Grid mapping method for dendritic crystal growth calculation based on molten pool dynamics and phase field method

Abstract

The invention discloses a grid mapping method for dendritic crystal growth calculation of a finite element method or a finite volume method and a phase field method. The invention relates to the technical field of welding simulation. The method specifically comprises the following steps that 1, field variable distribution in finite element method or finite volume method welding process numerical simulation calculation is obtained; 2, exporting coordinates and field variable data of nodes of which the temperature is greater than a metal melting point; 3, triangulation is conducted on the melting area according to the node coordinates; 4, drawing a Voronoi diagram of the melting area according to the outer center of the Delaunay triangle; step 5, setting phase field method nodes; 6, the units in the Voronoi diagram are sequentially processed, the base points of the units and the base points directly connected with the units serve as known points, and values of field variables of phase field method nodes are obtained through an interpolation method; and step 7, using the obtained value of the field variable for calculation of phase-field method grain growth.

Description

Technical Field

[0001] The invention relates to the technical field of welding simulation, in particular to a grid mapping method for calculating molten pool dynamics and dendrite growth using a phase field method. Background Art

[0002] Molten pool dynamics simulation is a numerical simulation technology that studies the physical phenomena of metal melting and solidification processes. It involves multi-scale and multi-influencing factors and is related to multi-physical phenomena, such as temperature field, fluid dynamics, thermal stress distribution, etc. During the simulation, the distribution of temperature field and temperature gradient in the calculation domain can be obtained, so the distribution of dynamic dimensional gradient and advancement speed of the molten pool solidification process can be obtained. The phase field method uses a unified control equation to describe the micro-scale growth process of the new phase in the solid phase, liquid phase and solid-liquid interface during metal solidification, and analyzes the crystallization process during metal solidification. During the welding process, the 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 the action of high temperature, a part of the unmelted part near the fusion line is also affected by the high temperature, and the morphology of the metal grains changes. The phase field method can simulate the growth process of metal grains during metal 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 the existing phase field method for calculating dendrite growth, the growth of dendrites is usually calculated in a rectangular plane or a cuboid space. The meshes required for the simulation of the molten pool dynamics and the phase field method for simulating dendrite growth are very different. Usually the mesh size of the latter is much smaller. Therefore, it is necessary to obtain the temperature field of the finer phase field method mesh through the mesh mapping method based on the temperature field of the coarser mesh and the morphology of the molten pool during the welding process. Summary of the invention

[0004] In view of the deficiencies in the prior art, the present invention provides a grid mapping method for melt pool dynamics and phase field dendrite growth calculation, which solves the problems mentioned in the above background technology.

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

[0006] A grid mapping method for melt pool dynamics and phase field dendrite growth calculation, specifically comprising the following steps:

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

[0008] S2, derive the coordinates and temperature and other field variables of the nodes whose temperature is greater than the melting point of the metal;

[0009] S3, performing Delaunay triangulation on the area where the exported finite element nodes are located;

[0010] S4, calculating the circumcenter of the triangle obtained after triangulation;

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

[0012] S6. Draw a rectangular area to include the scattered point area, and set the nodes of the phase field method in it;

[0013] S7. Perform interpolation processing on each unit of the Voronoi diagram in turn.

[0014] Preferably, in S3, the Delaunay triangulation generation algorithm adopts a point-by-point insertion method, and the steps are as follows:

[0015] A1. Create a super triangle, include all base points in it, and add the super triangle to the triangle list;

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

[0017] A3. Insert point B and find the triangle in the triangle list whose circumscribed circle contains the insertion point.

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

[0019] A5. Connect the insertion point to all vertices of the affected triangle;

[0020] A6. Put the newly formed triangle into the triangle list;

[0021] A7. Loop through A2-A6 until all nodes are inserted.

[0022] Preferably, in S5, the specific steps of forming the Voronoi diagram include:

[0023] B1. Delaunay triangulation is performed using the finite element nodes of the melt pool dynamics calculation as the base points of the Voronoi diagram;

[0024] B2. Calculate the center and radius of the circumscribed circle of each triangle in the triangulated network;

[0025] B3. Connect the circumcenters to form a Voronoi diagram.

