Friction stir welding analytical method and program

Abstract

A friction stir welding analytical method according to the present invention uses an analytical model including: a first mesh for a Lagrangian analysis and corresponding to a welding tool, which is a first analytical target; and a plurality of marker particles disposed in an element where a welding target member, which is a second analytical target, is present in a fixed second mesh. The analytical method according to the present invention is characterized by comprising an analytical step for using a contact model and a heat generation model to perform a thermo-elasto-plastic analysis and a thermal conduction analysis on the first and second meshes, and a step for moving the marker particles in the second mesh in accordance with the node flow rate obtained in the analytical step, wherein at least one of a temperature, an acceleration vector, a velocity difference, an equivalent plastic strain, an identifier, a stress tensor, and a velocity vector, is moved together with the marker particles.

Description

Friction stir welding analysis method and program

[0001] The present invention relates to a method and program for analyzing friction stir welding.

[0002] Friction stir welding (FSW), which joins materials in an unmolten state, is currently attracting attention as a next-generation joining method (see, for example, Patent Document 1). FSW mainly includes butt welding and lap welding. In butt welding, the ends of two workpieces (members to be joined) are fixed in a butted state, and a tool (joining tool) consisting of a shoulder and a probe is brought into contact with the interface between the two workpieces while rotating at high speed, generating frictional heat between the tool and the workpieces. The frictional heat softens the workpieces, and the rotation induces plastic flow near the joint interface, stirring and mixing the workpieces to join them. In lap welding, the ends of the two workpieces (members to be joined) are fixed in a lapped state, and a tool (joining tool) consisting of a shoulder and a probe is brought into contact with the overlapping area while rotating at high speed, joining the workpieces. As such, the movement of the materials constituting the workpieces in FSW is complex. Compared to conventional welding methods, with FSW the maximum temperature reached is below the melting point and the materials to be joined are joined while still in a solid state, so the heat input is small, welding residual stress and welding distortion can be kept small, and the loss of strength at the joint is smaller than with conventional fusion welding. In addition, FSW can join dissimilar materials such as aluminum and steel, which is not possible with conventional welding due to differences in thermal conductivity and melting point.

[0003] In recent years, the use of FSW, a non-melting, low-heat-input joining method for joining aluminum components, has expanded. FSW is now used in the manufacturing of railcars, ships, and aircraft. However, FSW presents numerous mechanical challenges, including tool wear and damage, difficulty visualizing whether the components are joined with sufficient strength, and the risk of internal defects during joining. Therefore, there is a need for the development of a simulation analysis system using the finite element method (FEM) to explore the tool shape, tool tilt angle, tool rotation speed, and tool movement speed (joining speed) to avoid these challenges. Lagrangian analysis is commonly used for welding simulation analysis using the finite element method. In Lagrangian analysis, a mesh consisting of multiple elements is placed on the target components, and the analysis proceeds by moving nodes located at the vertices of the elements.

[0004] Patent No. 6140863

[0005] As mentioned above, in FSW, the movement of materials that make up the workpieces is complex, so if you try to analyze FSW using Lagrangian analysis, the mesh will break down and the analysis will be difficult.The present invention has been made in consideration of these circumstances, and provides an analysis method that can efficiently analyze FSW without breaking down the mesh.

[0006] The present invention provides an analysis method for friction stir welding using an analytical model including a first mesh for Lagrangian analysis corresponding to a welding tool, which is a first analysis object, and a plurality of marker particles arranged in elements of a fixed second mesh, where the second analysis object, which is a member to be joined, is located. The analysis method of the present invention includes an analysis step of performing a thermal elastic-plastic analysis and a heat conduction analysis on the first and second meshes using a contact model and a heat generation model, and a step of moving the marker particles in the second mesh according to the nodal flow velocities obtained in the analysis step, and is characterized in that at least one of temperature, acceleration vector, velocity difference, equivalent plastic strain, identifier, stress tensor, and velocity vector is moved together with the marker particles.

[0007] The analysis method of the present invention uses a contact model and a heat generation model to analyze a first mesh for Lagrangian analysis corresponding to the welding tool, which is the first analysis object. This allows for simulation of the FSW tool movement and allows for calculation of the contact load and frictional heat between the welding tool and the workpieces. Furthermore, the analysis method of the present invention moves multiple marker particles located in elements of the fixed second mesh where the workpieces are located according to the nodal flow velocity, preventing mesh breakdown and making analysis difficult. Furthermore, the advection of variables such as temperature, acceleration vector, velocity difference, equivalent plastic strain, identifier, stress tensor, and velocity vector can be represented by marker particles, reducing the amount of calculations and enabling efficient analysis.

