JP2008224433A - Crystal grain analyzer, crystal grain analyzing method, and computer program - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To analyze how a crystal grain varies with the passage of time via an inclusion more easily and accurately than the conventional art. <P>SOLUTION: In a line change processing section 119, when the line whose both end points are two mutually adjacent grain boundary points on the same grain boundary of the crystal grain passes in an inhibitor set by an inhibitor setting section 118, a fixed point is generated in the inhibitor. A grain boundary energy E calculation section 121 calculates the grain boundary energy Ei in the grain boundary to which the fixed point belongs and the grain boundary energy Ei' in the grain boundary when the fixed point is moved from a fixed position to an equilibrium position. Then, a fixed point processing section 120, when the grain boundary energy Ei' is smaller than the grain boundary energy Ei, performs processing of releasing the fixed point, and allows simulation of the state that the grain boundary movement of the crystal grain is suppressed by the inhibitor. <P>COPYRIGHT: (C)2008,JPO&INPIT

Description

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

Conventionally, the state of crystal grains of a metal material has been analyzed by a computer.
Patent Document 1 discloses a technique for annealing a rolled thin steel plate to perform primary recrystallization, and finally annealing the primary recrystallized thin steel plate to obtain a secondary recrystallized thin steel plate. Yes. In such a technique, the particle size distribution of the primary recrystallized crystal grains is statistically obtained. Then, using the particle size distribution of the primary recrystallized grains, the integral value (integrated grain boundary energy) of the grain boundary energy of each primary recrystallized grain is obtained, and the obtained result is used. Estimate the optimal distribution of primary recrystallized grains. And in patent document 1, if it was made to obtain the crystal grain recrystallized primary so that it might become the distribution estimated in this way, the thin steel plate appropriately secondary recrystallized will be obtained. Yes.

  In Patent Document 2, the initial crystal grain size, the holding temperature, the holding time, and various coefficients obtained from the test pieces in each step of the Al slab in the soaking process or the Al plate material in the annealing process and predetermined coefficients are calculated. It is disclosed that the grain size after crystal growth is calculated by substituting into the equation.

  Furthermore, Patent Document 3 calculates the austenite grain size and average dislocation density after rolling based on the size of steel slab, component information and rolling conditions, and based on the calculated results and cooling conditions, the structure of the transformation structure It is disclosed that the fraction of each phase, the average formation temperature and the crystal grain size are calculated, and further, the fraction, particle size and carbide / precipitate size of each phase constituting the final structure are calculated based on the subsequent heat treatment conditions. Has been.

JP-A-6-158165 JP 2002-224721 A JP-A-5-87800

By the way, the primary recrystallized crystal grains grow while taking various behaviors during the secondary recrystallization.
However, the technique described in Patent Document 1 focuses on the primary recrystallized crystal grains, and does not consider the behavior until the primary recrystallized crystal grains are secondary recrystallized. Therefore, it has been difficult to obtain accurate knowledge about how the crystal grains change over time. Further, in the above-described conventional technique, since the particle size distribution of the primary recrystallized crystal grains is obtained statistically, a lot of data based on prior manufacturing and testing is necessary. Therefore, there is a problem that it is difficult to easily analyze the state of crystal grains.

Moreover, the technique described in Patent Document 2 only discloses a calculation model for crystal grain size. Therefore, there is a problem that it is difficult to analyze specifically what shape the crystal grains change with time.
In addition, the technique described in Patent Document 3 has a problem in that it does not indicate what model is used to calculate the crystal grain growth.

  Furthermore, as a metal material to be analyzed for crystal grains, for example, in a metal material of a magnetic steel sheet, it is necessary to enlarge the grain size of the crystal grains after secondary recrystallization. A technique of interposing an inhibitor as an inclusion between grains is used.

  In this case, while the inhibitor is present between the crystal grains, the growth proceeds while the crystal grain growth is suppressed. Therefore, it is essential to perform the calculation in consideration of the inclusion. In this regard, the conventional technique does not consider such inclusions, and there is a problem that it is difficult to calculate how the crystal grains grow through the inclusions.

