Contact Thermal Conductance Estimation Method, Contact Electrical Resistance Estimation Method, and Resistance Spot Welding Simulation Method

Abstract

To provide a contact thermal conductance estimation method that, when at least one of objects in contact with each other is an Al plating stamp steel plate, can efficiently and accurately estimate contact thermal conductance hc(ε).SOLUTION: The present invention is a method for, when a first object Ω1 and a second object Ω2 at least one of which is an Al plating stamp steel plate are in contact with each other on a contact surface S shared by a surface S1 and a surface S2 at a contact pressure P larger than 0, estimating the contact thermal conductance hc(ε) on the contact surface S. An Al plating layer of the Al plating stamp steel plate is approximated by a two-layer structure consisting of a first layer that is formed by diffusing Al in steel and distributed on the side of a base material of the Al plating stamp steel plate, and a second layer that is distributed on the side of the surface S1 or the side of the surface S2 as the remainder of the first layer.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to a contact thermal conductance estimation method for estimating the contact thermal conductance at the contact surface between a first object having a surface with minute irregularities and a second object having a surface with minute irregularities, a contact electrical resistance estimation method using the same, and a resistance spot welding simulation method for simulating the welding process of resistance spot welding using these. In particular, the present invention relates to a case where at least one of the first object and the second object is a hot stamping steel sheet having an Al plating layer on the surface side, and the Al plating layer is alloyed by heating before forming (stamping), and even when presenting a complex structure, a contact thermal conductance estimation method capable of efficiently and accurately estimating the contact thermal conductance, a contact electrical resistance estimation method using the same, and a resistance spot welding simulation method using these.

Background Art

[0002] Hot stamping steel sheets (sometimes referred to as quenched steel sheets) may have an Al plating layer (for example, a plating layer having a composition of Al-10%Si) on the surface side of the steel sheet before quenching for the purpose of preventing surface oxidation and improving corrosion resistance. However, when the steel sheet with this Al plating layer is heated to the austenitizing temperature range and held at a high temperature before forming, the alloying of the Al plating layer progresses, and it is known that the Al plating layer after quenching exhibits a complex multilayer structure (typically a 5-layer structure) with different chemical compositions, thermal properties, electrical properties, and mechanical properties, etc. (see, for example, Non-Patent Document 11). Therefore, in order to efficiently and accurately estimate the contact thermal conductance and contact electrical resistance at the contact surface shared by the surface of the first object and the surface of the second object when at least one of the first object and the second object is a hot stamping steel sheet having an Al plating layer on the surface side (hereinafter, this is appropriately referred to as an "Al-plated hot stamping steel sheet"), it is important to simply and appropriately model the Al plating layer after quenching.

[0003] However, a modeling method for the Al plating layer has not been proposed to efficiently and accurately estimate the contact thermal conductance and contact electrical resistance at the contact surface between the first object and the second object when at least one of the first object and the second object is an Al-plated hot stamping steel sheet. Therefore, there is a problem that the contact thermal conductance and contact electrical resistance at the contact surface between the first object and the second object cannot be efficiently and accurately estimated when at least one of the first object and the second object is an Al-plated hot stamping steel sheet. In particular, when numerically simulating the welding process of resistance spot welding in the case where the Al-plated hot stamping steel sheet is included in the workpiece to be welded, the estimation accuracy of the contact thermal conductance and contact electrical resistance at the contact surface between the Al-plated hot stamping steel sheet and other workpieces to be welded or electrodes in contact with this Al-plated hot stamping steel sheet greatly affects the accuracy of the simulation results. Therefore, it is extremely important to efficiently and accurately estimate the contact thermal conductance and contact electrical resistance.

Prior Art Documents

Non-Patent Documents

[0004]

Non-Patent Document 1

Non-Patent Document 2

Non-Patent Document 3

Non-Patent Document 9

Non-Patent Document 10

Non-Patent Document 11

Non-Patent Document 12

Summary of the Invention

Problems to be Solved by the Invention

[0005] The present invention has been made to solve the problems of the prior art as described above. Among the first object and the second object, at least one of them is a hot stamping steel sheet having an Al plating layer on the surface side. When the steel sheet having the Al plating layer is heated to the austenitizing temperature range and held at a high temperature before forming, alloying of the Al plating layer proceeds, and even when a complex multilayer structure (typically a five-layer structure) is exhibited, it is an object to provide a contact thermal conductance estimation method capable of efficiently and accurately estimating the contact thermal conductance, a contact electrical resistance estimation method using the same, and a resistance spot welding simulation method using these.

Means for Solving the Problems

[0006] To solve the above problems, the present inventor has conducted intensive studies. Generally, a hot stamping steel sheet having an Al plating layer on the surface side is heated in a heating furnace before forming. As a result, as described above, alloying of the Al plating layer proceeds, and it is known that the Al plating layer after hot stamping typically exhibits a five-layer structure. When this hot stamping steel sheet is subjected to resistance spot welding, among the five Al plating layers, the Al plating layers (diffusion layers) corresponding to the fourth and fifth layers from the surface side are hard and have a large electrical resistance, and thus are considered to have a great influence on the spot weldability. Therefore, the present inventor considered approximating a typically five-layer Al plating layer with a two-layer structure composed of a first layer (specifically, the fourth and fifth Al plating layers (diffusion layers) from the surface side) formed by diffusion of Al into steel and distributed on the base material side of the hot-stamped steel sheet, and a second layer (specifically, the first to third Al plating layers from the surface side) distributed on the surface side as the remainder of the first layer. By using the analysis model of this two-layer structure and giving physical property values such as hardness and thermal conductivity to each layer for simulation, since the actually typical five-layer Al plating layer is not directly modeled, the contact thermal conductance and contact electrical resistance can be accurately estimated with a small computational load. Consequently, by using these contact thermal conductance and contact electrical resistance, it has been found that the numerical simulation of the welding process of resistance spot welding when an Al-plated hot-stamped steel sheet is included in the material to be welded can be performed efficiently and accurately. Note that the above diffusion layer means an alloying layer mainly composed of αFe, Al, and FeAl, and continuously distributed with an Al concentration of generally 0% to 50% (weight% concentration) from the base material side to the surface side of the hot-stamped steel sheet. Also, depending on the heating conditions of the hot-stamped steel sheet, the Al plating layer may exhibit a multi-layer structure other than five layers. Even in this case, it has been found that if the multi-layer Al plating layer is approximated with a two-layer structure of the above diffusion layer and other layers, the contact thermal conductance and contact electrical resistance can be accurately estimated.

