Method and program for predicting liquid metal embrittlement cracking

Abstract

To provide a method for accurately predicting liquid metal embrittlement cracking on a surface of a plated steel plate in a plated steel plate welding step.SOLUTION: A method for accurately predicting liquid metal embrittlement cracking on a surface of a plated steel plate in a plated steel plate welding step comprises: a numeric simulation step ST1 of estimating a stress history and a temperature history near the surface of the plated steel plate in the welding step through numeric simulation simulating the welding step; a latent time consumption rate calculation step ST2 of calculating a latent time consumption rate ρ represented by an expression (1) below on the basis of the stress history and the temperature history which have been estimated; and a determination step ST3 of determining occurrence of liquid metal embrittlement cracking on the surface of the plated steel plate when the latent time consumption rate ρ is 1 or higher. Expression 17.SELECTED DRAWING: Figure 3

Description

Technical Field

[0001] The present invention relates to a method and a program for accurately predicting the occurrence of liquid metal embrittlement cracks on the surface of a plated steel sheet in the welding process of the plated steel sheet.

Background Art

[0002] In the welding process (for example, resistance spot welding process) of a plated steel sheet such as a galvanized steel sheet, cracks caused by liquid metal embrittlement (LME (Liquid Metal Embrittlement)) (hereinafter referred to as liquid metal embrittlement cracks or LME cracks) may occur in the welded part. When this LME crack is significant, there is a risk that the joint strength of the welded part will decrease.

[0003] Therefore, conventionally, for the purpose of suppressing LME cracks, for example, a steel sheet (LME crack-resistant steel sheet) with a plating component design in which LME cracks are less likely to occur, an LME crack prevention method for removing or modifying the plating surface before the welding process, or an LME crack prevention welding method in which welding conditions such as pressure and current are optimized as described in Patent Document 1 have been proposed.

[0004] However, conventionally, no method has been proposed for predicting the occurrence of LME cracks before actually performing the welding process of the plated steel sheet.

[0005] In addition, Non-Patent Documents 1 to 4 report research on the mechanism of liquid metal embrittlement cracks.

Prior Art Documents

Patent Documents

[0006]

Patent Document 1

Non-Patent Documents

[0007]

Non-Patent Document 1

[0008] The present invention has been made to solve the problems of the prior art as described above, and an object thereof is to provide a method and a program for accurately predicting the occurrence of liquid metal embrittlement cracks on the surface of a plated steel sheet in the welding process of the plated steel sheet. [Means for Solving the Problems]

[0009] In order to solve the above problems, the present invention provides a method for predicting the occurrence of liquid metal embrittlement cracking on the surface of a plated steel sheet in a welding process of the plated steel sheet, the method including: a numerical simulation step of estimating a stress history and a temperature history in the vicinity of the surface of the plated steel sheet in the welding process by a numerical simulation simulating the welding process; a latent time consumption rate calculation step of calculating a latent time consumption rate ρ represented by the following formula (1) based on the estimated stress history and temperature history; and a determination step of determining that liquid metal embrittlement cracking occurs on the surface of the plated steel sheet when the latent time consumption rate ρ is 1 or more. [Number] In the formula (1), Δt i means the time from the start to the end of welding in the welding process divided into an integer n, and specifically means the time (t i -t i+1 ) from the i-th time t i+1 to the (i + 1)-th time t i . i is an integer satisfying 1 ≦ i ≦ n. σ i means the stress (maximum principal stress at an arbitrary position X) in the vicinity of the surface of the plated steel sheet at the time Δt i . T i means the temperature (temperature at the position X) in the vicinity of the surface of the plated steel sheet at the time Δt i . t c means the latent time until the occurrence of liquid metal embrittlement cracking, and since it is expressed as a function of the stress σ i and the temperature T i , it is denoted as t c (σ i , T i ) in the above formula (1).

