Fatigue strength evaluation method for steel plates with spot welds

Abstract

To provide a method and the like for evaluating fatigue strength that properly evaluate fatigue strength of a steel plate having a spot weld zone.SOLUTION: The present invention includes: a first step ST1 that uses a plurality of analytic models of a steel plate in which a length L of a crack existing in a spot weld zone has been changed within a prescribed range when executing a respective finite element analysis, in order to calculate a relationship between the length L of a crack and a stress intensity factor K of the crack and derive a crack length Lref at which the stress intensity factor K indicates a maximal value Kmax; a second step ST2 that measures an actual crack length Lreal existing in a spot weld zone of a steel plate; and a third step ST3 that compares the crack length Lreal with the crack length Lref, and if an absolute value of a difference therebetween is larger than a prescribed threshold value Th, the fatigue strength of a steel plate is determined to be accepted, whereas if the absolute value of difference therebetween is equal to the threshold value Th or smaller, the fatigue strength of a steel plate is determined to have failed.SELECTED DRAWING: Figure 2

Description

[Technical Field]

[0001] The present invention provides a fatigue strength evaluation method capable of properly evaluating the fatigue strength of a steel plate having spot welds. law Regarding. [Background technology]

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

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

[0004] Generally, to evaluate the effect of cracks on fatigue strength, stress intensity factors calculated by treating the cracks as cracks are often used. The stress intensity factor is a fracture mechanics parameter that expresses the driving force for crack propagation based on the deformation field near the crack tip. Normally, as the crack length increases, the stress intensity factor also increases, and it is often thought that this is a factor that reduces fatigue strength. However, as a result of intensive research by the present inventors, it was found that in spot welds, even if the length of cracks such as LME cracks increases, the stress intensity factor may not increase monotonically. For this reason, it was found that the magnitude of the stress intensity factor cannot be evaluated simply based on the length of the crack present in the spot weld, as in the conventional thinking described above, and therefore the fatigue strength cannot be properly evaluated.

[0005] Non-Patent Document 1 presents a theoretical solution for the stress intensity factor of a crack. Furthermore, Non-Patent Document 2 describes a method for calculating a stress intensity factor based on the analysis results of the crack opening displacement. [Prior art documents] [Patent documents]

[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] Nakai, Yoshikazu and Kubo, Shiro, "Basic Course of Mechanical Engineering: Fracture Mechanics", Asakura Publishing, 2014, pp. 64-66 Summary of the Invention [Problem to be solved by the invention]

[0008] The present invention has been made to solve the above-mentioned problems of the conventional art, and provides a fatigue strength evaluation method that can properly evaluate the fatigue strength of a steel plate having spot welds. law The objective is to provide the following. [Means for solving the problem]

[0009] In order to solve the above problem, the inventors have conducted extensive research and found that, as mentioned above, in spot welds, the stress intensity factor does not always increase monotonically even when the crack length increases. Specifically, when an external force of a constant magnitude and direction is applied to a crack in a spot weld, and the crack length L is changed as shown in Figure 1, the stress intensity factor K increases with increasing crack length L. ref Although it increases up to the crack length L ref decreases as the stress intensity factor K increases (i.e., as the stress intensity factor K increases with the crack length L ref The maximum value K max In this case, the crack length L is ref Even if the crack length L is larger than the ref It was found that the fatigue strength was greater than that when As shown above, the stress intensity factor K reaches its maximum value K with respect to the change in the crack length L. max It is believed that the reason for this change, as shown in Fig. 1, is that the deformation of the spot weld is restricted. Specifically, in an actual vehicle body in which steel plates with spot welds are used, multiple steel plate pieces are joined by spot welds, and the spot welds cannot deform freely. For this reason, even if the crack length increases, the opening displacement does not increase monotonically. However, when the crack length exceeds a predetermined value (when the remaining thickness of the steel plate becomes less than a predetermined value), the load and moment borne by the part where the crack exists decrease significantly, and the opening displacement decreases.