[0007] The present invention has been completed based on the above findings of the present inventor. That is, to solve the above problems, the present invention provides a first object Ω1 having a surface S1 with minute irregularities and a second object Ω2 having a surface S2 with minute irregularities. When the surfaces S1 and S2 are in contact with each other at a contact pressure P greater than 0 at a contact surface S shared by the surfaces S1 and S2, and contact heat transfer occurs between the first object Ω1 and the second object Ω2 through the contact surface S, the contact thermal conductance h at the contact surface S cA method for estimating contact thermal conductance that estimates (ε), wherein at least one of the first object Ω1 and the second object Ω2 is a hot stamping steel sheet having an Al plating layer on the surface S1 side or the surface S2 side, and the Al plating layer is formed by diffusion of Al into the steel, and is approximated by a two-layer structure including a first layer distributed on the base material side of the hot stamping steel sheet and a second layer distributed on the surface S1 side or the surface S2 side as the remainder of the first layer. Provided is a method for estimating contact thermal conductance, characterized by the above.

[0008] In the present invention, the "Al plating layer" is a concept including not only a plating layer having a composition of Ai-10%Si but also a plating layer to which elements other than Al and Si are added for improving the characteristics of the plating layer. Also, in the present invention, the phrase "at least one of the first object Ω1 and the second object Ω2 is a hot stamping steel sheet having an Al plating layer on the surface S1 side or the surface S2 side" is a concept including the following aspects (1) to (3). (1) A mode in which only the first object Ω1 is an Al-plated hot stamping steel sheet and an Al plating layer is provided on the surface S1 side that contacts the second object Ω2 (including the case where an Al plating layer is provided not only on the surface S1 side but also on the surface side opposite to the surface S1). (2) A mode in which only the second object Ω2 is an Al-plated hot stamping steel sheet and an Al plating layer is provided on the surface S2 side that contacts the first object Ω1 (including the case where an Al plating layer is provided not only on the surface S2 side but also on the surface side opposite to the surface S2). (3) A mode in which both the first object Ω1 and the second object Ω2 are Al-plated hot stamping steel sheets, an Al plating layer is provided on the surface S1 side of the first object Ω1 (including the case where an Al plating layer is provided not only on the surface S1 side but also on the surface side opposite to the surface S1 of the first object Ω1), and an Al plating layer is provided on the surface S2 side of the second object Ω2 (including the case where an Al plating layer is provided not only on the surface S2 side but also on the surface side opposite to the surface S2 of the second object Ω2). According to the present invention, as the inventor has found, by approximating the Al plating layer with a two-layer structure, when at least one of the first object Ω1 and the second object Ω2 is a hot stamping steel sheet with an Al plating layer applied to the surface S1 side or the surface S2 side, the contact thermal conductance h c (ε) at the contact surface S can be estimated efficiently and accurately.

[0009] Also, in order to solve the above problems, in the present invention, the first object Ω1 and the second object Ω2 are metals, and the contact thermal conductance h c (ε) at the contact surface S estimated by the contact thermal conductance estimation method and the following formula (22) are used to estimate the contact electrical resistance R c (ε) at the contact surface S. The present invention also provides a contact electrical resistance estimation method characterized by this. R c (ε) = LT / h c (ε) ···(22) In the above formula (22), L is the Lorentz number, and T is the absolute temperature of the contact surface S. According to the present invention, as the inventor has found, by approximating the Al plating layer with a two-layer structure, when at least one of the first object Ω1 and the second object Ω2, which are metals, is a hot stamping steel sheet with an Al plating layer applied to the surface S1 side or the surface S2 side, the contact electrical resistance R c (ε) at the contact surface S can be estimated efficiently and accurately.

[0010] In order to solve the above problems, the present invention provides a resistance spot welding simulation method for numerically simulating a welding process of resistance spot welding in which a laminate ML in which a plurality of metal plates M are laminated is sandwiched between a pair of electrodes E and energized through the electrodes E to join the laminate ML. Among the plurality of metal plates M, at least one metal plate M is a hot-stamped steel plate having an Al plating layer on at least one surface S1 side thereof, and a contact thermal conductance h c (ε) at a contact surface S shared by the surface S1 on the side where the Al plating layer of the hot-stamped steel plate is provided and the surface S2 of the metal plate M or the electrode E in contact with the hot-stamped steel plate is estimated by the contact thermal conductance estimation method, and the welding process of the resistance spot welding is numerically simulated using the estimated contact thermal conductance h c (ε). Also provided is a resistance spot welding simulation method characterized by the above.

