A grid mapping method for pool dynamics and phase-field method dendrite growth calculation

Abstract

The application discloses a grid mapping method for finite element method or finite volume method and phase field method dendrite growth calculation. The application relates to the technical field of welding simulation. Specifically comprises the following steps: step 1, obtaining the field variable distribution in the numerical simulation calculation of the finite element method or the finite volume method welding process; step 2, exporting the coordinates and field variable data of the nodes with the temperature greater than the metal melting point; step 3, performing triangular partitioning on the melting area according to the node coordinates; step 4, drawing the Voronoi diagram of the melting area according to the circumcenters of the Delaunay triangles; step 5, setting the phase field method nodes; step 6, sequentially processing the units in the Voronoi diagram, taking the base point of the unit and the base point directly connected with the base point as known points, and obtaining the field variable value of the phase field method nodes by the interpolation method; and step 7, using the obtained field variable value for the calculation of the phase field method grain growth.

Description

Technical Field

[0001] This invention relates to the field of welding simulation technology, specifically to a mesh mapping method for calculating molten pool dynamics and dendrite growth using the phase field method. Background Technology

[0002] Molten pool dynamics simulation is a numerical simulation technique that studies the physical phenomena of metal melting and solidification processes. It involves multiple scales and influencing factors and is related to multiple physical phenomena, such as temperature fields, fluid dynamics, and thermal stress distribution. During the simulation, the distribution of temperature fields and temperature gradients within the computational domain can be obtained, thus revealing the distribution of dynamic dimensional gradients and propagation speeds during the molten pool solidification process. The phase-field method uses unified governing equations to describe the microscale growth process of new phases at the solid, liquid, and solid-liquid interfaces during metal solidification, analyzing the crystallization process during metal solidification. In welding, metal melts to form a weld. The boundary between the molten metal and the solid metal is called the fusion line. In addition to the molten metal, under high temperature, a portion of the unmelted area near the fusion line is also affected by the high temperature, causing changes in the morphology of metal grains. The phase-field method can simulate the growth process of metal grains during solidification near the fusion line and within the molten pool. The morphology of the grains is crucial to the quality of the weld.

[0003] In existing phase-field method calculations of dendrite growth, dendrite growth is typically calculated within a rectangular plane or cuboid space. The meshes required for molten pool dynamics simulation and phase-field method simulation of dendrite growth differ significantly. Typically, the latter uses a much smaller mesh size. Therefore, it is necessary to obtain the temperature field of a finer phase-field method mesh by mesh mapping, based on the temperature field of a coarser mesh and the morphology of the molten pool during welding. Summary of the Invention

[0004] To address the shortcomings of existing technologies, this invention provides a mesh mapping method for calculating molten pool dynamics and dendrite growth using the phase field method, thus solving the problems mentioned in the background section.

[0005] To achieve the above objectives, the present invention is implemented through the following technical solution: a mesh mapping method for calculating dendrite growth in molten pool dynamics and phase field method, which is mainly applied to the numerical simulation calculation of grain growth considering molten pool morphology during the welding process.

[0006] A mesh mapping method for calculating molten pool dynamics and dendrite growth using the phase field method specifically includes the following steps:

[0007] S1. Calculate the distribution of field variables such as temperature field on the base material during the welding process using the finite element method;

[0008] S2. Export the coordinates and temperature field variables of nodes with temperatures higher than the melting point of the metal;

[0009] S3. Perform Delaunay triangulation on the region where the exported finite element nodes are located;

[0010] S4. Calculate the circumcenter of the triangle obtained after triangulation;

[0011] S5. Connect the circumcenters of all adjacent triangles in sequence to form a Venn diagram, where the nodes of the finite element are the base points of the Venn diagram;

[0012] S6. Draw a rectangular area that includes the scattered point area, and set the nodes of the phase field method within it;

[0013] S7. Perform interpolation processing on each cell of the Vinonic diagram in sequence.

[0014] Preferably, in step S3, the Delaunay triangulation generation algorithm uses a point-by-point insertion method, with the following steps:

[0015] A1. Create a super triangle that includes all the base points, and add the super triangle to the triangle list;

[0016] A2. Insert base points point by point, as follows: Figure 4 Taking the triangulation of a base point as an example, first insert point A to form three triangles;

[0017] A3. Insert point B, and find the triangle whose circumcircle contains the insertion point in the triangle list;

[0018] A4. Delete the common edges that affect the triangle;

[0019] A5. Connect the insertion point to all vertices of the triangle that affect it;

[0020] A6. Add the newly formed triangle to the triangle list;

[0021] A7. Repeat steps A2-A6 until all nodes have been inserted.

