JP7135953B2 - Crystal grain analysis device, grain analysis method, and program - Google Patents

Description

The present invention relates to a crystal grain analysis apparatus, a crystal grain analysis method, and a program, and is particularly suitable for use in analyzing the state of crystal grains.

Primary recrystallized crystal grains grow while exhibiting various behaviors during secondary recrystallization. Therefore, conventionally, a computer analyzes the state of crystal grains of a metal material. When a computer analyzes the state of crystal grains of a metal material, a part of the metal material is cut out instead of the entire metal material, and the cut out region is analyzed. Therefore, it is necessary to consider the state of the boundaries (ends) of the area to be analyzed (analysis target area). As a technique for analyzing the state of crystal grains with a computer in consideration of such boundaries of analysis target regions, there is a technique described in Patent Document 1.

In Patent Document 1, a point is set at a position corresponding to a grain boundary of a crystal grain, and a line having two points adjacent to each other on the same grain boundary as endpoints is set. Then, the curvature of the arc determined by the boundary point, which is a point on the boundary line of the analysis target area, the point adjacent to the boundary point, and the virtual point, and the grain per unit length of the grain boundary to which the boundary point belongs A vector having a magnitude based on the product with the field energy and having a direction from the boundary point to the center of curvature of the arc is used as a driving force generated at the boundary point to calculate the position of the boundary point. Here, the virtual point is a virtual point arranged at a line-symmetrical position with respect to the boundary line of the analysis target area with respect to the point adjacent to the boundary point.

Japanese Patent No. 2937950

However, in the technique described in Patent Document 1, the driving force generated at the boundary point is repeatedly generated by the grain boundary in the analysis target region near the boundary point in the same manner as the analysis target region even outside the analysis target region. is derived as Therefore, for example, when the boundary of the analysis target region is the surface of an actual metal material, the behavior of the boundary point may deviate from the actual behavior. As described above, in the technique described in Patent Document 1, when analyzing the state of crystal grains in the vicinity of the boundary of the analysis target region, there is a risk that the state of the crystal grains will deviate from the actual state.

The present invention has been made in view of the above problems, and suppresses deviation of the state of the crystal grains from the actual state when analyzing the state of the crystal grains near the boundary of the analysis target area. intended to

The crystal grain analysis apparatus of the present invention comprises: image signal acquisition means for acquiring an image signal of a crystal in a metal material; point setting means for setting a boundary point corresponding to an intersection and a non-boundary point different from the boundary point and corresponding to a grain boundary of a crystal grain contained in the crystal; a surface grain boundary driving force deriving means for deriving a surface grain boundary driving force acting in a direction away from the boundary point along the boundary line to which the boundary point belongs; and the point setting means. At the boundary point set by the internal grain, the internal grain boundary driving force is the driving force acting in the direction away from the boundary point along the line connecting the boundary point and the point adjacent to the boundary point. a boundary driving force deriving means, the surface grain boundary driving force derived by the surface grain boundary driving force deriving means for the boundary point set by the point setting means, and the internal grain boundary for the boundary point boundary driving force deriving means for deriving a boundary driving force that is a vector sum of the internal grain boundary driving force derived by the driving force deriving means; A vector obtained by resolving the boundary driving force derived by the force deriving means, the direction being the direction along the boundary line to which the boundary point belongs, the magnitude of the boundary driving force, the boundary point being driving force deriving means for deriving a vector, which is the magnitude of a component in the direction along the boundary line, as the driving force generated at the boundary point; and driving force generated at the boundary point derived by the driving force deriving means. and boundary point position changing means for changing the position of the boundary point based on.

The crystal grain analysis method of the present invention includes an image signal acquisition step of acquiring an image signal of a crystal in a metal material, a grain boundary of a crystal grain contained in the crystal, and a boundary line of a region to be analyzed based on the image signal. a point setting step of setting a boundary point corresponding to the intersection and a non-boundary point different from the boundary point and corresponding to a grain boundary of a crystal grain included in the crystal; a surface grain boundary driving force deriving step of deriving a surface grain boundary driving force acting in a direction away from the boundary point along the boundary line to which the boundary point belongs, and the point setting step; At the boundary point set by the internal grain, the internal grain boundary driving force is the driving force acting in the direction away from the boundary point along the line connecting the boundary point and the point adjacent to the boundary point. a boundary driving force deriving step, the surface grain boundary driving force derived by the surface grain boundary driving force deriving step for the boundary point set by the point setting step, and the internal grain boundary for the boundary point a boundary driving force deriving step of deriving a boundary driving force that is a vector sum of the internal grain boundary driving force derived in the driving force deriving step; A vector obtained by decomposing the boundary driving force derived in the force derivation step, the direction being the direction along the boundary line to which the boundary point belongs, the magnitude of the boundary driving force, the boundary point being a driving force deriving step of deriving a vector, which is the magnitude of a component in the direction along the boundary line, as the driving force generated at the boundary point; and a boundary point position changing step of changing the position of the boundary point based on the boundary point position.

A program of the present invention is for causing a computer to function as each means of the grain analysis apparatus.

ADVANTAGE OF THE INVENTION According to this invention, when analyzing the state of a crystal grain near the boundary of the analysis object area|region, it can suppress that the state of a crystal grain diverges from an actual state.

It is a figure which shows notionally an example of the analysis method performed with a grain analyzer. It is a figure which shows an example of a mode that the crystal grain was modeled in the analysis object area|region vicinity. It is a block diagram which shows an example of the functional structure of a crystal grain analysis apparatus. FIG. 3 shows an example of a grain image, double and triple points, lines and grain boundaries; FIG. 4 is a diagram showing an example of points set on the boundary line of the analysis target area, and lines and grain boundaries set at positions including the boundary line of the analysis target area; It is a figure explaining an example of the calculation method of the driving force which arises in a double point. It is a figure explaining an example of the calculation method of the driving force which arises in a triple point. FIG. 5 is a diagram illustrating an example of a method of calculating a driving force generated at a point on a boundary line of an analysis target area; 4 is a flowchart for explaining an example of processing operations performed by a crystal grain analysis apparatus; FIG. 9-1 is a flowchart following FIG. 9-1; FIG. 9B is a flowchart following FIG. 9-2; FIG. FIG. 9-3 is a flowchart following FIG. 9-3;

An embodiment of the present invention will be described below with reference to the drawings. In this embodiment, a case where an electromagnetic steel sheet is applied as an example of a metal material (for example, a single-phase metal material) whose crystal grains are to be analyzed will be described.
FIG. 1 is a diagram conceptually showing an example of the analysis method performed by the grain analysis apparatus of this embodiment. For convenience of explanation, FIG. 1 shows only one crystal grain A among the many crystal grains that make up the electromagnetic steel sheet. It goes without saying that it will.

In the grain analysis apparatus of this embodiment, grains are modeled as shown in FIG.
First, as shown in FIG. 1A, triple points ia, ie, and if are set at positions corresponding to the end points of the three grain boundaries ua to uc of the crystal grain A, and the midpoints of the grain boundaries ua to uc are set. Double points ib to id and ig to ii are set at positions corresponding to . Here, the triple points ia, ie, and if refer to points where three lines p intersect (here, points in contact with three crystal grains), and the double points ib to id and ig to ii refer to two lines It means the point where p intersects (here, the point where two crystal grains are in contact). Then, a straight line is set to connect adjacent points (grain boundary points) i on the same grain boundaries ua to uc.
As described above, in this embodiment, the double points ib to id, ig to ii are set.

Driving force Fi(t) [N] generated at time t is calculated for each point (double point and triple point) ia to ii of the crystal modeled as described above. Then, based on the calculated driving force Fi(t), the position of each point (double point and triple point) ia to ii after Δt [sec] has passed (time t+Δt) is calculated. Then, the positions of the points (double points and triple points) ia to ii shown in FIG. 1(a) move to the positions shown in FIG. 1(b), for example.

In addition, in the grain analysis apparatus of the present embodiment, the point where the line modeled as described above intersects the boundary line of the region to be analyzed is set. FIG. 2 is a diagram showing an example of how crystal grains are modeled in the vicinity of the analysis target region.
As shown in FIG. 2, in the present embodiment, a single point ip is set at a point where one line p intersects the boundary line of the analysis target region (here, a point in contact with two crystal grains A1 and A2). A point where one line p intersects the boundary line of the analysis target area (here, a point in contact with the three crystal grains A3 to A5) is set as a double point iq, and a point where the three lines intersect the boundary line of the analysis target area ( Here, the point of contact with the four crystal grains A6 to A9) is set as the triple point ir.
As described above, in the present embodiment, points are set not only for the portions not partitioned by the boundary lines of the analysis target region, but also for the portions partitioned by the boundary lines of the analysis target region. In the following description, the point where the line intersects the boundary line of the analysis target area will be referred to as a boundary point as necessary in order to distinguish it from other points.

In the crystal grain analysis apparatus of the present embodiment, as described above, the triple points ia, ie, and if corresponding to the end points of the grain boundaries ua to uc included in the crystal grain A, and the intermediate points of the grain boundaries ua to uc Calculate the driving force Fi(t) generated at each of the corresponding double points ib to id, ig to ii, and the single point ip, double point iq, and triple point ir where the line intersects the boundary of the analysis target area. , triple points ia, ie, and if, double points ib-id, ig-ii, and single point ip, double point iq, and triple point ir are analyzed. As a result, for example, the crystal grain Aa shown in FIG. 1(a) changes with time like the crystal grain Ab shown in FIG. 1(b) as accurately as possible without imposing a large computational load. can be parsed into The behavior of crystal grains on the boundary line of the analysis target region will be described later using FIG. 8 and the like.

The configuration of the grain analysis apparatus will be described in detail below.
FIG. 3 is a block diagram showing an example of the functional configuration of the grain analysis apparatus. The hardware of the crystal grain analysis apparatus 100 can be realized using an information processing apparatus including a personal computer, CPU, ROM, RAM, hard disk, image input/output board, various interfaces, an interface controller, and the like. . Unless otherwise specified, each block shown in FIG. 3 is implemented by the CPU executing a control program stored in the ROM or hard disk using the RAM. By exchanging signals between the blocks shown in FIG. 3, the following processing is realized.
The main difference between the present embodiment and the technology described in Patent Document 1 is the processing in the boundary point driving force calculation unit 118 . In the following, for convenience of explanation, the same parts as the technique described in Patent Document 1 will also be explained in detail, but the parts other than the part related to the boundary point driving force calculation unit 118 are limited to the contents explained below. Instead, for example, the technology described in Patent Document 1 can be applied.

