JP5098901B2 - Calculation method of material property parameters - Google Patents

Description

  The present invention relates to a method for calculating material property parameters used in a simulation performed to evaluate the formability of a material (metal plate) used for a press-formed part such as an automobile.

  In order to evaluate the formability of materials (metal plates) used for press-molded parts such as automobiles, simulations using the finite element method are widely performed.

  Conventionally, in this simulation, it has been generally assumed that the yield behavior of a target material is constant regardless of the direction of the material, that is, isotropic.

  On the other hand, in recent years, in addition to the conventional evaluation of formability such as cracks and wrinkles, it is necessary to evaluate the mechanical properties of materials more strictly in order to predict the dimensional accuracy (spring back) after press molding. As a result, simulations taking into account the anisotropy of materials have been conducted.

  At that time, as an anisotropic material model, for example, a material model (Hill quadratic yield function) proposed by Hill described in Non-Patent Documents 1 and 2 has been used. A material model called Yld2000-2d (Yld2000-2d yield function) described in Non-Patent Document 3 has come to be used as a material model having a degree of freedom in expressing the directionality.

  Incidentally, the Yld2000-2d yield function φ is expressed by the following equations (1) to (3).

As described above, the Yld2000-2d yield function φ has _eight parameters α _{1 to} α ₈ and a parameter M as parameters based on material characteristics (material characteristic parameters). Yld2000 In order to calculate the −2d yield function φ, values α _{1 to} α ₈ and M are required.

Conventionally, regarding the values of the parameters α _{1 to} α ₈ , the yield stress (YP) and the Rankford value (r value) in a uniaxial tensile test in three directions (L direction, C direction, D direction), and the like It was calculated using the stress and elongation ratio in the biaxial stress tensile test (for example, see Non-Patent Document 4). Incidentally, with respect to the above three directions, in the plane of the material (metal plate), when the angle from the rolling direction is θ, the L direction is the rolling direction (θ = 0 °), and the C direction is the rolling cross direction ( θ = 90 °) and the D direction is an oblique direction (θ = 45 °).

On the other hand, for the parameter M, it is said that 6 or 8 is appropriate for metal materials.
"Plastics", Corona, 1.3 “Nonlinear Finite Element Method”, Corona, Chapter 7 F. Barlat et al., “Plane stress yield for aluminum alloy sheets”, International Journal of Plasticity, 19 (2003), p. 1297-1319 "Plate molding", Corona, Chapter 8

However, until now, in order to calculate the values of the _eight material property parameters α _{1 to} α ₈ in the Yld2000-2d yield function, a special test device called a biaxial tensile tester is required. It was not easy to determine the values of α _{1 to} α ₈ . Therefore, it has been difficult to routinely perform press forming analysis by the finite element method using the Yld2000-2d yield function.

The present invention has been made in view of the above circumstances, and the values of the eight material characteristic parameters α _{1 to} α ₈ in the Yld2000-2d yield function can be easily calculated, whereby Yld2000− An object of the present invention is to provide a method for calculating a material property parameter that enables daily press forming analysis by a finite element method using a 2d yield function.

  In order to solve the above problems, the present invention has the following features.

[1] A method for calculating material property parameters for calculating values of _eight material property parameters α _{1 to} α _{8 in} the Yld2000-2d yield function φ represented by the following formulas (1) to (3): ,
Eight material characteristic parameters α _{1 to} α ₈ in the Yld2000-2d yield function using the stress-strain relationship and the Rankford value obtained by conducting a uniaxial tensile test in four or more directions on the target material. A method for calculating material property parameters, characterized by calculating a value of.

[2] In the above [1], the material characteristics are characterized in that the values of the _eight material characteristic parameters α _{1 to} α ₈ in the Yld2000-2d yield function are calculated using the yield stress as the stress-strain relationship. Parameter calculation method.

[3] In the above [1], the values of the _eight material characteristic parameters α _{1 to} α _{8 in} the Yld2000-2d yield function are calculated using the stress at the equivalent plastic strain of 3% to 10% as the stress-strain relationship. A method for calculating a material property parameter.

According to the present invention, it is possible to easily obtain the _eight material characteristic parameters α _{1 to} α ₈ in the Yld2000-2d yield function without using a special test device that is not widely used such as a biaxial tensile tester. became. As a result, the press forming analysis by the finite element method using the Yld2000-2d yield function can be carried out on a daily basis, and the press formability evaluation of the material and the dimensional accuracy prediction of the press formed part are greatly increased. It became possible to improve.