[0010] The present invention was completed based on the above findings of the present inventors. That is, in order to solve the above-mentioned problem, the present invention provides a method for evaluating the fatigue strength of a steel plate having a spot weld in which a crack exists, characterized by comprising the following steps: (1) First step: Using a plurality of analytical models of the steel plate in which the length L of the crack existing in the spot weld is changed within a predetermined range, a finite element analysis is performed for each model to calculate the relationship between the length L of the crack and the stress intensity factor K of the crack, and the stress intensity factor K is calculated when the stress intensity factor K reaches a maximum value K. max The length of the crack L ref is derived. (2) Second step: The actual crack length L of the spot weld of the steel plate real Measure. (3) Third step: The length of the crack L real and the length of the crack L ref If the absolute value of the difference between the two is greater than a predetermined threshold value Th, the fatigue strength of the steel plate is judged to be acceptable, and if the absolute value of the difference between the two is equal to or less than the threshold value Th, the fatigue strength of the steel plate is judged to be unacceptable.

[0011] According to the present invention, in the first step, a relationship between the length L of a crack present in a spot weld of a steel plate and the stress intensity factor K of the crack is calculated by performing finite element analysis. Specifically, by performing finite element analysis on each of a plurality of analytical models of a steel plate in which the crack length L is changed within a predetermined range, the stress intensity factor K is calculated for each crack length L, and the above relationship can be calculated. Then, in the first step, the stress intensity factor K is calculated by the maximum value K. max The crack length L ref is derived. Next, in the second step, the actual crack length L real Measure the crack length L real The measurement method is not particularly limited, but for example, measurement can be performed using X-ray CT (Computed Tomography). Finally, in the third step, the crack length Lreal and the crack length L ref If the absolute value of the difference between the two is greater than a predetermined threshold value Th, the fatigue strength of the steel plate is judged to be acceptable. ref When the stress intensity factor K reaches its maximum value, K max The fatigue strength is considered to be at its lowest when the actual crack length L real is the length of this crack L ref If the difference between the crack length L and the stress intensity factor K is greater than the threshold value Th, the stress intensity factor K is sufficiently reduced, and the fatigue strength is considered to be sufficiently increased accordingly, so the fatigue strength of the steel plate can be judged to be acceptable. Conversely, if the absolute value of the difference between the two is less than the predetermined threshold value Th, the fatigue strength is considered to be acceptable when the crack length L is greater than the threshold value Th. ref Since it is considered that the fatigue strength is not sufficiently larger than that at time 1, it is possible to judge that the fatigue strength of the steel plate is unacceptable. As described above, according to the present invention, it is possible to properly evaluate the fatigue strength of a steel plate having spot welds. [Effects of the Invention]

[0013] According to the present invention, it is possible to properly evaluate the fatigue strength of steel plates having spot welds. As a result, there are cases where steel plates that would have been uniformly judged to have failed the fatigue strength test due to the long crack length in the past can now be judged to have passed the test, which contributes to improving yield. In addition, it is possible to reduce the cost required to take various measures to excessively reduce the crack length. [Brief explanation of the drawings]

[0014] [Figure 1] FIG. 1 is an explanatory diagram for schematically explaining the findings obtained by the present inventors. [Figure 2] 1 is a flow chart showing a schematic procedure of a method for evaluating fatigue strength of a steel plate having spot welds according to an embodiment of the present invention. [Figure 3] FIG. 1 is a diagram showing an analytical model for performing finite element analysis used in an embodiment of the present invention. [Figure 4]FIG. 1 is a diagram showing the relationship between the crack length L and the crack stress intensity factor K calculated in an example of the present invention. DETAILED DESCRIPTION OF THE INVENTION

[0015] Hereinafter, an embodiment of the present invention will be described with reference to the accompanying drawings. FIG. 2 is a flowchart showing an outline of the procedure of a method for evaluating the fatigue strength of a steel plate having spot welds according to one embodiment of the present invention (hereinafter, simply referred to as a "fatigue strength evaluation method" where appropriate). As shown in FIG. 2, the fatigue strength evaluation method according to this embodiment is a method for evaluating the fatigue strength of a steel plate having a spot weld in which a crack exists, and includes a first step ST1, a second step ST2, and a third step ST3. Steps ST1 to ST3 will be explained in order below.