[0010] In the present invention, "in the vicinity of the surface of the plated steel sheet" means the outermost surface of the plated steel sheet and the vicinity thereof (for example, a range of several μm in the thickness direction of the plated steel sheet from the outermost surface). In the present invention, the "numerical simulation simulating the welding process" means a numerical simulation in which the type and dimensions of the plated steel sheet and the welding conditions such as the pressing force and current are made the same as those of the actual welding process for predicting the occurrence of liquid metal embrittlement cracking. As the numerical simulation, for example, known finite element analysis can be used. In the present invention, the "stress history and temperature history" means the variation history of stress and the variation history of temperature from the start to the end of the welding process. According to the present invention, by the numerical simulation step, the stress history and temperature history in the vicinity of the surface of the plated steel sheet are estimated, and by the latent time consumption rate calculation step, the latent time consumption rate ρ represented by the formula (1) is calculated. As will be described later, when this latent time consumption rate ρ is 1 or more, it can be said that liquid metal embrittlement cracking occurs on the surface of the plated steel sheet. Therefore, in the determination step, when the latent time consumption rate ρ is 1 or more, by determining that liquid metal embrittlement cracking occurs on the surface of the plated steel sheet, the occurrence of liquid metal embrittlement cracking on the surface of the plated steel sheet can be accurately predicted. In addition, when the latent time consumption rate ρ represented by the formula (1) is less than 1, it can be determined that liquid metal embrittlement cracking of the plated steel sheet does not occur in the welding process to be predicted.

[0011] In the method for predicting liquid metal embrittlement cracking according to the present invention, it is possible to predict not only the occurrence or non-occurrence of liquid metal embrittlement cracking but also the occurrence time of liquid metal embrittlement cracking (the elapsed time from the start of welding until the occurrence of liquid metal embrittlement cracking starts). When predicting the occurrence time of liquid metal embrittlement cracking, in the latent time consumption rate calculation step, the latent time consumption rate ρ represented by the following formula (1)' N is calculated, and in the determination step, the latent time consumption rate ρ N is specified as the minimum N at which it becomes 1 or more, and it is preferable to determine that the (N + 1)-th time t N+1 is the occurrence time of liquid metal embrittlement cracking.

Number

[0012] According to the above preferred method, in the determination step, the minimum N at which the latency consumption rate ρ N becomes 1 or more is specified. In other words, the (N + 1)-th time t N when ρ N+1 becomes 1 or more is specified, and thus this time t N+1 can be determined as the occurrence time of liquid metal embrittlement cracking.

[0013] In the method for predicting liquid metal embrittlement cracking according to the present invention, for example, it is preferable to calculate the latency time t c in the formula (1) based on the following formulas (2) to (4).

Equation

[0014] In the above preferred method, the first term on the right side of the formula (2), (w c 0 / γ) 3 The value of can be determined using the values disclosed in Non-Patent Documents 1, 2, etc., for example. The value of the second term on the right side of the formula (2), (E *3 / G), is determined using the temperature history estimated in the numerical simulation step and known information for each of E, ν, D GB , Ω, k, and T i in the formulas (3) and (4). The value of the third term on the right side of the formula (2), 1 / (σ i -σ th ) 3 can be determined using the stress history estimated in the numerical simulation step and the values disclosed in Non-Patent Document 3, etc.

[0015] Also, in the method for predicting liquid metal embrittlement cracking according to the present invention, the latency time t c (=t c (σ i , T i )) in the formula (1) is expressed in the form of the following formula (5) (in other words, the formula (2) is rewritten in the form of the following formula (5)), and the latency time t c can also be calculated based on the following formula (5). Specifically, while maintaining the temperature T i in the temperature range where liquid metal embrittlement cracking can occur at the temperature T <j>< / j> , the stress σ i is changed to various stresses σ <m>< / m> , and a tensile test of the plated steel sheet is performed. Thus, the latency time t <m>< / m> until liquid metal embrittlement cracking occurs is measured for each stress σ c <m,j> , and the obtained point group (σ <m>< / m> , T <j>< / j> , t c <m,j> ) From the following formula (5) for φ(T i ) and σ th (T i ), by regression approximation, the following formula (5) is determined, and the latency time t c in the above formula (1) can also be calculated based on the determined following formula (5).

Equation

[0016] The liquid metal embrittlement crack prediction method according to the present invention is preferably used when the plated steel sheet is an electro-galvanized steel sheet, a hot-dip galvanized steel sheet, or an alloyed hot-dip galvanized steel sheet.

[0017] The liquid metal embrittlement crack prediction method according to the present invention is preferably used when the welding process is a resistance spot welding process.

[0018] Also, in order to solve the above problems, the present invention also provides a liquid metal embrittlement crack prediction program for causing a computer to execute the numerical simulation step, the latency time consumption rate calculation step, and the determination step included in the liquid metal embrittlement crack prediction method.