[0011] In the present invention, when at least one of the plurality of metal plates M constituting the laminate ML, which is a workpiece for resistance spot welding, is an Al-plated hot-stamped steel plate, when the laminate ML is resistance spot welded, the surface S1 on the side where the Al plating layer of a certain Al-plated hot-stamped steel plate is provided and another metal plate M (an Al-plated hot-stamped steel plate in contact with the certain Al-plated hot-stamped steel plate, a metal plate having a plating layer other than the Al plating layer, or a metal plate without a plating layer) or the surface S2 of the electrode E (the electrode in contact with the certain Al-plated hot-stamped steel plate) in contact with it share the contact surface S and come into contact. Then, if the certain Al-plated hot-stamped steel plate is considered as the first object Ω1 and the other metal plate M or the electrode E is considered as the second object Ω2, the contact thermal conductance h c (ε) at the contact surface S of the first object Ω1 and the second object Ω2 can be estimated efficiently and accurately by the contact thermal conductance estimation method for approximating the Al plating layer in a two-layer structure. Therefore, this contact thermal conductance h cBy using (ε), it is possible to efficiently and accurately perform a numerical simulation of the welding process of resistance spot welding when an Al-plated hot-stamped steel sheet is included in a laminate ML as a material to be welded.

[0012] Furthermore, in order to solve the above problems, the present invention numerically simulates the welding process of resistance spot welding in which a laminate ML in which a plurality of metal plates M are laminated is sandwiched between a pair of electrodes E and energized through the electrodes E to join the laminate ML. A resistance spot welding simulation method, wherein at least one of the plurality of metal plates M is a hot-stamped steel sheet having an Al plating layer on at least one surface S1 side thereof, and the surface S1 of the hot-stamped steel sheet on the side where the Al plating layer is provided and the surface S2 of the metal plate M or the electrode E in contact with the hot-stamped steel sheet The contact electrical resistance R at the contact surface S shared by c (ε) is estimated by the contact electrical resistance estimation method, and the estimated contact electrical resistance R c Using (ε) to numerically simulate the welding process of the resistance spot welding, it is also provided as a resistance spot welding simulation method characterized by this.

[0013] In the present invention, among a plurality of metal plates M constituting a laminate ML which is a material to be resistance spot welded, when at least one metal plate M is an Al-plated hot stamping steel plate, when resistance spot welding the laminate ML, the surface S1 on the side where the Al-plating layer of a certain one Al-plated hot stamping steel plate is applied and another metal plate M (an Al-plated hot stamping steel plate in contact with the certain one Al-plated hot stamping steel plate, a metal plate with a plating layer other than the Al-plating layer applied, or a metal plate without a plating layer) or the surface S2 of the electrode E (the electrode in contact with the certain one Al-plated hot stamping steel plate) share a contact surface S and come into contact. And if the certain one Al-plated hot stamping steel plate is regarded as the aforementioned first object Ω1 and the other metal plate M or the electrode E is regarded as the aforementioned second object Ω2, by the contact electrical resistance estimation method that approximates the aforementioned Al-plating layer in a two-layer structure, the contact electrical resistance R c (ε) at the contact surface S of the first object Ω1 and the second object Ω2 can be estimated efficiently and accurately. Therefore, by using this contact electrical resistance R c (ε), it is possible to efficiently and accurately perform a numerical simulation of the welding process of resistance spot welding when an Al-plated hot stamping steel plate is included in the laminate ML as a material to be welded.

Advantages of the Invention

[0014] According to the present invention, the contact thermal conductance and the contact electrical resistance can be estimated efficiently and accurately. By using these contact thermal conductance and contact electrical resistance, it is possible to efficiently and accurately perform a numerical simulation of the welding process of resistance spot welding when an Al-plated hot stamping steel plate is included in the material to be welded.

Brief Description of the Drawings

[0015]

Figure 1

Figure 2

Figure 3

Figure 4

MODE FOR CARRYING OUT THE INVENTION

[0016] Hereinafter, a contact thermal conductance estimation method according to an embodiment of the present invention, a contact electrical resistance estimation method using the same, and a resistance spot welding simulation method using these will be described.

[0017] <Contact Thermal Conductance Estimation Method> FIG. 1 is a diagram schematically showing an object for estimating the contact thermal conductance by the contact thermal conductance estimation method according to the present embodiment. As shown in FIG. 1, the contact thermal conductance estimation method according to the present embodiment includes a first object Ω1 having a surface S1 with minute irregularities and a second object Ω2 having a surface S2 with minute irregularities. When the surfaces S1 and S2 are in contact with each other at a contact pressure P greater than 0 at the contact surface S shared by the surfaces S1 and S2, and contact heat transfer occurs between the first object Ω1 and the second object Ω2 through the contact surface S, the contact thermal conductance h c (ε) on the contact surface S is a method for estimating.

[0018] In the example shown in FIG. 1, both the first object Ω1 and the second object Ω2 are hot stamp steel sheets (Al-plated hot stamp steel sheets) having Al plating layers on the surface S1 side and the surface S2 side, respectively. As shown in Fig. 1, the Al plating layer applied to the first object Ω1 is actually, on the surface S1 side of the first object Ω1 (the lower side in the example shown in Fig. 1), with respect to the base material of the first object Ω1 (the portion hatched with dots in Fig. 1), five Al plating layers C in order from the surface S1 side 11 ~C 15 It has become. Similarly, the Al plating layer applied to the second object Ω2 is actually, on the surface S2 side of the second object Ω2 (the upper side in the example shown in Fig. 1), with respect to the base material of the second object Ω2 (the portion hatched with dots in Fig. 1), five Al plating layers C in order from the surface S2 side 21 ~C 25 It has become.

