Performance evaluation method for spot welded joints

Abstract

This invention provides a method for evaluating the performance of spot-welded joints, which allows for the evaluation of joint strength according to the depth and circumferential length of the initial crack. [Solution] The method comprises a first preparation step (#5), a first analysis step (#10), an acquisition step (#15), a second preparation step (#20), a second analysis step (#25), a first derivation step (#30), a second derivation step (#35), a third derivation step (#40), a fourth derivation step (#45), a setting step (#50), a calculation step (#55), and an evaluation step (#60). From the first preparation step (#5) to the fourth derivation step (#45), a crack initiation fracture criterion function is derived with the depth and length of the initial crack as independent variables and the joint strength as the dependent variable. In the calculation step (#55), the evaluation joint strength corresponding to the depth and length set in the setting step (#50) is calculated using the crack initiation fracture criterion function, and in the evaluation step (#60), the evaluation joint strength is evaluated.

Description

Technical Field

[0001] The present disclosure relates to a method for evaluating the performance of spot weld joints.

Background Art

[0002] In the automotive industry, a large number of steel sheets are used, and resistance spot welding is widely used as a method for joining steel sheets. Conventionally, for example, when resistance spot welding is performed on high-tensile steel sheets having zinc-based plating, it is known that in rare cases, minute cracks occur in the welded portion. The occurrence of these cracks is attributed to Liquid Metal Embrittlement (LME). In spot weld joints formed by resistance spot welding, not limited to cracks caused by such LME, if minute cracks exist as initial cracks, there is a concern that the joint strength may decrease depending on the form of the initial cracks. Therefore, it is desired that the joint strength can be evaluated according to the form of the initial cracks.

[0003] Japanese Unexamined Patent Application Publication No. 2023-093288 (Patent Document 1) describes a method for estimating the performance of spot weld joints. In this estimation method, finite element analysis is performed to derive the relationship between the initial crack depth and the joint strength, and the limit of the initial crack depth that does not affect the joint strength is estimated from this relationship.

Prior Art Documents

Patent Documents

[0004]

Patent Document 1

Summary of the Invention

Problems to be Solved by the Invention

[0005] In spot-welded joints, when initial cracks form around the nugget, not only the depth of the initial cracks but also their circumferential length is considered a factor that affects the joint strength. This is because the circumferential length of the initial cracks corresponds to the area where the cracks exist, and if this area is large, the joint strength is expected to decrease. However, Patent Document 1 does not mention the circumferential length of the initial cracks. Therefore, there is room for improvement in evaluating the performance of spot-welded joints.

[0006] The purpose of this disclosure is to provide a method for evaluating the performance of spot-welded joints that can evaluate joint strength according to the depth and circumferential length of the initial crack. [Means for solving the problem]

[0007] The method for evaluating the performance of a spot welded joint according to this disclosure comprises a first preparation step, a first analysis step, an acquisition step, a second preparation step, a second analysis step, a first derivation step, a second derivation step, a third derivation step, a fourth derivation step, a setting step, a calculation step, and an evaluation step. The first preparation step involves preparing a crack-free spot welded joint in which no initial cracks exist. The first analysis step involves performing a finite element analysis under tensile conditions on the crack-free spot welded joint. The acquisition step involves obtaining the standard joint strength, which is the joint strength of the crack-free spot welded joint, from the results of the first analysis step. The second preparation step involves preparing a plurality of cracked spot welded joints in which initial cracks are formed around the nugget, and in which the depth and circumferential length of the initial cracks differ. The second analysis step involves performing a finite element analysis under tensile conditions on each of the cracked spot welded joints. The first derivation step involves deriving a crack initiation fracture function, expressed as a linear function with joint strength as the dependent variable, for each circumferential length of the initial crack, with the depth of the initial crack (after the fracture mode changes from normal fracture to fracture originating from the initial crack) as the independent variable and the joint strength as the dependent variable. The second derivation step involves deriving a slope function, expressed as a linear function with the circumferential length of the initial crack as the independent variable and the slope of the crack initiation fracture function as the dependent variable, based on the crack initiation fracture function derived in the first derivation step. The third derivation step involves deriving an intercept function, expressed as a linear function with the circumferential length of the initial crack as the independent variable and the intercept of the crack initiation fracture function as the dependent variable, based on the crack initiation fracture function derived in the first derivation step. The fourth derivation step involves substituting the slope function as the slope of the crack initiation fracture function derived in the first derivation step, and substituting the intercept function as the intercept, to derive a crack initiation fracture criterion function, which is expressed as a function with the initial crack depth and circumferential length as independent variables and joint strength as the dependent variable. The setting step involves setting the initial crack depth and circumferential length of the evaluation spot weld joint to be evaluated. The calculation step uses the crack initiation fracture criterion function derived in the fourth derivation step to calculate the evaluation joint strength, which is the joint strength corresponding to the initial crack depth and circumferential length set in the setting step, for the evaluation spot weld joint.The evaluation step assesses the joint strength of the spot welded joint being evaluated by comparing the joint strength of the evaluated joint with the standard joint strength. [Effects of the Invention]

[0008] According to the performance evaluation method for spot-welded joints described herein, the joint strength can be evaluated according to the depth and circumferential length of the initial crack. [Brief explanation of the drawing]

