JP4862408B2 - Fatigue life prediction method for spot welded structures - Google Patents

Description

  The present invention relates to a method for predicting the fatigue life of a spot welded structure formed by spot welding a plurality of metal plates at a plurality of locations, for example, the fatigue life of a portion where fatigue cracks may occur in the body of an automobile. It is related with the method of predicting.

  In the development of automobiles, in order to meet the challenges of weight reduction, development time reduction, and reduction of prototype vehicles, in recent years, various performance predictions by computer-aided engineering (CAE) using computers have been actively promoted. The strength evaluation of the car body is no exception, and the technology is also accelerating, and it has been verified that the finite element method is useful for strength analysis of structures. Some structures, such as automobile bodies, have multiple metal plates spot welded at multiple locations. When analyzing the strength of this type of spot welded structure using a computer, In general, a spot weld is modeled and a finite element method is applied to the model.

  Up to now, Rupp et al. Conducted a FEM (Finite Element Method) analysis of a spot welded part of an automobile body by modeling the weld nugget part with a beam element, and obtained it at the nodes at both ends of the beam element. A method has been proposed in which a nominal structural stress serving as an evaluation index is obtained using the measured force and moment, and the fatigue life of a spot weld is predicted using this (see Non-Patent Document 1).

  In Patent Document 1, an LP model as a spot welded structure is created by combining a flat plate and an L-shaped plate, a shell model for finite element method analysis is created for the LP model, and the created finite element method analysis Finite element method linear elastic analysis using a shell model for the load, the shared load of the weld nugget at the center of the spot weld, the deflection on the circumference of the diameter D drawn around the weld nugget, and the radial direction The nominal structural stress in the weld nugget is calculated using the disc theory of elasticity based on the calculated shared load, the deflection on the circumference, and the radial tilt. A method for predicting the fatigue life of a spot welded structure has been proposed. Here, the shell model for the finite element method analysis is created using shell elements, and is a model that divides the vicinity of the nugget portion into dense nest-like shell elements.

  Further, Patent Document 2 is a method for predicting a crack occurrence risk site of a structure formed by spot welding a plurality of panels at a plurality of locations, and a step of modeling a spot welded portion with a shared node model And applying a finite element method to the model to calculate a value corresponding to the peel distance in the perpendicular direction at a node adjacent to the shared node, and comparing the calculated value with a predetermined value. There has been proposed a method for predicting a crack occurrence risk site by providing the crack.

Further, Patent Document 3 discloses a fracture determination apparatus for determining fracture of a welded part, in which two plate elements to be welded are modeled as shell elements, a welded part is modeled as a beam element, and a beam is obtained by a finite element method. The stress generated at the outer edge of the beam is calculated, the reference stress that is the criterion for fracture determination at the weld site is calculated using the strain rate dependency of the shell element, and based on the stress generated at the outer edge of the beam and the reference stress, There has been proposed a break determination device for determining whether or not a welded portion is broken.
Andreas Rupp, Klaus Storzel, and Vatroslay Grubisic, “Computer Aided Dimensioning of Spot-Welded Automotive Structures”, International Congress and Exposition Detroit, Michigan, February 27-March 2,1995, p.1-11 JP 2003-149130 A JP 2002-35986 A JP 2005-205467 A

  However, in the method proposed by Rupp et al. In Non-Patent Document 1, the force and moment applied to the node from the beam element are calculated by FEM analysis, and the calculated force and moment are applied to the center of the weld nugget portion in the metal plate. Assuming that the stress around the weld nugget is calculated based on the theory of elasticity, there is a problem that the stress distribution has the same absolute value with the center of the weld nugget symmetric. Since the stress distribution around the weld nugget in a spot welded structure that is actually loaded is not the same in absolute value with the center of the weld nugget symmetrical, the accurate stress is not calculated by the method proposed by Rupp et al. The calculation could not be performed and the fatigue life of the dangerous part could not be accurately predicted.

Further, in the method proposed in Patent Document 1, it is necessary to create a finite element method analysis shell model that is a spider web model, but although the analysis accuracy is high, the model is dense and requires a great deal of time for creation. There was a problem that it would require.
Further, in the method proposed in Patent Document 2, since the spot welded portion is modeled with a shared node model, it can be easily modeled, and the modeling does not require many man-hours. However, since the spot weld is not modeled as a beam element, there is a problem in that there is a limit to the calculation accuracy of the force acting on the node.

Furthermore, although the method proposed in Patent Document 3 models a welded part as a beam element, the beam element is not connected to a node and the node is not shared. For this reason, there existed a subject that the calculation precision of the force which acts on a node has a limit.
Therefore, the present invention has been made to solve these problems, and the object of the present invention is to reduce the time for creating a finite element analysis model and to accurately predict the fatigue life of the spot welded structure. It is to provide a fatigue life prediction method.