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

[0027] Preferably, in S7, the specific steps of interpolation processing are:

[0028] C1. Since the units of the Voronoi diagram are all convex polygons, we can determine whether a point is within the polygon based on the sign of the dot product or cross product of the vectors. Determine the number of the phase field node contained in the unit;

[0029] C2. To facilitate interpolation, the node set is expanded from the nodes inside the unit to a rectangular range containing the internal nodes;

[0030] C3, obtain the coordinates and values ​​of field variables of the unit base point and the surrounding base points directly connected to it;

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

[0032] C5. Keep the field variable data of the phase field method nodes inside the unit, and delete the data of the phase field nodes within the rectangular range but not in the unit.

[0033] Preferably, in said C4, The cubic spline interpolation method is used to obtain the internal phase of the unit from the known data of the base point. The value of the field variable of the field node.

[0034] Beneficial Effects

[0035] The present invention provides a grid mapping method for calculating dendrite growth by a molten pool dynamics and a phase field method. Compared with the prior art, the present invention has the following beneficial effects: the grid mapping method for calculating dendrite growth by a molten pool dynamics and a phase field method specifically comprises the following steps: S1, calculating the distribution of field variables such as the temperature field on the base material during welding by a finite element method; S2, deriving the coordinates of the nodes whose temperature is greater than the melting point of the metal and the field variables such as the temperature; S3, performing Delaunay triangulation on the region where the derived finite element nodes are located; S4, calculating the circumcenter of the triangle obtained after triangulation; S5, sequentially connecting the circumcenters of all adjacent triangles to form a Voronoi diagram, wherein the nodes of the finite element are the base points of the Voronoi diagram; S6, drawing a rectangular region so that it contains a scattered point region, and uniformly setting the nodes of the phase field method in the rectangle according to the requirements of the phase field method; S7, sequentially performing interpolation processing on each unit of the Voronoi diagram; through the grid mapping method, the morphology of the molten pool obtained in the finite element simulation can be introduced into the simulation calculation of dendrite growth, so that the simulation process is more in line with the actual situation of welding, and therefore, the grid mapping method plays a very important role in this process. BRIEF DESCRIPTION OF THE DRAWINGS

[0036] Figure 1 A flowchart formed by a Voronoi diagram of the present invention;

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

[0038] Figure 3 Voronoi diagram unit interpolation processing flow chart;

[0039] Figure 4 This is the surface diagram and error analysis after interpolation of the present invention. DETAILED DESCRIPTION

[0040] The following will be combined with the drawings in the embodiments of the present invention to clearly and completely describe the technical solutions in the embodiments of the present invention. Obviously, the described embodiments are only part of the embodiments of the present invention, not all of the embodiments. Based on the embodiments of the present invention, all other embodiments obtained by ordinary technicians in this field without creative work are within the scope of protection of the present invention.

[0041] See also Figure 1-4 The present invention provides two technical solutions: a grid mapping method for melt pool dynamics and phase field dendrite growth calculation, specifically including the following embodiments:

[0042] Embodiment 1

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

[0044] S2, derive the coordinates and temperature and other field variables of the nodes whose temperature is greater than the melting point of the metal;

[0045] S3, performing Delaunay triangulation on the area where the exported finite element nodes are located;

[0046] S4, calculating the circumcenter of the triangle obtained after triangulation;

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

[0048] S6. Draw a rectangular area to include the scattered point area, and evenly set the nodes of the phase field method in the rectangle according to the requirements of the phase field method;

[0049] S7. Perform interpolation processing on each unit of the Voronoi diagram in turn, and use a linear interpolation method to obtain field variable data of the phase field nodes within the unit.

[0050] Embodiment 2

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

[0052] S2, derive the coordinates and temperature and other field variables of the nodes whose temperature is greater than the melting point of the metal;

[0053] S3, performing Delaunay triangulation on the area where the exported finite element nodes are located;

[0054] S4, calculating the circumcenter of the triangle obtained after triangulation;

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

[0056] S6. Draw a rectangular area to include the scattered point area, and evenly set the nodes of the phase field method in the rectangle according to the requirements of the phase field method;

[0057] S7. Process each unit of the Voronoi diagram in turn, and use a cubic spline interpolation method to obtain field variable data of the phase field nodes within the unit.