[0009] [Figure 1] Figure 1 is a perspective view showing a test specimen used to investigate the joint strength of a spot-welded joint. [Figure 2] Figure 2 is a perspective view showing the analytical model based on the test specimen shown in Figure 1. [Figure 3] Figure 3 is an enlarged side view of the welded area and its vicinity in the analysis model shown in Figure 2. [Figure 4A] Figure 4A is a plan view showing an example of initial cracking in the analysis model shown in Figure 2. [Figure 4B] Figure 4B is a plan view showing an example of initial cracking in the analysis model shown in Figure 2. [Figure 4C] Figure 4C is a plan view showing an example of initial cracking in the analysis model shown in Figure 2. [Figure 5A] Figure 5A shows the relationship between the depth of the initial crack and the joint strength when the circumferential length of the initial crack is 360°. [Figure 5B] Figure 5B shows the relationship between the depth of the initial crack and the joint strength when the circumferential length of the initial crack is 180°. [Figure 5C] Figure 5C shows the relationship between the depth of the initial crack and the joint strength when the circumferential length of the initial crack is 90°. [Figure 6] Figure 6 shows the relationship between the circumferential length of the initial crack and the slope of the fracture function at the crack initiation point. [Figure 7] Figure 7 shows the relationship between the circumferential length of the initial crack and the intercept of the fracture function at the crack initiation point. [Figure 8]Figure 8 is a flowchart showing the performance evaluation method for spot-welded joints according to this embodiment. [Modes for carrying out the invention]

[0010] To achieve the above objective, the inventors first created an analytical model of a spot-welded joint and performed finite element analysis (hereinafter also referred to as "FE analysis") to investigate the joint strength. The FE analysis process will be explained below with reference to Figures 1 to 4C.

[0011] Figure 1 is a perspective view showing a test specimen 10 for investigating the joint strength of a spot-welded joint assumed in finite element analysis. The test specimen 10 shown in Figure 1 assumes a tensile shear joint as the spot-welded joint. Using this test specimen 10, the tensile shear strength (TSS) can be investigated as the joint strength. The test specimen 10 consists of two steel plates 11 and 12. The steel plates 11 and 12 are stacked on top of each other with a displacement in the longitudinal direction LD of the test specimen 10, and a resistance spot weld 13 is formed in the center of the overlapping region.

[0012] Figure 2 is a perspective view showing an analysis model 20 based on the test specimen 10 shown in Figure 1. The analysis model 20 shown in Figure 2, like the test specimen 10 shown in Figure 1, is composed of two steel plates 21 and 22 stacked on top of each other, with a welded joint 23 formed in their overlapping region. However, due to the symmetry of the width direction WD of the test specimen 10, the analysis model 20 has the shape of the test specimen 10 cut at the center of the width direction WD, that is, half the shape of the test specimen 10. A nugget 24 is formed in the welded joint 23.

[0013] Figure 3 is an enlarged side view of the welded portion 23 of the analysis model 20 shown in Figure 2 and its vicinity. Referring to Figure 3, in the analysis model 20, a HAZ (heat affected zone) 25 is formed so as to surround the nugget 24, and a transition layer 26 is formed between the HAZ 25 and the base metal 27 of each steel plate 21, 22. In the analysis model 20, the nugget 24, the HAZ 25, the transition layer 26, and the base metal 27 are divided into element sets as different structures from each other, and a deformation resistance curve and a fracture criterion value are set for each of them.

[0014] In the analysis model 20, further, in the HAZ 25, an initial crack 28 is formed starting from the pressure contact portion between the steel plate 21 and the steel plate 22. The initial crack 28 is formed around the nugget 24. The initial crack 28 has a depth D. In this specification, the depth D of the initial crack 28 means the dimension (unit: mm) of the initial crack 28 in the plate thickness direction TD of the analysis model 20 (test piece 10). The initial crack 28 extends in the circumferential direction centered on the nugget 24 and has a circumferential length θ (see FIGS. 4A to 4C).

[0015] FIGS. 4A to 4C are respectively plan views showing an example of the initial crack 28 in the analysis model 20 shown in FIG. 2. The initial cracks 28 shown in FIGS. 4A to 4C have different circumferential lengths θ from each other. In this specification, the circumferential length θ of the initial crack 28 means the angle (unit: °) around the center of the nugget 24. Hereinafter, the depth of the initial crack is also referred to as the "initial crack depth", and the circumferential length of the initial crack is also referred to as the "initial crack length".

[0016] In the example shown in FIG. 4A, the initial crack 28 is formed over the entire circumference around the nugget 24. That is, the initial crack 28 extends in the range of 360° in the circumferential direction centered on the nugget 24. In this case, the circumferential length θ of the initial crack 28 is 360°.

[0017] In the example shown in FIG. 4B, the initial crack 28 is formed over a half circumference around the nugget 24. That is, the initial crack 28 extends in the range of 180° in the circumferential direction centered on the nugget 24 among the circumference around the nugget 24. In this case, the circumferential length θ of the initial crack 28 is 180°.

[0018] In the example shown in FIG. 4C, the initial crack 28 is formed in a quarter circle around the nugget 24. That is, the initial crack 28 extends in a range of 90° in the circumferential direction centered on the nugget 24 among the periphery of the nugget 24. In this case, the circumferential length θ of the initial crack 28 is 90°.