To solve the above problems, fatigue life prediction method for a spot welded structure according to the present onset Ming, a method of predicting the fatigue life of the spot welded structure in which a plurality of metal plates are spot welded at a plurality of positions by computer A first step of modeling the metal plate with a shell element by a computer and modeling one weld nugget with one beam element , wherein the shell element and the beam element are connected to each other. Each of the plurality of shell elements connected to the shared node is a quadrilateral element and the number of the shell elements is four , and the model modeled in the first step by the computer is finite. Applying the element method, the force and mode applied to the shared node from a plurality of shell elements connected to the shared node where the shell element and the beam element are connected. A second step of calculating the instrument,
A third step of calculating an evaluation stress using a value obtained by adding a force of an adjacent shell element and a value of an adjacent shell element from the force and moment calculated in the second step by a computer; and The fourth step is to predict the fatigue life based on the evaluation stress calculated in the third step and the fatigue life diagram prepared in advance by the computer .

  According to the fatigue life prediction method for a spot welded structure according to the present invention, a metal plate is modeled by a shell element and one weld nugget part is modeled by one beam element. Creation time can be shortened. Then, the force and moment applied to the shared node are calculated from a plurality of shell elements connected to the shared node where the shell element and the beam element are connected, the evaluation stress is calculated from the calculated force and moment, and the calculated evaluation is calculated. Since the fatigue life is predicted based on the stress and the fatigue life diagram prepared in advance, the calculation accuracy of the force and moment acting on the shared node is increased, and the fatigue life can be predicted with high accuracy.

  Next, embodiments of the present invention will be described with reference to the drawings. FIG. 1 shows a finite element analysis model and load load of a T-shaped spot welded structure made of a steel plate (metal plate) having a thickness of 1.2 mm and made up of a first hat cross-section member A and a second hat cross-section member B. It is a figure for demonstrating conditions. FIG. 2 is an enlarged view of one spot welded portion of the finite element analysis model shown in FIG.

As shown in FIG. 1, the first hat cross-section member A and the second hat cross-section member B made of a steel plate (metal plate) having a plate thickness of 1.2 mm are spot-welded (spot welded portion 2) at a plurality of locations. In the T-shaped spot welded structure 1 as described above, a structural analysis was performed by a finite element method under a condition in which a load of 1 kN was applied to the tip of the second hat cross-section member B in both the tensile and compression directions.
In this structural analysis, first, as shown in FIG. 2, in the spot welded portion 2, two steel plates to be welded are modeled by the shell element 3, and one weld nugget portion 4 is modeled by the beam element 5. Turn into. Here, both ends of the shell element 3 and the beam element 5 are connected by two shared nodes 6, and four shell elements 3 ₁ , 3 ₂ , 3 ₃ , 3 ₄ are connected to each shared node 6. Each shell element 3 ₁ , 3 ₂ , 3 ₃ , 3 ₄ is a quadrilateral element.

For each of the two shared nodes 6, the force and moment applied to the shared node 6 from the _four shell elements 3 ₁ , 3 ₂ , 3 ₃ , 3 ₄ are calculated. FIG. 3 shows the forces and moments applied from the _four shell elements 3 ₁ , 3 ₂ , 3 ₃ , 3 ₄ to one common node 6 in the model of the spot weld 2. As shown in FIG. 3A, the force f _ij in the shell element plane is applied to each shared node 6 from the four shell elements 3 ₁ , 3 ₂ , 3 ₃ , 3 ₄ , and FIG. As shown, a bending moment m _ij acting on the shell element surface from the _four shell elements 3 ₁ , 3 ₂ , 3 ₃ , 3 ₄ is added to each shared node 6, as shown in FIG. A stress f _zj perpendicular to the shell element surface is applied to each shared node 6 from the four shell elements 3 ₁ , 3 ₂ , 3 ₃ , 3 ₄ .

Next, an evaluation stress is calculated from the calculated force and moment. That is, the evaluation stress is calculated from the force f _ij in the shell element plane, the bending moment m _ij acting on the shell element plane, and the stress f _{zj in the} direction perpendicular to the shell element plane. In calculating this evaluation stress, a value obtained by adding the forces of the adjacent shell elements and a value obtained by adding the moments of the adjacent shell elements are used. That is, the value obtained by adding the force f _ij in the adjacent shell element surface, the value obtained by adding the bending moment m _ij acting on the adjacent shell element surface, and the vertical stress f _zj on the adjacent shell element surface are added. The calculated value is used to calculate the evaluation stress.

