Method for estimating stress intensity factor of welded joint

Abstract

To provide a method for estimating a stress intensity factor of a welded joint capable of simply and accurately estimating the stress intensity factor of a crack existing in the welded joint.SOLUTION: A step ST1 of calculating stress intensity factors of the crack for the respective shape coefficient indices and the respective dimensions of the crack by performing a finite element analysis on the reference joint; a step ST2 of calculating stress intensity factors of the crack for the respective shape coefficient indices and the respective dimensions of the crack by performing a finite element analysis on the reference joint; The method includes a step ST3 of calculating stress intensity factors of a crack having specific dimensions by performing a finite element analysis, a step ST3 of calculating shape factor indices of a target joint based on the stress intensity factors calculated in the step ST4 and a reference relationship, and a step ST5 of estimating stress intensity factors of a crack having arbitrary dimensions of the target joint based on the shape factor indices of the target joint and the reference relationship.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present invention relates to a method for estimating the stress intensity factor of a welded joint, which is capable of easily and accurately estimating the stress intensity factor of a crack present in a welded joint using finite element analysis. [Background technology]

[0002] In recent years, the automotive industry has been required to reduce the weight of vehicle bodies to improve fuel efficiency and to increase the strength of vehicle bodies to improve collision safety. To achieve both of these requirements, it is effective to use high-strength steel sheets as the material for vehicle bodies. Furthermore, from the viewpoint of improving rust prevention, zinc-based plated steel sheets, which have excellent corrosion resistance, are used among high-strength steel sheets.

[0003] Spot welding is primarily used to assemble automobile bodies, joining multiple steel sheets stacked in the thickness direction to form welded joints, but spot welding of zinc-based plated steel sheets can sometimes cause cracks in the spot welds. This cracking is said to be caused by what is known as liquid metal embrittlement (abbreviated as "LME" below), and is thought to be caused by the temperature rise and tensile stress generated during the welding process, which cause the molten zinc-based plated metal to penetrate the grain boundaries of the steel sheet, reducing the grain boundary strength. If the cracking caused by LME (LME cracking) is severe, the static strength of the spot weld may decrease. For this reason, in order to suppress LME cracking, techniques have been proposed, such as controlling the chemical composition and structure of the steel sheet and coating, and controlling the welding conditions, as described in Patent Document 1. However, the effect of LME cracking on fatigue strength has not been clearly understood. Therefore, from the viewpoint of fatigue strength, in addition to the development of technologies to suppress LME cracking, a method to accurately evaluate the effect of LME cracking on fatigue strength is desired.

[0004] Generally, to evaluate the effect of cracks on fatigue strength, stress intensity factors calculated by regarding the crack as a crack are often used. The stress intensity factor is a fracture mechanics parameter that expresses the driving force for crack propagation based on the deformation field near the crack tip. For example, as described in Non-Patent Document 1, a theoretical solution capable of accurately evaluating the stress intensity factor of a crack has been obtained when the mechanical conditions are simple. However, because LME cracks that occur in spot welds have a three-dimensional shape resembling an arc surface along the outer edge of a spot weld that is approximately circular when viewed from the thickness direction of the steel sheet, and because the mechanical conditions differ depending on the location of the spot weld in the automotive part, no theoretical solution capable of expressing the stress intensity factor exists.

[0005] In such cases, it is common to use finite element analysis to calculate the stress intensity factor, but creating a three-dimensional analytical model and performing the analysis requires a huge amount of time and effort. In particular, because automotive parts have complex shapes, Patent Document 2, for example, proposes a stress evaluation method for spot welds that combines theoretical solutions and finite element analysis. However, the method described in Patent Document 2 has problems in that it requires a complicated procedure for combining theoretical solutions and finite element analysis, and its applicability to cracks is unclear because it does not target cracks in the first place. Therefore, a method is desired that can easily and accurately estimate the stress intensity factor of a crack under various mechanical conditions, such as various crack dimensions (depth and length).

[0006] Non-Patent Document 2 describes a method for calculating a stress intensity factor based on the analysis results of the crack opening displacement. [Prior art documents] [Patent documents]

[0007] [Patent Document 1] Patent No. 7040330 [Patent Document 2] Japanese Patent Application Laid-Open No. 2003-149130 [Non-patent literature]

[0008] [Non-Patent Document 1] Y. Murakami et al., “STRESS INTENSITY FACTORS HANDBOOK”, Volume 1, Pergamon Press, 1987, p.11 [Non-patent document 2] Nakai, Yoshikazu and Kubo, Shiro, "Basic Course of Mechanical Engineering: Fracture Mechanics", Asakura Publishing, 2014, pp. 64-66 Summary of the Invention [Problem to be solved by the invention]

[0009] The present invention has been made to solve the problems of the conventional art as described above, and an object of the present invention is to provide a method for estimating the stress intensity factor of a welded joint, which is capable of simply and accurately estimating the stress intensity factor of a crack present in a welded joint using finite element analysis. [Means for solving the problem]

[0010] In order to solve the above problems, the present inventors have conducted extensive research. If the stress intensity factor is K, the shape factor is F, the nominal stress acting on the welded joint is σ, the crack depth (the dimension in the thickness direction of the steel plate) is a, and pi is the circular constant, it is known that the relationship between these can be expressed by the following equation (1). F=K / (σ·(π·a) 1 / 2 ) ···(1)

[0011] The shape factor F in the above formula (1) is a term that represents the state of deformation near the crack tip, but it is extremely difficult to calculate this theoretically and accurately. A large shape factor F is thought to correspond to large deformation near the crack tip (easiness of crack opening). Furthermore, large deformation near the crack tip is thought to correspond to a large area in which the steel plate can deform (easiness of steel plate deformation). Therefore, the inventors hypothesized that the shape factor corresponds to the size of the area in which the steel plate can deform, and further that the shape factor corresponds to the size of the representative dimension corresponding to this area (hereinafter referred to as the "shape factor index"), and investigated a method for estimating the stress intensity factor based on this shape factor index.