[0022] Preferably, in step S5, the specific steps for forming the Vinyasa diagram include:

[0023] B1. Delaunay triangulation is performed using the finite element nodes calculated from the molten pool dynamics as the base points of the Vinograph.

[0024] B2. Calculate the circumcenter and radius of each triangle in the triangulation network;

[0025] B3. Connect the ectodes to form the Vinio diagram.

[0026] Preferably, in step S6, the maximum and minimum values ​​of the vertex coordinates of the scattered convex hull are first calculated, and the nodes of the phase field method are uniformly set within the rectangular area according to the requirements of the phase field method.

[0027] Preferably, in step S7, the specific steps of the interpolation process are as follows:

[0028] C1. Since the elements of a Vinograph are all convex polygons, the sign of the dot product or cross product of vectors can be used to determine whether a point is within the polygon. Determine the number of the phase field nodes contained in the element;

[0029] C2. To facilitate interpolation, the node set is expanded from the nodes inside the cell to a rectangular area that includes the internal nodes.

[0030] C3. Obtain the coordinates and field variable values ​​of the unit's base point and the surrounding base points directly connected to it;

[0031] C4. Using the above base points as known points, the values ​​of the field variables of the phase field method nodes within the above rectangular area are obtained by interpolation.

[0032] C5. Retain the field variable data of the phase field nodes within the element, and delete the data of the phase field nodes that are within the rectangular area but not within the element.

[0033] Preferably, in C4, The cubic spline interpolation method is used to obtain the phase within the cell from the known data of the base point. The values ​​of the field variables at the field nodes.

[0034] Beneficial effects

[0035] This invention provides a mesh mapping method for calculating molten pool dynamics and dendrite growth using the phase-field method. Compared with existing technologies, it has the following advantages: This mesh mapping method for calculating molten pool dynamics and dendrite growth using the phase-field method specifically includes the following steps: S1, calculating the distribution of temperature and other field variables on the base material during welding using the finite element method; S2, deriving the coordinates and temperature and other field variables of nodes with temperatures higher than the metal melting point; S3, performing Delaunay triangulation on the region where the derived finite element nodes are located; S4, calculating the circumcenters of the triangles obtained after triangulation; S5, sequentially connecting the circumcenters of all adjacent triangles to form a Venn diagram, where the finite element nodes are the base points of the Venn diagram; S6, drawing a rectangular region that includes the scattered point region, and uniformly setting phase-field method nodes within the rectangle according to the requirements of the phase-field method; S7, sequentially performing interpolation processing on each element of the Venn diagram; Through the mesh mapping method, the morphology of the molten pool obtained from the finite element simulation can be introduced into the simulation calculation of dendrite growth, making the simulation process more consistent with the actual welding situation. Therefore, the mesh mapping method plays a very important role in this process. Attached Figure Description

[0036] Figure 1 This is a flowchart illustrating the formation of the Vinograph in this invention;

[0037] Figure 2This is a nodal diagram of the phase-field method of the present invention;

[0038] Figure 3 Flowchart of Vinograph cell interpolation processing;

[0039] Figure 4 This is the interpolated surface plot and error analysis of the present invention. Detailed Implementation

[0040] The technical solutions of the embodiments of the present invention will be clearly and completely described below with reference to the accompanying drawings. Obviously, the described embodiments are only some embodiments of the present invention, and not all embodiments. Based on the embodiments of the present invention, all other embodiments obtained by those skilled in the art without creative effort are within the scope of protection of the present invention.

[0041] Please see Figure 1-4 This invention provides two technical solutions: a mesh mapping method for calculating molten pool dynamics and dendrite growth using the phase field method, specifically including the following embodiments:

[0042] Example 1

[0043] S1. Calculate the distribution of field variables such as temperature field on the base material during the welding process using the finite element method;

[0044] S2. Export the coordinates and temperature field variables of nodes with temperatures higher than the melting point of the metal;

[0045] S3. Perform Delaunay triangulation on the region where the exported finite element nodes are located;

[0046] S4. Calculate the circumcenter of the triangle obtained after triangulation;

[0047] S5. Connect the circumcenters of all adjacent triangles in sequence to form a Venn diagram, where the nodes of the finite element are the base points of the Venn diagram;

[0048] S6. Draw a rectangular area that includes the scattered point area, and uniformly set the nodes of the phase field method within the rectangle according to the requirements of the phase field method.