[0008] 1 is an explanatory diagram of friction stir welding (butt welding). (a) and (b) are schematic cross-sectional views of a welding tool and members to be welded. (a) is a schematic diagram of an analytical model used in an analysis method for friction stir welding of one embodiment of the present invention. (b) is a schematic diagram of an analytical model used in an analysis method for friction stir welding of one embodiment of the present invention. (c) is a schematic diagram of an analytical model used in an analysis method for friction stir welding of one embodiment of the present invention. (d) is a schematic diagram of an analytical model used in an analysis method for friction stir welding of one embodiment of the present invention. (e) is a flowchart of an analysis method for friction stir welding of one embodiment of the present invention. (f) is a formula and an explanatory diagram representing an interface representation using the VOF method. (f) is a formula and an explanatory diagram representing a contact model. (f) is a formula representing a heat generation model. (f) is an explanatory diagram of finite element method analysis performed on a first mesh. (f) is an explanatory diagram of finite element method analysis performed on a second mesh. (f) is a first mesh corresponding to the welding tool included in the analytical model used in the analysis of friction stir welding. (f) is a second mesh included in the analytical model used in the analysis of friction stir welding. (a) is an analysis result (temperature distribution) when the moving speed of the welding tool is 250 mm / min, and (b) is an analysis result (temperature distribution) when the moving speed of the welding tool is 750 mm / min. 1A to 1E are diagrams showing the distribution of marker particles, which are analysis results for when burrs are generated; 2A are graphs showing the distribution of residual stress, which are analysis results; 3A are diagrams showing the distribution of marker particles, which are analysis results for when surface defects are generated; 4A to 4E are diagrams showing the distribution of marker particles, which are analysis results when the tool tilt angle TL is set to 0°, 2°, 3°, 6°, and 10°; 5A to 5E are diagrams showing the distribution of pressure on the welding tool surface, which are analysis results when the tool tilt angle TL is set to 0°, 3°, and 6°.

[0009] The present invention relates to a friction stir welding analysis method, and an analytical model including a first mesh for Lagrangian analysis corresponding to a welding tool, which is a first analysis object, and a fixed second mesh, in which a plurality of marker particles are arranged in elements where the second analysis object, which is a member to be welded, is located. The present invention also relates to a computer-implemented program for causing a computer to execute the present invention. The present invention also relates to a program for causing a computer to execute the present invention. The present invention also relates to a program for causing a computer to execute the present invention. The present invention also relates to a program for causing a computer to execute the present invention. The present invention also relates to a program for causing a computer to execute the present invention.

[0010] Hereinafter, an embodiment of the present invention will be described with reference to the drawings. The configurations shown in the drawings and the following description are examples, and the scope of the present invention is not limited to those shown in the drawings and the following description.

[0011] First, friction stir welding will be described. FIG. 1 is an explanatory diagram of friction stir welding (butt welding), and FIGS. 2(a) and (b) are schematic cross-sectional views of a welding tool and workpieces to be joined. In friction stir welding (butt welding), workpieces to be joined 3a and 3b are first fixed in a butt-jointed state. In FIG. 1, the dashed-dotted line A-A represents the interface between the workpieces 3a and 3b. When a welding tool 2 including a shoulder 8 and a probe 9 is brought into contact with and pressed into this interface while rotating at high speed, frictional heat is generated between the welding tool 2 and the workpieces 3a and 3b. The frictional heat softens the workpieces 3a and 3b, causing them to plastically flow. In this manner, the probe 9 can be inserted into the workpieces 3a and 3b. The welding tool 2 is then moved along the interface between the workpieces 3a and 3b while rotating at high speed. This allows the materials near the interface between the members to be joined 3a, 3b to be stirred and mixed by plastic flow, and the members to be joined 3a, 3b (members to be joined 3) can be joined. After that, the welding tool 2 is rotated at high speed and pulled out from the members to be joined 3. The side of the members to be joined 3 on which the direction of movement and rotation of the welding tool 2 is the same is called the AS (advancing side), and the side of the members to be joined 3 on which the direction of movement and rotation of the welding tool 2 is opposite is called the RS (retreating side).