[0012] Specifically, a welded joint whose shape factor index, which is a representative dimension corresponding to the area of ​​the deformable region, can be easily quantitatively evaluated (for example, if the welded joint is a circular plate joint made by overlapping multiple steel plates of the same circular shape in the plate thickness direction, the area of ​​the deformable region can be considered to be the area of ​​the overlapping region of each steel plate, i.e., the area of ​​each steel plate as viewed in the plate thickness direction, and the shape factor index, which is a representative dimension, can be the diameter or radius of the circular plate joint (the diameter or radius of each circular steel plate)) is used as a reference joint, and finite element analysis is performed using multiple analytical models of the reference joint in which the shape factor index and crack dimensions (for example, crack depth) are changed under the condition that an external force is applied to the crack in a certain direction, thereby calculating a reference relationship, which is the relationship between the shape factor index and the stress intensity factor of the crack, for each crack dimension.

[0013] Next, for a target joint (a welded joint of a different type from the reference joint, i.e., a welded joint with different shape, dimensions, boundary conditions, etc.) from the reference joint, for which a stress intensity factor is to be estimated, a finite element analysis is performed using an analytical model of the target joint having a crack of a specific size under conditions in which an external force acts on the crack in the same direction as in the reference joint. The stress intensity factor of the crack of a specific size in the target joint is calculated by performing a finite element analysis using an analytical model of the target joint. Then, a hypothesis is made that the above-mentioned reference relationship also applies to the target joint. The shape factor index for the target joint is calculated based on the calculated stress intensity factor of the crack of the specific size and the above-mentioned reference relationship. The shape factor index calculated for this target joint does not need to be easily quantitatively evaluated like the shape factor index of the reference joint. Because it is calculated (estimated) using the reference relationship, it is referred to as an "equivalent shape factor index" in this specification. In other words, the equivalent shape factor index corresponds to the shape factor index when the target joint is replaced with a reference joint that is considered to have the same deformation state as the target joint.

[0014] If it is hypothesized that the equivalent shape factor index is a value specific to the target joint, it is possible to estimate the stress intensity factor of a crack of any size that the target joint has based on this equivalent shape factor index and the reference relationship. That is, it is possible to estimate the stress intensity factor of a crack of a size different from the crack of the specific size without performing a finite element analysis using an analytical model of the target joint that has the crack of the different size. In other words, for the target joint, it is sufficient to simply perform a finite element analysis using an analytical model of the target joint that has a crack of the specific size. The inventors have found that the results of estimating the stress intensity factor of a crack of any size in a target joint based on the above hypothesis closely match the results calculated by performing finite element analysis using an analytical model of a target joint actually having a crack of any size (they have found that the above hypothesis is correct).

[0015] The present invention has been completed based on the above findings of the present inventors. That is, in order to solve the above-mentioned problems, the present invention provides a method for estimating stress intensity factors of welded joints, which uses finite element analysis to estimate the stress intensity factors of cracks present in a welded joint comprising a plurality of steel plates overlapping each other in the plate thickness direction and a spot weld that joins the overlapping steel plates, and which performs finite element analysis on a reference joint, which is a type of welded joint, using a representative dimension corresponding to the area of ​​the overlapping region of the plurality of steel plates as a shape factor index, under the condition that an external force is applied to the crack in a fixed direction, and using a plurality of analytical models of the reference joint in which the shape factor index and the size of the crack are changed, thereby calculating the stress intensity factor of the crack for each of the shape factor index and the size of the crack; a second stress intensity factor calculation step of calculating a stress intensity factor of a crack of a specific dimension in a target joint, the target joint being a welded joint of a different type from the reference joint and being a target for estimating a stress intensity factor, by performing finite element analysis using an analytical model of the target joint having a crack of a specific dimension under conditions in which an external force acts on the crack in the same direction as in the reference joint; a shape factor index calculation step of calculating the shape factor index for the target joint based on the stress intensity factor calculated in the second stress intensity factor calculation step and the reference relationship; and a stress intensity factor estimation step of estimating a stress intensity factor of the crack of an arbitrary dimension in the target joint based on the shape factor index for the target joint calculated in the shape factor index calculation step and the reference relationship.

