JP5896150B2 - Break determination device, break determination method, and break determination program - Google Patents

Description

  The present invention relates to a rupture determination device, a rupture determination method, and a rupture determination program, and in particular, a rupture determination device, a rupture determination method, and a rupture determination method for determining a rupture of a joint that joins a plurality of mutually stacked plate members. The present invention relates to a fracture determination program.

2. Description of the Related Art Conventionally, a technique for evaluating the amount of deformation of a structure due to an external force and the stress acting on the structure by computer simulation is known.
For example, in the field of automotive engineering, it is attempted to improve the collision safety performance of a vehicle by simulating deformation of a vehicle body or destruction of structural members at the time of a vehicle collision. Particularly in recent years, due to the demand for weight reduction of the vehicle body, the metal plate constituting the vehicle body has been made thinner, and stress concentration around the spot welded part joining the metal plates is more likely to occur. Therefore, in order to further improve the collision safety performance, it is required to predict the fracture of the spot welded portion with higher accuracy.

  For example, Patent Literature 1 discloses a fracture determination method for determining fracture of a spot weld by a finite element method. In this method, in a spot weld having a structure in which two metal plates are joined by a nugget, the metal plate is modeled by a shell element, and the nugget is modeled by a beam element, and the axial force acting on the beam element The nugget peripheral edge breakage is determined based on the bending moment and the shearing force.

Japanese Patent Laid-Open No. 2007-24788

By the way, in order to improve the analysis accuracy, it is assumed that the mesh size becomes smaller than the nugget diameter of the spot weld as the mesh is refined when the structure is modeled.
However, in the method of Patent Document 1 described above, since the beam element modeling the nugget and the shell element modeling the metal plate are coupled at one point, the mesh size of the shell element is larger than the actual nugget diameter. If it is small, local distortion different from the actual phenomenon may occur in the vicinity of the coupling point with the beam element, which may reduce the analysis accuracy.
In addition, when modeling a nugget with a beam element, the fracture of the beam element is only evaluated by the tensile load, shear load and moment acting on the beam element. It may be difficult to predict accurately.

  The present invention has been made to solve the above-described problems of the prior art, and can accurately determine the breakage of a joint portion that joins a plurality of plate members while suppressing an increase in calculation load. An object of the present invention is to provide a break determination device, a break determination method, and a break determination program.

また、破断判定方法は、相互に重ねられた複数の板材を接合する接合部の破断を判定する破断判定方法であって、接合部に作用する応力テンソルを特定するステップと、特定された応力テンソルと、接合部の破断応力とに基づき、接合部の破断リスクを算出するステップと、算出された破断リスクに基づき、接合部の破断を判定するステップと、を有し、破断リスクを算出するステップにおいて、板材の法線方向を直交座標系のｚ軸とする応力テンソルを（σ_x、σ_y、σ_z、τ_zy、τ_zx）、破断応力を（σ_T）、重み付け係数を（Ａ、Ｂ、Ｃ）とした場合、以下の式により破断リスク（ＦＲ）を算出することを特徴とする。

また、破断判定プログラムは、相互に重ねられた複数の板材を接合する接合部の破断をコンピュータに判定させるための破断判定プログラムであって、コンピュータに、接合部に作用する応力テンソルを特定するステップと、特定された応力テンソルと、接合部の破断応力とに基づき、接合部の破断リスクを算出するステップと、算出された破断リスクに基づき、接合部の破断を判定するステップと、を実行させ、破断リスクを算出するステップにおいて、板材の法線方向を直交座標系のｚ軸とする応力テンソルを（σ_x、σ_y、σ_z、τ_zy、τ_zx）、破断応力を（σ_T）、重み付け係数を（Ａ、Ｂ、Ｃ）とした場合、以下の式により破断リスク（ＦＲ）を算出させることを特徴とする。

このように構成された本発明によれば、接合部に作用する応力テンソルと、接合部の破断応力とに基づき、上記式を用いて接合部の破断リスクを算出し、この破断リスクに基づき、接合部の破断を判定するので、計算負荷の増大を抑制しつつ、複数の板材を接合する接合部の破断を高精度に判定することができる。 In order to achieve the above object, according to the present invention, a fracture determination device is a fracture determination device that determines a fracture of a joint portion that joins a plurality of stacked plates, and a stress acting on the joint portion. By means of a stress tensor specifying means for specifying a tensor, a stress tensor specified by the stress tensor specifying means, a fracture risk calculating means for calculating a fracture risk of the joint based on the fracture stress of the joint, and a fracture risk calculating means Rupture determining means for determining rupture of the joint based on the calculated rupture risk. The rupture risk calculating means has a stress tensor (σ _x) with the normal direction of the plate material as the z-axis of the orthogonal coordinate system. , Σ _y , σ _z , τ _zy , τ _zx ), rupture stress is (σ _T ), and weighting factors are (A, B, C), the rupture risk (FR) is calculated by the following formula: Features.