[0019] Returning to FIG. 2, in the FE analysis, one end of the analysis model 20 (the open end 21a in the longitudinal direction LD of the steel plate 21) is completely constrained, and a tensile load (thick arrow in FIG. 2) in the longitudinal direction LD is applied to the other end of the analysis model 20 (the open end 22a in the longitudinal direction LD of the steel plate 22). The FE analysis is carried out under the condition that the tensile load is applied. As a result of the FE analysis, the joint strength is obtained. Also, the fracture mode can be recognized. The joint strength is the maximum value of the load applied to the analysis model 20, that is, the test piece 10 during tension. In the FE analysis, elements that have reached the fracture criterion value are deleted to reduce the rigidity, and thus, the FE analysis simulates a tensile test using the actual test piece 10.

[0020] Referring to FIGS. 3 to 4C, in the FE analysis, a number of analysis models 20 were created. Specifically, as common conditions, the steel plates 21 and 22 were 980 MPa grade high-tensile steel plates. The plate thickness t of the steel plate 21 was the same as the plate thickness t of the steel plate 22, and each plate thickness t was 1.6 mm. Also, regarding the nugget diameter (k√t) represented by the product of the coefficient k and the square root of the plate thickness t, the coefficient k was set to 5.0. For this reason, the nugget diameter regarding the nugget 24 was 5√1.6, which was approximately 6.3 mm.

[0021] Then, the circumferential length θ of the initial crack 28 was variously changed. The initial crack length θ was set to three levels of 360° (FIG. 4A), 180° (FIG. 4B), and 90° (FIG. 4C). Further, in each of the analysis models 20 in which the initial crack length θ differed at three levels, the depth D of the initial crack 28 was variously changed. The initial crack depth D included 0 (zero), and further increased at a pitch of 0.1 mm from 0.1 mm. The maximum value of the initial crack depth D was set to 1.4 mm.

[0022] Figures 5A to 5C show the FE analysis results. Figure 5A shows the relationship between the initial crack depth D and the joint strength TSS when the circumferential length θ of the initial crack is 360°. Figure 5B shows the relationship between the initial crack depth D and the joint strength TSS when the circumferential length θ of the initial crack is 180°. Figure 5C shows the relationship between the initial crack depth D and the joint strength TSS when the circumferential length θ of the initial crack is 90°.

[0023] In each figure, open marks (□, 〇, ◇) indicate fracture originating from an initial crack. Hereafter, this type of fracture originating from an initial crack will also be called "crack-initiated fracture." On the other hand, solid marks (■, ●, ◆) indicate fracture that does not originate from an initial crack, similar to the case where there is no initial crack, i.e., when the depth D of the initial crack is zero. Hereafter, this type of fracture that does not originate from an initial crack will also be called "normal fracture."

[0024] Referring to Figure 5A, when the initial crack length θ is 360°, the joint strength for crack initiation fracture, indicated by the open mark (□), is lower than the joint strength for normal fracture, indicated by the solid mark (■). If the initial crack depth D is small, the fracture mode is normal fracture, and the joint strength is maintained at the same level as when there is no initial crack, i.e., when the initial crack depth D is zero. The joint strength when there is no initial crack is called the standard joint strength (TSSporp). On the other hand, when the initial crack depth D exceeds a certain value, the fracture mode changes to crack initiation fracture, and the joint strength decreases. Referring to Figures 5B and 5C, when the initial crack depth θ is 180° and 90°, the joint strength and fracture mode also show the same trend as when the initial crack length θ is 360° as shown in Figure 5A.

[0025] As shown in Figures 5A to 5C, in the range where the fracture mode is crack initiation fracture (open mark (□,〇,◇)), the joint strength TSS decreases as the initial crack depth D increases, regardless of whether the initial crack length θ is 360°, 180°, or 90°. Specifically, the joint strength TSS for crack initiation fracture can be approximated by a negative linear function of the initial crack depth D. Furthermore, the larger the initial crack length θ, the greater the decrease in joint strength TSS in relation to the initial crack depth D.

[0026] From this FE analysis, for each initial crack length θ, a crack initiation fracture function can be derived, which is a linear function in which the initial crack depth D after the fracture mode changes from normal fracture to crack initiation fracture is the independent variable and the joint strength TSS is the dependent variable. For example, referring to Figure 5A, the crack initiation fracture function when the initial crack length θ is 360° has a slope of "-16.357" and an intercept of "31.590". Referring to Figure 5B, the crack initiation fracture function when the initial crack length θ is 180° has a slope of "-9.722" and an intercept of "31.478". Referring to Figure 5C, the crack initiation fracture function when the initial crack length θ is 90° has a slope of "-6.467" and an intercept of "30.563".

[0027] Thus, since the fracture functions derived for each initial crack length θ are all expressed as linear functions, it is considered that there is a relationship between the initial crack length θ and the fracture function. Therefore, the inventors focused on the relationship between the initial crack length θ and the slope a of the fracture function, and the relationship between the initial crack length θ and the intercept b of the fracture function, and conducted thorough investigations. As a result, the following findings were obtained.

