Method for estimating the stress intensity factor of welded joints

Abstract

To provide a method for estimating stress intensity factor of a welded joint that can easily and accurately estimate the stress intensity factor of a crack that exists along the outer edge of a spot weld in the welded joint.SOLUTION: The present invention performs finite element analyses using a plurality of analytical models for the welded joint with a constant crack length and varying crack depth a, including steps: ST1 to calculate a first relationship between crack depth a and crack stress intensity factor K; ST2 to calculate a second relationship between the crack depth a and shape factor F; ST3 of calculating a third relationship between the crack depth a and corrected shape factor F'; ST4 to calculate the corrected shape factor F' corresponding to a depth a' of a crack in a target welded joint; ST5 to calculate the shape factor F corresponding to the depth a' of the crack in the target welded joint; and ST6 to estimate the stress intensity factor K of the crack in the target welded joint.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention relates to a method for estimating the stress intensity factor of a welded joint, which can easily and accurately estimate the stress intensity factor of a crack existing along the outer edge of a spot weld in a welded joint using finite element analysis. [Background technology]

[0002] In recent years, the automotive sector has demanded both lighter vehicle bodies for improved fuel efficiency and stronger vehicle bodies for enhanced collision safety. To achieve both of these requirements, using high-strength steel sheets as the vehicle body material is effective. Furthermore, from the perspective of enhancing corrosion resistance, zinc-plated steel sheets, which offer superior corrosion resistance among high-strength steel sheets, are frequently used.

[0003] In the assembly of automobile bodies, spot welding is primarily used to join multiple overlapping steel plates to form welded joints. However, when spot welding is performed on zinc-plated steel plates, cracks may occur at the spot welds. These cracks are said to be caused by so-called liquid metal embrittlement (LME), and it is believed that the molten zinc-plated metal penetrates the grain boundaries of the steel plate due to the rise in temperature and the generation of tensile stress during the welding process, thereby reducing the grain boundary strength. When LME-induced cracking (LME cracking) is severe, the static strength of the spot weld may decrease. For this reason, techniques have been proposed to suppress LME cracking, such as controlling the composition and structure of the steel plate or plating, or, as described in Patent Document 1, controlling the welding conditions. However, the effect of LME cracking on fatigue strength has not been clearly established. Therefore, from the perspective of fatigue strength, there is a need not only for developing technologies to suppress LME cracking, but also for methods that can properly evaluate the effect of LME cracking on fatigue strength.

[0004] Generally, to evaluate the effect of cracking on fatigue strength, the stress intensity factor, calculated by treating the crack as a fissure, is often used. The stress intensity factor is a fracture mechanics parameter that expresses the driving force of crack propagation based on the deformation field near the crack tip. For example, as described in Non-Patent Document 1, theoretical solutions have been obtained that can accurately evaluate the stress intensity factor of cracks when the mechanical conditions are simple. However, LME cracks that occur in spot welds have a three-dimensional shape in the form of an arc-shaped surface along the outer edge of the spot weld, when viewed from the thickness direction of the steel plate, and the mechanical conditions differ depending on the location of the automobile part where the spot weld is located. Therefore, there is no theoretical solution that can express the stress intensity factor of LME cracks. Non-Patent Document 2 proposes a theoretical solution for the stress intensity factor when the crack has a three-dimensional shape, but it is a theoretical solution for specific mechanical conditions, is complex, and lacks generality. In such cases, finite element analysis is typically used to calculate the stress intensity factor, but creating a three-dimensional analysis model and performing the analysis requires an enormous amount of time and effort. Therefore, there is a need for a method that can easily and accurately estimate the stress intensity factor of a crack for various mechanical conditions, such as the length and depth of the crack.

[0005] Non-patent document 3 describes a method for calculating the stress intensity factor based on the analysis results of the crack opening displacement. [Prior art documents] [Patent Documents]

[0006] [Patent Document 1] Japanese Patent Publication No. 2020-11253 [Non-patent literature]

[0007] [Non-Patent Document 1] Y. Murakami et al., “STRESS INTENSITY FACTORS HANDBOOK”, Volume 1, Pergamon Press, 1987, p.11 [Non-Patent Document 2] J. C. Newman, Jr. and I. S. Raju, “STRESS-INTENSITY FACTOR EQUATIONS FOR CRACKS IN THREE-DIMENSIONAL FINITE BODIES SUBJECTED TO TENSION AND BENDING LOADS”, NASA TM-85793, 1984 [Non-Patent Document 3] Zenichi Nakai and Shiro Kubo, “Fracture Mechanics in Basic Mechanical Engineering Courses”, Asakura Shoten, 2014, p.64-66 [Summary of the Invention] [Problems to be Solved by the Invention]