  One embodiment of the present invention is described below.

  First, as described above, the Yld2000-2d yield function φ is expressed by the following equations (1) to (3).

And, between the stress σ _{θ in the} uniaxial tensile test in the direction inclined by θ from the x direction (for example, the rolling direction) (θ direction) and σ _x , σ _y , σ _z in the absolute coordinate system, Since there is a relationship of 4), the expressions (2) and (3) become as the expressions (5) and (6). When Expression (6) is set as shown in Expression (7), the Yld2000-2d breakdown function φ can be expressed as σ _θ as shown in Expression (8). Furthermore, σ _θ is expressed by equation (9).

Further, the r value (r _θ ) in the θ direction is defined by the equation (10), and thus is expressed by the equation (11). Further, from the related flow law, there is a relationship of Expression (12), and Expression (11) can be written as Expression (13).

Further, from the theorem of the homogeneous equation of Euler's theorem, the relationship of Equation (14) is established, and considering the uniaxial tensile test, σ _w = σ _θw = 0, and therefore, Equation (15) is obtained. From Expressions (13) to (15) and Expressions (1) to (3), the r value in the θ direction can be finally expressed by Expression (16).

If the parameter M = 6 (or 8) is determined, in the equations (9) and (16), the eight parameters α _{1 to} α ₈ are unknown, so that the equations (9) and (16) Thus, eight parameters α _{1 to} α ₈ can be calculated by using the measured values of σ _θ and r _θ in four directions or more.

Specifically, when the measured values are σ _θ and r _θ and the values according to equations (9) and (16) are σ _θ ^* and r _θ ^* , α that minimizes the evaluation function g in equation (17) seek _{1 ~α 8.} Note that w is a weighting coefficient.

In the above, the measured value σ _θ may be determined based on the stress-strain relationship (stress-strain curve) of the target material, the yield stress YP may be used, or a predetermined equivalent plastic strain may be used. The stress at may be used. In addition, about predetermined | prescribed equivalent plastic strain, although it depends on the stress-strain curve of the said material, it is preferable to use the stress in 3-10% of equivalent plastic strain.

In this way, in this embodiment, the eight material characteristic parameters α _{1 to} α ₈ in the Yld2000-2d yield function can be easily obtained without using a special test apparatus that is not widely used such as a biaxial tensile tester. Can be requested. As a result, the press forming analysis by the finite element method using the Yld2000-2d yield function can be carried out on a daily basis, and the press formability evaluation of the material and the dimensional accuracy prediction of the press formed part are greatly increased. It becomes possible to improve.

As Example 1 of the present invention, eight material characteristic parameters α _{1 to} α ₈ in the Yld2000-2d yield function were calculated for JSC590R having a relatively strong material anisotropy in a steel material. The parameter M was 6.

  First, the target JSC590R plate material was subjected to a uniaxial tensile test in five directions shown in Table 1 with the rolling direction (L direction) being an angle θ = 0 °. Table 1 shows the yield stress YS and the r value obtained thereby. The r value is a value measured at the time of 8% strain.

Then, based on the measurement result of Table 1, the material characteristic parameters α _{1 to} α ₈ were obtained by the above formula (17), with the C direction (θ = 90 °) as the reference direction of equivalent strain and equivalent stress. . The results are shown in Table 2.

Table 1 shows the yield stress (initial yield stress) and the calculated r value obtained from the equations (9) and (16) using the material characteristic parameters α _{1 to} α ₈ obtained as described above. The yield stress and r value were compared. The results are shown in FIGS. In addition, what was calculated | required with Hill secondary yield function was plotted simultaneously for reference.

It can be seen that the Yld2000-2d yield function using the material characteristic parameters α _{1 to} α ₈ calculated in Example 1 matches the measured value better than the Hill secondary yield function.

  Further, assuming that the isoplastic work surface is equal to the yield surface, the stress in the L direction and D direction (θ = 45 °) is determined from the measured stress-strain relationship in the C direction, Yld2000-2d yield function, and material property parameters. The result of obtaining the strain relationship is shown in FIG.

  When the plastic strain is small, the measured value and the calculated value are in good agreement. However, when the plastic strain increases, there is a discrepancy between the measured value and the calculated value.

As Example 2 of the present invention, as in Example 1 above, eight material characteristic parameters α _{1 to} α ₈ in the Yld2000-2d yield function were calculated for JSC590R.

However, in Example 1, the measured value of the yield stress YP was used when calculating the material characteristic parameters α _{1 to} α _{8. In} Example 2, however, the equivalent plastic strain is 0.055 instead. When stress was used.