[0016] In the present invention, "crack dimension" means "crack depth" or "crack length." "Crack depth" means the crack dimension in the thickness direction of the steel plate. "Crack length" means the crack dimension when viewed from the thickness direction of the steel plate. In the present invention, "changing the crack dimensions" means changing the depth of the crack while keeping the length of the crack constant, or changing the length of the crack while keeping the depth of the crack constant. According to the present invention, in the first stress intensity factor calculation step, a finite element analysis is performed on a reference joint, which is a type of welded joint, with a shape factor index and crack dimensions changed, under conditions where an external force is applied to the crack in a certain direction, thereby calculating the stress intensity factor of the crack for each shape factor index (a representative dimension corresponding to the area of ​​the overlapping region of multiple steel plates) and crack dimension, and in the reference relationship calculation step, a reference relationship, which is the relationship between the shape factor index and the stress intensity factor of the crack, is calculated for each crack dimension. Next, in a second stress intensity factor calculation step, a finite element analysis is performed on a target joint, which is a welded joint of a different type from the reference joint and for which a stress intensity factor is to be estimated, under conditions in which an external force acts on the crack in the same direction as in the reference joint, to calculate a stress intensity factor of a crack of a specific size in the target joint. According to the findings of the inventors, the above-mentioned reference relationship also holds for the target joint, and therefore, in the shape factor index calculation step, a shape factor index (equivalent shape factor index) for the target joint can be calculated based on the stress intensity factor calculated in the second stress intensity factor calculation step and the reference relationship. Finally, according to the findings of the present inventors, the shape factor index (equivalent shape factor index) calculated in the shape factor index calculation step is a value specific to the target joint, and therefore, in the stress intensity factor estimation step, it is possible to estimate the stress intensity factor of a crack of any size that the target joint has, based on the shape factor index (equivalent shape factor index) for the target joint and the reference relationship.

[0017] According to the present invention, the stress intensity factor of a crack of any size that the target joint has is estimated by utilizing the fact that the reference relationship calculated for the reference joint by performing finite element analysis also holds for a target joint of a different type from the reference joint, and that the shape factor index for the target joint is a value specific to the target joint.Therefore, as long as the reference relationship is calculated accurately in advance, the stress intensity factor of a crack of any size that the target joint has can be accurately estimated. Furthermore, according to the present invention, finite element analysis is performed only in the first stress intensity factor calculation step and the second stress intensity factor calculation step, and finite element analysis does not need to be performed in the reference relationship calculation step, the shape factor index calculation step, and the stress intensity factor estimation step. In other words, for a target joint, it is only necessary to perform finite element analysis using an analytical model of a target joint having a crack of a specific size in the second stress intensity factor calculation step, so that the stress intensity factor of a crack of any size in the target joint can be easily estimated.

[0018] Specifically, in the present invention, in the first stress intensity factor calculation step, the shape factor index and the depth of the crack are changed and a finite element analysis is performed using a plurality of analytical models of the reference joint in which the length of the crack is set to a constant value, thereby calculating the stress intensity factor of the crack for each of the shape factor index and the depth of the crack; in the reference relationship calculation step, the reference relationship is calculated for each depth of the crack; in the second stress intensity factor calculation step, a finite element analysis is performed using an analytical model of the target joint having the crack of the same constant length as the reference joint and at a specific depth, thereby calculating the stress intensity factor of the crack at a specific depth that the target joint has; and in the stress intensity factor estimation step, the stress intensity factor of the crack at an arbitrary depth that the target joint has is estimated based on the shape factor index for the target joint calculated in the shape factor index calculation step and the reference relationship.

[0019] In the present invention, preferably, the reference joint is a disc joint, and the shape factor index is a diameter or a radius of the disc joint. [Effects of the Invention]

[0020] According to the present invention, it is possible to simply and accurately estimate the stress intensity factor of a crack present in a welded joint. [Brief explanation of the drawings]

[0021] [Figure 1] FIG. 1 is a flowchart showing an outline of a method for estimating a stress intensity factor of a welded joint according to an embodiment of the present invention. [Figure 2] 2 is an explanatory diagram for schematically explaining the first stress intensity factor calculation step ST1 and the reference relationship calculation step ST2 shown in FIG. 1. FIG. [Figure 3] 2 is an explanatory diagram for schematically explaining the second stress intensity factor calculation step ST3, the shape factor index calculation step ST4, and the stress intensity factor estimation step ST5 shown in FIG. 1. FIG. [Figure 4] FIG. 2 is a diagram showing an analytical model of a welded joint used in an example of the present invention. [Figure 5] FIG. 10 is a diagram showing a reference relationship calculated in an example of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0022] Hereinafter, an embodiment of the present invention will be described with reference to the accompanying drawings. FIG. 1 is a flowchart showing an outline of the procedure of a method for estimating a stress intensity factor of a welded joint according to one embodiment of the present invention (hereinafter, simply referred to as a "stress intensity factor estimation method" where appropriate). The stress intensity factor estimation method according to this embodiment uses finite element analysis to estimate the stress intensity factor of a crack present in a welded joint that includes multiple steel plates (two in this embodiment) stacked in the plate thickness direction and a spot weld that joins the multiple stacked steel plates. In this embodiment, consider a case in which the spot weld is approximately circular when viewed in the plate thickness direction of the steel plates, and a crack extending in the plate thickness direction of the steel plates exists along the outer edge of the approximately circular spot weld. As shown in FIG. 1, the stress intensity factor estimation method according to this embodiment includes a first stress intensity factor calculation step ST1, a reference relationship calculation step ST2, a second stress intensity factor calculation step ST3, a shape factor index calculation step ST4, and a stress intensity factor estimation step ST5. Steps ST1 to ST5 will be explained in order below.