[0012] In friction stir welding, for example, the material of the workpieces 3 to be joined is stirred and mixed on the tool side of the broken line shown in the cross-sectional view of Figure 2(a). This stirring and mixing generates plastic heat. In friction stir welding, the welding tool 2 can be rotated and moved at an angle θ (tool tilt angle TL) between the direction perpendicular to the surfaces of the workpieces 3 to be joined (the direction in which the welding tool 2 is inserted) and the rotation axis of the welding tool 2, as shown in the cross-sectional view of Figure 2(b).

[0013] In friction stir welding, depending on the material of the workpieces 3 to be joined, the material, shape, rotation speed, movement speed, and tool tilt angle of the joining tool 2, burrs, surface defects, internal defects, and damage / wear of the joining tool 2 may occur. The analysis method of this embodiment can be used to search for the material, shape, joining conditions, etc. of the joining tool 2 that can suppress the occurrence of such burrs, defects, damage / wear, etc.

[0014] 3 to 5 are schematic diagrams of analytical models used in the friction stir welding analysis method of this embodiment, and FIG. 6 is a flowchart of the friction stir welding analysis method of this embodiment. The friction stir welding analysis method of this embodiment uses an analytical model 7 including a first mesh 4 for Lagrangian analysis corresponding to the welding tool 2, which is the first analysis object, and a plurality of marker particles 6 arranged in elements of a fixed second mesh 5 where the welding target member 3, which is the second analysis object, is located. The friction stir welding analysis method of this embodiment also includes an analysis step of performing a thermal elastic-plastic analysis and a heat conduction analysis of the first mesh 4 and the second mesh 5 using a contact model and a heat generation model, and a step of moving the marker particles 6 in the second mesh 5 according to the nodal flow velocity obtained in the analysis step. The analysis step is characterized in that at least one of the temperature, acceleration vector, velocity difference, equivalent plastic strain, identifier, stress tensor, and velocity vector is moved along with the marker particles 6. The analysis method of this embodiment can be implemented by running a program on a computer. In this embodiment, the "mesh" refers to the mesh used in the analysis using the finite element method.

[0015] In the friction stir welding analysis method of this embodiment, the solid interface can be represented by the VOF method. Figure 7 is an explanatory diagram of interface representation using the VOF method. For example, the solid interface identifier φ of elements corresponding to solids (elements where marker particles 6 are present) among the elements constituting the second mesh 5 can be set to 1.0, the solid interface identifier φ of elements where no solids are present (elements where marker particles 6 are not present) among the elements constituting the second mesh 5 can be set to 0.0, and the solid interface identifier φ of elements present at the interface between these elements can be set to 0.5. Furthermore, a stabilized FEM using the SUPG method can be adopted, time can be discretized using the Wilson θ method, and analysis can be performed using the GPBiCG method.

[0016] The contact model used in the analysis method of friction stir welding of this embodiment can be a penalty-based contact model. Fig. 8 is an explanatory diagram of the contact model. Using the equation shown in Fig. 8, the contact reaction force (volumetric contact force) can be calculated according to the solid fraction and temperature of each space.

[0017] The heat generation model used in the analysis method for friction stir welding of this embodiment can be a model that calculates the amount of heat generated from the plastic work increment and frictional heat. The amount of heat generated can be calculated, for example, using the equation shown in Fig. 9. By performing a heat conduction analysis using the amount of heat generated by the plastic work increment and frictional heat, the mechanical phenomenon of friction stir welding can be stably calculated.

[0018] The first mesh 4 is a mesh for Lagrangian analysis using the finite element method and is composed of multiple elements. Nodes are placed at the vertices of the elements. The first mesh 4 has a shape corresponding to the welding tool 2, which is the object to be analyzed. In friction stir welding, the welding tool 2 moves while rotating. The first mesh 4 is rotated and moved while moving the nodes to correspond to this rotation and movement. The tool tilt angle TL of the first mesh 4 shown in FIG. 3 is 0°.

[0019] A Lagrangian FEM analysis is performed on the elements that make up the first mesh 4. For example, as shown in Fig. 10, the analysis can be performed by discretizing the governing equations of the solid using the finite element method. In the analysis of the elements that make up the first mesh 4, the contact model and heat generation model described above can be used.