In FIG. 3, the crystal image acquisition unit 101 is, for example, an image signal of the crystal grain A of the electromagnetic steel sheet obtained by the EBSP (Electron Back Scattering Pattern) method and the orientation of each crystal grain A included in the image signal. signal indicating ξ" and the like, and store them in a hard disk or the like. Incidentally, in the following description, the image of the crystal grain A of the electromagnetic steel sheet will be referred to as a crystal grain image as needed. The crystal image acquisition unit 101 may directly acquire the above-described signals from an analyzer that performs crystal analysis by the EBSP method, or may acquire the above-described signals from a removable storage medium such as a DVD or CD-ROM. It may be obtained indirectly.

The crystal image display unit 102 causes the display device 200 to display a crystal grain image based on the crystal grain image signal acquired by the crystal image acquisition unit 101, for example, based on the operation of the operation device 300 by the user. The display device 200 includes a computer display such as an LCD (Liquid Crystal Display). The operation device 300 also includes user interfaces such as a keyboard and a mouse.

The point setting unit 103 allows the user, using the operation device 300, to display the crystal grain image displayed by the crystal image display unit 102 within the analysis target region based on the crystal grain image signal acquired by the crystal image acquisition unit 101. acquires points (single points, double points, and triple points) i specified by The vector shown is set (stored) in the RAM or hard disk. In this embodiment, the user can arbitrarily specify the number of points i (single points, double points and triple points) and initial positions. As described above, in the present embodiment, not only the point i on the crystal grain A that is not partitioned by the boundary line of the analysis target area (the boundary of the crystal grain image), but also the crystal grain A that is partitioned by the boundary line of the analysis target area can be analyzed. A point i on the boundary line of the target area is also specified. Note that the setting of the point i may be performed automatically without being specified by the user.
Further, the point setting unit 103 determines that a vector indicating the position ri(t+Δt) after Δt [sec] at the point (single point, double point, or triple point) i to be calculated is obtained by the position calculation unit 116 as described later. Once calculated, a vector indicating the position ri(t+Δt) of that point i is set (stored) in RAM or hard disk.
Furthermore, as will be described later, when a double point is driven as a boundary point on the boundary line of the analysis target area, the boundary point is divided into two (see the right diagram of FIG. 8B). Therefore, when driving the boundary point i, which is a double point, the point setting unit 103 adds "1" to the total number NI of calculation target points.
Also, when driving a triple point as a boundary point on the boundary line of the analysis target area, the boundary point is divided into three (see the right diagram of FIG. 8(c)). Therefore, when driving the boundary point i, which is the triple junction, the point setting unit 103 adds "2" to the total number of calculation target points NI.

The line setting unit 104 relates to a line p specified by two points i adjacent to each other on the same grain boundary u among the points (single point, double point and triple point) i set by the point setting unit 103. Information is set (stored) in RAM or hard disk. Thus, the line p is a straight line having two points i adjacent to each other on the same grain boundary u.
The grain boundary setting unit 105 obtains information about the grain boundary u specified by the lines p, which are connected to each other with the triple point i set by the point setting unit 103, among the lines p set by the line setting unit 104. , RAM or hard disk. Further, the grain boundary setting unit 105 designates the triple point i of the line p set by the line setting unit 104 as one end, and the point (single point, double point, or triple point) on the boundary line of the analysis target region as the other end. Information about grain boundaries u identified by lines p connected to each other as edges is also set in the RAM or hard disk.

FIG. 4 shows a crystal grain image acquired by the crystal image display unit 102 (FIG. 4A) and points (double points and triple points) i set by the point setting unit 103 (FIG. 4B). , a line setting unit 104, and a line p and a grain boundary u set by a grain boundary setting unit 105 (FIG. 4C). For convenience of explanation, in FIGS. 4B and 4C, among the many crystal grains A included in the crystal grain image 31 shown in FIG. Only set points i, lines p and grain boundaries u are shown.

When the crystal grain image 31 is displayed as shown in FIG. 4A, the user uses the operation device 300 such as a mouse to designate the positions corresponding to the endpoints of the grain boundary u as the triple point i. Also, the position of the midpoint of the grain boundary u is designated as the double point i. Then, for example, as shown in FIG. is set.

Based on these double points and triple points i1 to i18, lines p1 to p18 and grain boundaries u1 to u4 are set as shown in FIG. 4(c). Here, for example, line p1 is specified by triple point i1 and double point i2. Also, the grain boundary u1 is specified by lines p1 to p4 mutually connected with the triple points i1 and i5 at both ends.
Incidentally, as shown in FIG. 4C, the grain boundary u1 is the grain boundary between the crystal grains A1 and A2, the grain boundary u2 is the grain boundary between the crystal grains A1 and A5, and the grain boundary u3 is the grain boundary between the crystal grains A1 and A5. A grain boundary u4 is a grain boundary between the grains A1 and A3.

FIG. 5 shows a point (single point, double point, and triple point) i set on the boundary line of the analysis target region by the point setting unit 103, and the boundary of the analysis target region by the line setting unit 104 and the grain boundary setting unit 105. It is a figure which shows an example of the line p set to the position containing a line, and the grain boundary u. For convenience of explanation, in FIG. 5, among the large number of crystal grains A included in the crystal grain image 31 shown in FIG. Only points i, lines p and grain boundaries u are shown. Here, FIG. 5(a) is a diagram corresponding to the area 33, FIG. 5(b) is a diagram corresponding to the area 34, and FIG. 5(c) is a diagram corresponding to the area 35. 5(d) is a diagram corresponding to the region 36. FIG.

The user uses the operating device 300 such as a mouse to specify a single point, double point, or triple point on the boundary line of the analysis target area. At this time, the user can specify any of single points, double points, and triple points in the crystal grain image 31, for example, according to the number of grain boundaries intersecting points on the boundary line of the region to be analyzed. . For example, in the crystal grain image 31, when there are one, two, and three grain boundaries that intersect points on the boundary line of the analysis target region, the points are defined as single points, double points, and triple points, respectively. specify.
As described above, when a single point, double point, or triple point is specified on the boundary line of the analysis target area, as shown in the left diagram of FIG. i22 and triple point i23 are set on the boundary line of the analysis target area.

Then, based on these single points, double points, and triple points i21 to i24 and the double points or triple points i25 to i34 designated for the intermediate points of the grain boundaries u as described above, the As shown in the right figure, lines p21 to p27 and grain boundaries u _i21 , u _i22-1 , u _i22-2 , u _i23-1 , u _i23-2 , u _i23-3 and u _i24 are set. . Here, for example, line p21 is specified by single point i21 and double point i25. In addition, the grain boundary u _i21 is connected to each other with the single point i21 and the triple point i (not shown) closest to the single point i21 among the triple points connected to the single point i21 via the line p as both ends. is specified by a line p (line p21, etc.).
_Incidentally , as shown in the right _diagram of FIG. u _i22-2 is the grain boundary between the crystal grains A19 and A20. Further, the grain boundary u _i23-1 is the grain boundary between the crystal grains A21 and A22, the grain boundary u _i23-2 is the grain boundary between the crystal grains A22 and A23, and the grain boundary u _i23-3 is the grain boundary between the crystal grains The grain boundary is between A23 and A24, and the grain boundary u _i24 is between the crystal grains A25 and A16.

The analysis temperature setting unit 106 acquires the analysis temperature θ (t) [° C.] of the electromagnetic steel sheet (crystal grain A) to be analyzed based on the operation of the operation device 300 by the user, and sets it in the RAM or hard disk ( Remember. Note that the analysis temperature θ(t) acquired by the analysis temperature setting unit 106 may be a constant value that does not depend on time or a value that depends on time (analysis temperature θ(t) change) is fine.

The orientation setting unit 107 determines all the crystal grains A is set (stored) in the RAM or hard disk.

The grain boundary energy storage unit 108 stores, for example, the grain boundary energy γ [J/m] per unit length and the absolute value of the difference Δξ between the orientations ξ of two crystal grains A adjacent to each other via the grain boundary u. , a graph, a numerical sequence, an expression, or a combination thereof showing the relationship with the analysis temperature θ(t). In the following description, these graphs, numerical sequences, formulas, or combinations thereof will be referred to as graphs and the like.
For example, the “grain boundary energy γ per unit length” at the grain boundary u1 shown in FIG. The “grain boundary energy γ per unit length” corresponding to the analysis temperature θ(t) set by the temperature setting unit 106 is obtained by reading from the graph or the like stored in the grain boundary energy storage unit 108 . In the following description, the grain boundary energy γ per unit length is abbreviated as grain boundary energy γ as necessary. Also, the grain boundary energy storage unit 108 is configured using, for example, a RAM or a hard disk.

The grain boundary energy setting unit 109 causes the grain boundary setting unit 105 to The grain boundary energies γ of all the set grain boundaries u are read out from the graph or the like stored in the grain boundary energy storage unit 108 as described above. Then, the grain boundary energy setting unit 109 sets (stores) the read grain boundary energy γ in the RAM or hard disk.

The mobility storage unit 110 stores the mobility Mi [cm ² /(V·sec)], the absolute value of the difference Δξ between the orientations ξ of two crystal grains A adjacent to each other via the grain boundary u, and Graphs, numerical sequences, formulas, or a combination thereof showing the relationship with temperature θ(t) are stored. In the following description, these graphs, numerical sequences, formulas, or combinations thereof will be referred to as graphs and the like.
For example, the mobility Mi at the grain boundary u1 shown in FIG. The mobility Mi corresponding to the analyzed temperature θ(t) is obtained by reading from the graph or the like stored in the mobility storage unit 110 . It should be noted that the mobility storage unit 110 is configured using, for example, a RAM or a hard disk.

The mobility setting unit 111 causes the grain boundary setting unit 105 to The mobilities Mi of all the set grain boundaries u are read out from the graph or the like stored in the mobility storage unit 110 as described above. Then, the mobility setting unit 111 sets (stores) the read mobility Mi in the RAM or hard disk.

