JP7747958B2 - Fatigue strength evaluation method for steel plates with spot welds - Google Patents

Description

The present invention relates to a fatigue strength evaluation method that can properly evaluate the fatigue strength of a steel plate having spot welds.

In recent years, the automotive industry has seen a demand for lighter vehicle bodies to improve fuel economy, while also increasing their strength to improve collision safety. To achieve both of these demands, it is effective to use high-strength steel sheets as the material for vehicle bodies. Furthermore, from the perspective of improving rust prevention, zinc-plated steel sheets, which have excellent corrosion resistance, are used among high-strength steel sheets.

Spot welding is primarily used for assembling automobile bodies, but spot welding of zinc-based coated steel sheets can result in cracks at the spot welds. This cracking is said to be caused by so-called liquid metal embrittlement (hereinafter abbreviated as "LME"), which is believed to be caused by temperature rise and tensile stress generation during the welding process, causing the molten zinc-based coated metal to penetrate into 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, for example, techniques for controlling the chemical composition and structure of the steel sheet and the coating, and techniques for controlling the welding conditions as described in Patent Document 1 have been proposed.
However, the effect of LME cracking on fatigue strength has not been clearly understood. Therefore, from the viewpoint of fatigue strength, not only is there a need for technological development to suppress LME cracking, but there is also a need for a method to properly evaluate the effect of LME cracking on fatigue strength.

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 a crack such as an LME crack 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 a crack present in a spot weld, as in the above-mentioned conventional thinking, and therefore the fatigue strength cannot be properly evaluated.

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.

Japanese Patent Application Laid-Open No. 2020-11253

Y.Murakami et al., “STRESS INTENSITY FACTORS HANDBOOK”, Volume 1, Pergamon Press, 1987, p.11 Nakai, Yoshikazu and Kubo, Shiro, "Fracture Mechanics: Basic Course in Mechanical Engineering", Asakura Publishing, 2014, pp. 64-66

The present invention has been made to solve the problems of the conventional technology as described above, and has an object of providing a fatigue strength evaluation method that can properly evaluate the fatigue strength of steel plates having spot welds.

To solve the above-mentioned problems, the present inventors conducted extensive research and found that, as described above, in spot welds, the stress intensity factor does not monotonically increase even as the crack length increases. Specifically, they found that 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 up to a predetermined crack length _Lref but decreases when the crack length exceeds _Lref (i.e., the stress intensity factor K reaches a maximum value _Kmax at the crack length _Lref ). In this case, the stress intensity factor K decreases even when the crack length L is longer than _Lref , resulting in a higher fatigue strength than when the crack length is _Lref .
As described above, the reason why the stress intensity factor K changes to reach a maximum value _Kmax with changes in the crack length L is thought to be due to the constraint on deformation of the spot weld. Specifically, in an actual vehicle body using steel plate with spot welds, multiple steel plate pieces are joined by spot welds, so the spot welds cannot deform freely. For this reason, even if the crack length increases, its 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.

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 a crack present 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 length _Lref of the crack at which the stress intensity factor K takes on a maximum value _Kmax is derived.
(2) Second step: The actual length L _real of the crack present in the spot weld of the steel plate is measured.
(3) Third step: The crack length L _real is compared with the crack length L _ref , and 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.

According to the present invention, in the first step, a finite element analysis is performed to calculate the 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. 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 crack length _Lref at which the stress intensity factor K shows a maximum value _Kmax is derived.
Next, in the second step, the actual length _Lreal of the crack present in the spot weld of the steel plate is measured. The method for measuring the crack length _Lreal is not particularly limited, but it can be measured using, for example, X-ray CT (Computed Tomography).
Finally, in the third step, the crack length _Lreal is compared with the crack length _Lref , and 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. That is, when the crack length L is _Lref , the stress intensity factor K reaches its maximum value _Kmax , and fatigue strength is considered to be at its lowest. Therefore, if the actual crack length _Lreal is separated from this crack length _Lref by more than the threshold value Th, the stress intensity factor K is considered to be sufficiently reduced, and accordingly, fatigue strength is considered to be sufficiently large, so that 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 equal to or less than the predetermined threshold value Th, it is considered that the fatigue strength is not sufficiently large compared to when the crack length L is _Lref , and therefore the fatigue strength of the steel plate can be judged to be 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.

The present invention makes it possible to properly evaluate the fatigue strength of steel plates with spot welds. As a result, steel plates that would previously have been uniformly judged to have failed the fatigue strength test due to large crack lengths can now be judged to pass, contributing to improved yields. It also reduces the costs required to take various measures to excessively reduce crack lengths.

FIG. 1 is an explanatory diagram for schematically explaining the findings obtained by the present inventors. 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. FIG. 1 is a diagram showing an analytical model for performing finite element analysis used in an embodiment of the present invention. 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.

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 the "fatigue strength evaluation method" as 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 described below in order.

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

One method for calculating the crack stress intensity factor K 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 node that constitutes the crack in the analytical 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 crack stress intensity factor is calculated based on the gradient 2u/r ^1/2 of the approximated line. Specifically, the crack stress intensity factor is calculated, for example, 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.

The relationship between the crack length L and the crack stress intensity factor K can be, for example, a function such as a polynomial function calculated by performing an approximation such as the least squares method on the crack stress intensity factor K calculated using each analytical model for each changed crack length L. It is also possible to represent the above relationship as a broken line connecting the crack stress intensity factors K calculated using each analytical model for each changed crack length L. Furthermore, if there are a large number of analytical models (the number of cracks with changed length L), it is also possible to represent the above relationship as a table correlating the crack length L with the crack stress intensity factor K.