[0016] <First step ST1> In the first step ST1, a finite element analysis is performed using a plurality of analytical models of a steel plate in which the length L of a crack existing in a spot weld is changed within a predetermined range (for example, an analytical model as shown in Fig. 3 described later). Then, in the first step ST1, the relationship between the crack length L and the stress intensity factor K of the crack is calculated, as shown in Fig. 1 described above. In this embodiment, the stress intensity factor K of the crack is the in-plane opening type (mode I) stress intensity factor (hereinafter referred to as "K I "), but this is not necessarily limited to this, and it is also possible to calculate the stress intensity factors of in-plane shear type (mode II) or out-of-plane shear type (mode III) depending on the load conditions (external force applied) in the finite element analysis.

[0017] One method for calculating the crack stress intensity factor K is to use the crack opening displacement. When calculating the stress intensity factor using the crack opening displacement, first, a finite element analysis is performed to calculate the displacement u of the node that constitutes the crack in the analysis model, and then the crack opening displacement 2u, which is double the displacement u, is calculated. Specifically, the crack opening displacement 2u is calculated for each distance r from the crack tip. Then, the relationship between the square root of the distance r from the crack tip and the crack opening displacement 2u is approximated by a straight line, and the gradient of the approximated line is 2u / r. 1 / 2 The stress intensity factor of the crack is calculated based on the following equation (1): Stress intensity factor = {E / 4(1-ν 2 )}·(2π / r) 1 / 2 ·u ···(1) In the above formula (1), E is the Young's modulus of the steel plate in which the crack exists, ν is the Poisson's ratio of the steel plate, and π is the ratio of the circumference of the steel plate to its diameter. The above formula (1) is a known formula that can be derived from formulas (4.8) and (4.16) described in Non-Patent Document 2.

[0018] The relationship between the crack length L and the crack stress intensity factor K can be expressed, for example, as a function such as a polynomial function calculated by performing an approximation calculation such as the least squares method on the crack stress intensity factor K calculated using each analytical model for each changed crack length L. Alternatively, the relationship can be expressed as a broken line connecting the crack stress intensity factors K calculated using each analytical model for each changed crack length L. Furthermore, when there are a large number of analytical models (the number of cracks whose length L is changed), the relationship can also be expressed as a table that associates the crack length L with the crack stress intensity factor K.

[0019] Then, in the first step ST1, based on the relationship between the crack length L and the stress intensity factor K of the crack, the stress intensity factor K is determined to be the maximum value K max The crack length L refAccording to the findings of the inventors, when an external force of a certain magnitude and direction is applied to a crack in a spot weld, the relationship between the crack length L and the stress intensity factor K of the crack has a single maximum value K max (There are no multiple maxima).

[0020] <Second step ST2> In the second step ST2, the actual crack length L real is measured using a known method such as X-ray CT.