The film stress obtained from the value obtained by adding the forces f _ij in the adjacent shell element planes is as shown in the following equations (1) to (4).
σ ₁ = σ (f _x1 + f _x4 ) = 2 (f _x1 + f _x4 ) · cos θ / (πdt)
0 ≦ θ ≦ π / 2, 3π / 2 ≦ θ ≦ 2π (1)
σ ₂ = σ (f _x2 + f _x3 ) = 2 (f _x2 + f _x3 ) · cos θ / (πdt)
π / 2 ≦ θ ≦ 3π / 2 (2)
σ ₃ = σ (f _y1 + f _y2 ) = 2 (f _y1 + f _y2 ) · sin θ / (πdt)
0 ≦ θ ≦ π (3)
σ ₄ = σ (f _y3 + f _y4 ) = 2 (f _y3 + f _y4 ) · sin θ / (πdt)
π ≦ θ ≦ 2π (4)
Here, sigma ₁ is adjacent shell element 3 _first surface of the x-axis direction along the force f _x1 and shell elements 3 ₄ side of the x-axis direction along the force f _x4 and film stress obtained from a value obtained by adding, sigma ₂ adjacent shell element 3 _second side of the x-axis direction along the force f _x2 and shell elements 3 ₃ side of x-axis direction along the force f _x3 and film stress obtained from a value obtained by adding, sigma ₃ is adjacent , The film stress obtained from the sum of the force f _y1 along the y-axis direction of the shell element 3 ₁ surface and the force f _y2 along the y-axis direction of the shell element 3 ₂ surface, σ ₄ is the adjacent shell element 3 _three surfaces of the y-axis direction along the force f _y3 and shell elements 3 ₄ side of the y-axis direction along the force f _y4 and film stress obtained from the value obtained by adding the nugget diameter d is shown in d in FIG. 2, t is the plate thickness, and θ is the angle from the x-axis indicated by θ in FIG.

The bending stress obtained from the value obtained by adding the bending moment m _ij acting on the adjacent shell element surfaces is as shown in the following equations (5) to (8).
σ ₅ = σ (m _x1 + m _x2 ) = 1.872.2 (m _x1 + m _x2 ) · sin θ / (dt ² )
0 ≦ θ ≦ π / 2, 3π / 2 ≦ θ ≦ 2π (5)
σ ₆ = σ (m _x3 + m _x4 ) = 1.8772 (m _x3 + m _x4 ) · sin θ / (dt ² )
π ≦ θ ≦ 2π (6)
_{σ 7 = σ (m y1 +} m y4) = 1.872 · 2 (m y1 + m y4) · cosθ / (dt 2)
0 ≦ θ ≦ π / 2, 3π / 2 ≦ θ ≦ 2π (7)
_{σ 8 = σ (m y2 +} m y3) = 1.872 · 2 (m y2 + m y3) · cosθ / (dt 2)
π / 2 ≦ θ ≦ 3π / 2 (8)
Here, σ ₅ is the bending stress obtained from the value obtained by adding the bending moment m _x1 about the x axis of the shell element 3 ₁ surface and the bending moment m _x2 about the x axis of the shell element 3 ₂ surface, and σ ₆ is Bending stress obtained from the sum of the bending moment m _x3 about the x axis of the adjacent shell element 3 ₃ plane and the bending moment m _x4 about the x axis of the shell element 3 ₄ plane, σ ₇ is the adjacent shell element 3 Bending stress obtained from the sum of the bending moment _my1 about the y-axis of _one surface and the bending moment _my4 about the y-axis of shell element 3 ₄ , σ ₈ is related to the y-axis of the adjacent shell element 3 ₂ surface it is obtained and bending moments m _y2 and shell elements 3 ₃ surface of the bending moment about the y-axis m _y3 from the value obtained by adding the bending stress.

Furthermore, the bending stress obtained from the value obtained by adding the stress f _{zj in the} vertical direction to the adjacent shell element surfaces is as shown in the following equation (9).
σ ₉ = σ (f _z1 + f _z2 + f _z3 + f _z4 ) = 1.744 (f _z1 + f _z2 + f _z3 + f _z4 ) / t ² (9)
Here, σ ₉ is a stress f _{z1 in the} vertical direction with respect to the adjacent shell element 3 ₁ surface, a stress f _{z2 in the} vertical direction with respect to the surface of the shell element 3 _2, and a stress f _{z3 in the} vertical direction with respect to the surface of the shell element 3 _3. a bending stress resulting from the value obtained by adding the vertical stress f _z4 for shell elements 3 ₄ sides.

The evaluation stress σ is calculated by adding all the film stresses σ ₁ to σ ₄ and bending stresses σ ₅ to σ ₉ . That is,
σ = σ ₁ + σ ₂ + σ ₃ + σ ₄ + σ ₅ + σ ₆ + σ ₇ + σ ₈ + σ ₉ (10)
And in the fatigue life prediction method of the spot welded structure according to the present embodiment, the fatigue life is calculated based on the evaluation stress σ calculated by the equation (10) and a fatigue life diagram (not shown) prepared in advance. Predict.