[0019] However, in the contact thermal conductance estimation method according to this embodiment, the Al plating layers applied to the first object Ω1 and the second object Ω2 are formed by the diffusion of Al into steel, and the first layer distributed on the base material sides of the first object Ω1 and the second object Ω2, and the second layer distributed on the surface S1 and S2 sides of the first object Ω1 and the second object Ω2 as the remainder of the first layer. An analytical model approximated by a two-layer structure is used. Specifically, for the first object Ω1, the first to third Al plating layers C from the surface side 11 ~C 13 Are regarded as one first Al plating layer C11 (corresponding to the above-mentioned second layer), and the fourth and fifth Al plating layers (diffusion layers) C from the surface side 14 、C 15 (Corresponding to the above-mentioned first layer) are regarded as another first Al plating layer C12, and an analytical model with a two-layer structure is used. Similarly, for the second object Ω1, the first to third Al plating layers C from the surface side 21 ~C 23 Are regarded as one second Al plating layer C21 (corresponding to the above-mentioned second layer), and the fourth and fifth Al plating layers (diffusion layers) C from the surface side 24 、C 25 Are regarded as another second Al plating layer C22 (corresponding to the above-mentioned first layer), and an analytical model with a two-layer structure is used. Then, using the analytical model approximated by the two-layer structure of this Al plating layer, the contact thermal conductance h at the contact surface S between the first object Ω1 and the second object Ω2 c (ε) is estimated.

[0020] Next, a specific example (the first example and the second example) of the estimation method of the contact thermal conductance h c (ε) will be described.

[0021] [First Example of the Estimation Method] As shown in FIG. 1, in the analysis model, the film thickness, thermal conductivity, and hardness of the first Al plating layer C11 are respectively t1 (1) , k1 (1) and H1 (1) , and the film thickness, thermal conductivity, and hardness of the first Al plating layer C12 are respectively t2 (1) , k2 (1) and H2 (1) . Also, the film thickness, thermal conductivity, and hardness of the second Al plating layer C21 are respectively t1 (2) , k1 (2) and H1 (2) , and the film thickness, thermal conductivity, and hardness of the second Al plating layer C22 are respectively t2 (2) , k2 (2) and H2 (2) . Further, as shown in FIG. 1, the thermal conductivities of the base materials of the first object Ω1 and the second object Ω2 are respectively k (1) , k (2) , and the hardnesses of the base materials of the first object Ω1 and the second object Ω2 are respectively H (1) , H (2) . Furthermore, although not shown in the figure, the RMS roughnesses of the surfaces S1 and S2 are respectively σ (1) , σ (2) , the average inclinations of the convex portions of the surfaces S1 and S2 are respectively m (1) , m (2) , and the hardnesses of the surfaces S1 and S2 are respectively H c,film (1) , H c,film (2) . Note that the hardness in this specification means microhardness (Vickers hardness or micro-Vickers hardness).

[0022] The physical property values (film thickness, thermal conductivity, and hardness) of the first Al plating layers C11 and C12 and the second Al plating layers C21 and C22 given to the analysis model may be directly measured by known measuring means, or the Al concentration (for example, at.% concentration) may be measured, and the physical property values may be estimated from the known correlation between the Al concentration and the physical property values. In the former case, for example, the physical property values of each Al plating layer C 11 ~C 13 are measured, and the average value (in the case where the physical property values are thermal conductivity and hardness) or the sum (in the case where the physical property value is film thickness) may be used as the physical property value of the first Al plating layer C11. Also, for example, the physical property values of each Al plating layer C 14 , C 15 are measured, and the average value or the sum may be used as the physical property value of the first Al plating layer C12. Similarly, the physical property values of each Al plating layer C 21 ~C 23 are measured, and the average value or the sum may be used as the physical property value of the second Al plating layer C21. Also, the physical property values of each Al plating layer C 24 , C 25 are measured, and the average value or the sum may be used as the physical property value of the second Al plating layer C22. Also, in the latter case, for example, the distribution of the Al concentration of each Al plating layer C 11 ~C 13 is measured, and the average value is used as the Al concentration of the first Al plating layer C11, and the physical property value of the first Al plating layer C11 may be estimated from this Al concentration. Also, for example, the distribution of the Al concentration of each Al plating layer C 14 , C 15 is measured, and the average value is used as the Al concentration of the first Al plating layer C12, and the physical property value of the first Al plating layer C12 may be estimated from this Al concentration. Similarly, the distribution of the Al concentration of each Al plating layer C 21 ~C 23 is measured, and the average value is used as the Al concentration of the second Al plating layer C21, and the physical property value of the second Al plating layer C21 may be estimated from this Al concentration. Also, the distribution of the Al concentration of each Al plating layer C 24 , C 25 is measured, and the average value is used as the Al concentration of the second Al plating layer C22, and the physical property value of the second Al plating layer C22 may be estimated from this Al concentration.

[0023] Thermal conductivities k1 of the first Al plating layers C11, C12 and the second Al plating layers C21, C22 (1) , k2 (1) , k1 (2) and k2 (2) can be obtained by measuring the thermal conductivity of each Al plating layer C 11 ~C 15 , C 21 ~C 25 using known measuring means for measuring the thermal conductivity. Alternatively, the thermal conductivities k1 of the first Al plating layers C11, C12 and the second Al plating layers C21, C22 (1) , k2 (1) , k1 (2) and k2 (2) are analyzed by using an apparatus such as an analytical scanning electron microscope (SEM-EDS) to analyze the composition of each Al plating layer C 11 ~C 15 , C 21 ~C 25 , and can be estimated by using the Al concentration distribution of each Al plating layer C 11 ~C 15 , C 21 ~C 25 obtained by the analysis and, for example, the correlation relationship (correlation relationship between Al concentration and thermal conductivity) described in Non-Patent Document 8.