[0008] The present invention has been made to solve the problems of the prior 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 that can simply and accurately estimate the stress intensity factor of a crack existing along the outer edge of a spot weld of a welded joint by using finite element analysis. [Means for Solving the Problems]

[0009] To solve the above problems, as a result of intensive studies, the inventors of the present invention focused on the fact that, as shown in FIG. 1(a), although the stress intensity factors of cracks calculated by finite element analysis show different values depending on the length (circumferential dimension of the crack when viewed from the plate thickness direction of the steel plate) and depth (dimension of the crack in the plate thickness direction of the steel plate) of the cracks existing along the outer edge of the spot weld, the relationship between the depth of the crack and the stress intensity factor of the crack when the length of the crack is set to a constant value is similar regardless of the length of the crack (the tendency of the change in the stress intensity factor of the crack according to the change in the depth of the crack is similar regardless of the length of the crack). In the example shown in FIG. 1(a), the relationship between the depth of the crack and the stress intensity factor of the crack when the length of the crack is "large", the relationship between the depth of the crack and the stress intensity factor of the crack when the length of the crack is "medium", and the relationship between the depth of the crack and the stress intensity factor of the crack when the length of the crack is "small" are all upwardly convex relationships, and the inventors focused on the fact that the tendency of the change in the stress intensity factor of the crack according to the change in the depth of the crack is similar regardless of the length of the crack ("large", "medium", "small"). Here, assuming that the stress intensity factor is K, the shape factor is F, the nominal stress acting on the welded joint is σ, the depth of the crack is a, and the pi is π, it is known that these relationships are represented by the following formula (1). The shape factor F is a term representing the deformed state near the tip of the crack. F = K / (σ · (π · a) 1 / 2 ) ···(1)

[0010] The inventors found that, although the shape factor F in equation (1) above shows different values ​​depending on the crack length and crack depth a, as shown in Figure 1(b), the relationship between the crack depth a and the shape factor F when the crack length is kept constant is similar regardless of the crack length (the trend of change in the shape factor F in response to changes in crack depth a is similar regardless of the crack length). In the example shown in Figure 1(b), the relationship between the crack depth a and the shape factor F when the crack length is "large", the relationship between the crack depth a and the shape factor F when the crack length is "medium", and the relationship between the crack depth a and the shape factor F when the crack length is "small" shows that the shape factor F is monotonically decreasing with respect to the crack depth a, and the inventors found that the trend of change in the shape factor F in response to changes in crack depth a is similar regardless of the crack length ("large", "medium", "small").

[0011] Therefore, the inventors further investigated whether these relationships could be uniformly organized regardless of the crack length. As a result, they found that, as described below, these relationships can be uniformly organized regardless of the crack length by using the concept of "equivalent virtual plate thickness." Specifically, by using the concept of "equivalent virtual plate thickness" and correcting the shape factor F to a corrected shape factor F', they found that the relationship between the crack depth a and this corrected shape factor F' becomes approximately the same regardless of the crack length, as shown in Figure 1(c). Therefore, by creating multiple analysis models of welded joints with varying crack depths a, while keeping the crack length at a certain value, and performing finite element analysis on each, it was found that if the relationship between crack depth a and the crack stress intensity factor K (for example, the relationship between crack depth a and the shape factor F when the crack length is "large" as shown in Figure 1(a)), and furthermore, the relationship between crack depth a and the corrected shape factor F' (for example, the relationship between crack depth a and the corrected shape factor F' when the crack length is "large" as shown in Figure 1(c)) can be calculated, then it is not necessary to create analysis models and perform finite element analysis for crack lengths that differ from the above-mentioned constant value. In other words, for different crack lengths (for example, "medium" and "small" crack lengths), a corrected shape factor F' corresponding to a certain crack depth a' is calculated using the aforementioned relationship between the crack depth a and the corrected shape factor F'. From the calculated corrected shape factor F', the shape factor F corresponding to the crack depth a' is calculated inversely. By substituting the calculated shape factor F and the crack depth a' into equation (1), it was found that the stress intensity factor K of a crack of depth a' can be estimated accurately without performing finite element analysis.

