Method and program for analyzing leakage of molten material

Abstract

To provide a leakage analysis method or the like capable of efficiently analyzing leakage of a molten material from a filled-material filled with the molten material without using fluid analysis.SOLUTION: The present invention relates to a method for analyzing leakage of a molten material from a filled-material in which the molten material is filled, the method including: a structure analysis step ST1 for modeling the molten material with an incompressible solid material to perform structural analysis to thereby calculate the pressure of the molten material; a leakage volume calculation step ST7 for calculating a leakage volume of the molten material on the basis of a difference between the pressures of the molten material and the pressure of an outside of the filled-material; and a volumetric strain calculation step ST8 for expressing the leakage volume by the volumetric strain of the molten material; wherein the structural analysis step, the leakage volume calculation step, and the volumetric strain calculation step are repeatedly executed in this order for each predetermined time step.SELECTED DRAWING: Figure 1

Description

Technical Field

[0001] The present invention relates to a method and a program for analyzing the leakage of molten material from a filled material (e.g., a non-molten metal material surrounding the molten metal) filled with a molten material (e.g., molten metal generated by resistance spot welding a plurality of metal plates stacked in the plate thickness direction). In particular, the present invention relates to a leakage analysis method and a leakage analysis program capable of efficiently analyzing the leakage of molten material using a structural analysis based on solid mechanics without using a fluid analysis with a large computational load.

Background Art

[0002] Conventionally, resistance spot welding has been used as a method for joining a plurality of metal plates in various industrial members such as automobiles. Resistance spot welding is a method in which metal plates such as a plurality of steel plates stacked in the plate thickness direction are sandwiched between electrodes and energized while pressing the metal plates with the electrodes. As a result, a part of the contact interface of the plurality of energized metal plates melts and is joined. The melted portion cools and solidifies to become a welded portion (nugget).

[0003] Here, spatter (splash), which is the scattering of the molten material (molten metal) generated by resistance spot welding (scattering from the non-molten metal material surrounding the molten metal), deteriorates the working environment and causes a decrease in product quality due to the adhesion of the scattered molten metal to the surface of the industrial member, which is the product. Further, when the metal plate is a zinc-based galvanized steel plate, it has been reported that the volume reduction of the molten metal due to this spatter promotes cracks called LME (Liquid Metal Embrittlement) cracks caused by LME in the welded portion. Therefore, if the volume reduction of the molten metal (leakage volume of the molten metal) due to the scattering (leakage) of the molten metal can be efficiently numerically analyzed, it can be expected to be effectively used for the evaluation of LME cracks and the like.

[0004] In the above description, the case of resistance spot welding has been described as an example. However, it is not necessarily limited to this. If the leakage of the molten material from the filled material filled with the molten material inside can be efficiently analyzed, it can be expected to be effectively utilized in various applications. Although it is conceivable to use fluid analysis to analyze the leakage of the molten material, fluid analysis is not efficient because of its large computational load.

[0005] For example, Patent Document 1 proposes a method for predicting the generation of spatter in resistance spot welding by using coupled numerical analysis of an electric field, a temperature field, and a stress field. However, the method described in Patent Document 1 only predicts the generation of spatter and does not calculate the volume reduction of the molten metal (the leakage volume of the molten metal) after the generation of spatter.

[0006] In addition, Patent Document 2 proposes a filling analysis method for the molten material that sequentially calculates the process of filling the cavity with the molten material in consideration of the leakage of gas from the cavity. However, the method described in Patent Document 2 does not analyze the leakage of the molten material.

Prior Art Documents

Patent Documents

[0007]

Patent Document 1

Patent Document 2

Summary of the Invention

Problems to be Solved by the Invention

[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 leakage analysis method and a leakage analysis program that can efficiently analyze the leakage of the molten material from the filled material filled with the molten material inside without using fluid analysis. [Means for solving the problem]

[0009] To solve the aforementioned problems, the inventors conducted diligent studies and found that by modeling the molten material as an incompressible solid material and representing the leakage volume of the molten material as the volumetric strain of the molten material, it is possible to efficiently analyze the leakage of the molten material using structural analysis based on solid mechanics, without using fluid analysis.

[0010] This invention was completed based on the inventor's findings described above. In other words, to solve the above problems, the present invention provides a method for analyzing leakage of molten material from a filler material which is filled with molten material, comprising: a structural analysis step of calculating the pressure of the molten material by modeling the molten material with an incompressible solid material and performing a structural analysis; a leakage volume calculation step of calculating the leakage volume of the molten material based on the difference between the pressure of the molten material and the external pressure of the filler material; and a volumetric strain calculation step of representing the leakage volume as the volumetric strain of the molten material, wherein the structural analysis step, the leakage volume calculation step, and the volumetric strain calculation step are repeatedly executed in this order at predetermined time steps.