For example, the analysis time setting unit 112 acquires the analysis completion time T [sec] based on the user's operation of the operation device 300, and sets (stores) it in the RAM or hard disk. Then, the analysis time setting unit 112 monitors the time t until the analysis completion time T elapses.
The analysis point determination unit 113 sequentially designates all the points (double points and triple points) i set by the point setting unit 103 as points to be calculated without duplication. Then, the analysis point determination unit 113 determines whether the designated point i is a double point or a triple point.

When the analysis point determination unit 113 determines that the calculation target point i is a double point that is not on the boundary line of the analysis target region, the double point driving force calculation unit 114 calculates the driving force Fi generated at the double point. Calculate (t).
FIG. 6 is a diagram illustrating an example of a method of calculating the driving force Fi(t) generated at a double point that is not on the boundary line of the analysis target area.

In FIG. 6, let Ri(t)[m] be the radius of curvature of an arc 41 defined by a double point i and two points i−1 and i+1 adjacent to the double point. Also, let γi be the magnitude (absolute value) of the grain boundary energy per unit length of the grain boundary u to which the double point i belongs. Then, the magnitude of the driving force Fi(t) generated at the double point i is expressed by the following equation (1). Also, the direction of the driving force Fi(t) generated at the double point i is the direction from the double point i toward the center of curvature O. FIG.

In order to obtain the driving force Fi(t) generated at the double point i using the equation (1), the double point driving force calculator 114 calculates the double point i to be calculated and the two adjacent double points i. Information on two points i−1 and i+1 is read from the point setting unit 103 . Next, the double point driving force calculator 114 calculates the center of curvature O and the radius of curvature Ri(t) of the arc 41 determined by the double point i and the two points i−1 and i+1 adjacent to the double point i. calculate. Further, the double point driving force calculator 114 acquires the grain boundary energy γi per unit length of the grain boundary u belonging to the double point i to be calculated from the grain boundary energy setting unit 109 .

Then, the double point driving force calculation unit 114 substitutes the radius of curvature Ri(t) and the grain boundary energy γi per unit length into the equation (1) to obtain the driving force Fi(t) generated at the double point i. ). Further, the double point driving force calculator 114 calculates the direction from the double point i to be calculated toward the center of curvature O, and determines the direction of the driving force Fi(t) generated at the double point i.

Returning to the description of FIG. 3, when the analysis point determination unit 113 determines that the point i to be calculated is a triple point that is not on the boundary line of the analysis target region, the triple point driving force calculation unit 115 Calculate the driving force Fi(t) occurring at the triple point. FIG. 7 is a diagram illustrating an example of a method of calculating the driving force Fi(t) generated at the triple point that is not on the boundary line of the analysis target region. In FIG. 7, the case of calculating the driving force Fi(t) generated at the triple point i will be described as an example. Also, in FIG. 7, three points adjacent to the triple point i are indicated by "1", "2", and "3", respectively.

First, the triple point driving force calculation unit 115 reads information on the triple point i to be calculated and the three points 1, 2, and 3 adjacent to the triple point i from the point setting unit 103 . Then, the triple junction driving force calculation unit 115 calculates a unit vector having a direction from the triple junction i to be calculated toward points 1, 2, and 3. FIG. Further, the triple junction driving force calculation unit 115 sets the magnitudes (absolute values) of the grain boundary energies γi1, γi2, and γi3 per unit length at the grain boundary u to which the points 1, 2, and 3 belong to the grain boundary energy setting Acquired from the unit 109 .
Then, the triple junction driving force calculation unit 115 calculates the magnitudes (absolute values) of the grain boundary energies γi1, γi2, and γi3 per unit length and the directions from the triple junction i to be calculated toward points 1, 2, and 3. and the unit vector (dij(t)/|dij(t)|) having the following equation (2) to calculate the driving force Fi(t) generated at the triple point i to be calculated.

In equation (2), j is a variable for identifying three points adjacent to the triple point i to be calculated.
Thus, in the present embodiment, the grain boundary energies γi1, γi2, and γi3 per unit length at the grain boundaries u to which the points 1, 2, and 3 belong have the same magnitudes (absolute values), and , the vector sum of three vectors Di1(t), Di2(t), Di3(t) with directions from the triple point i to be computed to points adjacent to that triple point i is the drive produced at the triple point i Calculated as force Fi(t).

Returning to the description of FIG. 3, the boundary point driving force calculation unit 118 detects boundary points (single points, double points, and triple points) where the calculation target point i is on the boundary line of the analysis target region by the analysis point determination unit 113. ), the driving force Fi(t) generated at the boundary point is calculated. FIG. 8 is a diagram illustrating an example of a method of calculating the driving force Fi(t) generated at a point (boundary point) on the boundary line of the analysis target area. 8(a) is a diagram corresponding to the area 33 shown in FIG. 4, FIG. 8(b) is a diagram corresponding to the area 34, and FIG. 8(c) is a diagram corresponding to the area 35. FIG. 8D is a diagram corresponding to the region 36. FIG.

The energy at the grain boundary set as the boundary line of the analysis target region is the surface energy, which is distinguished from the energy at the grain boundary set inside the analysis target region. Therefore, in this embodiment, the surface energy is used to set the driving force acting in the direction along the boundary line. In the following description, this driving force will be referred to as surface grain boundary driving force as required. In this embodiment, the absolute value (magnitude) of the surface grain boundary driving force depends on the angle between the normal direction of the boundary line and the orientation ξ of the crystal grain A. Therefore, in this embodiment, the relationship between the angle between the normal direction of the boundary line and the orientation ξ of the crystal grain A and the absolute value of the surface grain boundary driving force is derived in advance, and the information indicating the relationship is obtained from the crystal grains. It is stored in the analysis device 100 (the boundary point driving force calculation unit 118). In the following description, this relationship will be referred to as the surface grain boundary driving force-crystal orientation relationship as necessary. By changing the orientation ξ, the driving force at the boundary line of the crystal grain A of a certain orientation ξ existing in , is derived by numerical simulation. The information indicating the surface grain boundary driving force-crystal orientation relationship may be a formula (function) or a table.

The boundary point driving force calculator 118 derives the absolute value of the surface grain boundary driving force corresponding to the orientation ξ of the crystal grain A to which the boundary point i belongs from the information indicating the surface grain boundary driving force-crystal orientation relationship. The boundary point driving force calculation unit 118 faces in a direction away from the boundary point i along the boundary line of the crystal grain A to which the boundary point i belongs, and has the derived absolute value as the magnitude. A surface grain boundary driving force is derived as a surface grain boundary driving force generated on the grain A side at the boundary point i. The boundary point driving force calculator 118 derives the surface grain boundary driving force for each crystal grain A to which the boundary point i belongs and which has a boundary line.

In the example shown in FIG. 8A, the grains A16 and A17 to which the boundary point i21 belongs have boundary lines 801. In the example shown in FIG. The boundary point driving force calculation unit 118 calculates the absolute value |F _i21-1 (t) of the surface grain boundary driving force corresponding to the orientation ξ of the crystal grain A16 to which the boundary point i21 belongs and the normal direction of the boundary line 801. and the absolute value of the surface grain boundary driving force |F _i21-2 (t)| . The direction of the surface grain boundary driving force F _i21-1 (t) generated on the grain A16 side at the boundary point i21 is the direction (the second 1 direction). The direction of the surface grain boundary driving force F _i21-2 (t) generated on the grain A17 side at the boundary point i21 is the direction away from the boundary point i21 along the boundary line 801 of the grain A17 (the second 2 direction).

In the example shown in FIG. 8B, among the crystal grains A18, A19, and A20 to which the boundary point i22 belongs, the crystal grains having the boundary line 801 are the crystal grains A18 and A20. derives the absolute value of the surface grain boundary driving force |F _i22-1 (t)| The absolute value |F _i22-2 (t)| The direction of the surface grain boundary driving force F _i22-1 (t) generated on the grain A18 side at the boundary point i22 is the direction (the second 1 direction). The direction of the surface grain boundary driving force F _i22-2 (t) generated on the grain A20 side at the boundary point i22 is the direction (the second 2 direction).

In the example shown in FIG. 8C, among the crystal grains A21, A22, A23, and A24 to which the boundary point i23 belongs, the crystal grains having the boundary line are the crystal grains A21 and A24. 118 derives the absolute value of the surface grain boundary driving force | _Fi23-1 (t)| The absolute value |F _i23-2 (t)| The direction of the surface grain boundary driving force F _i23-1 (t) generated on the grain A21 side at the boundary point i23 is the direction (the second 1 direction). The direction of the surface grain boundary driving force F _i23-2 (t) generated on the grain A24 side at the boundary point i23 is the direction (the second 2 direction).

In the example shown in FIG. 8(d), grains A16 and A25 to which boundary point i24 belongs have boundary lines 801 and 802, respectively. The boundary point driving force calculator 118 calculates the absolute value |F _i24-1 (t) of the surface grain boundary driving force corresponding to the orientation ξ of the crystal grain A16 to which the boundary point i16 belongs and the normal direction of the boundary line 801. and the absolute value of the surface grain boundary driving force |F _i24-2 (t)| . The direction of the surface grain boundary driving force F _i24-1 (t) generated on the grain A16 side at the boundary point i24 is the direction (the second 1 direction). The direction of the surface grain boundary driving force F _i24-2 (t) generated on the grain A25 side at the boundary point i24 is the direction (the second 2 direction).

In addition, the boundary point driving force calculation unit 118 acts in a direction along the grain boundary from the boundary point i as a driving force due to energy at the grain boundary (grain boundary other than the boundary line) set inside the analysis target region. Derive the driving force. In the following description, this driving force will be referred to as internal grain boundary driving force as required. In this embodiment, the boundary point driving force calculator 118 calculates a unit vector (dij(t)/|dij( t) |) and the magnitude (absolute value) γij of the grain boundary energy γ per unit length at the grain boundary u to which the boundary points i and j belong (the grain boundary u to which the line p belongs) ( =γij×dij(t)/|dij(t)|) is derived as the internal grain boundary driving force generated on the grain boundary u side at the boundary point i. The boundary point driving force calculator 118 derives the internal grain boundary driving force for each grain boundary u (other than the boundary line) to which the boundary point i belongs.