[0012] This invention was completed based on the findings of the inventors described above. In other words, to solve the above problem, the present invention provides a method for estimating the stress intensity coefficient of a welded joint, which uses finite element analysis to estimate the stress intensity coefficient of a crack existing along the outer edge of a spot weld in a welded joint comprising a plurality of overlapping steel plates and a substantially circular spot weld that joins the plurality of steel plates, the method comprising: a first relationship calculation step of calculating a first relationship, which is the relationship between the crack depth a and the stress intensity coefficient K of the crack, by performing finite element analysis on a plurality of analysis models of the welded joint in which the length of the crack is set to a constant value and the depth a of the crack is changed; a second relationship calculation step of calculating a second relationship, which is the relationship between the crack depth a and the shape coefficient F expressed by the following equation (1), based on the first relationship; and the square root of the area of ​​the portion of the spot weld excluding the crack on the projection plane, when the spot weld is projected onto a projection plane that is a plane parallel to the thickness direction of the steel plate and perpendicular to the external force acting on the crack.c Let the square root of the area of the spot weld on the projection plane be t0, and based on the second relationship, a third relationship between the crack depth a and a correction shape coefficient F’ represented by the following formula (2) is calculated in a third relationship calculation step. For a target welded joint for which the stress intensity factor is to be estimated, and for a target welded joint having an arbitrary value of the crack length and depth, a correction shape coefficient calculation step of calculating the correction shape coefficient F’ corresponding to the crack depth a’ of the target welded joint based on the crack depth a’ of the target welded joint and the third relationship. And t calculated from the crack length and depth a’ of the target welded joint c Using t0 and the correction shape coefficient F’ corresponding to the crack depth a’, the shape coefficient F corresponding to the crack depth a’ is calculated by the following formula (3) in a shape coefficient calculation step. Using the crack depth a’ and the shape coefficient F corresponding to the crack depth a’, the stress intensity factor K of the crack of the target welded joint is estimated by the following formula (4) in a stress intensity factor estimation step. Provided is a method for estimating the stress intensity factor of a welded joint, which is characterized by having the above steps. F = K / (σ·(π·a) 1 / 2 ) ···(1) F’ = ((t c ) 3 / (t0) 3 )·F ···(2) F = F’ / ((t c ) 3 / (t0) 3 ) ···(3) K = F·σ·(π·a’) 1 / 2 ···(4) In the above formulas (1) and (4), σ means the nominal stress acting on the welded joint, and π means the pi.

[0013] In this invention, "crack length" refers to the circumferential dimension of the crack when viewed from the thickness direction of the steel plate. "Crack depth" refers to the dimension of the crack in the thickness direction of the steel plate. Furthermore, "area of ​​the spot weld on the projection plane" refers to the area of ​​the spot weld on the projection plane when there is no crack in the spot weld. According to the present invention, in the first relationship calculation step, the first relationship, which is the relationship between the crack depth a and the crack stress intensity factor K, is calculated by performing finite element analysis. Specifically, the first relationship is calculated by performing finite element analysis on multiple analysis models of welded joints in which the crack length is set to a constant value and the crack depth a is changed. As described in the inventors' findings above, this first relationship will be similar regardless of the crack length. That is, even if the crack length is changed, the first relationship will remain similar. Next, in the second relationship calculation step, the second relationship, which is the relationship between the crack depth a and the shape factor F expressed by equation (1), is calculated based on the first relationship. As mentioned in the inventors' findings above, this second relationship will also be similar regardless of the crack length. That is, even if the crack length is changed, the second relationship will remain similar. Next, in the third relationship calculation step, the third relationship, which is the relationship between the crack depth a and the corrected shape coefficient F' expressed by equation (2), is calculated based on the second relationship. Specifically, as will be described later, the concept of "equivalent virtual plate thickness" is used when calculating the corrected shape coefficient F' expressed by equation (2). As mentioned in the inventors' findings above, this third relationship is substantially the same regardless of the crack length. The first to third relationship calculation steps described above should be performed separately from the welded joint for which the crack stress intensity factor is to be estimated, and the calculated third relationship should be stored.

[0014] Next, according to the present invention, in the step of calculating the corrected shape coefficient, for a target welded joint for which the stress intensity coefficient is to be estimated, and for which the crack length and depth are arbitrary values, a corrected shape coefficient F' corresponding to the crack depth a' is calculated based on the crack depth a' of the target welded joint and the third relationship. This corrected shape coefficient F' is a value that depends only on the crack length a', regardless of the length of the crack in the target welded joint. Next, in the shape factor calculation step, the shape factor F corresponding to the crack depth a' is calculated inversely from the corrected shape factor F' calculated in the corrected shape factor calculation step. Specifically, the t calculated from the length and depth a' of the crack in the target welded joint is calculated. c Using t0 and the corrected shape factor F' corresponding to the crack depth a', the shape factor F corresponding to the crack depth a' is calculated by equation (3). This shape factor F is a value that also depends on the length of the crack in the welded joint in question. Finally, in the stress intensity factor estimation step, the stress intensity factor K of the crack at depth a' is estimated by substituting the shape factor F calculated in the shape factor calculation step and the crack depth a' into equation (1). Specifically, the stress intensity factor K of the crack in the target welded joint is estimated by equation (4), which is obtained by rearranging equation (1) using the crack depth a' and the shape factor F corresponding to the crack depth a'.