[0011] According to the present invention, in a structural analysis step that performs structural analysis based on solid mechanics, the molten material is modeled as an incompressible solid material, and in the volumetric strain calculation step, the leakage volume of the molten material calculated in the leakage volume calculation step is expressed as volumetric strain. Then, at predetermined time steps, the structural analysis step, the leakage volume calculation step, and the volumetric strain calculation step are repeatedly executed in this order (i.e., the structural analysis step is repeatedly executed using the volumetric strain of the molten material expressed in the volumetric strain calculation step). As the inventors have discovered, it is possible to efficiently analyze the leakage of the molten material without using fluid analysis, that is, to efficiently calculate the leakage volume (volume reduction of the molten material) from the start to the end of leakage of the molten material.

[0012] Here, if the pressure of the molten material is less than or equal to the pressure outside the filler material, it is assumed that the molten material will not leak out of the filler material. For this reason, in the present invention, the leakage volume calculation step and the volume strain calculation step are executed when the pressure of the molten material is greater than the pressure outside the filler material (i.e., when the molten material is leaking out of the filler material). In other words, after the time step in which the pressure of the molten material is less than or equal to the pressure outside the filler material, the leakage volume calculation step and the volume strain calculation step are not executed, and only the structural analysis step is executed.

[0013] In the leakage volume calculation step, for example, the leakage volume of the molten material can be calculated using Hagen-Poiseuille's law.

[0014] In the volumetric strain calculation step, for example, the leakage volume can be expressed as strain in the direction of the main volume reduction of the molten material.

[0015] The present invention can be suitably used for analyzing molten metal leakage in resistance spot welding. In this case, the molten material is molten metal produced by resistance spot welding multiple metal plates stacked in the thickness direction, the filler is a non-molten metal material surrounding the molten metal, the main direction of volume reduction of the molten metal due to spatter generated by the resistance spot welding is the thickness direction, and in the volume strain calculation step, the leakage volume can be expressed as the strain of the molten metal in the thickness direction.

[0016] Furthermore, in order to solve the above-mentioned problems, the present invention is also provided as a molten material leakage analysis program for causing a computer to perform the structural analysis step, the leakage volume calculation step, and the volume strain calculation step of the molten material leakage analysis method.

[0017] In summary, the present invention relates to the following matters [1] to [6]. [1] A method for analyzing leakage of molten material from a filler material which is filled with molten material, comprising: a structural analysis step of calculating the pressure of the molten material by modeling the molten material with an incompressible solid material and performing a structural analysis; a leakage volume calculation step of calculating the leakage volume of the molten material based on the difference between the pressure of the molten material and the external pressure of the filler material; and a volumetric strain calculation step of expressing the leakage volume as the volumetric strain of the molten material, wherein the structural analysis step, the leakage volume calculation step, and the volumetric strain calculation step are repeatedly executed in this order at predetermined time steps. [2] The method for analyzing leakage of a molten material according to [1], wherein the leakage volume calculation step and the volume strain calculation step are performed when the pressure of the molten material > the external pressure of the material to be filled. [3] The method for analyzing leakage of molten material according to [1] or [2], wherein the leakage volume of the molten material is calculated using the Hagen-Poiseuille law in the leakage volume calculation step. [4] A method for analyzing leakage of molten material according to any one of [1] to [3], wherein in the volume strain calculation step, the leakage volume is expressed as strain in the direction of the main volume reduction of the molten material. [5] The method for analyzing leakage of a molten material according to [4], wherein the molten material is molten metal produced by resistance spot welding a plurality of metal plates stacked in the thickness direction, the filler is a non-molten metal material surrounding the molten metal, the direction in which the main volume reduction of the molten metal due to spatter generated by the resistance spot welding occurs is the thickness direction, and in the volume strain calculation step, the leakage volume is expressed as the strain of the molten metal in the thickness direction. [6] A molten material leakage analysis program for causing a computer to perform the structural analysis step, the leakage volume calculation step, and the volume strain calculation step of the molten material leakage analysis method described in any of [1] to [5]. [Effects of the Invention]

[0018] According to the present invention, by performing structural analysis based on solid mechanics without using fluid analysis, it is possible to efficiently analyze the leakage of molten material from a filler material that is filled with molten material. [Brief explanation of the drawing]