In the example shown in FIG. 8A, the boundary point i21 is the endpoint. In this case, the grain boundary (other than the boundary line) to which the boundary point i21 belongs is the grain boundary u i21 connecting the boundary point i21 and the point _i25 . The boundary point driving force calculation unit 118 calculates a unit vector (dij(t)/|dij(t)|) having a direction from the boundary point i21 to the point _i25 and a grain boundary per unit length at the grain boundary u i21 The product of the magnitude (absolute value) of the energy γ and γij is derived as the internal grain boundary driving force F _i21-3 (t) generated on the grain boundary u _i21 side at the boundary point i21 (in this case, i=i21 , j=i25).

In the example shown in FIG. 8B, the boundary point i22 is a double point. In this case, the grain boundaries (other than the boundary line) to which the boundary point i22 belongs are the grain boundary u _i22-1 connecting the boundary points i22 and i26, and the grain boundary u _i22-2 connecting the boundary points i21 and i27. is. The boundary point driving force calculation unit 118 calculates a unit vector (dij(t)/|dij(t)|) having a direction from the boundary point _i22 to the point i26, and The product of the magnitude (absolute value) γij of the grain boundary energy γ is derived as the internal grain boundary driving force F _i22-3-1 (t) generated on the grain boundary u _i22-1 side at the boundary point i22 ( In this case i=i22 and j=i26). In addition, the boundary point driving force calculation unit 118 calculates a unit vector (dij(t)/|dij(t)|) having a direction from the boundary point i22 to the point 27 and a unit length at the grain boundary u _i22-2 The product of the magnitude (absolute value) γij of the grain boundary energy γ at the boundary point i22 is derived as the internal grain boundary driving force F _i22-3-2 (t) generated on the grain boundary u _i22-2 side at the boundary point i22 ( In this case, i=i22 and j=i27).

In the example shown in FIG. 8(c), the boundary point i23 is the triple point. In this case, the grain boundaries (other than the boundary line) to which the boundary point i23 belongs are the grain boundary u _i23-1 connecting the boundary point i23 and the point i28, and the grain boundary u _i23-2 connecting the boundary point i23 and the point i29. and a grain boundary u _i23-3 connecting the boundary point i23 and the point i30. The boundary point driving force calculation unit 118 calculates a unit vector (dij(t)/|dij(t)|) having a direction from the boundary point _i23 to the point i28, and The product of the magnitude (absolute value) γij of the grain boundary energy γ is derived as the internal grain boundary driving force F _i23-3-1 (t) generated on the grain boundary u _i23-1 side at the boundary point i23 ( In this case i=i23 and j=i28). Further, the boundary point driving force calculation unit 118 calculates a unit vector (dij(t)/|dij(t)|) having a direction from the boundary point i23 to the point i29 and a unit length at the grain boundary u _i23-2 The product of the magnitude (absolute value) γij of the grain boundary energy γ at the boundary point i23 is derived as the internal grain boundary driving force F _i23-3-2 (t) generated on the grain boundary u _i23-2 side at the boundary point i23 ( In this case, i=i23 and j=i29). Further, the boundary point driving force calculation unit 118 calculates a unit vector (dij(t)/|dij(t)|) having a direction from the boundary point i23 to the point i30 and a unit length at the grain boundary u _i23-3 The product of the magnitude (absolute value) γij of the grain boundary energy γ at the boundary point i23 is derived as the internal grain boundary driving force F _i23-3-3 (t) generated on the grain boundary u _i23-3 side at the boundary point i23 ( In this case, i=i23 and j=i30).

In the example shown in FIG. 8D, the boundary points i24 are points at the four corners of the analysis target area. In this case, the grain boundary (other than the boundary line) to which the boundary point i24 belongs is the grain boundary u _i24 connecting the boundary point i24 and the point i34. The boundary point driving force calculator 118 calculates a unit vector (dij(t)/|dij(t)|) having a direction from the boundary point i24 to the point i34 and a grain boundary per unit length at the grain boundary u _i24 The product of the magnitude (absolute value) of the energy γ and γij is derived as the internal grain boundary driving force F _i24-3 (t) generated on the grain boundary u _i24 side at the boundary point i24 (in this case, i=i24 , j=i34).

Then, the boundary point driving force calculation unit 118 calculates the vector sum of the surface grain boundary driving force generated on the grain A side at the boundary point i and the internal grain boundary driving force generated on the grain boundary u side to which the boundary point i belongs. to derive As shown in FIGS. 8A to 8C, when the boundary point i is not at the four corners of the analysis target region, the boundary point driving force calculation unit 118 generates a driving force on the grain A side at the boundary point i. A vector sum of (the vector sum of) the surface grain boundary driving force and the internal grain boundary driving force generated on the side of the grain boundary u to which the boundary point i belongs is derived. On the other hand, as shown in FIG. 8D, when the boundary point i is located at the four corners of the analysis target region, the boundary point driving force calculation unit 118 calculates the surface grain boundary driving force generated on the grain A side at the boundary point i. A vector sum of each of the forces and the internal grain boundary driving force generated on the side of the grain boundary u to which the boundary point i belongs is individually derived.
Specifically, in the example shown in FIG. 8A, the boundary point driving force calculator 118 calculates the surface grain boundary driving forces F _i21-1 (t), F _{i21 −2} (t) and the vector sum F _{i21-4 (t) of the internal grain boundary driving force F i21-3 (} t) generated on the side of the grain boundary u i21 to which the boundary point i21 _belongs is derived.

In the example shown in FIG. 8B, the boundary point driving force calculator 118 calculates the surface grain boundary driving forces F _i22-1 (t), F _i22-2 ( t) and the vector sum F _i21-4-1 (t) of the internal grain boundary driving force F _i22-3-1 (t) generated on the side of the grain boundary u _i21-1 to which the boundary point i22 belongs; , the surface grain boundary driving forces F _i22-1 (t) and F _i22-2 (t) generated on the grain A18 and A20 sides at the boundary point _i22 , and the internal and deriving the vector sum F _i22-4-2 (t) with the grain boundary driving force F _i22-3-2 (t).

In the example shown in FIG. 8C, the boundary point driving force calculator 118 calculates the surface grain boundary driving forces F _i23-1 (t), F _i23-2 ( t) and the vector sum F _i23-4-1 (t) of the internal grain boundary driving force F _i22-3-1 (t) generated on the side of the grain boundary u _i23-1 to which the boundary point i23 belongs; , the surface grain boundary driving forces F _i23-1 (t) and F _i23-2 (t) generated on the grain A21 and A24 sides at the boundary point _i23 , and the internal Deriving the vector sum F _i23-4-2 (t) with the grain boundary driving force F _i23-3-2 (t), and calculating the surface grain boundary driving force F Vector sum F _i23 of _i23-1 (t), F _i23-2 (t), and internal grain boundary driving force F _i23-3-3 (t) generated on the side of grain boundary u _i23-3 to which boundary point i23 belongs _{-4-3 Deriving} (t).

In the example shown in FIG. 8D, the boundary point driving force calculator 118 calculates the surface grain boundary driving force F _i24-1 (t) generated on the grain A16 side at the boundary point i24 and the grain boundary point i24 belongs to. Deriving the vector sum F _i24-4-1 (t) with the internal grain boundary driving force F _i24-3 (t) generated on the boundary u _i24 side, and the surface grain boundary generated on the grain A25 side at the boundary point i24 Derive the vector sum F _i24-4-2 (t) of the driving force F _i24-2 (t) and the internal grain boundary driving force F _i24-3 (t) generated on the side of the grain boundary u _i24 to which the boundary point i24 belongs Do and do.

In the following description, the vector sum of the surface grain boundary driving force generated on the grain A side at the boundary point i and the internal grain boundary driving force generated on the grain boundary u side to which the boundary point i belongs is expressed as It is called boundary driving force.
Then, the boundary point driving force calculation unit 118 calculates a vector obtained by decomposing the boundary driving force F _i (t) at the boundary point i, the direction of which is along the boundary line to which the boundary point i belongs, and is the magnitude of the component of the boundary driving force Fi(t) in the direction along the boundary line to which the boundary point _i belongs is derived as the driving force Fi(t) generated at the boundary point i. .

As shown in FIGS. 8A to 8C, when the boundary points i21, i22, and i23 are not at the four corners of the analysis target area, the boundary point driving force calculator 118 calculates the boundary driving force at the boundary point i. Force F _i21-4 (t), F _i22-4-1 (t)・F _i22-4-2 (t), F _i23-4-1 (t)・F _i23-4-2 (t)・F _{Decompose i23-4-3} (t) into a direction along the boundary line 801 and a direction perpendicular to the boundary line 801 . The boundary point driving force calculator 118 calculates boundary driving forces F _i21-4 (t), F _i22-4-1 (t), F _i22-4-2 (t), F _{i23-4- Driving force Fi21} (t), Fi22-1(t), Fi22-2(t), Fi23-1(t), Fi23-2(t), and Fi23-3(t).

By deriving the driving force Fi(t) generated at the boundary point i in this way, the boundary point i21 moves along the boundary line of the analysis target area as shown in the right diagram of FIG. , becomes a new boundary point i21'. Also, as shown in the right diagram of FIG. 8B, the boundary point i22, which is a double point, is divided into two boundary points i22' and i22''. Also, as shown in the right diagram of FIG. 8(c), the boundary point i23, which is the triple junction, is divided into three boundary points i23', i23'', and i23'''.
On the other hand, as shown in FIG. 8D, when the boundary point i24 is at the four corners of the analysis target region, the boundary point driving force calculator 118 calculates the boundary driving force F _i24-4-1 ( t) (first boundary driving force) is resolved into a direction along boundary line 801 and a direction perpendicular to boundary line 801, and boundary driving force F _i24-4-1 (t) (second boundary driving force) at boundary point i24. boundary driving force) is decomposed in the direction along the boundary line 801 to derive a vector Fi24-1(t). Further, the boundary point driving force calculation unit 118 decomposes the boundary driving force F _i24-4-2 (t) at the boundary point i24 into a direction along the boundary line 802 and a direction perpendicular to the boundary line 802, and calculates the boundary point A vector Fi24-2(t) is derived by resolving the boundary driving force F _i24-4-2 (t) at i24 in the direction along the boundary line 802 . The boundary point driving force calculation unit 118 calculates the vector Fi24-2(t), which has the greater magnitude (absolute value) of the vector Fi24-1(t) and the vector Fi24-2(t), at the boundary point i24. is derived as the driving force Fi24(t) generated at . By deriving the driving force Fi24(t) generated at the boundary point i in this manner, the boundary point i24 moves along the boundary line of the analysis target region as shown in the right diagram of FIG. 8(d). , becomes the new boundary point i24'.