[0019] Summarizing the above, the present invention relates to the matters shown in the following [1] to [7]. [1] A method for predicting the occurrence of liquid metal embrittlement cracks on the surface of a plated steel sheet in the welding process of the plated steel sheet, comprising: a numerical simulation step of estimating the stress history and temperature history near the surface of the plated steel sheet in the welding process by a numerical simulation simulating the welding process; a latent time consumption rate calculation step of calculating the latent time consumption rate ρ represented by the formula (1) based on the estimated stress history and temperature history; and a determination step of determining that liquid metal embrittlement cracks occur on the surface of the plated steel sheet when the latent time consumption rate ρ is 1 or more. A method for predicting liquid metal embrittlement cracks. [2] In the latent time consumption rate calculation step, the latent time consumption rate ρ represented by the formula (1)' N is calculated, and in the determination step, the latent time consumption rate ρ N The minimum N at which becomes 1 or more is specified, and the (N + 1)-th time t N+1 is determined to be the occurrence time of liquid metal embrittlement cracks. The method for predicting liquid metal embrittlement cracks according to [1]. [3] The latent time t in the formula (1) c is calculated based on the formulas (2) to (4). The method for predicting liquid metal embrittlement cracks according to [1] or [2]. [4] The latent time t in the formula (1) c is expressed in the form of the formula (5), and while maintaining the temperature T i at the temperature T <j>< / j> within the temperature range where liquid metal embrittlement cracks can occur, the stress σ i is changed to various stresses σ <m>< / m> , and a tensile test of the plated steel sheet is performed. Thus, for each stress σ <m>< / m> , the latent time t c <m,j> until the occurrence of liquid metal embrittlement cracks is measured, and from the obtained point group (σ <m>< / m> , T <j>< / j> , t c <m,j> ), φ(T i ) and σ th (T i ) in the formula (5) are regression approximated to determine the formula (5), and the latent time t in the formula (1) cThe liquid metal embrittlement crack prediction method according to [1] or [2], which is calculated based on the determined formula (5). [5] The liquid metal embrittlement crack prediction method according to any one of [1] to [4], wherein the plated steel sheet is an electrogalvanized steel sheet, a hot-dip galvanized steel sheet, or an alloyed hot-dip galvanized steel sheet. [6] The liquid metal embrittlement crack prediction method according to any one of [1] to [5], wherein the welding process is a resistance spot welding process. [7] A liquid metal embrittlement crack prediction program for causing a computer to execute the numerical simulation step, the latent time consumption rate calculation step, and the determination step included in the liquid metal embrittlement crack prediction method according to any one of [1] to [6].

Advantages of the Invention

[0020] According to the present invention, before actually performing the welding process of the plated steel sheet, it is possible to accurately predict the occurrence of liquid metal embrittlement cracks on the surface of the plated steel sheet. Specifically, it is possible to accurately predict the presence or absence of the occurrence of liquid metal embrittlement cracks. Further, it is possible to accurately predict the presence or absence of the occurrence of liquid metal embrittlement cracks for each position on the surface of the plated steel sheet, that is, it is possible to accurately predict the occurrence position (position on the surface of the plated steel sheet) of the liquid metal embrittlement cracks. Furthermore, according to a preferred method of the present invention, it is also possible to accurately predict the occurrence time of the liquid metal embrittlement cracks.

Brief Description of the Drawings

[0021]

Figure 1

Figure 2

Figure 3

Figure 4

[0022] Hereinafter, a liquid metal embrittlement cracking prediction method according to one embodiment of the present invention will be described using an example in which the plated steel sheet is a galvanized steel sheet such as an electro-galvanized steel sheet, a hot-dip galvanized steel sheet, or an alloyed hot-dip galvanized steel sheet, and the welding process is a resistance spot welding process.