[0023] <First stress intensity factor calculation step ST1> 2A and 2B are explanatory diagrams that schematically explain the first stress intensity factor calculation step ST1 and the reference relationship calculation step ST2. Fig. 2A is a perspective view showing an example of a reference joint used in the first stress intensity factor calculation step ST1, and Fig. 2B is a diagram showing the reference relationship calculated in the reference relationship calculation step ST2. Fig. 2A shows only half of the reference joint in consideration of symmetry. In the first stress intensity factor calculation step ST1, as shown in Figure 2(a), for a reference joint, which is a type of welded joint, a representative dimension corresponding to the area of ​​the overlapping region of multiple steel plates is used as a shape factor index, and finite element analysis is performed using multiple analytical models of the reference joint with different shape factor indexes and crack dimensions under the condition that an external force (load) in a certain direction is applied to the crack, thereby calculating the stress intensity factor of the crack for each shape factor index and crack dimension. Specifically, in the first stress intensity factor calculation step ST1 of this embodiment, the shape factor index and crack depth (the dimension in the thickness direction of the steel plate) are changed, and finite element analysis is performed using multiple analytical models of a reference joint in which the crack length (the dimension of the crack when viewed in the thickness direction of the steel plate; in this embodiment, the circumferential dimension of the crack) is set to a constant value, thereby calculating the stress intensity factor of the crack for each shape factor index and crack depth.

[0024] The example of the reference joint shown in FIG. 2(a) is a circular plate joint in which two circular steel plates with the same diameter are overlapped in the plate thickness direction. Therefore, in the case of the reference joint shown in FIG. 2(a), the area of ​​the overlapping region of the two steel plates corresponds to the area of ​​the steel plates as viewed in the plate thickness direction. The diameter D (diameter of the steel plates) or radius D / 2 (radius of the steel plates) of the circular plate joint can be considered as a representative dimension corresponding to this area. In the case of a circular plate joint as shown in FIG. 2(a), the area of ​​the deformable region can be considered as the area of ​​the overlapping region of the two steel plates, i.e., the area of ​​the circular steel plates as viewed in the plate thickness direction. Therefore, in this embodiment, the diameter D of the circular plate joint is used as the shape factor index (hence, hereinafter referred to as "shape factor index D" as appropriate). However, this is not limiting, and the radius D / 2 of the circular plate joint can also be used as the shape factor index. In the case of the reference joint (disc joint) shown in Figure 2(a), in the first stress intensity factor calculation step ST1, for example, a crack extending in the plate thickness direction is introduced from the top surface of the lower steel plate (the surface facing the upper steel plate), the entire outer edge of the upper steel plate is fixed, and a finite element analysis is performed under the conditions that an in-plane load is applied to part of the outer edge of the lower steel plate.

[0025] In the first stress intensity factor calculation step ST1 of this embodiment, an opening type (mode I) stress intensity factor is calculated as the stress intensity factor of the crack. The same applies to the second stress intensity factor calculation step ST3 described below. However, the present invention is not necessarily limited to this, and it is also possible to calculate an in-plane shear type (mode II) or an out-of-plane shear type (mode III) stress intensity factor depending on the load conditions (external forces acting on the crack) in the finite element analysis. One method for calculating the stress intensity factor of a crack is to use the crack opening displacement, for example. When calculating the stress intensity factor using the crack opening displacement, first, a finite element analysis is performed to calculate the displacement u of the nodes that make up the crack surface in the analytical model of the welded joint (in the first stress intensity factor calculation step ST1, the analytical model of the reference joint; in the second stress intensity factor calculation step ST3 described below, the analytical model of the target joint), and then the crack opening displacement 2u, which is double the displacement u, is calculated. Specifically, the crack opening displacement 2u is calculated for each distance r from the crack tip. Then, the relationship between the square root of the distance r from the crack tip and the crack opening displacement 2u is approximated by a straight line, and the gradient of the approximated line is 2u / r 1 / 2 The stress intensity factor of the crack is calculated based on the above equation. Specifically, for example, the stress intensity factor K of the crack is calculated based on the following equation (2). K={E / 4(1-ν 2 )}·(2π / r) 1 / 2 ·u ···(2) In the above equation (2), E is the Young's modulus of the welded joint (the steel plate that constitutes the welded joint) where the crack exists, ν is the Poisson's ratio of the welded joint (the steel plate that constitutes the welded joint), and π is the constant of the circumference of the welded joint. The above formula (2) is a known formula that can be derived from formulas (4.8) and (4.16) described in Non-Patent Document 2.

[0026] <Reference relationship calculation step ST2> In the reference relationship calculation step ST2, a reference relationship is calculated, which is the relationship between the shape factor index D and the crack stress intensity factor K for each crack dimension (depth), as shown in FIG. 2(b), based on the shape factor index D and the crack stress intensity factor K for each crack dimension (depth) calculated in the first stress intensity factor calculation step ST1. In the example shown in FIG. 2(b), for convenience, the reference relationship is calculated for each of three crack depths, A, B, and C (thus, in the first stress intensity factor calculation step ST1, finite element analysis is performed for three crack depths). However, this is not a limitation, and the reference relationship may be calculated for multiple crack depths. However, in order to estimate stress intensity factors K for cracks of many different depths in the stress intensity factor estimation step ST5 described below, it is preferable to calculate the reference relationship for as many different depths as possible in the reference relationship calculation step ST2. The reference relationship can be a function calculated by performing an approximation such as the least squares method on the crack stress intensity factor K calculated using each analytical model with a modified shape factor D for each crack dimension (depth). Alternatively, a broken line connecting the crack stress intensity factors K calculated using each analytical model with a modified shape factor D for each crack dimension (depth) can be used as the reference relationship. Furthermore, if there are a large number of analytical models (the number of finite element analyses with modified shape factor D), a table that associates the shape factor D with the crack stress intensity factor K for each crack dimension (depth) can also be used as the reference relationship. Furthermore, because the reference relationship is also a function of the crack dimension (depth), a unified formulation of the relationship with the stress intensity factor K can be used as the reference relationship by performing a multiple regression analysis or the like using both the shape factor D and the crack dimension (depth) as variables. As shown in Figure 2(b), the reference relationship indicates that for the same crack size (depth), the larger the shape factor index D (diameter D of the disc joint), the larger the stress intensity factor K.