[0020] The second mesh 5 is a mesh composed of multiple fixed elements, such as those used in Euler-type analysis using the finite element method. Nodes are located at the vertices of the elements. Analysis such as thermo-elastic-plastic analysis and heat conduction analysis is performed on the multiple elements constituting the second mesh 5. Marker particles 6 are located in elements of the multiple elements constituting the second mesh 5 that contain the second analysis target component 3. Marker particles 6 are not located in elements of the multiple elements constituting the second mesh 5 that do not contain the second analysis target component 3. At the start of the analysis, the number of marker particles 6 located in each element of the multiple elements constituting the second mesh 5 that contains the second analysis target component 3 is not particularly limited, but may be, for example, 1, 2, 4, 6, 8, 9, 12, 18, or 27. In the analysis model 7 shown in FIG. 3 , four marker particles 6 are located in each element. Physical variables possessed by the marker particles 6 present in the element can be used to analyze the elements included in the second mesh 5.

[0021] When simulating friction stir welding for joining a member to be joined 3a made of a first material and a member to be joined 3b made of a second material using the analysis method of this embodiment, marker particles 6 having an identifier for the first material can be placed in the element where the member to be joined 3a exists among the multiple elements constituting the second mesh 5, and marker particles 6 having an identifier for the second material can be placed in the element where the member to be joined 3b exists among the multiple elements constituting the second mesh 5. This makes it possible to simulate friction stir welding for joining members to be joined 3a and 3b made of different materials.

[0022] For the elements constituting the second mesh 5, an analysis similar to the Eulerian solid FEM analysis shown in FIG. 11 is performed using the contact model and heat generation model described above. However, the advection analysis using the advection equation shown in FIG. 11 is not performed. Instead, marker particles 6 are moved. Specifically, marker particles 6 having physical variables (temperature, acceleration vector, velocity difference, equivalent plastic strain, discriminator, stress tensor, velocity vector, etc.) are moved based on nodal flow velocities (advection velocities). The nodal flow velocities can be calculated by thermo-elastic-plastic analysis and heat conduction analysis of the elements constituting the first mesh 4 and thermo-elastic-plastic analysis and heat conduction analysis of the elements constituting the second mesh 5. In the second mesh 5, at least one of the temperature, acceleration vector, velocity difference, equivalent plastic strain, discriminator, stress tensor, and velocity vector is moved along with the marker particles 6. This allows for simulation of stirring and mixing of the workpieces 3 during friction stir welding.

[0023] The analysis method for friction stir welding according to this embodiment can proceed, for example, as shown in the flowchart in Fig. 6. In step S1, marker particles 6 are placed in the second mesh 5. The second mesh 5 of the analysis model 7 shown in Figs. 3 to 5 has 7 x 18 = 126 elements. Of these elements, marker particles 6 are placed in 5 x 16 = 80 elements. Furthermore, four marker particles 6 are placed in one element.

[0024] In steps S2 to S6, the above-described thermo-elastic-plastic analysis and heat conduction analysis are performed on the elements constituting the first mesh 4, and the above-described thermo-elastic-plastic analysis and heat conduction analysis are performed on the elements constituting the second mesh 5, and the nodal flow velocity at the nodes included in the second mesh 5 is calculated. Then, in step S7, the marker particles 6 are moved according to the nodal flow velocity (advection velocity). In step S8, it is determined whether the friction stir welding has been completed, and if not, the process returns to step S2. Thereafter, steps S2 to S7 are performed after a predetermined time (e.g., 0.01 seconds) has passed. In this manner, steps S2 to S7 are repeated from the start to the end of the friction stir welding.

[0025] In the analysis method for friction stir welding according to this embodiment, as shown in the analysis model of FIGS. 3 and 4 , the first mesh 4 (corresponding to the welding tool) is rotated (e.g., rotation speed: 1000 rpm) and pushed into elements of the second mesh 5 (corresponding to the members to be welded 3) where the marker particles 6 are present, and the probe portion of the first mesh 4 is inserted into the elements of the second mesh 5 where the marker particles 6 are present. Then, while rotating the first mesh 4 (corresponding to the welding tool), the first mesh 4 is moved through the elements of the second mesh 5 (corresponding to the members to be welded 3) where the marker particles 6 are present, as shown in FIGS. 4 and 5 (e.g., rotation speed: 1000 rpm, movement speed: 500 mm / min). Then, while rotating the first mesh 4 (corresponding to the welding tool), the first mesh 4 is pulled out of the elements of the second mesh 5 (corresponding to the members to be welded 3) where the marker particles 6 are present. In this manner, steps S2 to S7 are repeated while moving the first mesh 4 from the start to the end of the friction stir welding. This makes it possible to simulate the stirring and mixing of the materials of the workpieces 3 during friction stir welding by moving the marker particles 6. For example, as shown in Figures 3 to 5, the marker particles 6 can be mixed and stirred in the second mesh 5. Furthermore, by moving the marker particles 6 in the second mesh 5, it is possible to determine the position of the surfaces of the workpieces 3 after welding, and it is also possible to visualize the flow shape during friction stir welding.