[0023] <Outline of liquid metal embrittlement cracking prediction method> First, an overview of the liquid metal embrittlement cracking prediction method according to the present embodiment will be described, including how the liquid metal embrittlement cracking prediction method according to the present embodiment was conceived. There are various theories proposed for the mechanism of liquid metal embrittlement cracking (LME cracking) that occurs during welding processes such as resistance spot welding. One of the leading theories is that in the case of galvanized steel sheets, a wedge-shaped embrittlement region is formed due to stress-induced grain boundary diffusion of zinc (Zn), a surface embrittlement element. Fig. 1 is a schematic diagram showing the vicinity of the surface of a plated steel sheet to explain the above-mentioned concept. As shown in Fig. 1, a molten coating 2 contacts a surface 11 (surface of a base steel sheet 1) of a plated steel sheet 100 at a temperature T, and a tensile stress σ is applied perpendicularly to a grain boundary 3 having a width δ located directly below the molten coating 2. GB When the metal atoms (atomic volume = Ω) of the molten plating 2 are subjected to a tensile stress σ GB The driving force is the diffusion coefficient D along the grain boundary 3. GB The brittleness penetrates into the base steel sheet 1 at a temperature of 100° C., forming a wedge-shaped embrittled region 4. This wedge-shaped embrittled region 4 develops over time, and the width w 0 There is a critical dimension w c 0 When this is reached, LME cracking occurs. According to Non-Patent Document 4, when a stress σ perpendicular to the grain boundary 3 acts in the vicinity of the grain boundary 3, σ causes dislocations required for the movement of dislocations to be distributed such that the dislocations induce LME cracks in the grain boundary 3, and the stress σ th required for depositing dislocations on the grain boundary 3, and the stress σ p can be expressed as the sum of them, and the relationship of the following formula (6) holds. And σ that becomes the driving force for forming the wedge-shaped embrittlement region 4 described above GB is considered to be caused by the stress σ p expressed by formula (6). σ p = σ - σ th ···(6)

[0024] The elapsed time until reaching the above critical dimension is referred to as the incubation time until the occurrence of LME cracks, and in this specification, it is represented by t c This existence of the incubation time has been clarified by past experimental studies such as those shown in Non-Patent Document 3. As described above, the occurrence of LME cracks depends on the microscopic stress σ GB acting on the grain boundary and the existence of the molten plating, but the stress σ GB which is difficult to directly evaluate, is associated with the macroscopic stress σ acting on average in the vicinity of the surface of the plated steel sheet including the grain boundary, and the existence of the molten plating is associated with the temperature T in the vicinity of the surface of the plated steel sheet. Then, the incubation time t c can be expressed by the following formula (7) as a function of the stress σ and the temperature T. t c = t c (σ, T) ···(7)

[0025] Now, in a state of a constant temperature T where there is sufficient molten plating, if the plated steel sheet is held at a constant stress σ for a time t, from formula (7), the condition for the occurrence of LME cracks is the condition where the incubation time is completely consumed, that is, the condition where the incubation time consumption rate ρ obtained by dividing the time t by the incubation time t c is 1 or more, and is given by the following formula (8). ρ = t / t c(σ,T) ≥ 1 ···(8)

[0026] However, in the actual welding process, since the temperature T and stress σ near the surface of the plated steel sheet change moment by moment from the start to the end of welding, it is difficult to directly determine the occurrence of LME cracks according to Equation (8). Therefore, in the method for predicting liquid metal embrittlement cracks according to the present embodiment, it is considered to discretize the history of the stress σ and the history of the temperature T near the surface of the plated steel sheet in the welding process with respect to time t. FIG. 2 is a diagram for explaining the concept of discretization applied in the method for predicting liquid metal embrittlement cracks according to the present embodiment. FIG. 2(a) shows the concept of discretizing the history of the stress σ, and FIG. 2(b) shows the concept of discretizing the history of the temperature T. The curves shown by the thick solid lines in FIG. 2 are the histories of the stress σ and the temperature T. As shown in FIG. 2, in the method for predicting liquid metal embrittlement cracks according to the present embodiment, the time t from the start of welding (t = 0) to the end of welding is divided by a sufficiently large integer n (not necessarily equally divided). And at the i-th time t i from the i + 1-th time t i+1 (where i is an integer satisfying 1 ≤ i ≤ n) to the minute time Δt i (= t i+1 − t i ), it is approximated that the stress is a constant value of σ i and the temperature is a constant value of T i . The broken line shown by the thick dashed line in FIG. 2 is the approximation line. In this case, the condition for the occurrence of LME cracks, based on the same concept as Equation (8), can be given as the condition that the integrated value of the consumption rate Δt i / t c (σ i , T i ) of the latency time t i in each minute time Δt c (σ i , T i ), that is, the latency time consumption rate ρ represented by the product is 1 or more. That is, when the latency time consumption rate ρ represented by Equation (1) is 1 or more, it can be determined that LME cracks occur on the surface of the plated steel sheet. [Number]

[0027] Also, considering an integer N satisfying 1 ≦ N ≦ n, the latency consumption rate ρ represented by the following formula (1)' N if the smallest N for which ρ becomes 1 or more is considered, the (N + 1)-th time t N+1 can be regarded as the occurrence time of LME cracking (the elapsed time from the start of welding until the occurrence of LME cracking starts).