[0028] Figures 6 and 7 show the relationship between the initial crack length θ and the fracture function at the crack initiation point. Figure 6 shows the relationship between the initial crack length θ and the slope a of the fracture function at the crack initiation point. In Figure 6, the horizontal axis represents the initial crack length θ, and the vertical axis represents the slope a of the fracture function at the crack initiation point derived from the FE analysis described above. Figure 7 shows the relationship between the initial crack length θ and the intercept b of the fracture function at the crack initiation point. In Figure 7, the horizontal axis represents the initial crack length θ, and the vertical axis represents the intercept b of the fracture function at the crack initiation point derived from the FE analysis described above.

[0029] As shown in Figure 6, the negative slope a of the fracture initiation function increases linearly as the initial crack length θ increases. Specifically, the slope a of the fracture initiation function can be approximated by a negative linear function depending on the initial crack length θ. In short, based on the fracture initiation function, a slope function aθ can be derived, which is a linear function in which the initial crack length θ is the independent variable and the slope a of the fracture initiation function is the dependent variable. For example, referring to Figure 6, in the slope function aθ, the slope is "-0.037" and the intercept is "-3.150".

[0030] As shown in Figure 7, the intercept b of the fracture function increases linearly as the initial crack length θ increases. Specifically, the intercept b of the fracture function can be approximated by a linear function depending on the initial crack length θ. In short, based on the fracture function, an intercept function bθ can be derived, which is a linear function with the initial crack length θ as the independent variable and the intercept b of the fracture function as the dependent variable. For example, referring to Figure 7, the slope of the intercept function bθ is "0.003" and the intercept is "30.507".

[0031] Then, by substituting the slope function aθ as the slope and the intercept function bθ as the intercept into the crack initiation fracture function, we can derive a crack initiation fracture criterion function (TSSfrac) which is expressed as a function with initial crack depth D and initial crack length θ, and joint strength TSS as the dependent variable.

[0032] After deriving such a crack initiation fracture criterion function (TSSfrac), the initial crack depth D and initial crack length θ of the evaluation spot weld joint (evaluation joint) to be evaluated can be set, and the evaluation joint strength (TSSeval) can be calculated using the crack initiation fracture criterion function (TSSfrac). Then, by comparing the evaluation joint strength (TSSeval) with the standard joint strength (TSSporp), it is possible to evaluate the joint strength of the evaluation spot weld joint. Specifically, if the evaluation joint strength (TSSeval) is greater than or equal to the standard joint strength (TSSporp), it can be determined that there will be no decrease in joint strength due to initial cracking. In other words, the joint strength can be evaluated as equal to the standard joint strength (TSSporp). On the other hand, if the evaluation joint strength (TSSeval) is lower than the standard joint strength (TSSporp), it can be determined that there will be a decrease in joint strength due to initial cracking. In other words, the joint strength can be evaluated as equal to the evaluation joint strength (TSSeval). In short, joint strength can be evaluated according to the initial crack depth D and initial crack length θ.

[0033] The performance evaluation method for spot-welded joints according to this embodiment was completed based on the above findings.

[0034] The method for evaluating the performance of a spot welded joint according to this embodiment comprises a first preparation step, a first analysis step, an acquisition step, a second preparation step, a second analysis step, a first derivation step, a second derivation step, a third derivation step, a fourth derivation step, a setting step, a calculation step, and an evaluation step. The first preparation step involves preparing a crack-free spot welded joint in which no initial cracks exist. The first analysis step involves performing a finite element analysis under tensile conditions on the crack-free spot welded joint. The acquisition step involves obtaining the standard joint strength, which is the joint strength of the crack-free spot welded joint, from the results of the first analysis step. The second preparation step involves preparing a plurality of cracked spot welded joints in which initial cracks are formed around the nugget, and in which the depth and circumferential length of the initial cracks differ. The second analysis step involves performing a finite element analysis under tensile conditions on each of the cracked spot welded joints. The first derivation step involves deriving a crack initiation fracture function, expressed as a linear function with joint strength as the dependent variable, for each circumferential length of the initial crack, with the depth of the initial crack (after the fracture mode changes from normal fracture to fracture originating from the initial crack) as the independent variable and the joint strength as the dependent variable. The second derivation step involves deriving a slope function, expressed as a linear function with the circumferential length of the initial crack as the independent variable and the slope of the crack initiation fracture function as the dependent variable, based on the crack initiation fracture function derived in the first derivation step. The third derivation step involves deriving an intercept function, expressed as a linear function with the circumferential length of the initial crack as the independent variable and the intercept of the crack initiation fracture function as the dependent variable, based on the crack initiation fracture function derived in the first derivation step. The fourth derivation step involves substituting the slope function as the slope of the crack initiation fracture function derived in the first derivation step, and substituting the intercept function as the intercept, to derive a crack initiation fracture criterion function, which is expressed as a function with the initial crack depth and circumferential length as independent variables and joint strength as the dependent variable. The setting step involves setting the initial crack depth and circumferential length of the evaluation spot weld joint to be evaluated. The calculation step uses the crack initiation fracture criterion function derived in the fourth derivation step to calculate the evaluation joint strength, which is the joint strength corresponding to the initial crack depth and circumferential length set in the setting step, for the evaluation spot weld joint.The evaluation step involves evaluating the joint strength of the spot-welded joint being evaluated by comparing it with the standard joint strength (first configuration).