[0015] According to the present invention, by utilizing the fact that the third relationship is substantially the same regardless of the length of the crack, the stress intensity factor K of the crack in the target welded joint can be estimated. Therefore, if the third relationship is calculated accurately, the stress intensity factor K of the crack in the target welded joint can be estimated accurately. Furthermore, according to the present invention, finite element analysis is performed only in the first relationship calculation step, and it is not necessary to perform finite element analysis in the second relationship calculation step, the third relationship calculation step, the corrected shape factor calculation step, the shape factor calculation step, and the stress intensity factor estimation step. In other words, it is not necessary to create an analysis model of the target welded joint. For this reason, the stress intensity factor K of the crack in the target welded joint can be easily estimated. [Effects of the Invention]

[0016] According to the present invention, the stress intensity factor of a crack existing along the outer edge of a spot weld in a welded joint can be easily and accurately estimated. [Brief explanation of the drawing]

[0017] [Figure 1] This is an explanatory diagram that schematically illustrates the findings obtained by the inventors. [Figure 2] This is a flowchart illustrating the general procedure for estimating the stress intensity factor of a welded joint according to one embodiment of the present invention. [Figure 3] Figure 1 is a schematic diagram illustrating the steps from the first relationship calculation step ST1 to the corrected shape coefficient calculation step ST4. [Figure 4] This is an explanatory diagram illustrating "equivalent virtual plate thickness". [Figure 5] This figure shows the analysis model of a welded joint that performs finite element analysis, as used in the embodiment of the present invention. [Figure 6] This figure shows the relationship between the crack depth a, the crack stress intensity factor K, the shape factor F, and the corrected shape factor F', as calculated in an embodiment of the present invention. [Figure 7] The results of evaluating the estimation accuracy of the stress intensity factor K of the crack in the target welded joint estimated in the embodiment of the present invention are shown. [Modes for carrying out the invention]

[0018] An embodiment of the present invention will be described below with reference to the attached drawings as appropriate. Figure 2 is a flowchart showing the general procedure of a method for estimating the stress intensity factor of a welded joint according to one embodiment of the present invention (hereinafter, as may be, simply referred to as the "stress intensity factor estimation method"). Figure 3 is an explanatory diagram schematically illustrating the first relationship calculation step ST1 to the corrected shape factor calculation step ST4 shown in Figure 2. The stress intensity factor estimation method according to this embodiment is a method for estimating the stress intensity factor of a crack existing along the outer edge of a spot weld in a welded joint comprising a plurality of overlapping steel plates and a substantially circular spot weld that joins the plurality of steel plates, using finite element analysis. As shown in Figure 2, the stress intensity factor estimation method according to this embodiment comprises a first relationship calculation step ST1, a second relationship calculation step ST2, a third relationship calculation step ST3, a corrected shape factor calculation step ST4, a shape factor calculation step ST5, and a stress intensity factor estimation step ST6. The following explains each step, ST1 to ST6, in order.

[0019] <First Relationship Calculation Step ST1> In the first relationship calculation step ST1, as shown in Figure 3(a), the first relationship, which is the relationship between the crack depth a and the crack stress intensity factor K, is calculated by performing finite element analysis on multiple analysis models of welded joints with varying crack depths a (for example, the analysis models shown in Figure 5 described later) while keeping the crack length constant (crack length = L). In this embodiment, the stress intensity factor K of the crack is calculated as the stress intensity factor for an open crack (mode I), but it is not necessarily limited to this. Depending on the load application conditions (external forces acting on the crack) in the finite element analysis, it is also possible to calculate the stress intensity factors for in-plane shear cracks (mode II) or out-of-plane shear cracks (mode III).

[0020] One method for calculating the stress intensity factor K of a crack is to use the crack opening displacement. When calculating the stress intensity factor K using the crack opening displacement, first, a finite element analysis is performed to calculate the displacement u of the nodes constituting the crack surface in the analysis model. Then, the crack opening displacement 2u is calculated by doubling this displacement u. Specifically, the crack opening displacement 2u is calculated for every 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 / 2Based on this, the stress intensity factor K of the crack is calculated. Specifically, for example, the stress intensity factor K of the crack is calculated based on the following equation (5). K={E / 4(1-ν 2 )}·(2π / r) 1 / 2 ·u ···(5) In equation (5) above, E is the Young's modulus of the welded joint (the steel plate constituting the welded joint) where the crack exists, ν is the Poisson's ratio of the welded joint (the steel plate constituting the welded joint), and π is the ratio of the circumference to its diameter (pi). Furthermore, equation (5) above is a known equation that can be derived from equations (4.8) and (4.16) described in Non-Patent Document 3.