The fracture determination method is a fracture determination method for determining a fracture of a joint portion that joins a plurality of stacked plate materials, the step of identifying a stress tensor acting on the joint portion, and the identified stress tensor. And calculating a fracture risk based on the calculated fracture risk and a step of determining the fracture of the joint based on the calculated fracture risk. , The stress tensor with the normal direction of the plate as the z-axis of the orthogonal coordinate system (σ _x , σ _y , σ _z , τ _zy , τ _zx ), the breaking stress (σ _T ), and the weighting factor (A, In the case of B, C), the fracture risk (FR) is calculated by the following formula.

The rupture determination program is a rupture determination program for causing a computer to determine a rupture of a joint that joins a plurality of stacked plate members, and the computer specifies a stress tensor that acts on the joint. And a step of calculating a fracture risk of the joint based on the identified stress tensor and a fracture stress of the joint, and a step of determining the fracture of the joint based on the calculated fracture risk. In the step of calculating the fracture risk, the stress tensor with the normal direction of the plate as the z-axis of the Cartesian coordinate system (σ _x , σ _y , σ _z , τ _zy , τ _zx ) and the rupture stress (σ _T ) When the weighting coefficient is (A, B, C), the fracture risk (FR) is calculated by the following equation.

According to the present invention configured as described above, based on the stress tensor acting on the joint and the fracture stress of the joint, the fracture risk of the joint is calculated using the above formula, and based on this fracture risk, Since the breakage of the joint portion is determined, it is possible to determine the breakage of the joint portion joining a plurality of plate members with high accuracy while suppressing an increase in calculation load.

In the present invention, preferably, the stress tensor specifying means specifies a stress tensor acting on a joint modeled as a single solid element substantially equal to the size of the joint.
In the present invention configured as described above, it is possible to prevent the occurrence of local distortion and to prevent a decrease in analysis accuracy, compared with the case where the joint portion is modeled by the beam element.

このように構成された本発明においては、引張せん断、十字引張、及びピールの各破断モードによる破断リスクを、応力テンソルの各成分を用いて破断モード毎に算出し、その算出結果に基づき接合部の破断を判定するので、接合部の破断リスクをさらに高精度に予測することができ、接合部の破断を正確に判定することができる。 In the present invention, it is preferable that the fracture risk calculating means calculates the fracture stress of the joint due to tensile shear (σ _TSS ), the fracture stress of the joint due to cross tension (σ _CTS ), and the fracture stress of the joint due to peel. (Σ _LTS ), the fracture risk (FR _TSS ) of the joint due to tensile shear, the fracture risk (FR _CTS ) of the joint due to cross tension, and the fracture risk (FR _LTS ) of the joint due to peel, respectively It is calculated by the following formula.

In the present invention configured as described above, the fracture risk due to each fracture mode of tensile shear, cross tension, and peel is calculated for each fracture mode using each component of the stress tensor, and based on the calculation result, the joint portion is calculated. Therefore, it is possible to predict the risk of rupture of the joint with higher accuracy and accurately determine the rupture of the joint.

Moreover, in this invention, Preferably, the fracture | rupture of the spot weld part which joins the several metal plate piled up mutually is determined.
In this invention comprised in this way, the fracture | rupture of the spot weld part which joins the several metal plate piled up mutually can be determined with high precision, suppressing the increase in calculation load.

  According to the rupture determination device, the rupture determination method, and the rupture determination program according to the present invention, it is possible to determine the rupture of a joint portion that joins a plurality of plate members with high accuracy while suppressing an increase in calculation load.

It is a block diagram which shows the electric constitution of the collision simulation apparatus provided with the fracture determination apparatus by embodiment of this invention. It is a perspective view which shows roughly the model of the two metal plates piled up mutually and the spot welding part which joins these metal plates. It is a flowchart of a collision simulation process. It is a perspective view which shows the fracture mode of a spot weld part.