  The present invention has been made in view of such a problem, and makes it easier and more accurate to analyze how crystal grains change over time through inclusions. For the purpose.

  The crystal grain analyzer of the present invention corresponds to image signal acquisition means for acquiring an image signal of a crystal in a metal material and inclusions included in the metal material, and both end points of a grain boundary of the crystal grain included in the crystal. And a triple point in contact with the three crystal grains including the crystal grain, and a double point corresponding to the midpoint of the grain boundary of the crystal grain included in the crystal and in contact with the two crystal grains including the crystal grain. The grain boundary point setting means for setting the specified triple point and double point grain boundary point, and the grain boundary point set by the grain boundary point setting means. A line setting means for setting a line having two grain boundary points adjacent to each other on the same grain boundary, and when the inclusion is designated based on the image signal, the designated intervention Inclusion setting means for setting an object, and the line setting When a line set by a step passes through the inclusion, a fixed point is generated in the inclusion, and a line change processing means for performing a change process of the line with the fixed point as an end point; and the fixed point is The first grain boundary energy at the grain boundary to which it belongs and the grain when the fixed point is released from the fixed position and moved to the equilibrium position where the grain boundary energy is the minimum in the region excluding the inclusions. Grain boundary energy calculating means for calculating the second grain boundary energy in the boundary, and fixing for performing processing for releasing the fixed point when the second grain boundary energy is less than the first grain boundary energy And point processing means.

  In another aspect of the crystal grain analyzer of the present invention, image signal acquisition means for acquiring an image signal of a crystal in a metal material and inclusions included in the metal material, and a grain boundary of the crystal grain included in the crystal When a triple point corresponding to the two end points of and in contact with three crystal grains including the crystal grain is designated based on the image signal, the grain boundary point for setting the grain boundary point of the designated triple point A line setting unit that sets a line that is a grain boundary point set by the grain boundary point setting unit and has two grain boundary points adjacent to each other on the same grain boundary; and When the inclusion is designated based on the image signal, the inclusion setting means for setting the designated inclusion, and when the line set by the line setting means passes through the inclusion, the inclusion Generate a fixed point in the object Line change processing means for changing the line with the fixed point as an end point, the first grain boundary energy at the grain boundary to which the fixed point belongs, the fixed point is released from the fixed position, and the inside of the inclusion is excluded Grain boundary energy calculating means for calculating the second grain boundary energy at the grain boundary when moved to the equilibrium position where the grain boundary energy is the minimum at the region, and the second grain boundary energy is And fixing point processing means for performing processing for releasing the fixing point when the energy is less than the first grain boundary energy.

  The crystal grain analysis method of the present invention corresponds to an image signal acquisition step of acquiring an image signal of a crystal in a metal material and inclusions included in the metal material, and both end points of a grain boundary of the crystal grain included in the crystal. And a triple point in contact with the three crystal grains including the crystal grain, and a double point corresponding to the midpoint of the grain boundary of the crystal grain included in the crystal and in contact with the two crystal grains including the crystal grain. The grain boundary point set by the grain boundary point setting step and the grain boundary point setting step for setting the grain boundary point of the designated triple point and double point when specified based on the image signal. A line setting step for setting a line having two adjacent grain boundary points on the same grain boundary as both end points, and when the inclusion is designated based on the image signal, the designated intervention Inclusion setting step And a line change processing step for generating a fixed point in the inclusion when the line set by the line setting step passes through the inclusion and performing a line changing process with the fixed point as an end point, and , The first grain boundary energy at the grain boundary to which the fixed point belongs, and the fixed point is released from the fixed position and moved to an equilibrium position where the grain boundary energy is the minimum in the region excluding the inclusions. A grain boundary energy calculating step for calculating a second grain boundary energy at the grain boundary at the time of the release, and when the second grain boundary energy is less than the first grain boundary energy, the fixed point is released And a fixed point processing step for performing the processing.