[0021] As the first relationship between crack depth a and crack stress intensity factor K, for example, a polynomial function can be used, which is calculated by performing an approximation calculation such as the least squares method on the crack stress intensity factor K calculated using each analysis model for each modified crack depth a. Alternatively, a piecewise linear relationship can be used, connecting the crack stress intensity factors K calculated using each analysis model for each modified crack depth a. Furthermore, if the number of analysis models (number of finite element analyses with modified depth a) is large, a table mapping crack depth a and crack stress intensity factor K can also be used as the first relationship.

[0022] <Second Relationship Calculation Step ST2> In the second relationship calculation step ST2, based on the first relationship between the crack depth a and the crack stress intensity factor K, the second relationship, which is the relationship between the crack depth a and the shape factor F expressed by the following equation (1), is calculated as shown in Figure 3(b). F = K / (σ·(π·a)) 1 / 2 ) ···(1) In equation (1) above, σ represents the nominal stress acting on the welded joint, and π represents pi. As mentioned above, when a polynomial function or similar function is used as the first relation, the second relation will also be expressed as a polynomial function or similar function. Similarly, when a polyline is used as the first relation, the second relation will also be expressed as a polyline, and when a table is used as the first relation, the second relation will also be expressed as a table.

[0023] <Third Relationship Calculation Step ST3> In the third relationship calculation step ST3, based on the second relationship between crack depth a and shape factor F, the third relationship, which is the relationship between crack depth a and the corrected shape factor F', is calculated as shown in Figure 3(c). Here, in calculating the corrected shape coefficient F', we use the concept of "equivalent virtual plate thickness" devised by the inventors. The "equivalent virtual plate thickness" will be explained below.

[0024] As shown in Figure 1(b) above, the inventors believe that the relationship between the crack depth a and the shape factor F (second relationship) differs for each crack length because the deformation state near the crack tip differs for each crack length, and this is due to the difference in stiffness depending on the crack area. Furthermore, since the deformation of welded joints in which steel plates are spot-welded is mainly in the bending mode, the inventors decided to focus on the bending stiffness D of the plate. Based on the theory of elastic deformation of plates, the bending stiffness D of a plate is expressed by the following equation (6). D = E·t 3 / 12(1-ν 2 ) ···(6) In equation (6) above, E is the Young's modulus of the plate, t is the plate thickness, and ν is the Poisson's ratio of the plate. As can be seen from equation (6) above, the bending stiffness D is proportional to the cube of the plate thickness t. Also, the bending stress of the plate is considered to be inversely proportional to the bending stiffness D. Therefore, considering the case without a crack as the baseline, when a crack is present, the apparent plate thickness t decreases according to the length of the crack, and the bending stiffness D decreases, so the bending stress is expected to increase. For this reason, it is thought that the relationship between the crack depth a and the shape factor F expressed in equation (1) above shows different values ​​for each crack length.

[0025] Based on the above idea, the inventors considered correcting the shape factor F to a corrected shape factor F' represented by the following equation (7). F'=(D c / D0)·F=(D c / D0)·K / (σ·(π·a) 1 / 2 ) ···(7) In equation (7) above, D0 is the bending stiffness D when there is no crack, and D c This is the bending stiffness D when a crack is present. As shown in equation (6) above, the bending stiffness D0 and D c While each of these is thought to be proportional to the cube of the plate thickness t, the question arises as to what value of plate thickness t should be used when calculating the corrected shape coefficient F' shown in equation (7). Bending stiffness D c When considering this, simply using the remaining plate thickness (= plate thickness when there is no crack - crack depth a) does not take into account the effect of the crack length. Therefore, the inventors of this invention conceived the concept of "equivalent virtual plate thickness," which also includes the case when there is no crack.