[0026] The friction stir welding analysis method of this embodiment includes a step of determining the presence or absence of at least one of burrs, kissing bonds, cutting defects, and void defects based on the positions of the marker particles 6 after movement. This makes it possible to predict the occurrence of burrs, kissing bonds, cutting defects, void defects, etc., and to search for tool shapes, tool tilt angles, tool rotation speeds, tool movement speeds (welding speeds), etc. that will prevent these problems from occurring. This step may be performed during or after the analysis of friction stir welding. Kissing bonds are thought to be caused by insufficient stirring at the tip of the welding tool 2, cutting defects are thought to be caused by insufficient contact between the welding tool and the workpieces 3, void defects near the back surface are thought to be caused by insufficient heat input, and void defects near the front surface are thought to be caused by excessive heat input.

[0027] The method for analyzing friction stir welding according to this embodiment can include a step of determining whether the pressure applied to the welding tool 2 calculated using the contact model exceeds a predetermined value. This makes it possible to predict damage and frictional wear of the welding tool 2, and to search for a tool shape, tool tilt angle, tool rotation speed, tool movement speed (welding speed), and the like that will prevent these problems from occurring. This step may be performed during or after the analysis of friction stir welding.

[0028] The analysis method for friction stir welding of this embodiment can include a step of calculating the movement amount of the marker particles 6. The movement amount of the marker particles 6 corresponds to the movement amount of the material of the members to be joined 3, and therefore, the stirrability of the members to be joined 3 can be evaluated based on the movement amount of the marker particles 6.

[0029] Analysis of friction stir welding: Analysis was performed using the friction stir welding analysis method described above. For the analysis, a first mesh (corresponding to the welding tool) for Lagrangian analysis, as shown in Figure 12, was used. Specifically, the probe diameter was 5.0 mm, the probe extension length was 3.8 mm, and the shoulder diameter was 15.0 mm. The number of nodes in the first mesh was 6,072, and the number of elements in the first mesh was 5,320.

[0030] The analysis used a fixed second mesh as shown in Figure 13. Marker particles with the identifiers of the components to be joined were placed on elements of the second mesh where the components to be joined were present. One marker particle was placed on each element. The dimensions of the second mesh were 200.0 mm in length, 200.0 mm in width, and 14.0 mm in height. At the start of the analysis, the dimensions of the multiple elements in the second mesh where the components to be joined were 200.0 mm in length, 200.0 mm in width, and 4.0 mm in thickness. The number of nodes in the second mesh was 1,219,581, and the number of elements in the second mesh was 1,169,280. The material constants of the components to be joined, which were represented by the marker particles, were set to those of aluminum alloy AA5083. The analysis also analyzed the sequence of the insertion of the welding tool into the components to be joined, the movement of the welding tool while inserted, and the withdrawal of the welding tool from the components to be joined. Furthermore, the analysis steps S2 to S7 in FIG. 6 were repeated every 0.01 seconds.

[0031] Figure 14(a) shows the temperature distribution obtained by analyzing friction stir welding with the welding tool moving speed set to 250 mm / min and the welding tool rotating speed set to 1250 rpm. Figure 14(b) shows the temperature distribution obtained by analyzing friction stir welding with the welding tool moving speed set to 750 mm / min and the welding tool rotating speed set to 1250 rpm. It was confirmed that these temperature distributions have the same tendency as the temperature distributions when actual friction stir welding is performed.

[0032] Figure 15 shows the distribution of marker particles, which is the analysis result, and indicates the area where burrs occurred. The analysis result showed that larger burrs occurred on the RS (retreating side) than on the AS (advancing side). This coincides with the tendency of burrs occurring in actual friction stir welding. Therefore, it was found that the occurrence of burrs can be accurately predicted using the analysis method of the present invention.