  In another aspect of the crystal grain analysis method of the present invention, an image signal acquisition step of acquiring an image signal of a crystal in a metal material and inclusions included in the metal material, and a grain boundary of the crystal grain included in the crystal When a triple point corresponding to the two end points of and in contact with three crystal grains including the crystal grain is designated based on the image signal, the grain boundary point for setting the grain boundary point of the designated triple point A setting step; a line setting step for setting a line that is a grain boundary point set by the grain boundary point setting step and has two grain boundary points adjacent to each other on the same grain boundary; and When the inclusion is designated based on the image signal, the inclusion setting step for setting the designated inclusion, and when the line set by the line setting step passes through the inclusion, the inclusion object A fixed point is generated, a line change processing step for changing the line with the fixed point as an end point, a first grain boundary energy at the grain boundary to which the fixed point belongs, and the fixed point is released from the fixed position. And a grain boundary energy calculating step for calculating a second grain boundary energy at the grain boundary when moved to an equilibrium position where the grain boundary energy is the position of the region excluding the inside of the inclusions, and A fixed point processing step of performing a process of releasing the fixed point when the second grain boundary energy is less than the first grain boundary energy.

  The computer program of the present invention corresponds to an image signal acquisition step of acquiring an image signal of a crystal in a metal material and inclusions included in the metal material, and both end points of grain boundaries of crystal grains included in the crystal, and The triple point in contact with the three crystal grains including the crystal grain, and the double point corresponding to the intermediate point of the grain boundary of the crystal grain included in the crystal and in contact with the two crystal grains including the crystal grain, When specified based on the image signal, a grain boundary point setting step for setting the specified triple point and double point grain boundary point, and the grain boundary point set by the grain boundary point setting step, A line setting step for setting a line with two grain boundary points adjacent to each other on the same grain boundary, and when the inclusion is specified based on the image signal, the specified inclusion is Inclusion settings to be set And a line change processing step for generating a fixed point in the inclusion and changing the line with the fixed point as an end point when the line set in the line setting step passes through the inclusion. And the first grain boundary energy at the grain boundary to which the fixed point belongs, and the equilibrium position where the fixed point is released from the fixed position and is in the region excluding the inside of the inclusions, where the grain boundary energy is minimized. Grain boundary energy calculation step for calculating the second grain boundary energy at the grain boundary when moved, and when the second grain boundary energy is less than the first grain boundary energy, the fixed point is A fixed point processing step for performing the cancellation processing is executed by a computer.

  According to another aspect of the computer program of the present invention, an image signal acquisition step of acquiring an image signal of a crystal in a metal material and inclusions included in the metal material, and both ends of grain boundaries of crystal grains included in the crystal Grain boundary point setting step for setting a grain boundary point of the designated triple point when a triple point corresponding to the point and in contact with three crystal grains including the crystal grain is designated based on the image signal A line setting step for setting a line which is a grain boundary point set by the grain boundary point setting step and has two grain boundary points adjacent to each other on the same grain boundary, and the image signal When the inclusion is designated based on the inclusion, the inclusion setting step for setting the designated inclusion and the line set by the line setting step pass through the inclusion. A fixed point is generated in the inclusion, a line change processing step for changing the line with the fixed point as an end point, a first grain boundary energy at the grain boundary to which the fixed point belongs, and the fixed point are fixed. Grain boundary energy calculation step for calculating the second grain boundary energy at the grain boundary when the grain boundary energy is moved to an equilibrium position where the grain boundary energy is minimum and is located in a region excluding the inside of the inclusion. And, when the second grain boundary energy is less than the first grain boundary energy, a computer executes a fixed point processing step of performing a process of releasing the fixed point.

  According to the present invention, it is possible to more easily and accurately analyze how the crystal grains change with the passage of time through inclusions.

  Hereinafter, embodiments of the present invention will be described with reference to the drawings. In the following embodiments of the present invention, an example will be described in which an electromagnetic steel sheet manufactured using an inhibitor, which is an inclusion, is applied as a metal material to be analyzed for crystal grains.

(First embodiment)
Hereinafter, a first embodiment of the present invention will be described.
FIG. 1 is a diagram conceptually illustrating an example of an analysis method performed by the crystal grain analysis apparatus according to the first embodiment. In FIG. 1, for convenience of explanation, only one crystal grain A is shown among the many crystal grains constituting the electromagnetic steel sheet, but actually, the electromagnetic steel sheet is formed by the many crystal grains. Needless to say.