[0027] <Second stress intensity factor estimation step ST3> 3A and 3B are explanatory diagrams that schematically explain the second stress intensity factor calculation step ST3, the shape factor index calculation step ST4, and the stress intensity factor estimation step ST5. Fig. 3A is a perspective view showing an example of a target joint used in the second stress intensity factor calculation step ST3, Fig. 3B is an explanatory diagram that explains the shape factor index calculation step ST4, and Fig. 3C is an explanatory diagram that explains the stress intensity factor estimation step ST5. Fig. 3A shows only half of the target joint in consideration of symmetry. In the second stress intensity factor estimation step ST3, as shown in Figure 3(a), for a target joint, which is a welded joint of a different type from the reference joint (Figure 2(a)) and is the welded joint for which the stress intensity factor K is to be estimated, a finite element analysis is performed using an analytical model of the target joint having a crack of a specific dimension under conditions in which an external force (load) is applied to the crack in the same direction as in the reference joint, thereby calculating the stress intensity factor of a crack of a specific dimension in the target joint. Specifically, in the second stress intensity factor calculation step ST3 of this embodiment, as shown in Figure 3(a), a finite element analysis is performed using an analytical model of a target joint having a crack of a specific depth (e.g., crack depth = A) with the same constant length (circumferential dimension of the crack) as the reference joint, to calculate the stress intensity factor K of the crack of the specific depth that the target joint has. In the second stress intensity factor calculation step ST3, unlike the first stress intensity factor calculation step ST1, which requires finite element analysis to be performed for multiple crack depths (in the example shown in Figure 2(b), three crack depths: A, B, and C), it is only necessary to perform finite element analysis for a specific crack depth (for example, crack depth = A).

[0028] The example of the target joint shown in Figure 3(a) is a tension-shear joint in which two steel plates are partially overlapped in the plate thickness direction. 3(a), in the second stress intensity factor calculation step ST3, for example, a crack extending in the plate thickness direction from the top surface of the lower steel plate (the surface facing the upper steel plate) is introduced, one end of the lower steel plate is fixed, and a finite element analysis is performed under the conditions that an in-plane load is applied to one end of the upper steel plate. Then, the stress intensity factor of the crack is calculated based on the above-mentioned formula (2).

[0029] <Shape coefficient index calculation step ST4> In the shape factor index calculation step ST4, a shape factor index for the target joint is calculated based on the stress intensity factor K calculated in the second stress intensity factor calculation step ST3 and the reference relationship. Specifically, as shown in FIG. 3( b), if the stress intensity factor K calculated in the second stress intensity factor calculation step ST3 is the stress intensity factor K1 for the crack depth = A, the shape factor index D1 for the target joint is calculated based on the stress intensity factor K1 and the reference relationship for the crack depth = A (the reference relationship shown by the dashed-dotted line in FIG. 3( b)). In the case of the target joint shown in FIG. 3( a), the deformable region is not circular, so the shape factor index D1 calculated for this target joint cannot be easily quantified like the shape factor index D for the reference joint. For this reason, in the shape factor index calculation step ST4, the shape factor index D1 is calculated (estimated) using the reference relationship calculated in the reference relationship calculation step ST2, assuming that the reference relationship also holds for the target joint. Because this shape factor index D1 is calculated (estimated) using the reference relationship, in this embodiment, it is referred to as an equivalent shape factor index.

[0030] <Stress intensity factor estimation step ST5> In stress intensity factor estimation step ST5, a stress intensity factor K of a crack of any dimension (any depth in this embodiment) that the target joint has is estimated based on the shape factor index (equivalent shape factor index) for the target joint calculated in shape factor index calculation step ST4 and the reference relationship. Stress intensity factor estimation step ST5 is based on the premise that the equivalent shape factor index for the target joint calculated in shape factor index calculation step ST4 is a value specific to the target joint. Specifically, as described above, if the equivalent shape factor index for the target joint calculated in shape factor index calculation step ST4 is the equivalent shape factor index D1 calculated based on the stress intensity factor K1 for crack depth = A and the reference relationship for crack depth = A, then in stress intensity factor estimation step ST5, as shown in Figure 3(c), the stress intensity factor K2 of a crack of depth B in the target joint is estimated based on the equivalent shape factor index D1 and the reference relationship for crack depth = B (the reference relationship shown by the dashed line in Figure 3(c)), and the stress intensity factor K3 of a crack of depth C in the target joint is estimated based on the equivalent shape factor index D1 and the reference relationship for crack depth = C (the reference relationship shown by the solid line in Figure 3(c)).

[0031] According to the stress intensity factor estimation method of this embodiment described above, the stress intensity factor K of a crack of any depth in the target joint is estimated by utilizing the fact that the reference relationship (see FIG. 2(b)) calculated for the reference joint (disc joint) by performing finite element analysis also holds for a target joint (tension-shear joint) of a different type from the reference joint, and that the equivalent shape factor index D for the target joint is a value specific to the target joint.Therefore, as long as the reference relationship is calculated accurately in advance, it is possible to accurately estimate the stress intensity factor K of a crack of any depth in the target joint. Furthermore, according to the stress intensity factor estimation method of this embodiment, finite element analysis is performed only in the first stress intensity factor calculation step ST1 and the second stress intensity factor calculation step ST3, and finite element analysis does not need to be performed in the reference relationship calculation step ST2, the shape factor index calculation step ST4, and the stress intensity factor estimation step ST5. In other words, for the target joint, it is only necessary to perform finite element analysis using an analytical model of the target joint having a crack of a specific depth in the second stress intensity factor calculation step ST3, so that the stress intensity factor K of a crack of any depth that the target joint has can be easily estimated.