[0026] Figure 4 is an explanatory diagram illustrating "equivalent virtual plate thickness". As shown in Figure 4(a), when considering the "equivalent virtual plate thickness," we consider projecting the spot weld onto a projection plane that is parallel to the thickness direction of the steel plate (the direction perpendicular to the plane of the paper in Figure 4(a)) and perpendicular to the external force acting on the crack. Specifically, of the spot welds joining multiple steel plates, we project the portion corresponding to one steel plate (the portion corresponding to the thickness of one steel plate) onto the projection plane. Figure 4(b) shows the spot welds projected onto the projection plane, from left to right: no crack, large crack, medium crack, and small crack. In Figure 4(b), the hatched areas represent the joint regions of the spot welds on the projection plane, and the white areas represent the regions corresponding to cracks on the projection plane. The inventors considered calculating the area of ​​the hatched portion (joining region) shown in Figure 4(b) and taking its square root as the "equivalent virtual plate thickness." As shown in Figure 4(b), even if the crack depth a is the same, if the crack length is different, the area of ​​the hatched portion will also be different. Therefore, the "equivalent virtual plate thickness" calculated in the above manner takes into account the effect of the crack length. The inventors then considered using the "equivalent virtual plate thickness" as the plate thickness t in the aforementioned equation (6) and calculating the corrected shape coefficient F' using equation (7). As a result, it was found that the relationship between the crack depth a and this corrected shape coefficient F' is approximately the same regardless of the crack length, as shown in Figure 1(c) above.

[0027] In the third relationship calculation step ST3, the third relationship between the crack depth a and the corrected shape coefficient F' is calculated using the "equivalent virtual plate thickness" concept described above, as previously stated. Specifically, in the third relationship calculation step ST3, the square root of the area of ​​the spot weld excluding the crack on the projection plane (for example, the area of ​​the hatched portion in Figure 4(b) for crack lengths of "large," "medium," and "small") is used to calculate the equivalent virtual plate thickness t. c Then, using the square root of the area of ​​the spot weld on the projection plane (for example, the area of ​​the hatched portion in the case of no crack in Figure 4(b)) as the equivalent virtual plate thickness t0, the third relationship between the crack depth a and the corrected shape coefficient F' expressed by the following equation (2) is calculated based on the second relationship. F'=((t c ) 3 / (t0) 3 )·F ···(2) Equation (2) above is D in the aforementioned equation (7). c / D0 is calculated based on the above equation (6), (t c ) 3 / (t0) 3 This is the formula obtained by substituting the following: The area of ​​the spot weld area excluding the crack in the projected surface, and therefore the equivalent virtual plate thickness t cThis can be calculated using the diameter of the spot weld, the thickness of the steel plate, the length of the crack, and the depth a of the crack. Furthermore, the area of ​​the spot weld on the projection plane, and thus the equivalent virtual plate thickness t0, can be calculated using the diameter of the spot weld and the thickness of the steel plate.

[0028] Furthermore, the first relationship calculation steps ST1 to the third relationship calculation steps ST3 described above should be performed separately from the welded joint for which the stress intensity factor of the crack is to be estimated, and the calculated third relationship should be stored.

[0029] <Correction of Shape Factor Calculation Step ST4> In step ST4, the calculation of the corrected shape coefficient, for a welded joint to be used for estimating the stress intensity factor, where the crack length and depth are arbitrary values, the corrected shape coefficient F' corresponding to the crack depth a' is calculated based on the crack depth a' of the target welded joint and the third relationship, as shown in Figure 3(c). This corrected shape coefficient F' is a value that depends only on the crack length a', regardless of the length of the crack in the target welded joint.

[0030] <Shape Factor Calculation Step ST5> In the shape factor calculation step ST5, the shape factor F corresponding to the crack depth a' is calculated inversely from the corrected shape factor F' calculated in the corrected shape factor calculation step ST4. Specifically, in the shape factor calculation step ST5, the t calculated from the length and depth a' of the crack in the target welded joint is calculated. c Using t0 and the corrected shape factor F' corresponding to the crack depth a', the shape factor F corresponding to the crack depth a' is calculated by the following equation (3). F=F' / ((t c ) 3 / (t0) 3 ) ···(3) Equation (3) above is obtained by rearranging equation (2) mentioned earlier. This shape factor F is a value that also depends on the length of the crack in the welded joint in question.

[0031] <Stress Intensity Factor Estimation Step ST6> In the stress intensity factor estimation step ST6, the stress intensity factor K of the crack at depth a' is estimated by substituting the shape factor F calculated in the shape factor calculation step ST5 and the crack depth a' into the aforementioned equation (1). Specifically, the stress intensity factor K of the crack in the target welded joint is estimated by the following equation (4), which is obtained by rearranging equation (1) using the crack depth a' and the shape factor F corresponding to the crack depth a'. K = F·σ·(π·a') 1 / 2 ...(4) In equation (4) above, σ represents the nominal stress acting on the welded joint, and π represents pi.