In the crystal grain analyzer of the first embodiment, the crystal grains are modeled as shown in FIG.
First, as shown in FIG. 1 (a), triple points ia, ie, if are set at positions corresponding to both end points of three grain boundaries ua to uc of crystal grain A, and intermediate points of grain boundaries ua to uc. The grain boundary points of the double points ib to id and ig to ii are set at positions corresponding to. Here, the triple points ia, ie, and if are points where three straight lines intersect (that is, a point in contact with three crystal grains), and the double points ib to id and ig to ii intersect two straight lines. Points (points in contact with two crystal grains). And the straight line (line) which mutually connects the point (grain boundary point) i mutually adjacent on the same grain boundary ua-uc is set.

  As described above, in the present embodiment, not only the positions of both ends of the grain boundaries ua to uc but also the double points ib to id, so that the shape in the middle of the grain boundaries ua to uc can be represented as faithfully as possible. ig to ii are set.

  The 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. 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 elapsed (time t + Δt) is calculated. If it does so, the position of each point (double point and triple point) ia-ii shown in Drawing 1 (a) will move to the position shown in Drawing 1 (b), for example.

  In the crystal grain analysis apparatus of the present embodiment, as described above, the triple points ia, ie, if corresponding to both 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 are used. The driving force Fi (t) generated at each of the corresponding double points ib to id and ig to ii is calculated, and the triple points ia, ie, if and the double points ib to id and ig to ii move. Is analyzed. Thereby, for example, the state in which the crystal grain Aa shown in FIG. 1 (a) changes with the passage of time as the crystal grain Ab shown in FIG. 1 (b) is as accurate as possible without imposing a large calculation load. Can be analyzed. Incidentally, the behavior of the crystal grains via the inhibitor (inclusion) will be described in detail in the explanation using FIG. 8 and FIG.

Below, the structure of a crystal grain analyzer is demonstrated in detail.
FIG. 2 is a block diagram illustrating an example of a functional configuration of the crystal grain analysis apparatus according to the first embodiment. Note that the hardware of the crystal grain analysis apparatus 100 can be realized by using an information processing apparatus including a personal computer, a CPU, a ROM, a RAM, a hard disk, an image input / output board, various interfaces, an interface controller, and the like. . Unless otherwise specified, each block shown in FIG. 2 is realized by the CPU executing a control program stored in the ROM or the hard disk using the RAM. And the following processes are implement | achieved by exchanging a signal between each block shown in FIG.

  In FIG. 2, the crystal image acquisition unit 101 obtains, for example, an “image signal of an inhibitor existing between the crystal grain A of the electromagnetic steel sheet and the crystal grain A of the electromagnetic steel sheet obtained by an EBSP (Electron Back Scattering Pattern) method, A signal indicating the orientation ξ of each crystal grain A included in the image signal is acquired and stored in a hard disk or the like. In the following description, the image of the inhibitor existing between the crystal grain A of the magnetic steel sheet and the crystal grain A of the magnetic steel sheet is referred to as a crystal grain image as necessary. The crystal image acquisition unit 101 may directly acquire the signal described above from an analyzer that performs crystal analysis by the EBSP method, or may receive the signal described above from a removable storage medium such as a DVD or a CD-ROM. You may acquire indirectly.

  For example, 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 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). In addition, the operation device 300 includes a user interface such as a keyboard and a mouse.

  The point setting unit 103 acquires points (double points and triple points) i specified by the user using the operation device 300 for the image of the crystal grain A displayed by the crystal image display unit 102, and the acquired points (Double point and triple point) The number of i and a vector indicating the initial position ri (0) of the point i are set (stored) in the RAM or the hard disk. In this embodiment, the user can arbitrarily designate the number of points (double points and triple points) i and the initial position.