[0019] [Figure 1] This is a flowchart showing the general procedure for a leakage analysis method of molten material according to one embodiment of the present invention. [Figure 2] This figure shows an example of the results obtained by structural finite element analysis of the final welded joint (nugget) NA when three metal plates M1, M2, and M3, stacked in the thickness direction, are resistance spot welded using a molten material leakage analysis method according to one embodiment of the present invention. [Modes for carrying out the invention]

[0020] The following describes a method for analyzing leakage of molten material according to one embodiment of the present invention (hereinafter, as may be simply referred to as the "leakage analysis method"), using as an example a case in which the molten material is molten metal produced by resistance spot welding (molten metal produced by resistance spot welding multiple metal plates stacked in the thickness direction), and the molten metal leaks from the overlapping surface of the metal plates due to spatter produced by resistance spot welding. Figure 1 is a flowchart showing the schematic procedure of the leakage analysis method according to this embodiment. As shown in Figure 1, the leakage analysis method according to this embodiment has steps ST1 to ST8. Step ST1 corresponds to the structural analysis step of the present invention, step ST7 corresponds to the leakage volume calculation step of the present invention, and step ST8 corresponds to the volume strain calculation step of the present invention. The leakage analysis method according to this embodiment repeatedly executes the structural analysis step (step ST1), the leakage volume calculation step (step ST7), and the volume strain calculation step (step ST8) in this order at predetermined time steps. The leakage analysis method according to this embodiment is executed by a leakage analysis program that causes a computer to execute each of steps ST1 to ST8.

[0021] At time step t, when the analysis begins, in step ST1, the molten material (molten metal) is modeled as an incompressible solid material (the Poisson's ratio of the molten material is set to approximately 0.5), and a structural analysis (e.g., structural finite element analysis) is performed to calculate the pressure P1 of the molten material. In the above time step t, the result in step ST2 is "NO" because the previous time step does not exist, and in step ST3, it is determined whether or not the leakage initiation condition is satisfied (in other words, whether or not the sputter generation condition is satisfied). For determining whether or not this leakage initiation condition is satisfied, a method described in Patent Document 1, for example, can be used, although a detailed explanation is omitted here. However, it is not necessarily limited to this.

[0022] In step ST3, if the leakage initiation condition is not met (resulting in "NO" in step ST3), in step ST4, it is determined whether the above time step t is equal to or greater than the predetermined analysis end time. Since the time step t at which the analysis begins is less than the analysis end time (resulting in "NO" in step ST4), in step ST5, the time step t is incremented by a predetermined small amount of time Δt, and the structural analysis (step ST1) is performed again. On the other hand, in step ST3, if the leakage initiation condition is satisfied (if the answer is "YES" in step ST3), it is determined that the molten material leaks out of the filler material through the leakage path L formed inside the filler material (the non-molten metal material surrounding the molten metal, excluding the molten metal from the stacked metal plates) (on the overlapping surface of the metal plates), and steps ST7 (leakage volume calculation step) and ST8 (volume strain calculation step) are executed. Below, the specific contents of steps ST7 and ST8 will be explained using as an example the case where the leakage initiation condition is satisfied at time step t+Δt, which is an increment of a small time Δt in step ST5.

[0023] When the volume of a solid (continuum) material changes from V to V+ΔV between time step t and time step t+Δt, the volume strain ε, given by the trace of the total strain tensor ε of the solid material, isV When it can be assumed that it is a minute strain, the strain components ε x in the three directions x, y, and z of the three-dimensional orthogonal coordinate system, ε y and ε z can be approximated by the following formula (1). ε V =tr(ε)=ε x +ε y +ε z =ΔV / V ···(1) In the above formula (1), tr(·) means the trace inside the parentheses. When the above formula (1) is rewritten for the volume change ΔV, it becomes the following formula (2). ΔV=V·ε V ···(2)

[0024] On the other hand, when a fluid (molten material) with a volume V filled (enclosed) at a pressure P1 inside the filler leaks to the outside of the filler at a pressure P2 through a certain leakage path L, if the conductance (ease of leakage) is represented by C, the leakage amount (volume flow rate = outflow volume per unit time) Q of the fluid is proportional to the pressure difference (P1 - P2) inside and outside the leakage path L and is represented by the following formula (3). Q=dV / dt=C·(P1-P2) ···(3) Assuming that the leakage amount Q is constant from time step t to time step t + Δt, the volume change ΔV due to leakage is calculated by the following formula (4). ΔV=Q·Δt ···(4) Therefore, from the above formulas (3) and (4), the volume change ΔV can be represented by the following formula (5). ΔV=C·(P1-P2)·Δt ···(5) In step ST7 (leakage volume calculation step), based on the above formula (5), the leakage volume of the molten material is calculated. That is, based on the difference between the pressure P1 of the molten material and the pressure P2 outside the filler, the leakage volume ΔV of the molten material is calculated.