Hereinafter, a break determination device, a break determination method, and a break determination program according to embodiments of the present invention will be described with reference to the accompanying drawings.
First, referring to FIG. 1, the configuration of a fracture determination device according to an embodiment of the present invention will be described. FIG. 1 is a block diagram illustrating an electrical configuration of a collision simulation apparatus including a fracture determination apparatus according to an embodiment of the present invention.

A collision simulation apparatus 1 shown in FIG. 1 analyzes a deformation or breakage of a vehicle component at the time of a collision, and includes a vehicle body analysis unit 2 and a breakage determination apparatus 4.
The vehicle body analysis unit 2 includes a vehicle body model that expresses the shapes and physical properties of various members constituting the vehicle body, the position and number of spot welds, the nugget diameter, and the boundary conditions of the analysis (initial velocity at the time of collision and the object to be collided And the like, and the load and displacement acting on each element constituting the vehicle body model are calculated by the finite element method based on these vehicle body models and boundary conditions. In this calculation process, the vehicle body analysis unit 2 calculates the deformation amount of the node between the metal plate constituting the vehicle body and the spot welded part, and outputs it to the fracture determination device 4.

The fracture determination device 4 according to the present embodiment determines the breakage of a spot weld that is a joint that joins a plurality of metal plates stacked on each other. As shown in FIG. 1, the fracture determination device 4 includes a stress tensor identifying unit 6 that identifies a stress tensor acting on a spot weld, a stress tensor identified by the stress tensor identifying unit 6, and a fracture stress of the spot weld. The fracture risk calculation unit 8 that calculates the fracture risk of the spot welded portion based on the above, and the fracture determination unit 10 that determines the fracture of the spot welded portion based on the fracture risk calculated by the fracture risk calculation unit 8.
In particular, the stress tensor specifying unit 6 specifies a stress tensor acting on the spot welded portion based on the deformation amount of the node between the metal plate and the spot welded portion input from the vehicle body analyzing unit 2. Further, the break determination unit 10 outputs the determination result of the breakage of the spot welded portion to the vehicle body analysis unit 2.
Each of these components includes a CPU, various programs that are interpreted and executed on the CPU (including basic control programs such as an OS and application programs that are activated on the OS to realize specific functions), programs, and various types It is constituted by a computer having an internal memory such as a ROM or RAM for storing data.

Next, with reference to FIG. 2, a model used by the fracture determination device 4 according to the embodiment of the present invention to determine the fracture of the spot weld will be described. FIG. 2 is a perspective view schematically showing a model of two metal plates stacked on each other and a spot welded portion for joining these metal plates. As shown in FIG. 2, the metal plate is modeled as a shell element having a mesh size smaller than the actual nugget diameter of the spot weld. The spot weld is modeled as a single solid element having a rectangular parallelepiped whose length of each side is substantially equal to the actual nugget diameter. In the model shown in FIG. 2, the normal direction of the metal plate is the z-axis of the orthogonal coordinate system, and the normal direction of the side surface (surface perpendicular to the metal plate) of the solid element representing the spot weld is the x-axis. And y-axis.
A model as shown in FIG. 2 is incorporated into the vehicle body model for each spot weld, and a collision simulation is executed.

  Next, each process of the collision simulation performed by the collision simulation apparatus 1 including the fracture determination apparatus 4 according to the embodiment of the present invention will be described with reference to FIG. FIG. 3 is a flowchart of the collision simulation process.

  As shown in FIG. 3, when the collision simulation process is started, in step S1, the vehicle body analysis unit 2 determines the shape and property values of various members constituting the vehicle body, the position and number of spot welds, the nugget diameter, and the like. A vehicle body model to be expressed and boundary conditions for analysis (initial velocity at the time of collision, shape of an object to be collided, etc.) are acquired. The vehicle body model is stored in advance in a storage device, for example, and the vehicle body analysis unit 2 reads the vehicle body model from the storage device. The boundary condition is input by the user via the input device.

  Next, in step S2, the vehicle body analysis unit 2 calculates a load, a displacement, and the like acting on each element constituting the vehicle body model by a finite element method based on the vehicle body model and boundary conditions acquired in step S1. At this time, the vehicle body analysis unit 2 calculates the deformation amount of each node between the metal plate constituting the vehicle body and each spot welded part, and outputs it to the fracture determination device 4.