As described above, in the technique described in Patent Document 1, the driving force generated at the boundary point is generated by the grain boundary in the analysis target region in the vicinity of the boundary point in the same manner as the analysis target region even outside the analysis target region. It is derived using equation (1) assuming that . Then, the boundary point i is moved so that the length of the line p connecting the boundary point i and the point adjacent to the boundary point i at the shortest distance becomes shorter than before the movement of the boundary point i. . On the other hand, in the present embodiment, a driving force (surface grain boundary driving force) acting from the boundary point i in a direction away from the boundary point i along the boundary line to which the boundary point i belongs, and from the boundary point i, A vector of a driving force (internal grain boundary driving force) acting in a direction away from the boundary point i along a line p (grain boundary u) connecting the boundary point i and a point i adjacent to the boundary point i The sum (boundary driving force) is decomposed in the direction along the boundary line to derive the driving force Fi(t) generated at the boundary point i. Here, the surface grain boundary driving force at the boundary point i is the driving force generated corresponding to the surface energy of the analysis target region (electromagnetic steel sheet) at the boundary point i. The internal grain boundary driving force is a driving force generated corresponding to the energy generated in the grain boundary (grain boundary other than the boundary line) inside the analysis target area (magnetic steel sheet). In this embodiment, for example, the surface grain boundary driving force (the angle formed by the normal direction of the boundary line and the orientation ξ of the crystal grain A) causes the boundary point i and the point i adjacent to the boundary point i to be separated by the shortest distance can be longer than before moving the boundary point i (the length of the line p can be shorter or longer than before moving the boundary point i).

Returning to the description of FIG. 3, the position calculator 116 calculates changes in the positions of the single point i, the double point i, and the triple point i over time.
First, an example of a method for calculating changes in the positions of the boundary point i and the double point i that is not the boundary point i over time will be described.
The position calculation unit 116 acquires a vector indicating the driving force Fi(t) calculated by the double point driving force calculation unit 114 (a vector indicating the driving force Fi(t) generated at the point i to be calculated). Further, the position calculation unit 116 acquires the mobility Mi of the grain boundary u to which the point i to be calculated belongs from the mobility setting unit 111 .
Here, when the calculation target point i is a boundary point and is a double point (triple point), the position calculation unit 116 calculates the mobility Mi of the grain boundary u to which the calculation target point i belongs as You will get two (three). In the example shown in FIG. 8B, the mobility Mi1 of the grain boundaries u of the crystal grains A18 and A19 and the mobility Mi2 of the grain boundaries u of the crystal grains A19 and A20 are obtained. In the example shown in FIG. 8C, the mobility Mi1 of the grain boundaries u of the crystal grains A21 and A22, the mobility Mi2 of the grain boundaries u of the crystal grains A22 and A23, and the mobility Mi2 of the grain boundaries u of the crystal grains A23 and A24 Obtain the mobility Mi3 of the grain boundary u.

Then, the position calculation unit 116 converts the mobility Mi of the grain boundary u to which the calculation target point i belongs and the vector indicating the driving force Fi(t) of the calculation target point i to the following equation (3): Substitute to compute a vector indicating the velocity vi(t) of the point i being computed.
Here, when the point i to be calculated is a boundary point and is a double point (triple point), the position calculation unit 116 divides the vector indicating the velocity vi(t) of the point i to be calculated by 2 one (three) will be calculated.

After that, the position calculation unit 116 acquires “the vector indicating the current position ri(t) of the point i to be calculated” set in the point setting unit 103 . Then, the position calculation unit 116 converts a vector indicating the velocity vi(t) of the calculation target point i, a vector indicating the current position ri(t) of the calculation target point i, and the time Δt into the following ( 4) Calculate a vector indicating the position ri(t+Δt) where the point i to be calculated exists when Δt [sec] has passed from the current time t by substituting into the equation. In this embodiment, the change in the position of the point i to be calculated over time is calculated in this manner.
Here, if the point i to be calculated is a boundary point and is a double point (triple point), the position calculation unit 116 calculates We will compute two (three) vectors indicating the position ri(t+Δt) where the point i of interest lies.
The time Δt defines the timing (interval) for calculating the position of the point i, and is predetermined according to the type of electromagnetic steel sheet to be analyzed, analysis conditions, analysis accuracy, and the like.

Position calculation section 116 then outputs to point setting section 103 a vector indicating position ri(t+Δt) at which point i to be calculated exists. By doing so, the point setting unit 103 sets a vector indicating the current position ri(t) of the point i to be calculated, as described above.

Next, an example of a method for calculating the positional change over time of the triple point i, which is not a boundary point, will be described.
The position calculation unit 116 acquires from the mobility setting unit 111 the mobilities Mi1 to Mi3 of the three grain boundaries u to which the triple point i to be calculated belongs.

Then, the position calculation unit 116 calculates the mobility Mi of the triple junction i to be calculated using the mobilities Mi1 to Mi3 of the three grain boundaries u to which the triple junction i to be calculated belongs. Specifically, the position calculation unit 116 calculates a unit vector (dij(t)/|dij(t)|) having a direction from the target triple point i to points 1, 2, and 3, The mobilities Mi1 to Mi3 of the three grain boundaries u to which i belongs are substituted into the following equation (5) to calculate the mobility Mi of the triple junction i to be calculated.

In equation (5), j is a variable for identifying three points adjacent to the triple point i to be calculated.
Further, the position calculation unit 116 obtains a vector indicating the driving force Fi(t) calculated by the triple junction driving force calculation unit 115 (a vector indicating the driving force Fi(t) generated at the triple point i to be calculated). do. Then, the position calculation unit 116 calculates the mobility Mi of the grain boundary u to which the triple junction i to be calculated belongs and the vector indicating the driving force Fi(t) of the triple junction i to be calculated, as described in (3) above. Substitute into the equation to calculate a vector indicating the velocity vi(t) of the triple point i to be calculated.

After that, the position calculation unit 116 acquires “the vector indicating the current position ri(t) of the triple point i to be calculated” set in the point setting unit 103 . Then, the position calculation unit 116 calculates the vector indicating the velocity vi(t) of the triple point i to be calculated, the vector indicating the current position ri(t) of the triple point i to be calculated, and the time Δt as described above. (4) to calculate a vector indicating the position ri(t+Δt) where the triple point i to be calculated exists when Δt [sec] has passed from the current time t. In this embodiment, the change in the position of the triple point i to be calculated over time is calculated in this manner. As described above, the time Δt defines the timing (interval) for calculating the position of the point i. It is defined.

Position calculation section 116 then outputs to point setting section 103 a vector indicating position ri(t+Δt) at which triple point i to be calculated exists. By doing so, the point setting unit 103 sets a vector indicating the current position ri(t) of the triple point i to be calculated, as described above.

The analysis time setting unit 112 determines whether the position calculation unit 116 has calculated the position ri(t+Δt) when the analysis completion time T has passed or after the analysis completion time T has passed. By judging whether or not the analysis has been completed until the analysis completion time T is judged.

When the analysis time setting unit 112 determines that the analysis has been completed by the analysis completion time T, the analysis image display unit 117 displays the "vector of the position ri(t+Δt) of the point i" calculated by the position calculation unit 116. Based on this, the display device 200 is caused to display an image showing how the state of the crystal grain A changes during the time t from 0 (zero) to T [sec].

Next, an example of the processing operation performed by the crystal grain analysis apparatus 100 will be described with reference to the flow charts of FIGS. 9-1 to 9-4. It should be noted that the processing of the flowchart shown in FIG. 9A is started when the CPU reads the control program from the ROM or hard disk and starts executing it based on the operation of the operation device 300 by the user.

First, in step S1 in FIG. 9-1, the crystal image acquisition unit 101 receives an image signal of the crystal grains A of the electromagnetic steel plate and a signal indicating the orientation ξ of each crystal grain A included in the image signal. wait until When the image signal (crystal grain image signal) of the crystal grains A of the electromagnetic steel sheet and the signal indicating the orientation ξ of each crystal grain A included in the image signal are input, the process proceeds to step S2.
As described above, in the present embodiment, an example of image signal acquisition means is realized by performing the process of step S1, for example.

When the process proceeds to step S2, the crystal image display unit 102 causes the display device 200 to display the crystal grain image 31 based on the crystal grain image signal acquired in step S1. At this time, the crystal image display unit 102 also displays on the display device 200 an image for prompting the user to input the analysis temperature θ(t) of the electromagnetic steel sheet (crystal grain A) to be analyzed and the analysis completion time T. Let Here, after the analysis temperature θ(t) and the analysis completion time T are sequentially input, the user designates the point i (single point, double point, or triple point) while referring to the grain image 31. A case where it is possible will be described as an example.

Next, in step S3, the analysis temperature setting unit 106 waits until the analysis temperature θ(t) of the electromagnetic steel sheet (grain A) to be analyzed is input based on the operation of the operation device 300 by the user. . Then, when the analysis temperature θ(t) of the electromagnetic steel sheet (crystal grain A) to be analyzed is input, the process proceeds to step S4. When the process proceeds to step S4, the analysis temperature setting unit 106 sets the input analysis temperature θ(t) of the electromagnetic steel sheet (grain A) to be analyzed in the RAM or hard disk. In the flowcharts of FIGS. 9-1 to 9-4, the case where the analysis temperature θ(t) of the electromagnetic steel sheet (crystal grain A) to be analyzed is a constant value will be described as an example.

Next, in step S<b>5 , the analysis time setting unit 112 waits until the analysis completion time T is input based on the operation of the operation device 300 by the user. Then, when the analysis completion time T is input, the process proceeds to step S6. When the process proceeds to step S6, the analysis time setting unit 112 sets the input analysis completion time T in the RAM or hard disk.
Next, in step S7, the point setting unit 103 waits until a point i (single point, double point, or triple point) is specified for the crystal grain image displayed by the crystal image display unit 102. FIG. As described above, in the present embodiment, any single point, double point, or triple point can be designated on the boundary line of the analysis target area. Any one of the weights can be specified.