Equation

[0028] For example, referring to Non-Patent Document 1 and Non-Patent Document 4, the latency time t in formula (1) c can be expressed by the following formula (2).

Equation

Equation

[0029] The outline of the liquid metal embrittlement crack prediction method according to this embodiment is as described above. Hereinafter, the specific content of the liquid metal embrittlement crack prediction method according to this embodiment will be described.

[0030] <Specific Content of the Liquid Metal Embrittlement Crack Prediction Method> Figure 3 is a flowchart showing the schematic procedure of the liquid metal embrittlement crack prediction method according to this embodiment. As shown in Figure 3, the liquid metal embrittlement crack prediction method according to this embodiment includes a numerical simulation step ST1, a latent time consumption rate calculation step ST2, and a determination step ST3. The liquid metal embrittlement crack prediction method according to this embodiment is executed by a liquid metal embrittlement crack program for causing a computer to execute each of the steps ST1 to ST3. Hereinafter, each of the steps ST1 to ST3 will be described in order.

[0031] [Numerical Simulation Step ST1] In the numerical simulation step ST1, the stress history and temperature history near the surface of the plated steel sheet in the welding process are estimated by a numerical simulation that simulates the actual welding process (resistance spot welding process) to be predicted for LME crack generation. In this numerical simulation, for example, using known finite element analysis, the mechanical response and temperature response in the welding process are sequentially calculated for each small time Δt i to obtain the stress σ i and temperature T i at each small time Δt ican be obtained. That is, in the numerical simulation step ST1, the approximate line shown by the thick dashed line in FIG. 2 described above is estimated as the stress history and temperature history near the surface of the plated steel sheet in the welding process. In addition, in the numerical simulation step ST1, the stress history and temperature history will be estimated for a plurality of points on the surface of the plated steel sheet. In other words, the distribution of the stress history and temperature history on the surface of the plated steel sheet will be estimated.

[0032] [Latency time consumption rate calculation step ST2] In the latency time consumption rate calculation step ST2, based on the stress history and temperature history estimated in the numerical simulation step ST1 (the stress σ i and temperature T i at each micro time Δt i ), the latency time consumption rate ρ represented by the above formula (1) is calculated. Here, since the stress-induced grain boundary diffusion involved in LME cracking continues when the molten plating exists on the surface of the plated steel sheet near the grain boundary, for each micro time Δt i in the formula (1), the integration of the consumption rate Δt c / t i (σ i , T i ) of the latency time t c (σ i , T i ) is preferably performed only when the following formula (9) is satisfied. Melting point of plating ≤ T i ≤ Boiling point of plating ···(9) The melting point and boiling point of the plating in the above formula (9) may be set according to the type of plating and the plating method (electro-galvanizing, hot-dip galvanizing, etc.). In addition, in the numerical simulation step ST1, since the distribution of the stress history and temperature history on the surface of the plated steel sheet is estimated, in the latency time consumption rate calculation step ST2 as well, the distribution of the latency time consumption rate ρ on the surface of the plated steel sheet will be calculated.

[0033] The latency time t ccan be calculated by, for example, either the first method or the second method described below.

[0034] (First method) The first method is a method of calculating the latency time t in Equation (1) c based on the aforementioned Equations (2) to (4). The right side of Equation (2) is represented by the product of a first term that is a constant term, a second term that is a temperature-dependent term, and a third term that is a stress-dependent term. The value of the first term on the right side of Equation (2), which is (w c 0 / γ) 3 can be determined using, for example, values proposed in prior studies such as Non-Patent Documents 1 and 2. Specifically, referring to Non-Patent Document 1, γ = 0.386, and referring to Non-Patent Document 2, it is conceivable that w c 0 = 2b (where b is the magnitude of the Burgers vector corresponding to the crystal structure of the plated steel sheet). Here, b can use values disclosed in textbooks of metallurgy and the like. The value of the second term on the right side of Equation (2), which is (E *3 / G), can be determined using the temperature history estimated in the numerical simulation step ST1 and known information for each of E, ν, D GB , Ω, k, and T i involved in Equations (3) and (4). The value of the third term on the right side of Equation (2), which is 1 / (σ i -σ th ) 3 can be determined using the stress history (the history of σ i ) estimated in the numerical simulation step ST1 and the value of σ th disclosed in Non-Patent Document 3 and the like. At this time, since the development of the wedge-shaped embrittlement region due to stress-induced grain boundary diffusion is limited to the case where a tensile stress is acting, the consumption rate Δt i of the latency time t c (σ i , T i ) in each micro-time Δt in Equation (1) i / t c (σi , T i The integration of ( ) is subject to the condition regarding stress shown in the following formula (10) in addition to the condition regarding temperature in formula (9). σ i -σ th > 0 ···(10)

