
         [0101]    A mild steel sheet having a thickness of 0.7 mm was used as a blank  1 . Lockbeads were provided on the outer periphery of the portion at which a product is formed and complete stretch forming was performed to verify the effects of the invention. 
         [0102]    For comparison,  FIG. 6( a )  illustrates a preforming shape that has been typically formed. The preforming shape used for comparison ( FIG. 6( a ) ) is a preforming shape formed by stretch forming the sheet in a shape having a round head without using the method according to the invention. The preforming shape used for comparison is formed into a hemispheric shape. 
         [0103]      FIG. 6( b )  illustrates a preforming shape acquired by the method according to the invention. This preforming shape is a shape having a slightly recessed center portion so as to satisfy the conditions of the acquired cross-sectional line lengths. 
         [0104]    Here, in determination of the preforming shape according to the invention, a final shape forming analysis was performed using an analytic model and a preforming punch shape (preforming shape) was calculated from the result of the analysis. 
         [0105]    The mesh size of the analytic model was determined as 5 mm and the die set was a rigid body. The forming analysis was performed by a dynamic explicit method using LS-DYNA version 9.7.1R5. As illustrated in  FIG. 3 , in the above-described coordinate system, 60 cross sections were taken in the XZ plane and 60 cross sections were taken in the YZ plane, 120 cross sections were taken in total, as cross sections for acquiring the preforming shape. The preforming shape was designed by defining the above-described coordinate system in the space in which the preforming shape is designed, determining 60 cross sections each in the XZ plane and the YZ plane, 120 cross sections in total, at the same coordinates as those of the above-described 120 cross sections, and determining the ratio of the cross-sectional line length in the preforming shape to the cross-sectional line length in the final shape at the respective cross section positions so that the ratio falls within the range of 0.8 times to 1.2 times. At this time, the shape was calculated in such a state that the outlines of the preforming stretch forming in a round head used for comparison and the preforming shape according to the example coincide with each other in a top view. 
         [0106]    Table 1 shows the results of experiments. 
         [0000]    
       
         
               
               
               
             
           
               
                 TABLE 1 
               
               
                   
               
               
                 Method 
                 Cracks 
                 Wrinkles 
               
               
                   
               
             
             
               
                 Existing Method 
                 Occurred 
                 Not Occurred 
               
               
                 (Single Forming) 
               
               
                 Existing Method 
                 Dangerous 
                 Occurred 
               
               
                 (Preforming in Round Head) 
               
               
                 Method According to Invention 
                 Not Occurred 
                 Not Occurred 
               
               
                   
               
             
          
         
       
     
         [0107]    As found from Table 1, in the case of manufacture with single forming without performing preforming, cracks occurred as a result of strain being localized on a portion corresponding to a die shoulder. In the case of designing the preforming shape without the method according to the invention, significant wrinkles occurred at a portion corresponding to the punch bottom and necking occurred at a portion corresponding to the punch shoulder since the cross-sectional line length was not taken into consideration. In contrast, it was confirmed that none of wrinkles, cracks, necking, and other problems occurred in the case where the preforming shape was determined by the method according to the invention. In this manner, preferable results can be acquired by providing the method according to the invention. 
       Example 2 
       [0108]    Example 2 is an example in which cross sections at each of which the cross-sectional line length is adjusted are determined so as to be in a radial form. 
         [0109]    In Example 2, an internal set point P 0  is determined in the final shape acquired using the analytic model at the centroid position of the final shape when the final shape is viewed from the direction parallel to the direction of pressing, as illustrated in  FIG. 7 . Multiple lines are determined so as to extend radially from the internal set point P 0 . The positions of broken lines indicate the positions of the multiple lines. 
         [0110]    Subsequently, on the basis of the cross-sectional line lengths at the determined positions of the multiple lines, the ratio of the cross-sectional line length in the preforming shape to the cross-sectional line length in the final shape was calculated so as to fall within 0.8 times to 1.2 times at each cross section position.  FIG. 8  illustrates the shape subjected to preforming on the basis of the results. The positions of the broken lines indicate the positions of the cross-sectional line lengths. 
         [0111]    Here, properties other than the cross section positions, such as those of a blank or a final shape, are similarly determined as in the case of Example 1. 
         [0112]    Also in Example 2, it was confirmed that none of wrinkles, cracks, necking, and other problems occurred. In this manner, preferable results can be also acquired by providing this method according to the invention. 
       Example According to Second Embodiment 
       [0113]    The final shape designed after an automobile wheelhouse part illustrated in  FIG. 13  was fabricated with multiple steps in the press forming process. 
         [0114]    A mild steel sheet having a thickness of 0.7 mm was used as a blank  1 . Lockbeads were provided on the outer periphery of the portion at which a product is formed and complete stretch forming was performed to verify the effects of the invention. 
         [0115]    The internal reference point was determined at the centroid position in the final shape, multiple points were disposed on the peripheral border line (outline) of the forming area of the final shape, division points, at which each of cross-sectional lines individually connects the internal reference point to the corresponding multiple points, are determined at such positions that the corresponding one of the cross-sectional lines is divided into ten equal parts at the division points, and nine cross-sectional lines (first endless annular lines) were determined in accordance with the division positions (see  FIG. 14 ). 
         [0116]    Subsequently, the preforming shape was designed so that the line lengths at the nine cross-sectional line positions fall within 0.8 times to 1.2 times as long as the lengths in the final shape.  FIG. 15  illustrates an example of the preforming shape. 
         [0117]    Here, when the preforming shape was determined in accordance with the invention, a final shape forming analysis was performed using an analytic model and a preforming punch shape (preforming shape) was calculated from the result of the analysis. 
         [0118]    For comparison, processing into a final shape was performed with a single forming without performing preforming. 
         [0119]    Table 2 shows the results of experiments. 
         [0000]    
       
         
               
               
               
             
           
               
                 TABLE 2 
               
               
                   
               
               
                 Method 
                 Cracks 
                 Wrinkles 
               
               
                   
               
             
             
               
                 Existing Method 
                 Occurred 
                 Not Occurred 
               
               
                 (Single Forming) 
               
               
                 Method According to Invention 
                 Not Occurred 
                 Not Occurred 
               
               
                   
               
             
          
         
       
     
         [0120]    As found from Table 2, in the case of manufacture with single forming without performing preforming, cracks occurred as a result of strain being localized on a portion corresponding to a die shoulder. In the case of designing the preforming shape without the method according to the invention, significant wrinkles occurred at a portion corresponding to the punch bottom and necking occurred at a portion corresponding to the punch shoulder since the cross-sectional line length was not taken into consideration. 
         [0121]    In contrast, it was confirmed that none of wrinkles, cracks, necking, and other problems occurred in the case where the preforming shape was determined by the method according to the invention. In this manner, preferable results can be acquired by providing the method according to the invention. 
       REFERENCE SIGNS LIST 
       [0000]    
       
           1  blank  1   
         P 0  internal set point 
         A internal reference point 
         AF internal point 
         B 11  to B 82  division point 
         B 1  to B 8  external reference point 
         BF 1  to BF 8  external point 
         C 1 , C 2  first endless annular line 
         D 1  to D 7  cross-sectional line