[0032] In this embodiment, the case where the crack length is kept constant and the crack depth is changed has been described as an example. Specifically, in this embodiment, in the first stress intensity factor calculation step ST1, the shape factor index D and the crack depth are changed and finite element analysis is performed using multiple analytical models of a reference joint in which the crack length is kept constant, thereby calculating the stress intensity factor K of the crack for each shape factor index D and crack depth. In the reference relationship calculation step ST2, a reference relationship is calculated for each crack depth. In the second stress intensity factor calculation step ST3, finite element analysis is performed using an analytical model of a target joint having a crack of the same constant length as the reference joint and of a specific depth, thereby calculating the stress intensity factor K of a crack of a specific depth that the target joint has. In the stress intensity factor estimation step ST5, the stress intensity factor K of a crack of any depth that the target joint has is estimated based on the equivalent shape factor index D for the target joint calculated in the shape factor index calculation step ST4 and the reference relationship. However, the present invention is not limited to this, and it is also possible to keep the crack depth constant and vary the crack length. Specifically, in the first stress intensity factor calculation step ST1, the shape factor index D and the crack length are changed, and finite element analysis is performed using multiple analytical models of a reference joint with a constant crack depth to calculate the stress intensity factor K of the crack for each shape factor index D and crack length. In the reference relationship calculation step ST2, a reference relationship is calculated for each crack length. In the second stress intensity factor calculation step ST3, finite element analysis is performed using an analytical model of a target joint having a crack of a specific length at the same constant depth as the reference joint to calculate the stress intensity factor K of a crack of a specific length that the target joint has. In the stress intensity factor estimation step ST5, the stress intensity factor K of a crack of any length that the target joint has can be estimated based on the equivalent shape factor index D for the target joint calculated in the shape factor index calculation step ST4 and the reference relationship.

[0033] Furthermore, in this embodiment, a tensile shear joint, which has relatively simple mechanical conditions, is used as an example of the target joint, but the present invention is not limited to this, and a welded joint having spot welds that constitute an automobile body part can also be used as the target joint. In this case, for example, the following method can be used. First, a finite element analysis is performed using an analytical model with a coarse mesh division to calculate the deformation state near the spot weld of the vehicle body part. Next, an analytical model with a fine mesh division and a crack is created by extracting an arbitrary region including the spot weld as the analytical model of the target joint. Then, a finite element analysis is performed using the analytical model with a fine mesh division, with the deformation state of the outer edge of the region calculated by the finite element analysis using the coarse mesh division model as the boundary condition. In this case, the equivalent shape factor index D is calculated from the analysis results for a crack of a specific depth, and the stress intensity factor K for a crack of any depth can be calculated. As described above, according to the present invention, it is possible to easily and accurately estimate the stress intensity factor K of a wide range of target joints.

[0034] Furthermore, in this embodiment, a disc joint is exemplified as the reference joint, but the present invention is not limited to this, and for example, a welded joint in which multiple steel plates of the same square shape are overlapped in the plate thickness direction can also be used as the reference joint. In this case, the shape factor index of the reference joint can be the length of one side of each square steel plate.

[0035] Hereinafter, the features of the present invention will be further clarified by describing examples of the stress intensity factor estimation method according to the present invention.

[0036] FIG. 4 is a diagram showing an analytical model of a welded joint used in this example. FIG. 4(a) is a perspective view showing the element division and boundary conditions of the analytical model of the reference joint used in this example. FIG. 4(b) is a perspective view showing the element division and boundary conditions of the analytical model of the target joint used in this example. FIG. 4(c) is an enlarged perspective view of the vicinity of a spot weld that is common to the analytical models shown in FIG. 4(a) and FIG. 4(b). In FIG. 4, only half of the welded joint (reference joint and target joint) is modeled in consideration of symmetry (in an actual welded joint, the same structure exists in front of the analytical models shown in FIG. 4(a) to FIG. 4(c)). As shown in Figure 4(a), in this example, a circular plate joint in which two circular steel plates with the same diameter D were overlapped in the plate thickness direction was used as the reference joint. Four types of diameter D were used for the circular plate joints: 25 mm, 33 mm, 40 mm, and 50 mm. Also, as shown in Figure 4(b), in this example, a tensile shear joint in which two steel plates were partially overlapped in the plate thickness direction was used as the target joint. For both the reference joint and the target joint, the steel plate thickness was 1.6 mm, the Young's modulus of the steel plate was 206 GPa, and the Poisson's ratio was 0.3. For both the reference joint and the target joints, the diameter of the spot weld (nugget diameter) was set to 6 mm, and a crack was introduced along the outer edge of the spot weld, extending in the thickness direction from the top surface of the lower steel plate (the surface facing the upper steel plate, shown by the dashed line in Figure 4(c)). For both the reference joint and the target joints, the crack depth (dimension in the thickness direction of the steel plate) a was set to four values: 0.5 mm, 0.8 mm, 1.0 mm, and 1.2 mm, and the crack length (dimension in the circumferential direction of the crack when viewed from the thickness direction of the steel plate) was set to the length equivalent to one circumference around the outer edge of the spot weld.