[0035] (Second method) The second method is a method of expressing the latency time t in formula (1) in the form of the following formula (5) and calculating it based on the following formula (5). c

Number

[0036] Specifically, in the second method, while maintaining the temperature T i at the temperature T <j>< / j> (j = 1, 2, ···, J, where j is an integer satisfying 1 ≤ j ≤ J (J is an integer)), the stress σ i is changed to various stresses σ <m>< / m> (m = 1, 2, ···, M(j), where m is an integer satisfying 1 ≤ m ≤ M(j) (M(j) is an integer)), and a tensile test of the plated steel sheet is performed. Thus, the latency time t <m>< / m> until LME cracking occurs is measured for each stress σ c <m,j> . By performing regression approximation of φ(T <m>< / m> ) and σ <j>< / j> (T c <m,j> ) from the obtained point group (σ i , T th , t i ), formula (5) is determined (φ(T i ) and σ th (T​i ) to determine). Then, based on the determined formula (5), the latency time t in formula (1) c is calculated. Specifically, the stress history (σ i history) and temperature history (T i history) estimated in the numerical simulation step ST1 are applied to the determined formula (5) to calculate the latency time t c in formula (1). As more specific content of this second method, the following second - 1 method and second - 2 method can be considered.

[0037] <The second - 1 method> In the second - 1 method, the temperature T i is maintained at a constant temperature T <j>< / j> , and the tensile test of the plated steel sheet is performed under M(j) (M(j) is an integer of 2 or more) conditions where the stress σ i is selected as various values σ <m>< / m> (provided that any condition is a condition under which LME cracking occurs), and the latency time t c <m,j> until LME cracking occurs is measured. For all m, the latency time t <m>< / m> measured under the test conditions (σ <j>< / j> , T c <m,j> ), and the latency time t c (σ <m>< / m> , T <j>< / j> ) calculated by applying the same test conditions to formula (5) are approximated so that the sum of the squares of the errors is minimized, that is, approximate calculation is performed so that S(j) represented by the following formula (11) is minimized, thereby determining the function value φ(T <j>< / j> ) and σ <j>< / j> ) for the temperature condition T th (T <j>< / j> ).

Number

[0038] For all temperature conditions T <j>< / j> (1 ≤ j ≤ J) of all tensile tests, φ(T <j>< / j> ) and σth (T <j>< / j> ) is repeatedly determined, and using these results, φ(T i ) and σ th (T i ) are respectively regression approximated by J - 1 degree polynomials of temperature T i to determine φ(T i ) and σ i ) at any temperature T th (T i ) as determined by the following formulas (12) and (13) respectively.

Equation

[0039] <Second - 2nd Method> As a result of intensive studies by the inventors from a thermodynamic consideration, it was found that φ(T i ) and σ th (T i ) in formula (5) can be approximated by potential - type formulas shown in the following formulas (14) and (15) respectively using unknown coefficients A, B, C, and D. The second - 2nd method is a method of determining φ(T i ) and σ th (T i ) in formula (5) using the following formulas (14) and (15).

Equation

[0040] Note that the method for determining φ(T i ) and σ th (T i ) in the second method is not limited to the above-described first and second methods. Whichever method is used, the number of test conditions required to determine φ(T i ) and σ th (T i ) only needs to be set to a sufficient number to determine the unknowns.

[0041] In the latency time consumption rate calculation step ST2, calculate the latency time consumption rate ρ represented by equation (1) as described above. Note that in the latency time consumption rate calculation step ST2, it is also preferable to calculate the latency time consumption rate ρ N represented by the aforementioned equation (1)'.