[0025] Here, the total strain tensor ε of a solid material is, as shown in equation (6) below, an elastic strain tensor e that is linked to stress through Hooke's law and an eigen strain tensor ε that is not linked to stress. * It is expressed as the sum of the two. ε = e + ε * ...(6)

[0026] As mentioned above, if we treat the molten material (fluid) as a solid material with a Poisson's ratio set to approximately 0.5, that is, an incompressible solid material, then the volumetric strain due to the elastic strain tensor e becomes approximately zero. Considering the traces of both sides of equation (6) above, the volumetric strain ε V This is the Eigen strain tensor ε * Volume strain ε due to V * It is calculated using only the following formula (7). ε V =ε V * ...(7) Therefore, from equations (2) and (7) above, the volume change due to leakage of molten material (leakage volume of molten material) ΔV is equal to the volume strain ε of the solid material. V * Using this, it can be expressed by the following equation (8). ΔV = V·ε V * ...(8) In particular, in resistance spot welding of this embodiment, when the volume change due to leakage of molten material mainly occurs in a specific direction (for example, the z direction), ε V * In equation (9) below, the Eigin strain ε in the x direction is x * and the Eigin strain ε in the y direction y * Assuming both are 0, the Eigin strain ε in the z direction z * It is approximated by only this. ε V * =tr(ε * )=ε x * +ε y* +ε z * =ε z * ...(9) In step ST8 (volume strain calculation step), based on equations (8) and (9) above, the leakage volume ΔV of the molten material was treated as an incompressible solid material (Poisson's ratio set to approximately 0.5), and the z-direction Eingin strain ε of the molten material was calculated. z * It is represented as follows. Furthermore, if the above time step t+Δt is less than the predetermined end time of the analysis (if "NO" is selected in step ST4), then this strain ε z * Using this method, we will perform structural analysis again (step ST1) for the next time step.

[0027] Furthermore, the conductance C in equation (5) above can be determined using the principles of fluid dynamics. For example, when a molten material with viscosity coefficient μ leaks from a small hole of radius R and length S, the conductance C can be determined by the following equation (10) according to Hagen-Poiseuille's law. C=π·R 4 / (8·μ·S) ···(10) In equation (10) above, π is the ratio of a circle's circumference to its diameter (pi). The value of R in equation (10) can be selected to be an appropriate value so as to reproduce the actual leakage phenomenon. In this embodiment, when molten material (molten metal) leaks from the overlapping surface of metal plates due to spatter generated by resistance spot welding, it is preferable to set the value to a surface roughness of several μm to several tens of μm, which is typical for metal plates (e.g., steel plates). However, the method for determining the conductance C is not limited to using equation (10) above; for example, it is also possible to use the conductance when passing through the orifice instead of the small hole.

[0028] Furthermore, as in this embodiment, if molten material (molten metal) leaks from the overlapping surface of the metal plates due to spatter generated by resistance spot welding, the volume of the molten material is VN The viscosity coefficient of the molten material is μ N The contact diameter (contact radius) of the overlapping surfaces of the metal plates where sputtering occurs (typically, the contact interface is circular) is r c (See Figure 2(a) below), the melting diameter (typically the radius at the contact interface of the molten material that is concentric with the circular contact interface) is r N (See Figure 2(a) below) If we set V as shown in equations (1) to (5) above, then V N , μ as shown in equation (10) above N , S to r c -r N You can replace it with this. Furthermore, if we consider that the main direction of volume reduction of the molten material (molten metal) due to sputtering is the plate thickness direction (z direction), then (i.e., the volume reduction of the molten material is mainly due to strain ε in the z direction) z * It manifests as a strain ε in the x-direction. x * = 0, strain ε in the y direction y * (Assuming = 0), from equations (5), (8), (9), and (10), the strain ε z * This can be expressed by the following equation (11). ε z * =ΔV / V=π·R 4 (P1-P2)Δt / {8·V} N ·μ N ·(r c -r N )} ···(11) The strain ε expressed by equation (11) z * Using this, it is possible to perform the structural analysis again (step ST1) for the next time step. Note that ε z * This represents the volume reduction due to leakage of molten material, so in structural analysis (step ST1), ε is calculated from the strain in the z direction. z * This will reduce it.