[0037] In each of the analytical models described above, as shown in Fig. 4(a), for the reference joint, the entire outer edge of the upper steel plate was fixed, and a load of 2000 N was applied in the in-plane direction to part of the outer edge of the lower steel plate, and deformation in the plate thickness direction was constrained (only deformation in the in-plane direction was allowed) at the position where the load was applied. As a result, for the reference joint, the stress intensity factor K (mode I) was calculated for each crack depth and disc joint diameter D (corresponding to the first stress intensity factor calculation step ST1 in this embodiment). 4(b), for the target joint, a finite element analysis was performed under the following conditions: one end of the lower steel plate was fixed, and a load of 2000 N was applied to one end of the upper steel plate in the in-plane direction (the same direction as the load applied to the reference joint), while deformation in the plate thickness direction was constrained (only deformation in the in-plane direction was allowed) at the load application position. As a result, a stress intensity factor K (mode I) was calculated for each crack depth for the target joint (corresponding to the second stress intensity factor calculation step ST3 in this embodiment; however, in actual second stress intensity factor calculation step ST3, the stress intensity factor K is calculated for any one crack depth).

[0038] Then, based on the results of calculating the stress intensity factor K for each crack depth a and disc joint diameter D for the reference joint as described above, a reference relationship was calculated, which is the relationship between the shape factor index D, represented by the disc joint diameter D, and the stress intensity factor K of the crack for each crack depth a (corresponding to reference relationship calculation step ST2 in this embodiment). Figure 5 shows the calculated reference relationship. As shown in Figure 5, the reference relationship differs depending on the crack depth a, but all of them share the common relationship that the larger the shape factor index D (diameter D of the disc joint), the larger the stress intensity factor K. This is thought to be because the larger the diameter D of the disc joint, the larger the area of ​​the region where the steel plates can deform, which reduces the rigidity of the disc joint and makes it easier for cracks to open.

[0039] In this example, as shown by the dashed line in FIG. 5, the reference relationship for each crack depth a was approximated by the power law shown in the following equation (3) using the least squares method. K=A·D B ···(3) The values ​​of the coefficient A and the index B in the above formula (3) are shown in Table 1 below. [Table 1] The reason why the power law was used in this example is that it was thought that as the shape factor index (diameter of the disc joint) D becomes smaller, that is, as the rigidity of the disc joint increases, the stress intensity factor K approaches 0 and becomes consistent with the deformation behavior. However, as long as it can appropriately express the deformation behavior, the function expressing the reference relationship is not limited to the power law.

[0040] Next, for the target joint, a shape factor index D (referred to as an equivalent shape factor index Deq in this embodiment) was calculated for each crack depth a based on the stress intensity factor K calculated for each crack depth a and the reference relationship shown in Equation (3). (This corresponds to shape factor index calculation step ST4 in this embodiment. However, in actual shape factor index calculation step ST4, the equivalent shape factor index Deq is calculated for any one crack depth a.) Specifically, the equivalent shape factor index Deq for a crack depth a = 0.5 mm was calculated by back-calculating the shape factor index D based on the stress intensity factor K calculated by performing finite element analysis for a crack depth a = 0.5 mm and the reference relationship shown in Equation (3) for a crack depth a = 0.5 mm (coefficient A = 5.325, exponent B = 0.131). The equivalent shape factor index Deq for crack depths a = 0.8 mm, 1.0 mm, and 1.2 mm was calculated in a similar manner.

[0041] Table 2 below shows the equivalent shape coefficient index Deq of the target joint calculated for each crack depth a, and the stress intensity factor K (analytical value of stress intensity factor K) for each crack depth a of the target joint used to calculate the equivalent shape coefficient index Deq. In Table 2, the analytical value of the stress intensity factor K for each crack depth a of the target joint is shown in the column "Stress intensity factor K (analysis)". [Table 2] As shown in Table 2, the equivalent shape factor index Deq for a crack depth a = 0.5 mm is slightly larger than the equivalent shape factor index Deq for crack depths a = 0.8 mm, 1.0 mm, and 1.2 mm. However, at crack depths a = 0.8 mm, 1.0 mm, and 1.2 mm, the equivalent shape factor index Deq is approximately 400 mm, and can be considered to be a nearly constant value. In other words, in practice, the equivalent shape factor index Deq calculated in this example can be considered to be a value specific to the target joint. Furthermore, from the perspective of the deformation behavior of the steel plates, it can be determined that the tensile shear joint used as the target joint in this example can be considered to be equivalent to a circular plate joint having a diameter Deq. The reason why the equivalent shape factor index Deq is larger than the diameter D (25 to 50 mm) of the reference joint, which is a circular plate joint, is thought to be because the deformation constraint around the spot weld in a tensile shear joint is weaker than in a circular plate joint, making the steel plate more susceptible to deformation.

[0042] Finally, in this example, the average value (404 mm) of the equivalent shape factor index Deq for crack depths a = 0.8 mm, 1.0 mm, and 1.2 mm was used as the equivalent shape factor index Deq specific to the target joint. Based on this equivalent shape factor index Deq and the reference relationship shown in Equation (3), the stress intensity factor K of a crack at any depth a (a = 0.5 mm, 0.8 mm, 1.0 mm, 1.2 mm) in the target joint was estimated (corresponding to the stress intensity factor estimation step ST5 in this example. However, in the actual stress intensity factor estimation step ST5, the equivalent shape factor index Deq for any one crack depth a is used to estimate the stress intensity factor K of a crack at any depth a in the target joint). That is, by substituting Deq (= 404 mm) for D on the right side of Equation (3), the estimated stress intensity factor K of the crack in the target joint for each crack depth a was calculated.