[0032] According to the stress intensity factor estimation method of this embodiment described above, the stress intensity factor K of the crack in the target welded joint is estimated by utilizing the fact that the third relationship (the relationship between the crack depth a and the corrected shape factor F') is substantially the same regardless of the crack length. Therefore, if the third relationship is calculated accurately, the stress intensity factor K of the crack in the target welded joint can be estimated accurately. Furthermore, according to the stress intensity factor estimation method of this embodiment, finite element analysis is performed only in the first relationship calculation step ST1, and it is not necessary to perform finite element analysis in the second relationship calculation step ST2, the third relationship calculation step ST3, the corrected shape factor calculation step ST4, the shape factor calculation step ST5, and the stress intensity factor estimation step ST6. In other words, it is not necessary to create an analysis model of the target welded joint. For this reason, the stress intensity factor K of the crack in the target welded joint can be easily estimated.

[0033] The features of the present invention will be further clarified by describing an example of the stress intensity factor estimation method according to the present invention.

[0034] Figure 5 shows the analysis model of a welded joint used in this embodiment for finite element analysis. Figure 5(a) is a perspective view showing the outline of the analysis model. Figure 5(b) is a perspective view showing the element division and boundary conditions of the analysis model. Figure 5(c) is an enlarged front view of the vicinity of the spot weld of the analysis model. Figure 5(d) is a cross-sectional view taken along the line AA in Figure 5(c). The analytical model shown in Figure 5 is an analytical model of a welded joint formed by spot welding together the flange portions of two steel plates bent into an L-shape in a front view. Considering symmetry, only half of the welded joint is modeled (actual welded joints have the same structure in front of the analytical models shown in Figures 5(a) and 5(b)). Point C shown in Figures 5(c) and 5(d) is the center of the spot weld. The thickness of the steel plates was set to 1.6 mm in all cases, the Young's modulus of the steel plates was set to 206 GPa, and the Poisson's ratio was set to 0.3. The diameter of the spot weld (nugget diameter) was set to 6 mm, and a crack extending in the thickness direction was introduced along the outer edge of the spot weld from the inner surface of one steel plate (the surface facing the other steel plate). Specifically, a crack extending in the thickness direction was introduced from the inner surface of the right steel plate shown in Figures 5(a) to 5(c) (the surface facing the left steel plate shown in Figures 5(a) to 5(c)). The crack depth (dimension in the thickness direction) was set to five types: 0.2 mm, 0.5 mm, 0.8 mm, 1.0 mm, and 1.2 mm (0.8 mm in the example shown in Figure 5(c)). The crack length (circumferential dimension when viewed from the thickness direction) was expressed by the central angle θ shown in Figure 5(d), and was set to three types: θ = 90°, 45°, and 22.5° (90° in the example shown in Figure 5(d)). The analysis model shown in Figure 5 is a 1 / 2 model; therefore, the actual crack length corresponds to half the circumference of the outer edge of the spot weld when θ = 90°. Similarly, when θ = 45° and 22.5°, it corresponds to one-quarter and one-eighth the circumference of the spot weld, respectively. Therefore, from here on, the crack lengths will be expressed as half, one-quarter, and one-eighth of the circumference, respectively.

[0035] In the analysis model described above, as shown in Figure 5(b), one end of the left steel plate was fixed, and a load of 500N in the in-plane direction (direction of the thick arrow shown in Figure 5(a)) was applied to one end of the other steel plate. Finite element analysis was performed under the condition that deformation in the thickness direction was constrained at the point of load application (only deformation in the in-plane direction was allowed). As a result, the stress intensity factor K (mode I) was calculated for each crack. Furthermore, a shape factor F was calculated for each crack based on the calculated stress intensity factor K and equation (1). Note that the nominal stress σ shown in equation (1) can be considered a constant value regardless of the analytical model in which the cracks exist; therefore, for simplicity, it was omitted in this embodiment (i.e., σ = 1). Furthermore, a corrected shape factor F' was calculated for each crack based on the calculated shape factor F and equation (3).

[0036] Figure 6 shows the relationship between the crack depth a and the crack stress intensity factor K, shape factor F, and corrected shape factor F' calculated in this embodiment. Figure 6(a) shows the relationship between the crack depth a and the crack stress intensity factor K. Figure 6(b) shows the relationship between the crack depth a and the shape factor F. Figure 6(c) shows the relationship between the crack depth a and the corrected shape factor F'. As shown in Figure 6(a), although the stress intensity factor K of a crack shows different values ​​depending on the crack length and depth a, it can be seen that the relationship between the crack depth and the stress intensity factor of a crack is similar regardless of the crack length when the crack length is kept constant. Furthermore, as shown in Figure 6(b), although the shape factor F shows different values ​​depending on the crack length and depth a, it can be seen that the relationship between the crack depth a and the shape factor F is similar regardless of the crack length when the crack length is kept constant. In contrast, as shown in Figure 6(c), the relationship between the crack depth a and the corrected shape factor F' is approximately the same regardless of the crack length.