  Next, in step S3, the vehicle body analysis unit 2 calculates the strain that occurs on the metal plate of the vehicle body and the stress that acts on the metal plate based on the load and displacement that act on each element calculated in step S2.

In step S4, the stress tensor specifying unit 6 determines the stress tensor acting on each spot welded portion based on the deformation amount of each node between the metal plate and each spot welded portion input from the vehicle body analyzing unit 2 in step S2. Six components (σ _x , σ _y , σ _z , τ _zy , τ _zx , τ _xy ) are calculated.

  Next, in step S5, the rupture risk calculation unit 8 calculates the rupture risk of each spot welded part based on the stress tensor calculated in step S4 and the rupture stress of the spot welded part. A detailed method for calculating the fracture risk will be described later.

Next, in step S6, the fracture determination unit 10 determines the fracture of each spot weld based on the fracture risk calculated by the fracture risk calculation unit 8 in step S5. Then, the spot welded portion determined to have a fracture is excluded from the calculation targets in steps S4 to S6.
In addition, the process of step S3 which the vehicle body analysis part 2 performs, and the process of step S4 thru | or S6 which the fracture | rupture determination apparatus 4 performs are performed in parallel.

After the process of step S3 or S6, in step S7, the vehicle body analysis unit 2 determines whether or not a predetermined end condition of the collision simulation process is satisfied. When it is determined that the predetermined end condition is not satisfied, the vehicle body analysis unit 2 returns to step S2.
On the other hand, when it is determined in step S7 that the predetermined end condition is satisfied, the vehicle body analysis unit 2 ends the collision simulation process.

Next, the calculation method of the fracture risk by the fracture risk calculation unit 8 will be described in detail.
FIG. 4 is a perspective view showing a fracture mode of a spot weld. The fracture mode of the spot welded portion includes three modes of tensile shear (TSS) shown in FIG. 4 (a), cross tension (CTS) shown in FIG. 4 (b), and peel (LTS) shown in FIG. 4 (c). There is. Further, there are two types of spot welding rupture modes: base material rupture (metal plate rupture) and interface rupture (nugget rupture). Therefore, the rupture risk calculation unit 8 calculates the respective rupture risks for the six conditions obtained by combining the three rupture modes and the two rupture modes.

In any of the three break modes described above, the spot welded portion is composed of a combination of tension along the plate surface of the metal plate and bending the metal plate to be concave or convex toward the normal direction of the plate surface. It works in the same way. When this is applied to the model shown in FIG. 2, the stress tensor acting on a single solid element representing a spot weld by tension becomes four components (σ _x , σ _y , τ _zx , τ _zy ). In addition, the stress tensor acting on a single solid element by bending has three components (σ _z , τ _xz , τ _yz ).
Therefore, the state of the stress acting on the spot weld is expressed as a function f (σ _x , σ _y , τ _zx , τ _zy , σ _z , τ _xz , τ _yz ) of these stress tensors, and experimentally in advance. It is considered that the rupture risk of the spot welded part can be calculated by comparing with the derived rupture stress.

First, the stress tensors (σ _x , σ _y , τ _zx , τ _zy ) acting on a single solid element by tension will be examined. The spot weld may be pulled from any direction along the plate surface of the metal plate (any direction along the xy plane in FIG. 2). Therefore, the square root of the sum of squares of the normal stress components (σ _x , σ _y ) ((σ _x ² + σ _y ² ) ^{1 / 2} ) and the square root ((τ _zx ² + τ _zy ² ) ^1/2 ) of the sum of squares of the shear stress components (τ _zx , τ _zy ) and the function f (σ _x , σ _y , τ _zx , τ _zy , Σ _z , τ _xz , τ _yz ).

Next, the stress tensors (σ _z , τ _xz , τ _yz ) acting on a single solid element by bending will be examined. Since each of these components is a component along the z-axis direction, it is not necessary to consider the influence of the direction along the plate surface of the metal plate. Therefore, the normal stress component (σ _z ) and the shear stress component (τ _xz + τ _yz ) are expressed as terms of the function f (σ _x , σ _y , τ _zx , τ _zy , σ _z , τ _xz , τ _yz ). I will include it.