After the point i (single point, double point, or triple point) is designated as described above, the process proceeds to step S8. When proceeding to step S8, the point setting unit 103 calculates a vector indicating the position ri(t) of the point i determined to be designated in step S7, and sets it in the RAM or hard disk.
As described above, in the present embodiment, an example of point setting means is realized by performing the process of step S8.
Next, in step S9, the point setting unit 103 determines whether or not an instruction to end the work of designating a point (single point, double point, or triple point) i has been given based on the operation of the operating device 300 by the user. judge. As a result of this determination, if no instruction has been given to end the work specifying the point i, the process returns to step S7, and the already specified point (single point, double point, or triple point) i and another point (single point) point, double point or triple point) waits until i is specified.
On the other hand, if an instruction to end the work of designating point i is given, the process proceeds to step S10. When the process proceeds to step S10, the point setting unit 103 determines the number of points (single point, double point, or triple point) i determined to be specified in step S7 (that is, the number of times the process of step S7 is performed) NI is calculated and set in RAM or hard disk.

Next, in step S11, the line setting unit 104 selects two points i adjacent to each other on the same grain boundary u among the points (single point, double point, or triple point) i set in step S8. The specified line p is set in RAM or hard disk. That is, the line setting unit 104 defines the line p by two points i specifying the line p. For example, the line p1 shown in FIG. 4(c) is defined by the following equation (5).
p1={i1, i2} (5)

Next, in step S12, the grain boundary setting unit 105 selects the grain boundary u specified by the line p, which is connected to each other with the triple point i set in step S8 as both ends, among the lines p set in step S11. is set in RAM or hard disk. Further, the grain boundary setting unit 105 sets the grain boundary u specified by a line p having the triple point i set in step S8 as one end and the boundary point i set in step S8 as the other end and connected to each other. also set in RAM or hard disk. That is, the grain boundary setting unit 105 defines the grain boundary u by a plurality of lines p specifying the grain boundary u. For example, the grain boundary u1 shown in FIG. 4(c) is defined by the following equation (6).
u1={p1, p2, p3, p4} (6)

Next, in step S13, the orientation setting unit 107 converts the crystal grain image 31 into The orientations ξ of all crystal grains A included are set in the RAM or hard disk.
Next, in step S14, the grain boundary energy setting unit 109 stores grain boundary energy based on the orientation ξ of the crystal grain A set in step S14 and the analysis temperature θ(t) set in step S4. Grain boundary energy γ per unit length of all grain boundaries u set in step S12 is read out from the graph or the like stored in the unit 108 . Then, the grain boundary energy setting unit 109 sets the read grain boundary energy γ per unit length in the RAM or hard disk.

Next, in step S15, the mobility setting unit 111 stores the mobility based on the orientation ξ of the crystal grain A set in step S14 and the analysis temperature θ(t) set in step S4. From the graph or the like stored in the unit 110, the mobilities Mi of all the grain boundaries u set in step S12 are read. Then, the mobility setting unit 111 sets the read mobility Mi in the RAM or hard disk.

Next, at step S16 in FIG. 9B, the point setting unit 103 sets "0 (zero)" to the number NJ of boundary points i that increases by separating the boundary points i.
Next, in step S17, the point setting unit 103 sets "1" to the variable i indicating the point to be calculated.
Next, in step S18, the analysis point determination unit 113 determines whether or not the point (calculation target point) specified by the variable i indicating the calculation target point is a boundary point. As a result of this determination, if the point to be calculated is a boundary point, the process proceeds to step S22, which will be described later.

On the other hand, if the point to be calculated is not a boundary point, the process proceeds to step S19. When the process proceeds to step S19, the analysis point determination unit 113 determines whether or not the variable i indicating the points to be calculated is smaller than the total number NI of points to be calculated. As a result of this determination, if the variable i indicating the points to be calculated is smaller than the total number of points NI to be calculated, it is determined that all the currently set points i have not been judged as to whether they are boundary points or not. Then, the process proceeds to step S20.

When the process proceeds to step S20, the point setting unit 103 adds "1" to the variable i indicating the point to be calculated to change the point to be calculated. Then, the process after step S18 is performed again for the changed points.
On the other hand, if it is determined in step S19 that the variable i indicating the points to be calculated is greater than or equal to the total number of points to be calculated NI, it is determined whether or not all the currently set points i are boundary points. It is determined that the determination has been made, and the process proceeds to step S21. When the process proceeds to step S21, the point setting unit 103 adds the number NJ of boundary points i, which is increased by dividing the boundary point i, to the total number of calculation target points NI, and obtains the total number of calculation target points NI. to update. Then, the process proceeds to step S26 in FIG. 9-3, which will be described later.

If it is determined in step S18 that the point to be calculated is a boundary point, the process proceeds to step S22. When proceeding to step S22, the analysis point determination unit 113 determines whether or not the boundary point to be calculated is a single point. As a result of this determination, if the boundary point to be calculated is a single point, the process proceeds to step S19 described above, and it is determined whether or not the variable i indicating the point to be calculated is smaller than the total number of points to be calculated NI. judge.

On the other hand, if the boundary point to be calculated is not a single point, the process proceeds to step S23. After proceeding to step S23, the analysis point determination unit 113 determines whether or not the boundary point i to be calculated is a double point. As a result of this determination, if the boundary point i to be calculated is a double point, the process proceeds to step S24. When the process proceeds to step S24, the point setting unit 103 adds "1" to the number NJ of boundary points i that increases by separating the boundary points i. Then, the process proceeds to step S19 described above, and it is determined whether or not the variable i indicating the points to be calculated is smaller than the total number NI of points to be calculated.

On the other hand, if the boundary point to be calculated is not a double point but a triple point as a result of the determination in step S23, the process proceeds to step S25. When the process proceeds to step S25, the point setting unit 103 adds "2" to the number NJ of boundary points i that is increased by separating the boundary points i. Then, the process proceeds to step S19 described above, and it is determined whether or not the variable i indicating the points to be calculated is smaller than the total number NI of points to be calculated.

When the total number NI of points to be calculated considering the separation of boundary points is determined as described above, the process proceeds to step S26 in FIG. 9-3. When the process proceeds to step S26, the analysis time setting unit 112 sets the time t to "0 (zero)".
Next, in step S27, the analysis point determination unit 113 sets the variable i indicating the point to be calculated to "1". This sets the point i to be calculated.

Next, in step S28, the analysis point determination unit 113 determines whether the point to be calculated is a boundary point. As a result of this determination, if the point to be calculated is a boundary point, the process proceeds to step S46 in FIG. 9-4, which will be described later.
On the other hand, if the point to be calculated is not a boundary point, the process proceeds to step S29. When proceeding to step S29, the analysis point determination unit 113 determines whether or not the point i to be calculated is a double point. As a result of this determination, if the point to be calculated is not a double point but a triple point, the process proceeds to step S42, which will be described later. On the other hand, if the point to be calculated is a double point, the process proceeds to step S30.
When the process proceeds to step S30, the double point driving force calculation unit 114 reads from the point setting unit 103 the information on the double point i to be calculated and the two points i−1 and i+1 adjacent to the double point. . Then, the double point driving force calculator 114 calculates the center of curvature O and the radius of curvature Ri(t) of the arc 41 determined by the double point i and the two points i−1 and i+1 adjacent to the double point i. do.

Next, in step S<b>31 , the double point driving force calculation unit 114 reads from the grain boundary energy setting unit 109 the grain boundary energy γi per unit length of the grain boundary u to which the calculation target point belongs.
Next, in step S32, the double point driving force calculation unit 114 calculates the curvature radius Ri(t) calculated in step S30 and the grain boundary energy γi per unit length read out in step S31 by the formula (1). to calculate the magnitude of the driving force Fi(t) generated at the double point i.

Further, the double point driving force calculation unit 114 reads from the point setting unit 103 a vector indicating the current position ri(t) of the double point i to be calculated. Then, the double point driving force calculation unit 114 calculates the curvature from the double point i to be calculated based on the vector indicating the current position ri(t) of the double point i to be calculated and the center of curvature O calculated in step S30. Calculate the direction toward the center O to determine the direction of the driving force Fi(t) occurring at the double point i. As a result, a vector representing the driving force Fi(t) generated at the double point i is obtained.

Next, in step S33, the position calculation unit 116 reads from the mobility setting unit 111 the mobility Mi corresponding to the grain boundary u to which the point (double point) to be calculated belongs.
Next, in step S<b>34 , the position calculation unit 116 receives from the point setting unit 103 a vector indicating the current position ri(t) of the point to be calculated.

Next, in step S35, the position calculation unit 116 calculates the "vector indicating the driving force Fi(t) generated at the point to be calculated" obtained in step S32 (or steps S43 and S49, which will be described later), and step S33 ( Alternatively, the "mobility Mi of the grain boundary u to which the point to be calculated belongs" read out in steps S44 and S50 described later) is substituted into the equation (3) to obtain the velocity vi of the point i to be calculated ( Compute a vector representing t).
Then, the position calculation unit 116 converts a vector indicating the velocity vi(t) of the point i to be calculated, a vector indicating the current position ri(t) of the point to be calculated, and the time Δt into equation (4): to calculate a vector indicating the position ri(t+Δt) where the point i to be calculated exists when Δt [sec] has passed from the current time t.

Next, in step S36, the analysis point determination unit 113 determines whether or not the variable i indicating the points to be calculated is smaller than the total number NI of points to be calculated. As a result of this determination, if the variable i indicating the points to be calculated is smaller than the total number of points NI to be calculated, it is determined that the positions at time t+Δt have not been calculated for all points i currently set. Then, the process proceeds to step S37.

When the process proceeds to step S37, the analysis point determination unit 113 adds "1" to the variable i indicating the point to be calculated to change the point to be calculated. Then, the processing after step S28 is performed again for the changed points.
On the other hand, if it is determined in step S36 that the variable i indicating the points to be calculated is greater than or equal to the total number of points to be calculated NI, the position at time t+Δt is set to It is determined that all points i have been calculated, and the process proceeds to step S38.

When the process proceeds to step S<b>38 , position calculation section 116 outputs to point setting section 103 a vector indicating position ri(t+Δt) at which point i to be calculated exists. As a result, the point setting unit 103 sets (or updates) a vector indicating the current position ri(t) of the point to be calculated.
Next, in step S39, the analysis time setting unit 112 determines whether the time t is longer than the analysis completion time T set in step S6. That is, it is determined whether or not the analysis completion time T has passed. As a result of this determination, if the time t is not longer than the analysis completion time T set in step S6 (if the analysis completion time T has not passed), the process proceeds to step 40. FIG. When the process proceeds to step S40, the analysis time setting unit 112 adds the time Δt to the currently set time t to update the time t. Then, the processing after step S27 is performed again, and the position ri(t+Δt) of the point i when the time Δt has passed from the updated time t is calculated.