[0037] In this embodiment, the first relationship was defined as the relationship between the crack depth a and the crack stress intensity factor K obtained when the crack length was half a circumference. The stress intensity factor K of the cracks in the target welded joints was estimated for cases where the crack length was 1 / 4 circumference and 1 / 8 circumference. In this case, the second relationship was defined as the relationship between the crack depth a and the shape factor F obtained when the crack length was half a circumference, and the third relationship was defined as the relationship between the crack depth a and the corrected shape factor F' obtained when the crack length was half a circumference. When estimating the stress intensity factor K of the cracks in the target welded joints, the third relationship was approximated by a cubic polynomial. Figure 7 shows the results of evaluating the estimation accuracy of the stress intensity factor K of the crack in the target welded joint estimated in this embodiment. The horizontal axis of Figure 7 shows the stress intensity factor K of the crack calculated by performing finite element analysis using the analysis model of the target welded joint. That is, the values ​​of the stress intensity factor K obtained for 1 / 4 and 1 / 8 of the circumference in Figure 6(a). The vertical axis of Figure 7 shows the stress intensity factor K of the crack estimated in this embodiment. The dashed line shown in Figure 7 is a straight line where the values ​​on the vertical axis and the values ​​on the horizontal axis coincide. As shown in Figure 7, the estimated stress intensity factor K is in good agreement with the analytical value. The estimation error is at most around 10%, indicating sufficient estimation accuracy for practical purposes. As described above, the stress intensity factor estimation method according to the present invention eliminates the need to create an analysis model and perform finite element analysis for the target welded joint, and makes it possible to easily and accurately estimate the stress intensity factor of cracks present in the target welded joint. [Explanation of symbols]

[0038] a, a'... depth of the crack F... Shape coefficient F'... Correction shape coefficient K... Stress intensity factor ST1...First Relationship Calculation Step ST2...Second Relationship Calculation Step ST3...Third Relationship Calculation Step ST4... Correction shape coefficient calculation step ST5... Shape Factor Calculation Step ST6... Stress Intensity Factor Estimation Step

Claims

[Claim 1] A method for estimating the stress intensity coefficient of a welded joint, comprising a welded joint having a plurality of overlapping steel plates and a substantially circular spot weld that joins the plurality of steel plates, wherein the stress intensity coefficient of a crack existing along the outer edge of the spot weld is estimated using finite element analysis, A first relationship calculation step involves calculating a first relationship, which is the relationship between the crack depth a and the crack stress intensity factor K, by performing finite element analysis on multiple analysis models of the welded joint in which the crack length is set to a constant value and the crack depth a is changed, respectively. Based on the first relationship, a second relationship calculation step is performed to calculate a second relationship, which is the relationship between the crack depth a and the shape factor F expressed by the following formula (1): When the spot weld is projected onto a projection plane that is parallel to the thickness direction of the steel plate and perpendicular to the external force acting on the crack, the square root of the area of ​​the portion of the spot weld excluding the crack on the projection plane is t ｃ The square root of the area of ​​the spot weld on the projection plane is t ０ Based on the second relationship, a third relationship calculation step is performed to calculate a third relationship, which is the relationship between the crack depth a and the corrected shape coefficient F' expressed by the following formula (2). For a welded joint to be used for estimating the stress intensity factor, where the length and depth of the crack are arbitrary values, a correction shape factor calculation step is performed to calculate the correction shape factor F' corresponding to the crack depth a' in the target welded joint based on the crack depth a' in the target welded joint and the third relationship. The t calculated from the length and depth a' of the crack in the target welded joint ｃ and the aforementioned t ０ A shape factor calculation step in which the shape factor F corresponding to the crack depth a' is calculated using the corrected shape factor F' corresponding to the crack depth a' by the following formula (3), The process includes a stress intensity factor estimation step in which the stress intensity factor K of the crack in the target welded joint is estimated using the following formula (4), with respect to the crack depth a' and the shape factor F corresponding to the crack depth a'. A method for estimating the stress intensity factor of a welded joint, characterized by the features described herein. F=K / (s・(π・a) １／２ ) ・・・(1) F’=((t ｃ ) ３ / (t ０ ) ３ )・F ・・・(2) F=F’ / ((t ｃ ) ３ / (t ０ ) ３ ) ・・・(3) K=F・s・(π・a') １／２ ・・・(4) In equations (1) and (4) above, σ represents the nominal stress acting on the welded joint, and π represents pi.

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