・・・（１） As described above, the function f (σ _x , σ _y , τ _zx , τ _zy , σ _z , τ _xz , τ _yz ) can be expressed by the following expression.

... (1)

・・・（２）

・・・（３）

・・・（４）
ここで、σ_TSSは引張せん断による母材破断時の破断応力であり、σ_CTSは十字引張による母材破断時の破断応力であり、σ_LTSはピールによる母材破断時の破断応力である。これらの破断応力は、破断試験の結果に基づいて導出される。また、添え字を付した応力テンソルの各成分は、それぞれの添え字に対応する破断モードによる母材破断時の境界条件に基づき算出された、応力テンソル各成分の算出値である。 For each of the three fracture modes described above, the test specimen of the fracture test is modeled, and each component of the stress tensor calculated by giving the load at the time of the fracture as a boundary condition is substituted into the following equation (1). The formula is obtained.

... (2)

... (3)

... (4)
Here, σ _TSS is the rupture stress when the base material is broken by tensile shear, σ _CTS is the rupture stress when the base material is broken by cross tension, and σ _LTS is the rupture stress when the base material is broken by peel. These breaking stresses are derived based on the result of the breaking test. Each component of the stress tensor with a subscript is a calculated value of each component of the stress tensor calculated based on the boundary condition at the time of the base material fracture in the fracture mode corresponding to each subscript.

・・・（５）
従って、式（２）乃至（４）を以下のように変更できる。

・・・（６）

・・・（７）

・・・（８）
これらの式（６）乃至（８）から、式（５）の係数Ａ、Ｂ、Ｃを決定することができる。 By determining the coefficients A, B ₁ , B ₂ , and C based on these equations (2) to (4), each component of the stress tensor acting on a single solid element is substituted into equation (1). And it becomes possible to evaluate whether the fracture | rupture of a spot weld part generate | occur | produces about each fracture | rupture mode.
However, while there are four coefficients A, B ₁ , B ₂ , and C in Equation (1) that are unknown, the equations for determining the unknown are Equations (2) to (4). Therefore, the coefficients A, B ₁ , B ₂ , and C cannot be determined as they are. Therefore, the term (τ _xz + τ _yz ) having a small influence on the calculation accuracy of the fracture risk is omitted from the equation (1) and changed to the following equation.

... (5)
Therefore, the equations (2) to (4) can be changed as follows.

... (6)

... (7)

... (8)
From these equations (6) to (8), the coefficients A, B, and C of equation (5) can be determined.

・・・（９）
同様に、十字引張による母材破断リスクＢＦＲ_CTS、及びピールによる母材破断リスクＢＦＲ_LTSは、以下のように算出できる。

・・・（１０）

・・・（１１） Then, if the value obtained by dividing the right side of Equation (5) by the breaking stress σ _TSS at the time of base material breakage due to tensile shear is defined as the base material breakage risk BFR _TSS due to tensile shear, BFR _TSS can be calculated by the following formula.

... (9)
Similarly, the base material fracture risk BFR _CTS due to cross tension and the base material fracture risk BFR _LTS due to peel can be calculated as follows.

... (10)

(11)

・・・（１２）

・・・（１３）

・・・（１４） Further, the interfacial fracture risk SFR _TSS due to tensile shear, the interfacial fracture risk SFR _CTS due to cross tension, and the interfacial fracture risk SFR _LTS due to peel can be calculated as follows based on the same examination as described above.

(12)

... (13)

(14)

In step S5 of the collision simulation process described with reference to FIG. 3, the fracture risk calculation unit 8 substitutes each component of the stress tensor specified by the stress tensor specifying unit 6 into the equations (9) to (14). To calculate the base material fracture risk BFR _TSS , BFR _CTS , BFR _LTS , and interface fracture risk SFR _TSS , SFR _CTS , SFR _LTS . Each fracture risk calculated by these equations (9) to (14) can take a value of 0 to 1.

  Furthermore, in step S6, when the fracture risk calculated by the fracture risk calculation unit 8 is 1 in any of the fracture modes, the fracture determination unit 10 determines that a fracture occurs in the spot welded portion in the fracture mode. .

  Next, functions and effects of the above-described break determination device, break determination method, and break determination program according to the present embodiment will be described.