[0035] According to the performance evaluation method of the first configuration, the joint strength can be evaluated according to the depth and circumferential length of the initial crack, by following steps in line with the above-mentioned knowledge.

[0036] In the performance evaluation method relating to the first configuration, preferably, the crack initiation fracture criterion function TSSfrac is expressed by equation (1) (second configuration). TSSfrac = aθ × D + bθ (1) In equation (1), the meaning of each symbol is as follows: D: Depth of initial crack, aθ: Slope function with the circumferential length of the initial crack as the independent variable, bθ: Intercept function with the circumferential length of the initial crack as the independent variable.

[0037] In the performance evaluation method relating to the second configuration, preferably, in equation (1), the slope function aθ is expressed by equation (i) and the intercept function bθ is expressed by equation (ii) (third configuration). aθ = c1 × θ + d1 (i) bθ = c² × θ + d² (ii) In equations (i) and (ii), the meaning of each symbol is as follows: θ: circumferential length of the initial crack, c1: A coefficient expressed as a value between -10 and 10. d1: A coefficient expressed as a number between -10 and 10. c2: A coefficient expressed as a value between -10 and 10, and d2: A coefficient expressed as a value between 0 and 50 (inclusive).

[0038] Embodiments of this disclosure will be described below with reference to the drawings. In each drawing, the same or equivalent components will be denoted by the same reference numerals, and redundant descriptions will not be repeated.

[0039] [Performance evaluation method for spot-welded joints] Referring to Figures 2 to 8, the performance evaluation method for spot welded joints according to this embodiment will be described. Figure 8 is a flowchart showing the performance evaluation method for spot welded joints according to this embodiment. Referring to Figure 8, the performance evaluation method comprises a first preparation step #5, a first analysis step #10, an acquisition step #15, a second preparation step #20, a second analysis step #25, a first derivation step #30, a second derivation step #35, a third derivation step #40, a fourth derivation step #45, a setting step #50, a calculation step #55, and an evaluation step #60. Each step #5 to #60 will be described in detail below.

[0040] [First Preparation Step #5] The first preparation step #5 involves preparing a crack-free spot welded joint in which no initial cracks exist. This crack-free spot welded joint is the analysis model 20 described with reference to Figures 2 and 3. This analysis model has no initial cracks and the initial crack depth D is set to 0 (zero). Hereafter, this analysis model will also be referred to as the "crack-free analysis model".

[0041] In this embodiment, as described above, in the crack-free analysis model, the two steel plates constituting the joint are 980 MPa class high-tensile steel plates. The thickness t of each steel plate is 1.6 mm. The coefficient k of the nugget diameter (k√t) is 5.0.

[0042] The steel type, plate thickness t, and nugget diameter coefficient k of the steel plate are set according to the spot welded joint being evaluated. Therefore, the steel plate may be a high-tensile steel plate of 980 MPa class or higher, for example, a 1180 MPa class high-tensile steel plate. Also, the plate thickness t of the steel plate may be other than 1.6 mm, for example, 1.2 mm or 2.0 mm. In the case of steel plates used in automobiles, the plate thickness t is, for example, in the range of 0.6 mm or more and 2.4 mm or less. Also, the nugget diameter coefficient k may be other than 5.0. In practice, the coefficient k is, for example, in the range of 3.0 or more and 5.5 or less.

[0043] [First analysis step #10] The first analysis step #10 involves performing a finite element (FE) analysis under tensile conditions for the crack-free spot-welded joint. Specifically, the FE analysis is performed on the crack-free analysis model as explained with reference to Figure 2. The joint strength is obtained as a result of the FE analysis. Furthermore, the fracture mode can be identified.

[0044] [Acquisition Step #15] Acquisition step #15 involves obtaining the standard joint strength (TSSporp), which is the joint strength of a crack-free spot welded joint, from the results of the first analysis step #10. That is, the standard joint strength (TSSporp) is obtained from the FE analysis results using the crack-free analysis model. In this embodiment, the standard joint strength TSSprop is determined to be 29.40 kN.

[0045] [Second Preparation Step #20] The second preparation step #20 involves preparing multiple spot welded joints with cracks. These multiple spot welded joints have initial cracks formed around the nugget, with varying initial crack depths and circumferential lengths. The spot welded joints with cracks are the same as the non-cracked spot welded joints described above, using the analysis model 20 explained with reference to Figures 2 and 3. This analysis model involves the formation of initial cracks around the nugget, with various variations in initial crack depth D and initial crack length θ. Hereafter, this analysis model will also be referred to as the "cracked analysis model."

[0046] In the cracked analysis model of this embodiment, the steel type of the two steel plates constituting the joint, the plate thickness t of the steel plates, and the coefficient k of the nugget diameter (k√t) are the same as in the non-cracked analysis model.

[0047] In this embodiment, as described above, the initial crack length θ in the cracked analysis model is set to three levels: 360° (Figure 4A), 180° (Figure 4B), and 90° (Figure 4C). Furthermore, in each of the three different cracked analysis models with varying initial crack lengths θ, the initial crack depth D is increased in increments of 0.1 mm from 0.1 mm, with a maximum value of 1.4 mm. This maximum value of the initial crack depth D (1.4 mm) is set according to the plate thickness t. For example, the maximum value of the initial crack depth D is effectively 85% of the plate thickness t (1.6 mm).