[0043] Table 3 below shows the estimated stress intensity factor K of the cracks in the target joint calculated for each crack depth a, the analytical value of the stress intensity factor K of the cracks in the target joint calculated by performing finite element analysis for each crack depth a, and the estimation error. In Table 3, the estimated value is shown in the "Stress Intensity Factor K (Estimated)" column, and the analytical value is shown in the "Stress Intensity Factor K (Analysis)" column. The value shown in the "Stress Intensity Factor K (Analysis)" column is the same as the value shown in the "Stress Intensity Factor K (Analysis)" column in Table 2. The estimation error was calculated using the following equation (4), assuming the analytical value to be the true value. Estimation error = |(Estimated value - Analysis value) / Analysis value × 100| (4) [Table 3] As shown in Table 3, for crack depths a = 0.8 mm, 1.0 mm, and 1.2 mm, the estimated values ​​are almost identical to the analytical values. Furthermore, for crack depth a = 0.5 mm, the estimation error is less than 5%, which is sufficient accuracy for practical purposes. From the above examples, it can be seen that the stress intensity factor K of a crack present in a target joint can be easily and accurately estimated based on the analytical values ​​of a finite element analysis using an analytical model of a reference joint.

[0044] In this example, the load applied to the reference joint and the load applied to the target joint are the same (2000 N) (thus, the same external force is applied to the crack), but the present invention is not limited to this. As long as an external force is applied to the crack in the same direction, it is also possible to apply different loads to the reference joint and the target joint. In this case, however, the ratio of the loads applied to the reference joint and the target joint must be taken into consideration when calculating the equivalent shape factor index Deq of the target joint in the shape factor index calculation step ST4 and when estimating the stress intensity factor K of a crack of any size that the target joint has in the stress intensity factor estimation step ST5. For example, if the load applied to the target joint is twice as large as the load applied to the reference joint (e.g., if the load applied to the reference joint is 2000 N and the load applied to the target joint is 4000 N), when calculating the equivalent shape factor index Deq of the target joint in the shape factor index calculation step ST4, it is necessary to multiply the stress intensity factor K of the target joint calculated in the second stress intensity factor calculation step ST3 by 0.5, and then calculate the equivalent shape factor index Deq of the target joint based on this and the reference relationship. Furthermore, when estimating the stress intensity factor K of a crack of any size that the target joint has in stress intensity factor estimation step ST5, it is necessary to double the stress intensity factor K calculated based on the equivalent shape factor index Deq of the target joint and the reference relationship, and use this as the estimated value of the stress intensity factor K. [Explanation of symbols]

[0045] ST1: First stress intensity factor calculation step ST2: Reference relationship calculation step ST3: Second stress intensity factor calculation step ST4: Shape factor index calculation step ST5: Stress intensity factor estimation step

Claims

1. A method for estimating a stress intensity factor of a welded joint, using finite element analysis, to estimate a stress intensity factor of a crack present in a welded joint including a plurality of steel plates overlapping each other in a plate thickness direction and a spot weld that joins the overlapping plurality of steel plates, a first stress intensity factor calculation step of calculating a stress intensity factor of the crack for each shape factor index and each size of the crack by performing finite element analysis on a reference joint, which is a type of welded joint, using a representative dimension corresponding to an area of ​​an overlapping region of the plurality of steel plates as a shape factor index, and using a plurality of analytical models of the reference joint in which the shape factor index and the size of the crack are changed, under the condition that an external force is applied to the crack in a fixed direction; a reference relationship calculation step of calculating a reference relationship between the shape factor index and a stress intensity factor of the crack for each dimension of the crack; a second stress intensity factor calculation step of calculating a stress intensity factor of a crack of a specific dimension in a target joint by performing a finite element analysis using an analytical model of the target joint, the target joint being a welded joint of a different type from the reference joint and being a welded joint for which a stress intensity factor is to be estimated, under conditions in which an external force is applied to the crack in the same direction as in the reference joint; a shape factor index calculation step of calculating the shape factor index for the target joint based on the stress intensity factor calculated in the second stress intensity factor calculation step and the reference relationship; a stress intensity factor estimating step of estimating a stress intensity factor of the crack of any dimension that the target joint has, based on the shape factor index for the target joint calculated in the shape factor index calculating step and the reference relationship. A method for estimating stress intensity factors of welded joints, comprising:

2. In the first stress intensity factor calculation step, the shape factor index and the depth of the crack are changed, and a finite element analysis is performed using a plurality of analytical models of the reference joint in which the length of the crack is set to a constant value, thereby calculating a stress intensity factor of the crack for each of the shape factor index and the depth of the crack; In the reference relationship calculation step, the reference relationship is calculated for each depth of the crack; In the second stress intensity factor calculation step, a finite element analysis is performed using an analytical model of the target joint having the crack at a specific depth with the same constant length as the reference joint, thereby calculating a stress intensity factor of the crack at the specific depth that the target joint has; In the stress intensity factor estimation step, a stress intensity factor of the crack at an arbitrary depth in the target joint is estimated based on the shape factor index for the target joint calculated in the shape factor index calculation step and the reference relationship.

2. The method for estimating a stress intensity factor of a welded joint according to claim 1.

3. the reference joint is a disc joint; The shape factor indicator is the diameter or radius of the disc joint; 3. The method for estimating a stress intensity factor of a welded joint according to claim 1 or 2.

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