[0042] [Judgment step ST3] In the determination step ST3, it is determined whether or not the latency consumption rate ρ calculated in the latency consumption rate calculation step ST2 is 1 or more (step ST31 shown in FIG. 3). When the latency consumption rate ρ is 1 or more (when "Yes" in step ST31 shown in FIG. 3), it is determined that LME cracks occur on the surface of the plated steel sheet (step ST32 shown in FIG. 3). On the other hand, when the latency consumption rate ρ is less than 1 (when "No" in step ST31 shown in FIG. 3), it is determined that LME cracks do not occur on the surface of the plated steel sheet (step ST33 shown in FIG. 3). In the latency consumption rate calculation step ST2, since the distribution of the latency consumption rate ρ on the surface of the plated steel sheet is calculated, the determination of the occurrence of LME cracks in the determination step ST3 is also made for each position on the surface of the plated steel sheet. In other words, in the determination step ST3, the presence or absence of LME cracks and the occurrence position of LME cracks (position on the surface of the plated steel sheet) when they occur are determined.

[0043] Note that when calculating the latency consumption rate ρ in the latency consumption rate calculation step ST2 N in the determination step ST3, the minimum N at which the latency consumption rate ρ N becomes 1 or more is specified, and it is preferable to determine that the (N + 1)-th time t N+1 is the occurrence time of LME cracks. Thereby, in the determination step ST3, the presence or absence of LME cracks, the occurrence position and the occurrence time of LME cracks are determined (predicted).

[0044] According to the method for predicting liquid metal embrittlement cracks according to the present embodiment described above, the stress history and the temperature history in the vicinity of the surface of the plated steel sheet are estimated by the numerical simulation step ST1, and the latency consumption rate ρ represented by the formula (1) is calculated by the latency consumption rate calculation step ST2. As described above, it can be said that LME cracks occur on the surface of the plated steel sheet when this latency consumption rate ρ is 1 or more. Therefore, in the determination step ST3, by determining that LME cracks occur on the surface of the plated steel sheet when the latency consumption rate ρ is 1 or more, the occurrence of LME cracks on the surface of the plated steel sheet can be accurately predicted.

[0045] FIG. 4 is a diagram showing an example of the result of predicting the occurrence of LME cracks on the surface of a plated steel sheet by the liquid metal embrittlement crack prediction method according to the present embodiment. The upper diagram of FIG. 4 is a cross-sectional photograph of a plated steel sheet on which LME cracks have occurred after performing a resistance spot welding process, and the lower diagram is a diagram showing the radial direction (the radial direction of the electrode used for resistance spot welding) distribution of the latent time consumption rate ρ calculated by the latent time consumption rate calculation step ST2 for the plated steel sheet corresponding to the upper diagram. The result shown in FIG. 4 is the result when two 980 MPa grade hot-dip galvanized steel sheets with a thickness of 1.4 mm, which were melted, rolled, and plated for laboratory tests, were stacked and subjected to a resistance spot welding process. In the latent time consumption rate calculation step ST2, Equation (5) was determined by the second method. In the ranges of A1 and A2 shown in the lower diagram of FIG. 4, the latent time consumption rate ρ is 1 or more. However, the starting points of the LME cracks shown in the upper diagram of FIG. 4 (the positions on the surface of the plated steel sheet indicated by "〇") are all approximately located within the ranges of A1 or A2. It can be seen that the occurrence of LME cracks on the surface of the plated steel sheet can be accurately predicted by the liquid metal embrittlement crack prediction method according to the present embodiment.

Description of Reference Numerals

[0046] ST1... Numerical simulation step ST2... Latent time consumption rate calculation step ST3... Judgment step