[0048] Regarding the initial crack length θ, the more levels (number of adjustments) available, the better, as this increases accuracy. Therefore, while two levels of initial crack length θ are acceptable, three or more are preferable. Similarly, regarding the initial crack depth D, the more levels available, the better, and the smaller the adjustment interval, the better, as this increases accuracy.

[0049] [Second Analysis Step #25] The second analysis step, #25, involves performing a finite element (FE) analysis under tensile conditions for each cracked spot-welded joint. That is, FE analysis is performed on multiple cracked analysis models, similar to the analysis model without cracks. The joint strength is obtained as a result of the FE analysis, and the fracture mode can also be identified.

[0050] [First Derivation Step #30] The first derivation step #30 derives the crack initiation fracture function for each initial crack length θ from the results of the second analysis step #25. The crack initiation fracture function is expressed as a linear function with the initial crack depth D after the fracture mode changes from normal fracture to crack initiation fracture as the independent variable and the joint strength TSS as the dependent variable. The method for deriving the crack initiation fracture function expressed as a linear function is described below.

[0051] The analysis results from the second analysis step #25 are shown in Figures 5A to 5C. Figures 5A to 5C also show the analysis results from the first analysis step #10. Figure 5A shows the relationship between the initial crack depth D and the joint strength TSS when the initial crack length θ is 360°, Figure 5B shows the relationship between the initial crack depth D and the joint strength TSS when the initial crack length θ is 180°, and Figure 5C shows the relationship between the initial crack depth D and the joint strength TSS when the initial crack length θ is 90°.

[0052] In Figures 5A to 5C, as described above, open marks (□, 〇, ◇) indicate fracture at the crack initiation point. On the other hand, solid marks (■, ●, ◆) indicate normal fracture. Referring to Figures 5A to 5C, in the range where the fracture mode is fracture at the crack initiation point (open marks (□, 〇, ◇)), the joint strength TSS decreases as the initial crack depth D increases, regardless of whether the initial crack length θ is 360°, 180°, or 90°. Therefore, the joint strength TSS for fracture at the crack initiation point can be approximated by a negative linear function of the initial crack depth D. This approximation is a linear function with the initial crack depth D at which fracture at the crack initiation point occurs as the independent variable and the joint strength TSS as the dependent variable. In other words, this approximation is the fracture initiation function.

[0053] Referring to Figure 5A, for an initial crack length θ of 360°, the fracture function at the crack initiation point has a slope of "-16.357" and an intercept of "31.590". Referring to Figure 5B, for an initial crack length θ of 180°, the fracture function at the crack initiation point has a slope of "-9.722" and an intercept of "31.478". Referring to Figure 5C, for an initial crack length θ of 90°, the fracture function at the crack initiation point has a slope of "-6.467" and an intercept of "30.563". In all cases, the slope is a negative value and the intercept is a positive value.

[0054] Referring to Figures 5A to 5C, it is clear from the slopes of the fracture functions at each crack initiation point that the larger the initial crack length θ, the greater the decrease in joint strength TSS corresponding to the initial crack depth D. In other words, the decrease in joint strength TSS corresponding to the initial crack depth D is greatest for initial crack lengths θ of 90°, 180°, and 360°.

[0055] Here, when deriving each crack initiation fracture function, we identify the abrupt transition point where the fracture mode changes from normal fracture to crack initiation fracture (dotted open marks in Figures 5A to 5C). The initial crack depth at the abrupt transition point is the average of the maximum initial crack depth at which normal fracture occurred and the minimum initial crack depth at which crack initiation fracture occurred. The joint strength at the abrupt transition point is the average of the joint strength corresponding to the maximum initial crack depth at which normal fracture occurred and the joint strength corresponding to the minimum initial crack depth at which crack initiation fracture occurred.

[0056] Based on the initial crack depth and joint strength at the identified abrupt point, the maximum initial crack depth (1.4 mm), and the joint strength corresponding to this maximum, a linear fracture function is derived for each initial crack length θ. However, the linear fracture function may also be derived based on the initial crack depth and joint strength at the abrupt point, the initial crack depth at which fracture originated, and the joint strength corresponding to each of these initial crack depths.

[0057] [Second Derivation Step #35] The second derivation step #35 derives the slope function aθ based on the fracture initiation function derived in the first derivation step #30. The slope function aθ is expressed as a linear function with the initial crack length θ as the independent variable and the slope a of the fracture initiation function as the dependent variable. The method for deriving the linear function aθ is explained below.

[0058] Based on the fracture initiation function derived in the first derivation step #30, the relationship between the initial crack length θ and the slope a of the fracture initiation function is shown in Figure 6. As shown in Figure 6, the negative slope a of the fracture initiation function increases linearly as the initial crack length θ increases. Therefore, the slope a of the fracture initiation function can be approximated by a negative linear function depending on the initial crack length θ. This approximation is a linear function with the initial crack length θ at which fracture initiation occurs as the independent variable and the slope a of the fracture initiation function as the dependent variable. In other words, this approximation is the slope function aθ.