[0021] <Third step ST3> In the third step ST3, the crack length L real and the crack length L ref and determine whether the absolute value of the difference between them is greater than a predetermined threshold value Th (ST31 in FIG. 2). As a result, if the absolute value of the difference between them is greater than the threshold value Th ("Yes" in ST31 in FIG. 2), the fatigue strength of the steel plate is determined to be acceptable (ST32 in FIG. 2). On the other hand, if the absolute value of the difference between them is equal to or less than the threshold value Th ("No" in ST31 in FIG. 2), the fatigue strength of the steel plate is determined to be unacceptable (ST33 in FIG. 2). The threshold value Th may be set to an appropriate value based on the stress intensity factor corresponding to the allowable fatigue strength. Specifically, the fatigue strength and the stress intensity factor K are quantitatively related based on the crack propagation characteristics of the steel plate (the relationship between the stress intensity factor K and the crack propagation rate). Therefore, if an allowable fatigue strength is given, the corresponding allowable stress intensity factor K (hereinafter referred to as K al ) is obtained, and the stress intensity factor K can be calculated from the relationship between the crack length L and the stress intensity factor K as shown in Figure 1. al The allowable crack length L (hereafter referred to as L al The crack length L al As shown in Figure 1, the crack length L ref (The stress intensity factor K is at its maximum value K maxThe threshold value Th is obtained by, for example, determining the crack length L ref and the length of one crack L al The absolute value of the difference between the crack length L ref and the length of the other crack L al The larger of the absolute value of the difference between the

[0022] Hereinafter, the features of the present invention will be further clarified by describing examples of the fatigue strength evaluation method according to the present invention.

[0023] <Calculation of the relationship between crack length L and crack stress intensity factor K using finite element analysis> FIG. 3 is a diagram showing an analytical model (analysis model of a spot-welded joint of steel plates) used in the finite element analysis in this example. The analytical model shown in FIG. 3(a) is an analytical model of a tensile-shear joint J (a standard test piece for measuring the fatigue strength of a weld, the shape and dimensions of which are specified in JIS Z 3138 "Fatigue test method for spot-welded joints") in which steel plate pieces Ja and Jb are spot-welded. The thickness of each steel plate piece is 1.6 mm, the Young's modulus of the steel plate pieces is 206 GPa, and the Poisson's ratio is 0.3. In consideration of symmetry, the analytical model shown in FIG. 3(a) models only half of the tensile-shear joint J. Figure 3(b) is an enlarged view of the spot weld in the analysis model shown in Figure 3(a). As shown in Figure 3(b), the diameter (nugget diameter) of the spot weld was set to 6 mm, and a crack was introduced extending from the interface between each steel sheet, indicated by the dashed line in Figure 3(b), in the thickness direction, around the entire circumference of the spot weld. Five crack lengths (dimension in the thickness direction) L were used: 0.2 mm, 0.5 mm, 0.8 mm, 1.0 mm, and 1.2 mm. Contact was defined between opposing crack surfaces and between opposing steel sheets. In the above analytical model, one steel plate, Ja, was fixed, and a load of 2000 N was applied (external force was applied) to the other steel plate, Jb, in the in-plane direction (the direction of the bold arrow in Figure 3(a)). Finite element analysis was performed under the following conditions: deformation in the thickness direction was constrained (only deformation in the in-plane direction was allowed) at the load application location. Therefore, although the geometry of the tension-shear joint is relatively simple, the state of deformation constraint at the spot weld is similar to that in an actual vehicle body. By performing the finite element analysis in this manner, the stress intensity factor (mode I) was calculated.

[0024] FIG. 4 is a diagram showing the relationship between the crack length L and the crack stress intensity factor K calculated in this example. As shown in FIG. 4, when the crack length L is 0.8 mm (L ref = 0.8 mm), the stress intensity factor K reaches its maximum value K max Therefore, whether the crack length L is greater or less than 0.8 mm, the stress intensity factor K becomes smaller and the fatigue strength is thought to improve.

[0025] <Verification by fatigue testing> Fatigue tests were conducted on an actual tension-shear joint, which had the same joint shape and dimensions and spot weld diameter as the analytical model shown in Figure 3, to verify the validity of the fatigue strength evaluation results from the finite element analysis described above. The steel sheet pieces used in the fatigue tests were zinc-plated steel sheets with a tensile strength of 980 MPa. By adjusting the welding conditions, a crack (LME crack) was introduced in the thickness direction of the weld. The crack lengths (target values) were 0.5 mm and 1.0 mm. The fatigue test was carried out at room temperature in the atmosphere under the condition of a stress ratio (minimum load / maximum load) = 0.1, and the fatigue strength was defined as the strength at 2 million cycles. The strength at 2 million cycles refers to the load range (maximum load - minimum load) where there is a 50% probability that the spot weld will break after 2 million cycles. In Figure 4, the stress intensity factor K for crack lengths L = 0.5 mm and 1.0 mm is similar (approximately 12.5 MPa mm 1 / 2), so the fatigue strength is expected to be equivalent. In the tension-shear joint used in this fatigue test, the crack only extends around half the circumference of the spot weld, but even in this case, it has been confirmed by separate finite element analysis that the relationship between the crack length L and the stress intensity factor K is similar to that shown in Figure 4.