  First, based on the stress tensor acting on the joint and the breaking stress of the joint, the fracture risk of the joint is calculated using the above-described equations (9) to (14). Therefore, it is possible to determine with high accuracy the breakage of the joint portion that joins the plurality of plate members while suppressing an increase in calculation load.

  In particular, the stress tensor acting on the joint modeled as a single solid element approximately equal to the joint size is identified, and the fracture risk of the joint is calculated based on each component of this stress tensor. Compared with the case where the joint is modeled by elements, it is possible to prevent the occurrence of local distortion and to prevent the analysis accuracy from being lowered.

  Furthermore, the fracture risk due to each fracture mode of tensile shear, cross tension, and peel is calculated for each fracture mode using each component of the stress tensor, and the fracture of the joint is determined based on the calculation result. Can be predicted with higher accuracy, and the fracture of the joint can be accurately determined.

Finally, modifications of the break determination device, the break determination method, and the break determination program will be described.
In embodiment mentioned above, although the fracture determination apparatus 4 demonstrated the case where the fracture | rupture of the spot weld part which is a junction part which joins the several metal plate piled up mutually was determined, it is different from this. You may make it determine a fracture. For example, it is possible to determine the breakage of a line welded portion that joins a plurality of metal plates stacked on each other, a bolt that joins a plurality of resin plates or glass plates stacked on top of each other, or an adhesive. .

DESCRIPTION OF SYMBOLS 1 Collision simulation apparatus 2 Car body analysis part 4 Break determination apparatus 6 Stress tensor specific part 8 Break risk calculation part 10 Break determination part

Claims (6)

A break determination device for determining breakage of a joint portion for joining a plurality of stacked plate materials,
A stress tensor specifying means for specifying a stress tensor acting on the joint,
A rupture risk calculating means for calculating a rupture risk of the joint based on the stress tensor specified by the stress tensor specifying means and a rupture stress of the joint;
A break determination means for determining breakage of the joint based on the breakage risk calculated by the breakage risk calculation means,
The fracture risk calculation means uses the stress tensor (σ _x , σ _y , σ _z , τ _zy , τ _zx ) with the normal direction of the plate material as the z-axis of the orthogonal coordinate system, and the rupture stress as (σ _T ), And the weighting coefficient is (A, B, C), the breakage risk (FR) is calculated by the following formula.

  The fracture determination device according to claim 1, wherein the stress tensor specifying means specifies a stress tensor acting on the joint modeled as a single solid element substantially equal to the size of the joint. The fracture risk calculation means calculates the fracture stress of the joint by tensile shear (σ _TSS ), the fracture stress of the joint by cross tension (σ _CTS ), and the fracture stress of the joint by peel (σ _LTS ). The fracture risk of the joint due to tensile shear (FR _TSS ), the fracture risk of the joint due to cross tension (FR _CTS ), and the fracture risk of the joint due to peel (FR _LTS ) are as follows: The fracture determination device according to claim 1 or 2, which is calculated by an equation.

  The break determination device according to any one of claims 1 to 3, wherein a break of a spot welded portion that joins a plurality of metal plates stacked on each other is determined. It is a rupture determination method for determining a rupture of a joint part that joins a plurality of stacked plate materials,
Identifying a stress tensor acting on the joint;
Calculating a fracture risk of the joint based on the identified stress tensor and the fracture stress of the joint;
Determining the breakage of the joint based on the calculated breakage risk, and
In the step of calculating the fracture risk, the stress tensor with the normal direction of the plate material as the z-axis of the orthogonal coordinate system (σ _x , σ _y , σ _z , τ _zy , τ _zx ), and the fracture stress ( A rupture determination method, wherein the rupture risk (FR) is calculated by the following formula when σ _T ) and weighting coefficients are (A, B, C).

A rupture determination program for causing a computer to determine a rupture of a joint that joins a plurality of stacked plate materials, the computer,
Identifying a stress tensor acting on the joint;
Calculating a fracture risk of the joint based on the identified stress tensor and the fracture stress of the joint;
Determining the breakage of the joint based on the calculated breakage risk, and
In the step of calculating the fracture risk, the stress tensor with the normal direction of the plate material as the z-axis of the orthogonal coordinate system (σ _x , σ _y , σ _z , τ _zy , τ _zx ), and the fracture stress ( A rupture determination program characterized by causing the rupture risk (FR) to be calculated by the following formula, when σ _T ) and weighting coefficients are (A, B, C).

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