[0049] S7. Perform interpolation on each element of the Vinonic diagram in sequence, and use linear interpolation to obtain the field variable data of the phase field nodes within the element.

[0050] Example 2

[0051] S1. Calculate the distribution of field variables such as temperature field on the base material during the welding process using the finite volume method;

[0052] S2. Export the coordinates and temperature field variables of nodes with temperatures higher than the melting point of the metal;

[0053] S3. Perform Delaunay triangulation on the region where the exported finite element nodes are located;

[0054] S4. Calculate the circumcenter of the triangle obtained after triangulation;

[0055] S5. Connect the circumcenters of all adjacent triangles in sequence to form a Venn diagram, where the nodes of the finite element are the base points of the Venn diagram;

[0056] S6. Draw a rectangular area that includes the scattered point area, and uniformly set the nodes of the phase field method within the rectangle according to the requirements of the phase field method.

[0057] S7. Process each element of the Vinonic diagram sequentially, and use cubic spline interpolation to obtain the field variable data of the phase field nodes within the element.

[0058] Furthermore, any content not described in detail in this specification is existing technology known to those skilled in the art.

[0059] It should be noted that, in this document, relational terms such as "first" and "second" are used only to distinguish one entity or operation from another, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Furthermore, the terms "comprising," "including," or any other variations thereof are intended to cover non-exclusive inclusion, such that a process, method, article, or apparatus that comprises a list of elements includes not only those elements but also other elements not expressly listed, or elements inherent to such process, method, article, or apparatus.

[0060] Although embodiments of the invention have been shown and described, it will be understood by those skilled in the art that various changes, modifications, substitutions and alterations can be made to these embodiments without departing from the principles and spirit of the invention, the scope of which is defined by the appended claims and their equivalents.

Claims

1. A mesh mapping method for calculating molten pool dynamics and dendrite growth using the phase field method, characterized in that: It is mainly used in the numerical simulation calculation of grain growth considering the morphology of the weld pool during the welding process; Specifically, the following steps are included: S1. Calculate the distribution of field variables such as temperature field on the base material during the welding process using the finite element method; S2. Export the coordinates and temperature field variables of nodes with temperatures higher than the melting point of the metal; S3. Perform Delaunay triangulation on the region where the exported finite element nodes are located; S4. Calculate the circumcenter of the triangle obtained after triangulation; S5. Connect the circumcenters of all adjacent triangles in sequence to form a Venn diagram, where the nodes of the finite element are the base points of the Venn diagram; S6. Draw a rectangular area that includes the scattered point area, and set the nodes of the phase field method within it; S7. Perform interpolation processing on each cell of the Vinograph in sequence; In step S5, the specific steps for forming the Vinyasa diagram include: B1. Delaunay triangulation is performed using the finite element nodes calculated from the molten pool dynamics as the base points of the Vinograph. B2. Calculate the circumcenter and radius of each triangle in the triangulation network; B3. Connect the circumcenters to form a Vinio diagram; In S6, the maximum and minimum values ​​of the vertex coordinates of the scattered convex hull are first calculated, and the nodes of the phase field method are uniformly set within the rectangular area according to the requirements of the phase field method. In step S7, the specific steps for processing each unit of the Vinograph include: C1. Since the elements of a Venn diagram are all convex polygons, the sign of the dot product or cross product of vectors can be used to determine whether a point is in the polygon and to determine the number of the phase field nodes contained in the element. C2. To facilitate interpolation, the node set is expanded from the nodes inside the cell to a rectangular area that includes the internal nodes. C3. Obtain the coordinates and field variable values ​​of the unit's base point and the surrounding base points directly connected to it; C4. Using the above base points as known points, the values ​​of the field variables of the phase field method nodes within the above rectangular area are obtained by interpolation. C5. Retain the field variable data of the phase field nodes within the element, and delete the data of the phase field nodes that are within the rectangular area but not within the element.

2. The mesh mapping method for calculating molten pool dynamics and phase-field dendrite growth according to claim 1, characterized in that: In S3, the Delaunay triangulation generation algorithm uses a point-by-point insertion method, and the steps are as follows: A1. Create a super triangle that includes all the base points, and add the super triangle to the triangle list; A2. Insert base points one by one. Taking the triangulation of four base points as an example, first insert point A to form three triangles. A3. Insert point B, and find the triangle whose circumcircle contains the insertion point in the triangle list; A4. Delete the common edges that affect the triangle; A5. Connect the insertion point to all vertices of the triangle that affect it; A6. Add the newly formed triangle to the triangle list; A7. Repeat steps A2-A6 until all nodes have been inserted.

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