[0026] Table 1 shows the fatigue strength of the tensile shear joint evaluated in this fatigue test. [Table 1] As shown in Table 1, the fatigue strength values ​​for crack lengths L = 0.5 mm and 1.0 mm are relatively close, and as mentioned above, the fact that the stress intensity factors K for both are similar can be said to correspond to the results of this fatigue test.

[0027] According to the theoretical solution described in Non-Patent Document 1, when a plate with a finite thickness (here, 1.6 mm) having a single-edge crack is subjected to a bending load (two-dimensional problem), the stress intensity factor K for a crack length of 1.0 mm can be calculated from the following equations (2) to (4): I is the stress intensity factor K for a crack length of 0.5 mm I This is about 2.6 times the original value. K I =σ·(πa) 1 / 2 F(α) (2) α=a / W (3) F(α)=1.122-1.40α+7.33α 2 -13.08α 3 +14.0α 4 ···(4) Here, a is the crack length [mm] (in this example, a=0.5 mm, 1.0 mm), and W is the plate thickness [mm] (1.6 mm in this example).

[0028] As described above, according to the theoretical solution, the fatigue strength of a crack 1.0 mm long is predicted to drop significantly compared to a crack 0.5 mm long due to an increase in the stress intensity factor K of approximately 2.6 times, which will result in a significant difference from the results of the fatigue test. Therefore, by calculating and understanding the relationship between the crack length L and the crack stress intensity factor K as shown in Figure 4 in advance by performing finite element analysis, it is possible to determine the allowable crack length (L) (at which the fatigue strength is judged to be acceptable). real ±Th) can be evaluated appropriately. In other words, if the relationship shown in Fig. 4 is not understood in advance, there is a risk of making the erroneous judgment that the fatigue strength decreases as the crack length increases, as suggested by the theoretical solution. As a result, if the crack length is large, the fatigue strength will be uniformly judged to be unacceptable, which could result in a decrease in yield or in unnecessary costs due to various measures to excessively reduce the crack length. [Explanation of symbols]

[0029] K stress intensity factor K max Maximum value of stress intensity factor L: length of the crack L ref The length of the crack at which the stress intensity factor reaches its maximum value L real Actual crack length ST1: First step ST2: Second step ST3: Third step

Claims

[Claim 1] A method for evaluating fatigue strength of a steel plate having a spot weld in which a crack exists, comprising: A finite element analysis is performed using a plurality of analytical models of the steel plate in which the length L of the crack present in the spot weld is changed within a predetermined range, and the relationship between the length L of the crack and the stress intensity factor K of the crack is calculated, and the stress intensity factor K is calculated to be a maximum value K. ｍａｘ The length L of the crack ｒｅｆ A first step of deriving The actual length L of the crack present in the spot weld of the steel plate ｒｅａｌ a second step of measuring The length of the crack L ｒｅａｌ and the length of the crack L ｒｅｆ and a third step of comparing the fatigue strength of the steel plate with the fatigue strength of the steel sheet, and determining that the fatigue strength of the steel sheet is acceptable if the absolute value of the difference between the two is greater than a predetermined threshold value Th, and determining that the fatigue strength of the steel sheet is unacceptable if the absolute value of the difference between the two is equal to or less than the threshold value Th. A method for evaluating fatigue strength of a steel plate having spot welds, characterized by:

Images