  That is, the stress in each direction when the equivalent plastic strain is 0.055 from the uniaxial tensile test in five directions in which the rolling direction (L direction) of the JSC590R plate material shown in Example 1 is θ = 0 °. (Stress in each direction, which is an isoplastic work when the plastic strain in the C direction is 0.055) was obtained. The results are shown in Table 3.

Then, based on the measurement results of Table 3, the material characteristic parameters α _{1 to} α ₈ were obtained by the above-described equation (17) with the C direction (θ = 90 °) as the reference direction of the equivalent strain and equivalent stress. . The results are shown in Table 4.

  Table 3 shows the calculated values of stress and r value when the equivalent plastic strain obtained from the equations (9) and (16) using the material characteristic parameters α1 to α8 obtained as described above is 0.055. The stress at the equivalent plastic strain of 0.055 and the measured value of the r value were compared. The results are shown in FIGS. In addition, what was calculated | required with Hill secondary yield function was plotted simultaneously for reference.

It can be seen that the Yld2000-2d yield function using the material characteristic parameters α _{1 to} α ₈ calculated in Example 2 matches the measured value better than the Hill secondary yield function.

  Further, assuming that the isoplastic work surface is equal to the yield surface, the stress in the L direction and D direction (θ = 45 °) is determined from the measured stress-strain relationship in the C direction, Yld2000-2d yield function, and material property parameters. -The result which calculated | required distortion relation is shown in FIG.

  In the portion where the plastic strain is small, the measured value and the calculated value are slightly different, but when the plastic strain is large, the measured value and the calculated value are in good agreement.

  As Example 3 of the present invention, based on Examples 1 and 2 above, the Yld2000-2d yield function was applied to the press forming of the JSC590R material, and analysis by the finite element method was performed. The object of analysis was press molding with a bent hat shape with a height of 45 mm shown in FIG. 7, and the amount of bending after bending (the amount of bending near the right end) was evaluated.

Here, the case where the material characteristic parameters α _{1 to} α ₈ calculated in Example 1 are used is referred to as Invention Example 1, and the case where the material characteristic parameters α _{1 to} α ₈ calculated in Example 2 are used is It was set as Example 2. A case where a Hill quadratic yield function was applied was used as a reference example. And the case where it actually measured by press-molding was made into the actual measurement example.

  In the actual measurement example, after performing the press molding with the wrinkle pressing pressure of 50 tonf, the shape was measured after performing the laser cutting of 15 mm from the radius of the flange, and the bending amount was calculated. On the other hand, in Inventive Example 1, Inventive Example 2, and Reference Example, after performing molding analysis, trim and springback analysis were performed to calculate the bending amount.

  FIG. 8 shows the amount of bending in each case. In the reference example, the amount of bending differs from the actual measurement example by about 2 mm, whereas in the inventive examples 1 and 2, the difference from the actual measurement example is 1 mm or less.

  Accordingly, it was confirmed that the dimensional accuracy (spring back) of the press-formed part can be predicted with high accuracy and easily by applying the present invention.

It is a comparison figure of the yield stress in Example 1. 6 is a comparison diagram of r values in Example 1. FIG. 2 is a comparative diagram of stress-strain curves in Example 1. FIG. It is a comparison figure of the yield stress in Example 2. 6 is a comparison diagram of r values in Example 2. FIG. 6 is a comparative diagram of stress-strain curves in Example 2. FIG. It is a figure which shows the press molding shape in Example 3. FIG. It is a comparison figure of the amount of bending after press molding in Example 3.

Claims (3)

A material property parameter calculation method for calculating the values of _eight material property parameters α _{1 to} α _{8 in} the Yld2000-2d yield function φ represented by the following equations (1) to (3):
Eight material characteristic parameters α _{1 to} α ₈ in the Yld2000-2d yield function using the stress-strain relationship and the Rankford value obtained by conducting a uniaxial tensile test in four or more directions on the target material. A method for calculating material property parameters, characterized by calculating a value of.

The method for calculating a material property parameter according to claim 1, wherein the value of the _eight material property parameters α _{1 to} α ₈ in the Yld2000-2d yield function is calculated using the yield stress as the stress-strain relationship. . In Claim 1, the value of _eight material characteristic parameters (alpha) _1- alpha8 in Yld2000-2d yield function is calculated using the stress in equivalent plastic strain 3%-10% as a stress-strain relationship. Calculation method of material property parameters.

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