More than the series of processes, it intends row at the computer.
Here, in the finite element analysis model of the spot welded structure 1 shown in FIG. 1, in the structural analysis by the finite element method performed under the condition in which a load 1 kN is applied to the tip portion of the second hat cross-section member B in both the tensile and compression directions, In the portion shown dark in FIG. 4, the evaluation stress at the spot welded portion 2 on the second hat cross-section member B side is high, and it was predicted that the portion was a fatigue fracture risk location.

  Next, in the finite element analysis model of the spot welded structure 1 shown in FIG. 1, a fatigue test was performed by changing the load range applied to the tip of the second hat cross-section member B within the range shown in Table 1, and the life in that case was It was measured. Moreover, the lifetime at the time of changing the load range given to the front-end | tip part of the 2nd hat cross-section member B in the range shown in Table 1 in the finite element analysis model of the spot welded structure 1 shown in FIG. Table 1 shows the fatigue test results and the prediction results according to the present invention.

  In Table 1, the predicted life is shown by the average life and the upper and lower limits of the 95% confidence interval. FIG. 5 shows the fatigue test results and prediction results shown in Table 1 in relation to the load range and life. In FIG. 5, the test results are indicated by ●, and the prediction results are indicated by the solid line for the average life and the upper and lower limits of the 95% confidence interval by the broken line.

Referring to Table 1 and FIG. 5, the test results and the prediction results according to the present invention corresponded well, and it was confirmed that the fatigue life prediction method according to the present invention is effective.
In addition, compared with the fatigue life prediction method according to the present invention, fatigue evaluation was performed by the method proposed by Rupp et al. In the finite element analysis model of the spot welded structure 1 shown in FIG. 1, a load 1 kN is applied to the tip of the second hat cross-section member B in both the tensile and compression directions, and the beam element is moved to the node by the method proposed by Rupp et al. The applied force and moment were obtained, and the evaluation stress was calculated from the force and moment. The results are shown in Table 2.

  As shown in Table 2, the evaluation stress at the spot welded portion on the first hat cross-section member A side is high, and the method proposed by Rupp et al. This result is different from the second hat cross-section member B side where the fracture occurred in the test, indicating that the prediction accuracy was not sufficient.

According to the fatigue life prediction method for a spot welded structure according to the embodiment of the present invention, the steel plate is modeled by the shell element 3 and one weld nugget portion 4 is modeled by one beam element 5, The time for creating the finite element analysis model can be shortened. Then, the force and moment applied to the shared node 6 are calculated from the plurality of shell elements 3 ₁ , 3 ₂ , 3 ₃ , and 3 ₄ connected to the shared node 6 where the shell element 3 and the beam element 5 are connected. Since the evaluation stress is calculated from the force and the moment, and the fatigue life is predicted based on the calculated evaluation stress and the fatigue life diagram prepared in advance, the calculation accuracy of the force and moment acting on the shared node 6 is increased. The fatigue life can be accurately predicted.

A finite element analysis model and load loading conditions of a T-shaped spot welded structure composed of two first hat cross-section members and a second hat cross-section member made of a steel plate (metal plate) having a thickness of 1.2 mm will be described. FIG. FIG. 2 is an enlarged view of a spot welded portion in the finite element analysis model shown in FIG. 1. It is a figure which shows the force and moment which are applied to one common node in the model of a spot weld from four shell elements. It is a figure which shows the stress distribution obtained by implementing the structural analysis by the finite element method in the fatigue life prediction method based on this invention. It is a graph which shows the fatigue test result and prediction result which are shown in Table 1 by the relationship between a load range and a lifetime.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Spot welding structure 2 Spot welding part 3 Shell element 3 ₁ , 3 ₂ , 3 ₃ , 3 ₄ Shell element 4 Welding nugget part 5 Beam element 6 Shared node A 1st hat cross-section member B 2nd hat cross-section member

Claims (1)

A method of predicting the fatigue life of a spot welded structure in which a plurality of metal plates are spot welded at a plurality of locations by a computer ,
The first step of modeling the metal plate with a shell element and modeling one weld nugget part with one beam element by a computer, and at a shared node where the shell element and the beam element are connected A first step in which each of the connected shell elements is a quadrilateral element and the number of the shell elements is four ;
Applying a finite element method to the model modeled in the first step by a computer, a force applied to the shared node from a plurality of shell elements connected to the shared node to which the shell element and the beam element are connected; A second step of calculating moments;
A third step of calculating an evaluation stress using a value obtained by adding a force of an adjacent shell element and a value of an adjacent shell element from the force and moment calculated in the second step by a computer; and ,
Fatigue life prediction of a spot welded structure comprising a fourth step of predicting a fatigue life based on the evaluation stress calculated in the third step and a fatigue life diagram prepared in advance by a computer Method.

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