[0024] Hardnesses H1 of the first Al plating layers C11, C12 and the second Al plating layers C21, C22 (1) , H2 (1) , H1 (2) and H2 (2) can be obtained by measuring the hardness of each Al plating layer C 11 ~C 15 , C 21 ~C 25 using known measuring means for measuring the hardness. Alternatively, the hardnesses H1 of the first Al plating layers C11, C12 and the second Al plating layers C21, C22 (1) , H2 (1) , H1 (2) and H2 (2) are each Al plating layer C 11 ~C 15 , C 21 ~C25 The composition of each Al plating layer C obtained by the analysis was analyzed using an analytical scanning electron microscope (SEM-EDS) and other devices. 11 ~C 15 , C 21 ~C 25 This can be estimated by using the distribution of Al concentration in the specimen and, for example, the correlation (correlation between Al concentration and hardness) described in Non-Patent Document 9.

[0025] Thickness t1 of the first Al plating layers C11, C12 and the second Al plating layers C21, C22 (1) , t2 (1) , t1 (2) and t2 (2) is measured by a known measuring means for measuring the thickness of each Al plating layer C. 11 ~C 15 , C 21 ~C 25 Alternatively, the thickness t1 of the first Al plating layers C11, C12 and the second Al plating layers C21, C22 can be obtained by measuring the thickness t1 of the first Al plating layers C11, C12 and the second Al plating layers C21, C22. (1) , t2 (1) , t1 (2) and t2 (2) can also be estimated by a diffusion analysis that simulates the thermal history of the hot stamping process. In carrying out this diffusion analysis, for example, the technology described in Non-Patent Document 10 can be referred to as the diffusion coefficient.

[0026] In the first example of the estimation method, the contact thermal conductance h is calculated using the following equations (1) to (17). c Estimate (ε).

number

[0027] As described above, the outline of the process of deriving the method for estimating the contact thermal conductance h c (ε) using equations (1) to (17) is as follows. The inventor first decided to represent the contact thermal conductance h c (ε) by equation (1) based on the concepts described in Non-Patent Documents 3 and 4. Specifically, the contact thermal conductance h cLet (ε) be the contact thermal conductance h when no plating layer is provided. c,bare (ε) (see Equation (3)), or the constriction parameter ψ when a plating layer is provided. film (i) (ε) and the constriction parameter ψ when no plating layer is provided. bare The constriction parameter correction coefficient C expressed as the ratio to (ε). L (i) It was decided to represent by Equation (1) using (ε) (see Equation (4)) and the like. Then, in order to solve the problem that the estimation accuracy of the equation representing the constriction parameter (the constriction parameter when no plating layer is provided) proposed in Non-Patent Document 1 deteriorates in the range where ε is large, the present inventor considered the constriction parameter ψ when no plating layer is provided. bare (ε) changes according to the change in ε (ε: 0 → 1), and the contact area ratio ε 2 When it is small (ε → 0), the constriction parameter ψ bare From the theoretical solution of (ε), the contact area ratio ε 2 When it is large (ε → 1), the constriction parameter ψ bare (ε) is considered to continuously transition to the theoretical solution of (ε), and a function β(ε) of ε representing the change is introduced. As shown in Equation (5), the constriction parameter ψ bare (ε) was conceived to be represented by the linear mixture of the above two theoretical solutions. Next, heat transfer finite element analysis of two contacting cylinders (flux tubes) with no plating layer, in which ε is varied variously in the range from 0 to 1, was performed. The constriction parameter ψ bare (ε) calculated from the analysis results and the constriction parameter ψ bare (ε) calculated from Equation (5) were made to approximately match, and β(ε) represented by Equation (7) was derived by least squares approximation. Also, by adding the ideas described in Non-Patent Documents 3 and 4 to the same concept as the constriction parameter ψ bare (ε) when no plating layer is provided, the constriction parameter ψ film (i) (ε) when a plating layer is provided was decided to be represented by Equation (6).

[0028] In addition, the inventor of the present invention has proposed the contact area ratio ε in Non-Patent Document 1 2 The formula representing is such that the volume change of the convex portion crushed (or smoothed) by the contact between the surface S1 and the surface S2 does not take into account the influence on the shape change of the non-contact surface (for example, the concave portion adjacent to the convex portion). In order to solve this problem, based on the concept described in Non-Patent Document 2, the contact area ratio ε 2 is represented by Equation (2) instead of the formula proposed in Non-Patent Document 1. The H shown in Equation (2) c,film is, as shown in Equation (18), the hardness H of the surface S1 of the first object Ω1 provided with the first Al plating layer c,film (1) and the hardness H of the surface S2 of the second object Ω2 provided with the second Al plating layer c,film (2) means the softer hardness among them.

[0029] According to the findings of the inventor of the present invention, the hardness H of the surface S1 c,film (1) and the hardness H of the surface S2 c,film (2) can be obtained, for example, as the solution of the system of simultaneous equations represented by the following Equations (19) to (21) with reference to the concepts described in Non-Patent Documents 5 and 6.

Equation

[0030] Hardness H of surface S1 c,film (1) and hardness H of surface S2 c,film (2) As a method for obtaining the above, as long as the method can consider the influence of the plating layer, it is not limited to the above example. For example, instead of the above formulas (19) and (21), it is also possible to obtain them using the estimation formulas described in Non-Patent Document 7.