On the other hand, when it is determined in step S39 that the time t is longer than the analysis completion time T set in step S6 (when the analysis completion time T has passed), the process proceeds to step S41. When the process proceeds to step S41, the analysis image display unit 117 displays the time t from 0 (zero) to T [sec] based on the "vector of the position ri (t+Δt) of the point i" calculated in step S35. The display device 200 is caused to display an image showing how the state of the crystal grain A changes during this period. Then, the flow chart of FIG. 9 ends.

If it is determined in step S29 that the point to be calculated is not the double point but the triple point, the process proceeds to step S42. When the process proceeds to step S42, the triple point driving force calculation unit 115 calculates the magnitude (absolute value) of the grain boundary energies γi1, γi2, and γi3 per unit length at the grain boundary u to which the points 1, 2, and 3 belong. is read out from the grain boundary energy setting unit 109 .
Further, the triple point driving force calculator 115 reads information on the triple point i to be calculated and three points 1, 2, and 3 adjacent to the triple point i from the point setting unit 103 . Then, the triple junction driving force calculation unit 115 calculates a unit vector having a direction from the triple junction i to be calculated toward points 1, 2, and 3. FIG.

Next, in step S43, the triple junction driving force calculation unit 115 combines the "magnitudes of grain boundary energies γi1, γi2, and γi3 per unit length" read out in step S42 with the "calculation target A unit vector having a direction from the triple point i of to points 1, 2 and 3" is substituted into the equation (2) to calculate the driving force Fi(t) generated at the triple point i to be calculated.

Next, in step S44, mobilities Mi1 to Mi3 corresponding to the three grain boundaries u to which the points (triple junctions) to be calculated belong are read out from the mobility setting unit 111. FIG.
Next, in step S45, the position calculation unit 116 determines the mobilities Mi1 to Mi3 of the three grain boundaries u to which the triple junctions to be calculated belong, and the directions from the triple junctions to be calculated to the points 1, 2, and 3. and the unit vector (dij(t)/|dij(t)|) is substituted into the equation (5) to calculate the mobility Mi of the triple junction i to be calculated. Note that the unit vector having the direction from the triple point i to the points 1, 2, and 3 to be calculated can be the one calculated in step S42. Then, the processes after step S34 described above are performed, and the vector of the position ri(t+Δt) of the triple point i at time t+Δt is calculated as described above.

If it is determined in step S28 that the point to be calculated is a boundary point, the process proceeds to step S46 in FIG. 9-4.
When the process proceeds to step S46, the boundary point driving force calculation unit 118 determines the boundary The absolute value of the surface grain boundary driving force corresponding to the orientation ξ of the grains A16/A17, A18/A20, A21/A24, A16/A25 having lines 801 and 802 indicates the surface grain boundary driving force-crystal orientation relationship. Derived from information. The boundary point driving force calculation unit 118 turns from the boundary points i21, i22, i23, and i24 to the direction along the boundary lines of the crystal grains A16/A17, A18/A20, A21/A24, A16/A25, and derives the A vector having the magnitude of the absolute value is a surface grain boundary drive at time t generated on the grain A16/A17, A18/A20, A21/A24, A16/A25 side at the boundary points i21, i22, i23, and i24. Forces F _i21-1 (t)・F _i21-2 (t), F _i22-1 (t)・F _i22-2 (t), F _i23-1 (t)・F _i23-2 (t), F It is derived as _i24-1 (t) and F _i24-2 (t).

Next, in step S47, the boundary point driving force calculation unit 118 obtains the boundary points i21, i22, i23, i24 and the line A unit vector having a direction toward points i25, i26/i27, i28/i29/i30, and i34 adjacent through p, and the boundary points i21, i22, i23, i24 and points i25, i26/i27, i28/i29・The _magnitude of the grain boundary energy γ per unit length at the grain boundaries _ui21 , _ui22-2 , _ui22-1 , _ui23-3 , _ui23-2 , _ui23-1 , and ui24 to which i30 and i34 belong (absolute value) γij at the boundary points i21, i22, i23, and i24 at the grain boundaries u _i21 , u _i22-1 · u _i22-2 , u _i23-1 · u _i23-2 , u _{i23- 3} , internal grain boundary driving force F _i21-3 (t), F _i22-3-1 (t), F _i22-3-2 (t), F _i23-3-1 at time t occurring on the u _i24 side (t) F _i22-3-2 (t) F _i22-3-3 (t) and F _i24-3 (t).

Next, in step S48, the boundary point driving force calculation unit 118 generates at time t on the grain A16/A17, A18/A20, A21/A24, and A16/A25 sides at the boundary points i21, i22, i23, and i24. surface grain boundary driving force F _i21-1 (t)・F _i21-2 (t), F _i22-1 (t)・F _i22-2 (t), F _i23-1 (t)・F _i23-2 (t), F _i24-1 (t)·F _i24-2 (t), and grain boundaries u _i21 , u _i22-1 ·u _i22-2 , u _i23 to which the boundary points i21, i22, i23, i24 belong ₋₁ ·u _i23-2 , u _i23-3 , internal grain boundary driving force F _i21-3 (t), F _i22-3-1 (t)·F _i22-3-2 (t) generated on the side of u _i24 , F _i23-3-1 (t), F _i23-3-2 (t), F _i23-3-3 (t), and F _i24-3 (t) is the boundary driving force at time t F _i21-4 (t), F _i22-4-1 (t)・F _i22-4-2 (t), F _i23-4-1 (t)・F _i23-4-2 (t)・F _{i23 -4-3} (t), F _i24-4-1 (t) and F _i24-4-2 (t) are derived.

As described above, for the boundary points i21, i22, and i23 that are not located at the four corners of the analysis target region, the boundary point driving force calculation unit 118 calculates the crystal grains A16/A17, A18/A20, Surface grain boundary driving force F _i21-1 (t)/F _i21-2 (t), F _i22-1 (t)/F _i22-2 (t), F _{i23- 1} (t)·F _i23-2 (t) and grain boundaries u _i21 , u _i22-1 · u _i22-2 , u _i23-1 · u _i23-2 , u Internal grain boundary driving force F _i21-3 (t), F _i22-3-1 (t), F _i22-3-2 (t), _{F i22-3-3 (} t), F _i23-3-1 (t), F _i23-3-2 (t), and F _i23-3-3 (t) are expressed as the boundary driving force F _i21-4 ( t), F _i22-4-1 (t), F _i22-4-2 (t), F _i23-4-1 (t), F _i23-4-2 (t), F _i23-4-3 ( t) respectively.

On the other hand, for the boundary point i24 that is not located at the four corners of the analysis target region, the boundary point driving force calculation unit 118 calculates the surface grain boundary driving force F _i24-1 at the time t generated on the grain A16/A25 side at the boundary point i24. (t) F _i24-2 (t) and the internal grain boundary driving force F _i24-3 (t) at time t generated on the grain boundary u _i24 side to which the boundary point i24 belongs, Derived as the boundary driving force F _i24-4 (t) at time t.

Next, in step S49, the boundary point driving force calculator 118 calculates the boundary driving forces F _i21-4 (t), F _i22-4-1 (t)·Fi22 at the boundary points i21, i22, i23, and _i24 . _-4-2 (t), F _i23-4-1 (t), F _i23-4-2 (t), F _i23-4-3 (t), F _i24-4-1 (t), F _{i24 -4-2} A vector that decomposes (t), the direction is the direction along the boundary line to which the boundary point i belongs, and the magnitude is the boundary driving force F _i (t). Driving forces Fi21(t) and Fi22-1(t) generated at the boundary point i at time t · Fi22-2(t), Fi23-1(t), Fi23-2(t), Fi23-2(t), Fi24-1(t), Fi24-2(t).

As described above, for the boundary points i21, i22, and i23 that are not located at the four corners of the analysis target region, the boundary point driving force calculator 118 calculates the boundary driving force F _i21-4 (t) at the boundary points i21, i22, and i23. , F _i22-4-1 (t)・F _i22-4-2 (t), F _i23-4-1 (t)・F _i23-4-2 (t)・F _i23-4-3 (t) is decomposed in the direction along the boundary line 801, and the driving forces Fi21(t), Fi22-1(t), Fi22-2(t), Fi23- 1(t), Fi23-2(t), and Fi23-3(t).
On the other hand, for the boundary point i24 that is not located at the four corners of the analysis target region, the boundary point driving force calculation unit 118 calculates the boundary driving forces F _i24-4-1 (t), F _i24-4-2 (t ) in the direction along the boundaries 801 and 802, the one with the larger magnitude (absolute value) (boundary driving force F _i24-4-2 (t)) is defined as the boundary point i24 at time t. is derived as the driving force Fi24(t) generated at .

Next, in step S50, the position calculation unit 116 reads from the mobility setting unit 111 the mobility Mi corresponding to the grain boundary u to which the boundary point i to be calculated belongs. As described above, when the point i to be calculated is a boundary point and is originally a double point (triple point), the position calculation unit 116 determines the granularity to which each separated boundary point i to be calculated belongs. One will acquire the mobility Mi of the realm u.
Then, the process proceeds to step S34 in FIG. 9-3 described above, and the position calculation unit 116 acquires a vector ri(t) indicating the current position of the boundary point to be calculated.
As described above, in this embodiment, for example, by performing the processing of steps S46, S47, S48, and S49, surface grain boundary driving force deriving means, internal grain boundary driving force deriving means, boundary driving force deriving means, driving force An example of derivation means is implemented. Further, for example, by performing the processing of steps S34 and S35, an example of boundary point position changing means is realized.

If the analyzed temperature θ(t) input in step S3 depends on time, for example, after step S39, the analyzed temperature θ(t+Δt) at time t+Δt set in step S40 is read, and the analyzed temperature θ After resetting the grain boundary energy γ per unit length at (t+Δt) and the mobility Mi, the processing after step S27 may be performed.