[0059] Specifically, the slope function aθ is expressed by equation (i). aθ = c1 × θ + d1 (i) In equation (i), the meaning of each symbol is as follows: θ: circumferential length of the initial crack, c1: A coefficient represented by a value between -10 and 10, and d1: A coefficient represented by a number between -10 and 10 (inclusive).

[0060] In the example shown in Figure 6, the slope function aθ has a slope c1 of "-0.037" and an intercept d1 of "-3.150".

[0061] [Third Derivation Step #40] The third derivation step #40 derives the intercept function bθ based on the fracture initiation function derived in the first derivation step #30. The intercept function bθ is expressed as a linear function with the initial crack length θ as the independent variable and the intercept b of the fracture initiation function as the dependent variable. The method for deriving the intercept function bθ, which is expressed as a linear function, is explained below.

[0062] Based on the fracture initiation function derived in the first derivation step #30, the relationship between the initial crack length θ and the intercept b of the fracture initiation function is shown in Figure 7. As shown in Figure 7, the intercept b of the fracture initiation function increases linearly as the initial crack length θ increases. Therefore, the intercept b of the fracture initiation function can be approximated by a linear function depending on the initial crack length θ. This approximation is a linear function where the initial crack length θ at which fracture initiation occurs is the independent variable, and the intercept b of the fracture initiation function is the dependent variable. In other words, this approximation is the intercept function bθ.

[0063] Specifically, the intercept function bθ is expressed by equation (ii). bθ = c² × θ + d² (ii) In equation (ii), the meaning of each symbol is as follows: θ: circumferential length of the initial crack, c2: A coefficient expressed as a value between -10 and 10, and d2: A coefficient expressed as a value between 0 and 50 (inclusive).

[0064] In the example shown in Figure 7, the slope c2 of the intercept function bθ is "0.003" and the intercept d2 is "30.507".

[0065] [Fourth Derivation Step #45] The fourth derivation step #45 is to derive the crack initiation fracture criterion function TSSfrac. The crack initiation fracture criterion function TSSfrac is obtained by substituting the slope function aθ as the slope and the intercept function bθ as the intercept of the crack initiation fracture function derived in the first derivation step #30. Thus, the crack initiation fracture criterion function TSSfrac can be expressed as a function with initial crack depth D and initial crack length θ as independent variables and joint strength as the dependent variable.

[0066] Specifically, the crack initiation fracture criterion function TSSfrac is expressed by equation (1). TSSfrac = aθ × D + bθ (1) In equation (1), the meaning of each symbol is as follows: D: Depth of initial crack, aθ: Slope function with the circumferential length of the initial crack as the independent variable, bθ: Intercept function with the circumferential length of the initial crack as the independent variable.

[0067] In other words, the crack initiation fracture criterion function TSSfrac is expressed by equation (1A). TSSfrac=(c1×θ+d1)×D+(c2×θ+d2) (1A)

[0068] More specifically, as shown in the examples in Figures 6 and 7, the crack initiation fracture criterion function TSSfrac is expressed by equation (1B). TSSfrac=(-0.037×θ-3.150)×D+(0.003×θ+30.507) (1B)

[0069] [Setup Step #50] Setting step #50 sets the initial crack depth D and initial crack length θ in the spot welded joint to be evaluated. In this embodiment, for example, the initial crack depth D is set to 0.3 mm and the initial crack length θ is set to 120°.

[0070] [Calculation Step #55] Calculation step #55 uses the crack initiation fracture criterion function TSSfrac derived in the fourth derivation step #45 to calculate the evaluated joint strength TSSeval, which corresponds to the initial crack depth D and initial crack length θ set in setting step #50 for the spot welded joint being evaluated. In this embodiment, in equation (1), or more directly in equation (1B), 0.3 (mm) is substituted for D and 120 (°) is substituted for θ. As a result, the evaluated joint strength TSSeval for the spot welded joint being evaluated is obtained to be 28.59 kN.

[0071] [Evaluation Step #60] Evaluation step #60 evaluates the joint strength of the spot welded joint being evaluated, i.e., the evaluated joint strength TSSeval, by comparing the evaluated joint strength TSSeval with the standard joint strength TSSprop. Specifically, if the evaluated joint strength TSSeval is greater than or equal to the standard joint strength TSSporp, it can be determined that there will be no decrease in joint strength due to initial cracking. In other words, the joint strength can be evaluated as equal to the standard joint strength (TSSporp). On the other hand, if the evaluated joint strength TSSeval is lower than the standard joint strength TSSporp, it can be determined that there will be a decrease in joint strength due to initial cracking. In other words, the joint strength can be evaluated as equal to the evaluated joint strength (TSSeval).

[0072] In this embodiment, the standard joint strength TSSprop is 29.40 kN, and the evaluated joint strength TSSeval is 28.59 kN. In this case, the evaluated joint strength TSSeval is lower than the standard joint strength TSSprop. Therefore, as set in setting step #50, it can be determined that a decrease in joint strength occurs in the case of an initial crack with a depth D of 0.3 mm and a circumferential length θ of 120°. That is, in the case of an initial crack with a depth D of 0.3 mm and a circumferential length θ of 120°, the joint strength can be evaluated as 28.59 kN.