[0031] The contact thermal conductance h c (ε) of the first example of the estimation method is derived so as to solve the problems of the estimation method described in Non-Patent Document 1 when plating layers are provided on the surface side of the first object Ω1 and the surface side of the second object Ω2. Therefore, even when the contact pressure P at the contact surface S is very large, such as in resistance spot welding, the contact thermal conductance h c (ε) can be accurately estimated.

[0032] [Second Example of Estimation Method] In the second example of the estimation method, the contact thermal conductance h c (ε) is estimated using the following formulas (1A) to (17A).

Equation

[0033] Since the formulas (5) and (6) used in the first example of the above-described estimation method include the sum with n = ∞, the estimation using these formulas requires a huge number of numerical operations including solving the zeros of the first-kind Bessel function of the first order, and the computational load is excessive. Therefore, as a result of intensive studies by the present inventor, when the film thicknesses and thermal conductivities of the first plating layer and the second plating layer are within a certain range, the constriction parameter correction coefficient C L (i) (ε) has characteristics in its distribution, and the constriction parameter correction coefficient C L (i) (ε) calculated by the above formulas (4) to (7) used in the first example of the estimation method is derived as an approximate formula that minimizes the error from the theoretical solution (the solution calculated by terminating the calculation at n (for example, n = 10000) where the sum converges within a certain range). By using this approximate formula (5A) in the second example of the estimation method, a huge number of numerical operations are unnecessary. Therefore, compared with the first example of the estimation method, the computational load is small, and the problems of the estimation method described in the above Non-Patent Document 1 can be solved. Even when the contact pressure P at the contact surface S is very large, the contact thermal conductance h c (ε) can be estimated accurately and simply. Regarding the second example of the estimation method as well, the hardness H of the surface S1 c,film (1) and the hardness H of the surface S2 c,film (2) can be obtained, for example, as the solution of the simultaneous equations represented by the above formulas (19) to (21). Also, instead of the above formulas (19) and (21), it is also possible to obtain them using the estimation formulas described in Non-Patent Document 7.

[0034] <Contact Electrical Resistance Estimation Method> The first object Ω1 and the second object Ω2 shown in FIG. 1 are both hot-stamping steel plates with an Al plating layer. Since they are metals, generally, the contact thermal conductance h c (ε) and the contact electrical resistance R c (ε) satisfy the Wiedemann-Franz law expressed by the following formula (22). R c (ε) = LT / h c (ε) ···(22) In the above formula (22), L is the Lorentz number, T is the absolute temperature of the contact surface S, and the average temperature of the absolute temperature of the surface S1 and the absolute temperature of the surface S2 can be used. Therefore, using the contact thermal conductance h c (ε) estimated by the first example or the second example of the contact thermal conductance estimation method described above and formula (22), it is also possible to estimate the contact electrical resistance R c (ε) on the contact surface S.

[0035] In the contact thermal conductance estimation method and the contact electrical resistance estimation method according to the present embodiment described above, the case where both the first object Ω1 and the second object Ω2 are Al-plated hot-stamping steel plates has been described as an example. However, the estimation method according to the present invention is not limited to this, and it is also applicable when at least one of the first object Ω1 and the second object Ω2 is an Al-plated hot-stamping steel plate. FIG. 2 is a diagram schematically showing an example of an object capable of estimating the contact thermal conductance h c (ε) or the contact electrical resistance R c (ε) by the estimation method (contact thermal conductance estimation method and contact electrical resistance estimation method) according to the present invention. FIG. 2(a) is a diagram showing the case where both the first object Ω1 and the second object Ω2 are Al-plated hot-stamping steel plates, and is a more schematic representation of FIG. 1. FIG. 2(b) shows that the first object Ω1 is an Al-plated stamp steel plate and the second object Ω2 is an object without a plating layer (contact electrical resistance R cThis is a diagram showing the case when estimating (ε) for a metal plate. Fig. 2(c) shows that the first object Ω1 is an Al-plated stamp steel plate, and the second object Ω2 is an object with one or two plating layers other than the Al plating layer (contact electrical resistance R c This is a diagram showing the case when estimating (ε) for a metal plate). The estimation method according to the present invention is applicable to any of the cases shown in Figs. 2(a) to 2(c).