[0029] As shown in Figure 1, steps ST7 (leakage volume calculation step) and ST8 (volume strain calculation step) described above are executed when the answer in step ST2 is "NO" and step ST3 is "YES", as well as when the answer in step ST2 is "YES" (i.e., the previous time step was during molten material leakage) and step ST6 is "NO". Step ST6 determines whether the leakage termination condition is met. Specifically, it determines whether the pressure P1 of the molten material (molten metal) is less than or equal to the external pressure P2 of the filler material (the non-molten metal material surrounding the molten metal). If this condition is not met (if the answer in Step ST6 is "NO"), i.e., if P1 > P2, it can be said that the molten material (molten metal) is still leaking, and Steps ST7 and ST8 are executed. On the other hand, if the condition is met (if the answer in Step ST6 is "YES"), there is no need to consider further leakage of the molten material (molten metal), and Steps ST7 and ST8 are not executed.

[0030] Each of the steps ST1 to ST8 described above is repeated in step ST4 if the current time step t is less than the predetermined analysis end time (if "NO" is selected in step ST4), and the analysis ends in step ST4 if the current time step t becomes equal to or greater than the predetermined analysis end time (if "YES" is selected in step ST4).

[0031] Figure 2 shows an example of the results obtained by structural finite element analysis of the final welded joint (nugget) NA when three metal plates M1, M2, and M3, stacked in the thickness direction, are resistance spot welded using the leakage analysis method according to this embodiment. Figure 2(a) shows the results when using the leakage analysis method according to this embodiment, and Figure 2(b) shows the results obtained by structural finite element analysis without considering the volume reduction of molten metal due to spatter. In both cases, an axisymmetric model with respect to the axis of symmetry (SYM) was used as the analytical model, and structural finite element analysis was performed by giving welding conditions that would cause spatter. Comparing the results shown in Figure 2(a) with the results shown in Figure 2(b), the thickness t of the nugget NA (area filled in dark gray) on the axis of symmetry (SYM) N and the total thickness t of metal plates M1 to M3 A For both of these, the values ​​obtained using the leakage analysis method according to this embodiment were smaller, indicating that the volume reduction of molten metal due to spatter is reflected. Although details are omitted, when resistance spot welding tests were actually performed under similar welding conditions and the cross-section after welding was examined, it was found that the nugget NA shape was the same as the result shown in Figure 2(a). [Explanation of symbols]

[0032] ST1...Structural analysis process ST7...Leakage volume calculation process ST8... Volumetric strain calculation process M1, M2, M3...metal plate NA...Welded part (nugget)

Claims

1. A method for analyzing leakage of molten material from a filler material that is filled with molten material inside, A structural analysis step is performed to calculate the pressure of the molten material by modeling the molten material with an incompressible solid material and performing a structural analysis. A leakage volume calculation step, which calculates the leakage volume of the molten material based on the difference between the pressure of the molten material and the external pressure of the material to be filled, The process includes a volume strain calculation step in which the leakage volume is expressed as the volume strain of the molten material, At predetermined time steps, the structural analysis step, the leakage volume calculation step, and the volume strain calculation step are repeatedly executed in this order. Method for analyzing leakage of molten material.

2. The leakage volume calculation step and the volume strain calculation step are executed when the pressure of the molten material is greater than the external pressure of the material to be filled. The method for analyzing leakage of molten material according to claim 1.

3. In the leakage volume calculation step, the leakage volume of the molten material is calculated using Hagen-Poiseuille's law. A method for analyzing leakage of molten material according to claim 1 or 2.

4. In the volumetric strain calculation step, the leakage volume is expressed as the strain in the direction of the main volume reduction of the molten material. A method for analyzing leakage of molten material according to claim 1 or 2.

5. The molten material is the metal produced by resistance spot welding multiple metal plates stacked in the thickness direction. The filler material is a non-molten metal material surrounding the molten metal, The main direction in which the volume reduction of the molten metal due to spatter generated by the resistance spot welding occurs is the plate thickness direction. In the volumetric strain calculation step, the leakage volume is expressed as the strain of the molten metal in the thickness direction of the plate. The method for analyzing leakage of molten material according to claim 4.

6. A molten material leakage analysis program for causing a computer to perform the structural analysis step, the leakage volume calculation step, and the volume strain calculation step of the molten material leakage analysis method according to claim 1 or 2.

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