Claims

1. A method for predicting the occurrence of liquid metal embrittlement cracking on the surface of the plated steel sheet in the welding process of the plated steel sheet, comprising: A numerical simulation step of estimating the stress history and temperature history in the vicinity of the surface of the plated steel sheet in the welding process by numerical simulation simulating the welding process; A latent time consumption rate calculation step of calculating a latent time consumption rate ρ represented by the following formula (1) based on the estimated stress history and temperature history; A determination step of determining that liquid metal embrittlement cracking occurs on the surface of the plated steel sheet when the latent time consumption rate ρ is 1 or more; having A method for predicting liquid metal embrittlement cracking. 【Number 13】 In the above formula (1), Δt ｉ means the time from the start to the end of the welding process in the welding step, when divided by an integer n, the time from the i-th time t ｉ to the (i + 1)-th time t ｉ＋１ (t ｉ＋１ - t ｉ ). i is an integer satisfying 1 ≦ i ≦ n. σ ｉ means the stress near the surface of the plated steel sheet at the time Δt ｉ . T ｉ means the temperature near the surface of the plated steel sheet at the time Δt ｉ . t ｃ means the latency time until liquid metal embrittlement cracking occurs, and since it is expressed as a function of the stress σ ｉ and the temperature T ｉ , in the above formula (1), it is denoted as t ｃ (σ ｉ , T ｉ ).

2. In the latency consumption rate calculation step, the latency consumption rate ρ represented by the following formula (1)' Ｎ is calculated, In the determination step, the minimum N for which the latency consumption rate ρ Ｎ becomes 1 or more is specified, and the (N + 1)-th time t Ｎ＋１ is determined to be the occurrence time of liquid metal embrittlement cracking. The method for predicting liquid metal embrittlement cracking according to Claim 1. 【Number 14】 In the formula (1)’, N is an integer satisfying 1 ≦ N ≦ n.

3. The latency time t in the formula (1) ｃ is calculated based on the following formulas (2) to (4): The method for predicting liquid metal embrittlement cracking according to Claim 1 or 2. 【Number 15】 In the above formula (2), γ is a predetermined constant. w ｃ ０ means the width of the wedge-shaped embrittlement region on the surface of the plated steel sheet, which corresponds to the critical dimension for the occurrence of liquid metal embrittlement cracking. E ＊ and G are the values represented by formula (3) and formula (4), respectively. σ ｔｈ means the minimum stress near the surface of the plated steel sheet that causes liquid metal embrittlement cracking. In the formula (3), E means the Young's modulus of the plated steel sheet. ν means the Poisson's ratio of the plated steel sheet. π is the ratio of the circumference of a circle to its diameter. In the formula (4), δ and D ＧＢ , Ω, and k respectively represent the width of crystal grain boundaries existing near the surface of the plated steel sheet, the diffusion coefficient of metal atoms of the plating in the crystal grain boundaries, the atomic volume of the metal atoms of the plating, and the Boltzmann constant.

4. The latency time t in the formula (1) ｃ is represented in the form of the following formula (5), At the temperature T within the temperature range where liquid metal embrittlement cracking can occur ｉ while maintaining at the temperature T ＜ｊ＞ and varying the stress σ ｉ to various stresses σ ＜ｍ＞ and performing a tensile test on the plated steel sheet, for each stress σ ＜ｍ＞ the latency time t until the occurrence of liquid metal embrittlement cracking is measured, and from the obtained point group (σ ｃ ＜ｍ，ｊ＞ , T ＜ｍ＞ , t ＜ｊ＞ ｃ ＜ｍ，ｊ＞ ), by regression approximation of φ(T ｉ ) and σ ｔｈ (T ｉ ) of the following formula (5), the following formula (5) is determined,​ The latency time t in the formula (1) ｃ is calculated based on the following determined formula (5): The method for predicting liquid metal embrittlement cracking according to Claim 1 or 2. 【Number 16】 In the above formula (5), φ(T ｉ ) means a coefficient that is a function of the temperature T ｉ . σ ｔｈ means the minimum stress near the surface of the plated steel sheet that causes liquid metal embrittlement cracking. Since it is expressed as a function of the temperature T ｉ , in the above formula (5), it is denoted as σ ｔｈ (T ｉ ). The j is an integer that satisfies 1 ≤ j ≤ J (J is an integer). The m is an integer that satisfies 1 ≤ m ≤ M(j) (M(j) is an integer).

5. The plated steel sheet is an electro-galvanized steel sheet, a hot-dip galvanized steel sheet, or an alloyed hot-dip galvanized steel sheet. The method for predicting liquid metal embrittlement cracking according to Claim 1 or 2.

6. The welding process is a resistance spot welding process. The method for predicting liquid metal embrittlement cracking according to Claim 1 or 2.

7. A liquid metal embrittlement cracking prediction program for causing a computer to execute the numerical simulation step, the latent time consumption rate calculation step, and the determination step included in the liquid metal embrittlement cracking prediction method according to Claim 1 or 2.

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