[0058] Meanwhile, the contents not described in detail in this specification belong to the prior art known to those skilled in the art.

[0059] It should be noted that, in this article, relational terms such as first and second, etc. are only used to distinguish one entity or operation from another entity or operation, and do not necessarily require or imply any such actual relationship or order between these entities or operations. Moreover, the terms "include", "comprise" or any other variants thereof are intended to cover non-exclusive inclusion, so that a process, method, article or device including a series of elements includes not only those elements, but also other elements not explicitly listed, or also includes elements inherent to such process, method, article or device.

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

Claims

1. A grid mapping method for melt pool dynamics and phase field dendrite growth calculation, characterized by: It is mainly used in the numerical simulation calculation of grain growth considering the molten pool morphology during welding process.

2. A grid mapping method for melt pool dynamics and phase field dendrite growth calculation, characterized by: The specific steps include: S1. Calculate the distribution of field variables such as temperature field on the base material during welding by finite element method; S2, derive the coordinates and temperature and other field variables of the nodes whose temperature is greater than the melting point of the metal; S3, performing Delaunay triangulation on the area where the exported finite element nodes are located; S4, calculating the circumcenter of the triangle obtained after triangulation; S5. Connect the circumcenters of all adjacent triangles in sequence to form a Voronoi diagram, where the nodes of the finite element are the base points of the Voronoi diagram; S6. Draw a rectangular area to include the scattered point area, and set the nodes of the phase field method in it; S7. Perform interpolation processing on each unit of the Voronoi diagram in turn.

3. A grid mapping method for melt pool dynamics and phase field dendrite growth calculation according to claim 2, characterized in that: In S3, the Delaunay triangulation generation algorithm adopts a point-by-point insertion method, and the steps are as follows: A1. Create a super triangle, include all base points in it, 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, insert point A first to form three triangles. A3. Insert point B and find the triangle in the triangle list whose circumscribed circle contains the insertion point. A4. Delete the common edges that affect the triangles; A5. Connect the insertion point to all vertices of the affected triangle; A6. Put the newly formed triangle into the triangle list; A7. Loop through A2-A6 until all nodes are inserted.

4. A grid mapping method for melt pool dynamics and phase field dendrite growth calculation according to claim 2, characterized in that: In S5, the specific steps of forming the Voronoi diagram include: B1. Delaunay triangulation is performed using the finite element nodes of the melt pool dynamics calculation as the base points of the Voronoi diagram; B2. Calculate the center and radius of the circumscribed circle of each triangle in the triangulated network; B3. Connect the circumcenters to form a Voronoi diagram.

5. A grid mapping method for melt pool dynamics and phase field dendrite growth calculation according to claim 2, characterized in that: In S6, the maximum and minimum values ​​of the vertex coordinates of the scattered point convex hull are first calculated, and the nodes of the phase field method are evenly arranged within the rectangular range according to the requirements of the phase field method.

6. A grid mapping method for melt pool dynamics and phase field dendrite growth calculation according to claim 2, characterized in that: In S7, the specific steps of processing each unit of the Voronoi diagram include: C1. Since the units of the Voronoi diagram are all convex polygons, we can determine whether a point is within the polygon based on the sign of the dot product or cross product of the vectors. Determine the number of the phase field node contained in the unit; C2. To facilitate interpolation, the node set is expanded from the nodes inside the unit to a rectangular range containing the internal nodes; C3, obtain the coordinates and values ​​of field variables of the unit base point and the surrounding base points directly connected to it; C4. Taking the above base points as known points, the values ​​of the field variables of the phase field method nodes within the above rectangular range are obtained by interpolation method; C5. Keep the field variable data of the phase field method nodes inside the unit, and delete the data of the phase field nodes within the rectangular range but not in the unit.

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