[0036] In the case shown in Fig. 2(a), the contact thermal conductance h at the contact surface S c (ε) and the contact electrical resistance R c The method for estimating (ε) is as described above. In the case shown in Fig. 2(b), in the first example of the above-described estimation method, C in Equation (1) L (2) is set to 1, and H in Equation (18) c,film (2) = H (2) is set, and the contact thermal conductance h at the contact surface S c (ε) is estimated, or in the second example of the above-described estimation method, C in Equation (1A) L (2) is set to 1, and H in Equation (9A) c,film (2) = H (2) is set, and the contact thermal conductance h at the contact surface S c (ε) may be estimated. Then, using this contact thermal conductance h c (ε) and Equation (22), the contact electrical resistance R at the contact surface S c (ε) may be estimated. In the case shown in Fig. 2(c), when there are two plating layers applied to the second object Ω2, in the first example of the above-described estimation method, m = 2 in Equation (19) for obtaining the hardness H of the surface S2, and k1 in Equations (11) to (14) c,film (2) , k2 (2) , t1 (2) , t2 (2) and t2 (2) and H1 in Equation (19) (2) and H2 (2)Then, by setting the thermal conductivity, film thickness, and hardness of each of the two plating layers applied to the second object Ω2, the contact thermal conductance h c (ε) at the contact surface S may be estimated. When there is one plating layer applied to the second object Ω2, in the first example of the aforementioned estimation method, the hardness H c,film (2) of the surface S2 is set to m = 1 in Equation (19) when obtaining it, and k1 (2) , t1 (2) in Equations (11) to (14), and H1 (2) in Equation (19). Then, by setting the thermal conductivity, film thickness, and hardness of the one plating layer applied to the second object Ω2, and setting k2 (2) = k (2) , t2 (2) = 0, the contact thermal conductance h c (ε) at the contact surface S may be estimated. Alternatively, in the case shown in Fig. 2(c), when there are two plating layers applied to the second object Ω2, in the second example of the aforementioned estimation method, the hardness H c,film (2) of the surface S2 is set to m = 2 in Equation (19) when obtaining it, and k1 (2) , k2 (2) , t1 (2) and t2 (2) in Equations (11A) to (14A), and H1 (2) and H2 (2) in Equation (19). Then, by setting the thermal conductivity, film thickness, and hardness of each of the two plating layers applied to the second object Ω2, the contact thermal conductance h c (ε) at the contact surface S may be estimated. When there is one plating layer applied to the second object Ω2, in the second example of the aforementioned estimation method, the hardness H c,film (2) of the surface S2 is set to m = 1 in Equation (19) when obtaining it, and k1 (2) , t1 (2) in Equations (11A) to (14A), and H1 (2) in Equation (19). Then, by setting the thermal conductivity, film thickness, and hardness of the one plating layer applied to the second object Ω2, and setting k2 (2) = k (2) , t2 (2)Set it to 0, and estimate the contact thermal conductance h c (ε) on the contact surface S. Then, using this contact thermal conductance h c (ε) and Equation (22), estimate the contact electrical resistance R c (ε) on the contact surface S.

[0037] <Resistance Spot Welding Simulation Method> FIG. 3 schematically shows an object for numerically simulating the welding process of resistance spot welding by the resistance spot welding simulation method according to an embodiment of the present invention. FIG. 3(a) shows an overall view of the object to be numerically simulated, and FIGS. 3(b) to 3(e) show specific examples of an object for estimating the contact thermal conductance h c (ε) or the contact electrical resistance R c (ε). As shown in FIG. 3(a), the resistance spot welding simulation method according to the present embodiment is a method for numerically simulating the welding process of resistance spot welding in which a laminate ML in which a plurality of metal plates M are laminated is sandwiched between a pair of electrodes E and energized through the electrodes E to join the laminate ML.

[0038] In the resistance spot welding simulation method according to the present embodiment, among the plurality of metal plates M constituting the laminate ML, at least one metal plate M is a hot-stamped steel plate (Al-plated hot-stamped steel plate) having an Al plating layer on at least one surface S1 side thereof. Then, in the resistance spot welding simulation method according to the present embodiment, the contact thermal conductance h c (ε) on the contact surface S shared by the surface S1 on the Al plating layer side of a certain Al-plated hot-stamped steel plate (considered as the aforementioned first object Ω1) and the surface S2 of the metal plate M or the electrode E (considered as the aforementioned second object Ω2) in contact with the Al-plated hot-stamped steel plate is estimated by the aforementioned contact thermal conductance estimation method, or the contact electrical resistance R c (ε) on the contact surface S is estimated by the aforementioned contact electrical resistance estimation method, and the estimated contact thermal conductance hc (ε) or contact electrical resistance R c Using (ε), numerically simulate the welding process of resistance spot welding.

[0039] Specifically, for example, the examples shown in FIGS. 3(b) to 3(e) can be considered. The left diagrams in FIGS. 3(b) to 3(e) show the case where an Al plating layer is provided only on one surface S1 side of the Al-plated hot-stamped steel sheet as the first object Ω1, and the right diagrams in FIGS. 3(b) to 3(e) show the case where Al plating layers are provided on both the one surface S1 side and the opposite surface side of the Al-plated hot-stamped steel sheet as the first object Ω1. The example shown in FIG. 3(b) shows the case where the second object Ω2 in contact with the first object Ω1, which is an Al-plated hot-stamped steel sheet, is also an Al-plated hot-stamped steel sheet. By the estimation method described above with reference to FIGS. 1 and 2(a), the contact thermal conductance h c (ε) and contact electrical resistance R c (ε) can be estimated. The example shown in FIG. 3(c) shows the case where the second object Ω2 in contact with the first object Ω1, which is an Al-plated hot-stamped steel sheet, is a metal plate M without a plating layer. By the estimation method described above with reference to FIG. 2(b), the contact thermal conductance h c (ε) and contact electrical resistance R c (ε) can be estimated. The example shown in FIG. 3(d) shows the case where the second object Ω2 in contact with the first object Ω1, which is an Al-plated hot-stamped steel sheet, is a metal plate M with one or two plating layers other than the Al plating layer. By the estimation method described above with reference to FIG. 2(c), the contact thermal conductance h c (ε) and contact electrical resistance R c (ε) can be estimated. The example shown in Fig. 3(e) shows a case where the second object Ω2 in contact with the first object Ω1, which is an Al-plated hot-stamping steel sheet, is the electrode E. Similar to the case where the second object Ω2 shown in Fig. 3(c) is the metal plate M without a plating layer, the contact thermal conductance h c (ε) and the contact electrical resistance R c (ε) can be estimated.

[0040] In addition, when both of the two metal plates M that constitute the laminate ML and are in contact with each other are not Al-plated hot-stamping steel sheets, the contact thermal conductance h c (ε) and the contact electrical resistance R c (ε) can be estimated as follows. That is, considering one metal plate M as the first object Ω1, on the condition that no plating layer is provided on the surface S1 side of the first object Ω1, or one or two plating layers other than the Al plating layer are provided on the surface S1 side of the first object Ω1, and considering the other metal plate M as the second object Ω2, on the condition that no plating layer is provided on the surface S2 side of the second object Ω2, or one or two plating layers other than the Al plating layer are provided on the surface S2 side of the second object Ω2, it is possible to estimate using the same concept as the above-described estimation method.