[0073] In contrast, for example, if the initial crack depth D is set to 0.2 mm and the initial crack length θ is set to 90° in setting step #50, the evaluated joint strength TSSeval will be 29.48 kN. In this case, the evaluated joint strength TSSeval is greater than or equal to the standard joint strength TSSporp. Therefore, in the case of an initial crack with a depth D of 0.2 mm and a circumferential length θ of 90°, it can be determined that there is no decrease in joint strength. That is, in the case of an initial crack with a depth D of 0.2 mm and a circumferential length θ of 90°, the joint strength can be evaluated as 29.40 kN.

[0074] The processes described in steps #5 through #60 above are executed on the computer where the program is installed.

[0075] [effect] According to the performance evaluation method for spot-welded joints of this embodiment, by following steps #5 to #60 described above in order, the joint strength can be evaluated according to the initial crack depth D and circumferential length θ. That is, it is possible to determine whether or not there is a decrease in joint strength according to the initial crack depth D and initial crack length θ, and to evaluate the joint strength.

[0076] The embodiments relating to this disclosure have been described above. However, the above embodiments are merely illustrative. Therefore, this disclosure is not limited to the above embodiments, and the above embodiments can be modified as appropriate without departing from the spirit thereof.

[0077] In the above embodiment, a tensile shear joint is assumed as the spot-welded joint. However, the spot-welded joint is not limited to a tensile shear joint, and may be, for example, a cross tensile joint or an L-shaped tensile joint. In the case of a cross tensile joint, the cross tensile strength (CTS) is used as the joint strength. In the case of an L-shaped tensile joint, the L-shaped tensile strength (LTS) is used as the joint strength. [Explanation of symbols]

[0078] 20: Analysis Model 21,22: Steel plate 23: Welded section 24: Nuggets 25:HAZ 28: Initial crack D: Depth of initial crack θ: Circumferential length of the initial crack

Claims

1. A method for evaluating the performance of spot welded joints, The first preparation step involves preparing a crack-free spot welded joint in which no initial cracks exist, The first analysis step involves performing a finite element analysis under tensile conditions on the aforementioned crack-free spot welded joint, Based on the results of the first analysis step, an acquisition step is made to obtain the standard joint strength, which is the joint strength of the crack-free spot welded joint. A second preparation step involves preparing multiple spot welded joints with cracks, each having an initial crack formed around the nugget and varying depths and circumferential lengths of the initial cracks. A second analysis step involves performing a finite element analysis under tensile conditions for each of the aforementioned cracked spot welded joints, Based on the results of the second analysis step, a first derivation step is performed to derive a crack initiation fracture function, which is a linear function in which the depth of the initial crack after the fracture mode changes from normal fracture to fracture originating from the initial crack is the independent variable and the joint strength is the dependent variable, for each circumferential length of the initial crack. A second derivation step involves deriving a slope function, which is a linear function in which the circumferential length of the initial crack is the independent variable and the slope of the crack initiation function is the dependent variable, based on the crack initiation fracture function derived in the first derivation step. A third derivation step involves deriving an intercept function, which is a linear function in which the circumferential length of the initial crack is the independent variable and the intercept of the crack initiation function is the dependent variable, based on the crack initiation fracture function derived in the first derivation step. A fourth derivation step involves substituting the slope function as the slope of the crack initiation fracture function derived in the first derivation step, and substituting the intercept function as the intercept, to derive a crack initiation fracture criterion function that is represented by a function in which the depth and circumferential length of the initial crack are independent variables and the joint strength is the dependent variable. A setting step to set the initial crack depth and circumferential length in the spot welded joint to be evaluated, A calculation step is performed to calculate the evaluated joint strength for the evaluated spot welded joint, which is the joint strength corresponding to the initial crack depth and circumferential length set in the setting step, using the crack initiation fracture criterion function derived in the fourth derivation step. A method for evaluating the performance of a spot welded joint, comprising: an evaluation step of evaluating the joint strength of the evaluated spot welded joint by comparing the evaluated joint strength with the standard joint strength.

2. A method for evaluating the performance of a spot welded joint according to claim 1, The aforementioned crack initiation fracture criterion function TSSfrac is expressed by equation (1), a method for evaluating the performance of spot welded joints. TSSfrac=aθ×D+bθ (1) In equation (1), the meaning of each symbol is as follows: D: Depth of initial crack, aθ: Slope function with the circumferential length of the initial crack as the independent variable, and bθ: Intercept function with the circumferential length of the initial crack as the independent variable.

3. A method for evaluating the performance of a spot welded joint according to claim 2, A method for evaluating the performance of a spot welded joint, wherein in equation (1), the slope function aθ is expressed by equation (i) and the intercept function bθ is expressed by equation (ii). aθ=c1×θ+d1 (i) bθ=c2×θ+d2 (ii) In equations (i) and (ii), the meaning of each symbol is as follows: θ: circumferential length of the initial crack, c1: A coefficient expressed as a number between -10 and 10. d1: A coefficient expressed as a number between -10 and 10. c2: A coefficient expressed as a number between -10 and 10, and d2: A coefficient expressed as a value between 0 and 50 (inclusive).

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