Then, in the first step ST1, the crack length Lref at which the stress intensity factor K shows a maximum value _Kmax is derived based on the relationship between the crack length L _and the crack stress intensity factor K. Note that, according to the findings of the present inventors, under conditions in which an external force of a certain magnitude and in a certain direction is applied to a crack present in a spot weld, the relationship between the crack length L and the crack stress intensity factor K has a single maximum value _Kmax (there are no multiple maximum values).

<Second step ST2>
In the second step ST2, the length L _real of the actual crack present in the spot weld of the steel plate is measured using a known technique such as X-ray CT.

<Third step ST3>
In the third step ST3, the crack length _Lreal is compared with the crack length _Lref , and it is determined 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 a stress intensity factor corresponding to the allowable fatigue strength. Specifically, fatigue strength and 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, a corresponding allowable stress intensity factor K (hereinafter referred to as K _a1 ) can be obtained. In turn, an allowable crack length L (hereinafter referred to as L a1) corresponding to the stress intensity factor K _a1 can be obtained from the relationship between the crack length L _{and the stress intensity factor K as shown in FIG. 1. As the crack length L a1 ,} two values can be obtained: one smaller than the crack length L _ref (the crack length at which the stress intensity factor K reaches its maximum value K _max ), and the other larger than it, as shown in FIG. 1. The threshold value Th may be set to, for example, the larger of the absolute value of the difference between the crack length _Lref and the length _Lal of one crack, and the absolute value of the difference between the crack length _Lref and the length _Lal of the other crack.

The following describes examples of the fatigue strength evaluation method according to the present invention, further clarifying the features of the present invention.

<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 of 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 shown by the dashed line in Figure 3(b) in the sheet thickness direction and around the entire circumference of the spot weld. The crack length (dimension in the sheet thickness direction) L was set to five lengths: 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 analysis model, finite element analysis was performed under the following conditions: 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 thick arrow in Figure 3(a)), and deformation in the plate thickness direction was constrained (only deformation in the in-plane direction was allowed) at the load application position. Therefore, although the shape of the tensile shear joint is relatively simple, the deformation constraint state of the spot weld is similar to that in an actual vehicle body. By performing finite element analysis in this manner, the stress intensity factor (mode I) was calculated.

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, the stress intensity factor K reaches its maximum value _Kmax when the crack length L is 0.8 mm ( _Lref = 0.8 mm). Therefore, it is considered that the stress intensity factor K decreases and the fatigue strength improves whether the crack length L is greater or less than 0.8 mm.

<Verification by fatigue test>
A fatigue test was 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 obtained by the finite element analysis described above. The steel sheet pieces used in the fatigue test were zinc-plated steel sheets with a tensile strength of 980 MPa. By adjusting the welding conditions, a crack (LME crack) was introduced into the weld in the thickness direction. The crack lengths (target values) were 0.5 mm and 1.0 mm.
The fatigue test was conducted at room temperature in air under a stress ratio (minimum load/maximum load) of 0.1, and the fatigue strength was defined as the 2 million cycles strength. The 2 million cycles strength refers to the load range (maximum load - minimum load) where the probability of the spot weld breaking after 2 million cycles is 50%. 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 similar. In the tension-shear joint used in this fatigue test, the crack only extends about halfway around the spot weld. However, separate finite element analysis confirmed that the relationship between the crack length L and the stress intensity factor K is similar to that shown in Figure 4 .

The fatigue strength of the tensile shear joint evaluated in this fatigue test is shown in 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 the fact that the stress intensity factors K for both are similar, as mentioned above, can be said to correspond to the results of this fatigue test.

According to the theoretical solution described in Non-Patent Document 1, if we consider an example in which a plate of finite thickness (here, 1.6 mm) with a one-side crack is subjected to a bending load (two-dimensional problem), the stress intensity factor K _I for a crack length of 1.0 mm is approximately 2.6 times the stress intensity factor K _I for a crack length of 0.5 mm, based on the following equations (2) to (4).
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).

As described above, according to the theoretical solution, the fatigue strength of a crack length of 1.0 mm is predicted to be significantly lower than that of a crack length of 0.5 mm due to an increase in the stress intensity factor K of approximately 2.6 times, which is significantly different from the results of the fatigue test. Therefore, by calculating and understanding in advance the relationship between the crack length L and the crack stress intensity factor K as shown in Figure 4 by performing finite element analysis, it is possible to properly evaluate the allowable crack length (L _real ±Th) (at which the fatigue strength is judged to be acceptable).
4, there is a risk of misjudging that the fatigue strength decreases as the crack length increases, as in the theoretical solution. As a result, there is a possibility that any crack with a large length will be uniformly judged to have a failure in fatigue strength, resulting in a decrease in yield, or that various measures to excessively reduce the crack length will result in unnecessary increases in costs.

K: stress intensity factor K _max : maximum value of stress intensity factor L: crack length L _ref : length of crack where stress intensity factor shows maximum value L _real : actual crack length ST1: first step ST2: second step ST3: third step

Claims (1)

A method for evaluating fatigue strength of a steel plate having a spot weld in which a crack exists, comprising:
a first step of performing finite element analysis on each of a plurality of analytical models of the steel plate in which the length L of a crack present in the spot weld is changed within a predetermined range, thereby calculating a relationship between the length L of the crack and a stress intensity factor K of the crack, and deriving a length _Lref of the crack at which the stress intensity factor K shows a maximum value _Kmax ;
A second step of measuring the actual crack length L _real present in the spot weld of the steel plate;
a third step of comparing the crack length L _real with the crack length L _ref , and determining that the fatigue strength of the steel plate 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 plate 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 :