[0041] In the resistance spot welding simulation method according to the present embodiment, during the welding process of resistance spot welding the laminate ML, specifically, the coupled behavior of heat - electricity - structure is simulated using general-purpose software capable of performing coupled analysis. The contact thermal conductance h c (ε) or the contact electrical resistance R c (ε) is defined to enable the simulation. For details of the coupled analysis, for example, a known method as described in Non-Patent Document 12 can be used, so detailed description is omitted here.

[0042] FIG. 4 shows an example of the result of comparing the range of appropriate welding current calculated for the resistance spot welding of two Al-plated hot-stamped steel sheets with a plate thickness t of 1.6 mm and a plating adhesion amount of 160 g / m 2 (80 g / m on each of the both surfaces S1 and S2 sides 2 ) with the range of appropriate welding current obtained by actually conducting a welding experiment. The horizontal axis of FIG. 4 represents the heating conditions before forming of the Al-plated hot-stamped steel sheet in the heating furnace. Condition 1 means the case where the steel sheet is held in a heating furnace at a furnace temperature of 950° C. for 1 minute, and Condition 2 means the case where the steel sheet is held in a heating furnace at a furnace temperature of 950° C. for 3.5 minutes. The vertical axis of FIG. 4 represents the welding current. When the thickness of the Al-plated hot-stamped steel sheet is t, the welding current at which the nugget diameter of the resistance spot weld portion becomes 4t 1 / 2 is shown as the lower limit value of the range of appropriate welding current, and the welding current at which spatter starts to occur is shown as the upper limit value of the range of appropriate welding current. Specifically, the vertical axis of FIG. 4 plots the values normalized based on the lower limit value of the range of appropriate welding current of the experimental results under Condition 1. As can be seen from FIG. 4, the range of appropriate welding current calculated using the resistance spot welding simulation method according to the present embodiment generally coincides with the range of appropriate welding current obtained by actually conducting a welding experiment. It can be said that by using the resistance spot welding simulation method according to the present embodiment, the welding process during resistance spot welding can be simulated.

Explanation of Signs

[0043] Ω1 ··· First object Ω2 ··· Second object S ··· Contact surface S1, S2 ··· Surfaces P ··· Contact pressure h c (ε) ··· Contact thermal conductance ε 2 ··· Contact area ratio

Claims

1. A first object Ω1 having a surface S1 with minute irregularities and a second object Ω2 having a surface S2 with minute irregularities are in contact with each other at a contact pressure P greater than 0 on a contact surface S shared by the surface S1 and the surface S2, and when contact heat transfer occurs between the first object Ω1 and the second object Ω2 through the contact surface S, the contact thermal conductance h ｃ (ε) on the contact surface S is estimated, and a method for estimating contact thermal conductance, comprising: At least one of the first object Ω1 and the second object Ω2 is a hot stamping steel sheet having an Al plating layer on the surface S1 side or the surface S2 side, The Al plating layer is approximated by a two-layer structure composed of a first layer formed by diffusion of Al into the steel and distributed on the base material side of the hot stamping steel sheet, and a second layer distributed on the surface S1 side or the surface S2 side as the remainder of the first layer, The method for estimating contact thermal conductance is characterized in that.

2. The first object Ω1 and the second object Ω2 are metals, The contact thermal conductance h ｃ (ε) on the contact surface S estimated by the method for estimating contact thermal conductance according to Claim 1 and the following formula (22) are used to estimate the contact electrical resistance R ｃ (ε) on the contact surface S, The method for estimating contact electrical resistance is characterized in that. R ｃ (ε) = LT / h ｃ (ε)... (22) In the above formula (22), L is the Lorentz number and T is the absolute temperature of the contact surface S.

3. A method for numerically simulating the welding process of resistance spot welding for joining a laminate ML in which a plurality of metal plates M are laminated by sandwiching the laminate ML as a workpiece between a pair of electrodes E and energizing the laminate ML through the electrodes E, Of the plurality of metal plates M, at least one metal plate M is a hot stamping steel plate having an Al plating layer on at least one of its surfaces S1, The contact thermal conductance h at the contact surface S shared by the surface S1 of the hot stamping steel plate on which the Al plating layer is provided and the surface S2 of the metal plate M or the electrode E in contact with the hot stamping steel plate ｃ Estimate (ε) by the contact thermal conductance estimation method according to claim 1, Using the estimated contact thermal conductance h ｃ (ε) to numerically simulate the welding process of the resistance spot welding, A resistance spot welding simulation method characterized by the above.

4. A resistance spot welding simulation method for numerically simulating the welding process of resistance spot welding in which a laminate ML in which a plurality of metal plates M are laminated is sandwiched between a pair of electrodes E and energized through the electrodes E to join the laminate ML, Of the plurality of metal plates M, at least one metal plate M is a hot stamping steel plate having an Al plating layer on at least one of its surfaces S1, The contact electrical resistance R at the contact surface S shared by the surface S1 of the hot stamping steel plate on which the Al plating layer is provided and the surface S2 of the metal plate M or the electrode E in contact with the hot stamping steel plate ｃ Estimate (ε) by the contact electrical resistance estimation method according to claim 2, Using the estimated contact electrical resistance R ｃ (ε) to numerically simulate the welding process of the resistance spot welding, A resistance spot welding simulation method characterized by the above.

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