[0033] Figure 16 shows the residual stress distribution in the welding direction (the direction of welding tool movement) obtained by analyzing friction stir welding at welding tool movement speeds of 250 mm / min, 500 mm / min, 750 mm / min, or 1000 mm / min and a welding tool rotation speed of 1250 rpm. This residual stress distribution reveals that tensile residual stress occurs in the weld and compressive residual stress occurs in the surrounding area. Furthermore, it was found that residual stress is small when the welding tool movement speed is fast (low heat input). These results show the same trend as the measured residual stress in components actually welded by friction stir welding. Therefore, it was found that the analysis method of the present invention can be used to predict residual stress occurring in components to be welded.

[0034] Friction stir welding was analyzed with the joining tool rotation speed set to 1000 rpm, the joining tool movement speed set to 500 mm / min, and the tool tilt angle TL set to -3°, 0°, 2°, 3°, 6°, or 10°. The amount of movement of marker particles near the joint in this analysis was calculated, and the stirability of the material of the components to be joined was evaluated. The presence or absence of internal defects was also determined from the distribution of marker particles corresponding to the cross-section of the joint. The pressure applied to the joining tool while it was being moved and rotated was also calculated. These results are summarized in Table 1. The remarks column in Table 1 also includes information on the occurrence of surface defects and large burrs.

[0035]

[0036] FIG. 17 shows the analysis results obtained by analyzing friction stir welding with a tool tilt angle TL of 0°, and is a distribution diagram of marker particles corresponding to a top view. FIGS. 18(a) to 18(e) show the analysis results obtained by analyzing friction stir welding with a tool tilt angle TL of 0°, 2°, 3°, 6°, or 10°, and are distribution diagrams of marker particles corresponding to cross-sectional views. As shown in Table 1, when the tool tilt angle TL was set to -3° and 0°, surface defects such as those shown in FIGS. 17 and 18(a) were observed. The locations of the surface defects shown in FIG. 17 almost coincided with the locations of surface defects that appear in actual friction stir welding. Also, as shown in Table 1, when the tool tilt angle TL was set to -3°, 0°, or 2°, internal defects such as those shown in FIGS. 18(a) and 18(b) were observed. It is believed that such defects occur when the tool tilt angle TL was set to -3°, 0°, or 2° because the movement of the marker particles (material of the materials to be joined) was relatively small and the stirring ability of the materials to be joined was low.

[0037] 18(c) and (d), it was found that when the tool tilt angle TL was set to 3° or 6°, friction stir welding could be performed satisfactorily without the generation of internal defects, surface defects, large burrs, etc. Furthermore, it was found that when the tool tilt angle TL was set to 10°, large burrs were generated, as shown in the analysis result of Fig. 18(e).

[0038] 19(a) to (c) show the analysis results obtained by analyzing friction stir welding with the tool tilt angle TL set to 0°, 3°, or 6°, and show the pressure distribution on the surface of the welding tool. It was found that the pressure on the outside of the shoulder and the side of the probe was high at any tool tilt angle. Since the outside of the shoulder of the welding tool and the side of the probe wear out in actual friction stir welding, it was found that the analysis method of the present invention can predict tool wear and damage. It was also found that the pressure on the probe was smallest when the tool tilt angle TL was set to 3°.

[0039] 2: Welding tool 3, 3a, 3b: Parts to be welded 4: First mesh 5: Second mesh 6: Marker particle 7: Analysis model 8: Shoulder 9: Probe

Claims

1. A method for analyzing friction stir welding using an analytical model including a first mesh for Lagrangian analysis corresponding to the welding tool, which is the first object of analysis, and a plurality of marker particles arranged in elements of a fixed second mesh where the components to be joined, which are the second object of analysis, are present, the method comprising: an analysis step of performing a thermal elastic-plastic analysis and a heat conduction analysis of the first and second meshes using a contact model and a heat generation model; and a step of moving the marker particles in the second mesh according to the nodal flow velocities obtained in the analysis step, characterized in that at least one of temperature, acceleration vector, velocity difference, equivalent plastic strain, identifier, stress tensor and velocity vector is moved together with the marker particles.

2. The analysis method according to claim 1, further comprising a step of determining the presence or absence of at least one of burrs, kissing bonds, cut defects and void defects based on the positions of the marker particles after they have been moved.

3. The analysis method according to claim 1, further comprising a step of determining whether or not the pressure applied to the welding tool calculated using the contact model exceeds a predetermined value.

4. The analysis method according to claim 1, further comprising a step of calculating the amount of movement of the marker particles.

5. The analysis method according to claim 1, wherein the members to be joined include a first member made of a first material and a second member made of a second material.

6. A program configured to cause a computer to execute the analysis method according to any one of claims 1 to 5.

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