As described above, in the present embodiment, the boundary point driving force calculation unit 118 generates a driving force (surface grain boundary Driving force F _i21-1 (t)/F _i21-1 (t), F _i22-1 (t)/F _i22-2 (t), F _i23-1 (t)/F _i23-2 (t), F _i24-1 (t) F _i24-2 (t)) and a line p (grain boundary u) connecting the boundary point i and a point i adjacent to the boundary point i driving force (internal grain boundary driving force F _i21-3 (t), F _i22-3-1 (t), F _i22-3-2 (t), F _{i23- 3-1} (t), F _i23-3-2 (t), F _i23-3-3 (t), F _i24-3-1 (t), F _i24-3-2 (t), F _{i24- 3-3} (t)) and the vector sum (boundary driving force F _i21-4 (t), F _i22-4-1 (t), F _i22-4-2 (t), F _i23-4-1 ( t) F _i23-4-2 (t) F _i23-4-3 (t), F _i24-4-1 (t) F _i24-4-2 (t)) to the boundary lines 801 and 802 Driving forces Fi21(t), Fi22-1(t), Fi22-2(t), Fi23-1(t), Fi23-2(t), Fi23-1(t), Fi23-2(t), Fi23-3(t), Fi24-1(t) and Fi24-2(t) are derived.

Therefore, considering both the surface energy of the analysis target region (electromagnetic steel sheet) and the energy generated at the grain boundary inside the analysis target region, the movement of each point i including the boundary point i with the passage of time can be analyzed. Therefore, it is possible to prevent the state of the crystal grains A (particularly in the vicinity of the boundary of the analysis target region) from deviating from the actual state.

In this embodiment, the absolute value of the surface grain boundary driving force (driving force acting in the direction along the boundary line to which the boundary point i belongs from the boundary point i) is the normal direction of the boundary line and the boundary line. The case where it depends on the angle formed with the orientation ξ of the crystal grain A included as the grain boundary u has been described as an example. However, the absolute value of the surface grain boundary driving force does not necessarily have to be determined in this manner. For example, the absolute value of the surface grain boundary driving force may depend on the attribute of the crystal grain A including the boundary line as the grain boundary u, other than the angle. For example, the absolute value of the surface grain boundary driving force, in addition to or instead of the angle formed by the normal direction of the boundary line and the orientation ξ of the crystal grain A containing the boundary line as the grain boundary u, It may depend on the size of the crystal grain A included as the grain boundary u (the volume when three-dimensional analysis is performed, and the area when two-dimensional analysis is performed). Further, when the boundary point i is not at the four corners of the analysis target region, the absolute value of the surface grain boundary driving force is determined by the boundary point i and the distance between both ends of the boundary line to which the boundary point i belongs.

In addition, in the present embodiment, the cases where the boundary point i is a single point, a double point, and a triple point are shown as examples, but even if the boundary point i is an m point (m is an integer of 4 or more), Changes in position over time can be made in the same manner as for double and triple points. In this case, since the number of boundary points i is divided into m, when moving such boundary points i, the total number of points NI to be calculated is increased by (m-1). Become.

Further, in the present embodiment, the material analyzed by the grain analysis apparatus 100 is an electromagnetic steel plate, and the plate is described as an example, but the material analyzed by the grain analysis apparatus 100 is limited to such a material. not. For example, the shape of the electromagnetic steel sheet is not particularly limited, and may be a thin plate, a thick plate, a wire rod, or the like. In addition to electromagnetic steel sheets, all metal materials such as stainless steel, titanium, and aluminum can be applied. When the material to be analyzed by the crystal grain analysis apparatus 100 is different, the contents of the graphs stored in the grain boundary energy storage unit 108, the mobility storage unit 110, and the boundary point driving force calculation unit 118 may differ from each other. The data input to the grain analysis device 100 will differ depending on the material.

Among the embodiments of the present invention described above, the part executed by the CPU can be realized by the computer executing the program. In addition, a means for supplying a program to a computer, for example, a computer-readable recording medium such as a CD-ROM recording such a program, or a transmission medium for transmitting such a program can be applied as an embodiment of the present invention. . A program product such as a computer-readable recording medium recording the above program can also be applied as an embodiment of the present invention. The above program, computer-readable recording medium, transmission medium and program product are included in the scope of the present invention.
Moreover, the above-described embodiments are merely examples of specific implementations of the present invention, and the technical scope of the present invention should not be construed to be limited by these. That is, the present invention can be embodied in various forms without departing from its technical concept or main features.

100: crystal grain analysis device, 101: crystal image acquisition unit, 102: crystal image display unit, 103: point setting unit, 104: line setting unit, 105: grain boundary setting unit, 106: analysis temperature setting unit, 107: orientation Setting unit 108: Grain boundary energy storage unit 109: Grain boundary energy setting unit 110: Mobility storage unit 111: Mobility setting unit 112: Analysis time setting unit 113: Analysis point determination unit 114 : double point driving force calculation unit 115: triple point driving force calculation unit 116: position calculation unit 118: boundary point driving force calculation unit 200: display device 300: operation device

Claims (9)

an image signal acquiring means for acquiring an image signal of crystals in the metal material;
A crystal included in the crystal, wherein the boundary point corresponds to the intersection of the grain boundary of the crystal grain included in the crystal and the boundary line of the analysis target area based on the image signal, and the boundary point is different from the boundary point. point setting means for setting non-boundary points corresponding to grain boundaries;
surface grain boundary driving force deriving means for deriving a surface grain boundary driving force acting in a direction away from the boundary point along the boundary line to which the boundary point belongs at the boundary point set by the point setting means; When,
At the boundary point set by the point setting means, an internal grain boundary driving force acting in a direction away from the boundary point along a line connecting the boundary point and a point adjacent to the boundary point is calculated. an internal grain boundary driving force deriving means for deriving;
The surface grain boundary driving force derived by the surface grain boundary driving force deriving means for the boundary point set by the point setting means, and the internal grain boundary driving force deriving means for the boundary point derived by the internal grain boundary driving force deriving means a boundary driving force deriving means for deriving a boundary driving force that is a vector sum of the internal grain boundary driving force and the
A vector obtained by resolving the boundary driving force derived by the boundary driving force deriving means for the boundary point set by the point setting means, the direction of which is along the boundary line to which the boundary point belongs a driving force deriving means for deriving a vector whose magnitude is the magnitude of a component of the boundary driving force in the direction along the boundary line to which the boundary point belongs, as the driving force generated at the boundary point;
and boundary point position changing means for changing the position of the boundary point based on the driving force generated at the boundary point derived by the driving force deriving means. The surface grain boundary driving force deriving means derives the surface grain boundary driving force for the boundary point set by the point setting means based on the attribute of the crystal grain including the boundary line to which the boundary point set by the point setting means belongs as a grain boundary. The crystal grain analysis apparatus according to claim 1, characterized in that: 3. The crystal grain analysis apparatus according to claim 2, wherein the attribute of the crystal grain including the boundary line to which the boundary point set by the point setting means belongs as the grain boundary includes the orientation of the crystal grain. The surface grain boundary driving force deriving means acts in a first direction and a second direction away from the boundary point set by the point setting means along the boundary line to which the boundary point belongs. 4. The crystal grain analysis apparatus according to claim 1, wherein two driving forces are respectively derived as the surface grain boundary driving forces. If the boundary point is not at a corner of the analysis target area,
The boundary driving force deriving means provides the two surface grain boundary driving forces derived by the surface grain boundary driving force deriving means for the boundary point and the internal grain boundary driving force deriving means for the boundary point. 5. The crystal grain analysis apparatus according to claim 4, wherein a vector sum with one of the internal grain boundary driving forces derived by is derived as the boundary driving force at the boundary point. If the boundary point is at a corner of the analysis target area,
The boundary driving force deriving means generates one of the two surface grain boundary driving forces derived by the surface grain boundary driving force deriving means for the boundary point and the boundary point with one of the internal grain boundary driving forces derived by the internal grain boundary driving force deriving means for the other surface grain boundary deriving the vector sum of the driving force and the internal grain boundary driving force as the second boundary driving force at the boundary point;
The driving force deriving means decomposes the first boundary driving force at the boundary point into a vector obtained by resolving the first boundary driving force at the boundary point in a direction along the boundary line that coincides with the direction of the one surface grain boundary driving force, and the A vector obtained by resolving the second boundary driving force in a direction along the boundary line corresponding to the direction of the one surface grain boundary driving force and a vector having a larger magnitude is generated at the boundary point. 6. The crystal grain analysis apparatus according to claim 4, wherein the driving force is derived. The internal grain boundary driving force derivation means includes a unit vector having a direction from the boundary point set by the point setting means to a point adjacent to the boundary point via the line, and a unit vector at the grain boundary to which the line belongs. The crystal grain analysis apparatus according to any one of claims 1 to 6, wherein the internal grain boundary driving force for the boundary point is derived based on the magnitude of grain boundary energy per unit length. . an image signal acquisition step of acquiring an image signal of crystals in the metal material;
A crystal included in the crystal, wherein the boundary point corresponds to the intersection of the grain boundary of the crystal grain included in the crystal and the boundary line of the analysis target area based on the image signal, and the boundary point is different from the boundary point. a point setting step of setting non-boundary points corresponding to grain boundaries;
A surface grain boundary driving force deriving step of deriving a surface grain boundary driving force acting in a direction away from the boundary point along the boundary line to which the boundary point belongs at the boundary point set by the point setting step. When,
At the boundary point set by the point setting step, an internal grain boundary driving force, which is a driving force acting in a direction away from the boundary point along a line connecting the boundary point and a point adjacent to the boundary point, is calculated. an internal grain boundary driving force derivation step to derive;
The surface grain boundary driving force derived by the surface grain boundary driving force deriving step for the boundary point set by the point setting step, and the internal grain boundary driving force derived for the boundary point by the internal grain boundary driving force deriving step a boundary driving force deriving step of deriving a boundary driving force that is a vector sum of the internal grain boundary driving force and the
A vector obtained by decomposing the boundary driving force derived by the boundary driving force deriving step with respect to the boundary point set by the point setting step, the direction of which is along the boundary line to which the boundary point belongs a driving force deriving step of deriving a vector whose magnitude is the magnitude of the component of the boundary driving force in the direction along the boundary line to which the boundary point belongs, as the driving force generated at the boundary point;
and a boundary point position changing step of changing the position of the boundary point based on the driving force generated at the boundary point derived by the driving force deriving step. A program for causing a computer to function as each means of the grain analysis apparatus according to any one of claims 1 to 7.

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