  In addition, the point setting unit 103 calculates a vector indicating the position ri (t + Δt) after Δt [sec] at the calculation target point (double point or triple point) i by the position calculation unit 116 as described later. Then, a vector indicating the position ri (t + Δt) of the point i is set (stored) in the RAM or the hard disk. Further, the point setting unit 103 changes the setting of the currently set point i based on inputs from the line change processing unit 119 and the fixed point processing unit 120 described later, and sets (stores) this in the RAM or hard disk. )

  The line setting unit 104 includes information on the line p specified by two points i adjacent to each other on the same grain boundary u among the points (double points and triple points) i set by the point setting unit 103. Set (store) in RAM or hard disk. As described above, the line p is a straight line having two points i adjacent to each other on the same grain boundary u. The line setting unit 104 also performs a process of changing the line p with the occurrence of a fixed point in the line change processing unit 119 described later.

  The grain boundary setting unit 105 includes information on the grain boundary u specified by the line p connected to each other with the triple point i set by the point setting unit 103 as both ends among the lines p set by the line setting unit 104. Set to RAM or hard disk.

  FIG. 3 shows the first embodiment, a crystal grain image displayed by the crystal image display unit 102 (FIG. 3A), and points (double points and triple points) i set by the point setting unit 103. FIG. 3B is a diagram illustrating an example of the line p and the grain boundary u (FIG. 3C) set by the line setting unit 104 and the grain boundary setting unit 105. For convenience of explanation, in FIGS. 3B and 3C, among the crystal grains A1 included in the crystal grain image 31 shown in FIG. Only the point i, the line p, and the grain boundary u set are shown. In addition, the crystal grain image 31 shown in FIG. 3A shows, as an example, inhibitors (k1 to k4) that are inclusions only around the crystal grain A1, but the inhibitors are actually It exists in the whole shown in the crystal grain image 31.

  When the crystal grain image 31 is displayed as shown in FIG. 3A, the user designates a position corresponding to both end points of the grain boundary u as a triple point i using the operation device 300 such as a mouse. At the same time, the position of the intermediate point of the grain boundary u is designated as the double point i. Then, as shown in FIG. 3B, for example, double points i2 to i4, i6 to i10, i12 to i15, i17, i18, and triple points i1, i5, i11, i16, and Each grain boundary point 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. Here, for example, the line p1 is specified by the triple point i1 and the double point i2. The grain boundary u1 is specified by lines p1 to p4 connected to each other with the triple points i1 and i5 as both ends. As shown in FIG. 3C, the grain boundary u1 is a grain boundary between the crystal grains A1 and A2, the grain boundary u2 is a grain boundary between the crystal grains A1 and A5, and the grain boundary u3 is a crystal boundary. It is a grain boundary of the grains A1 and A4, and the grain boundary u4 is a grain boundary of the crystal grains A1 and A3.

  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 (stores) it in the RAM or the hard disk. ) 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 (the analysis temperature θ (t) increases with time). It may be changed).

  The orientation setting unit 107, based on the “signal indicating the orientation ξ of each crystal grain A included in the crystal grain image 31” acquired by the crystal image acquisition unit 101, all the crystal grains A included in the crystal grain image 31. Is set (stored) in the RAM or hard disk.

  The grain boundary energy (γ) storage unit 108 is, for example, the difference Δξ between the grain boundary energy γ [J / m] per unit length and the orientation ξ of two crystal grains A adjacent to each other via the grain boundary u. A graph, a numerical string, a formula, or a combination thereof showing the relationship between the absolute value and the analysis temperature θ (t) is stored. In the following description, these graphs, numeric strings, formulas, or combinations thereof are referred to as graphs.

  For example, the “grain boundary energy γ per unit length” at the grain boundary u1 shown in FIG. 3C is the absolute value of the difference Δξ between the orientation ξ1 of the crystal grain A1 and the orientation ξ2 of the crystal grain A2, and the analysis. By reading “grain boundary energy γ per unit length” corresponding to the analysis temperature θ (t) set by the temperature setting unit 106 from a graph or the like stored in the grain boundary energy (γ) storage unit 108. can get. The grain boundary energy (γ) storage unit 108 is configured using, for example, a RAM or a hard disk.

  The grain boundary energy (γ) setting unit 109 sets the grain boundary based on the orientation ξ of the crystal grain A set by the orientation setting unit 107 and the analysis temperature θ (t) acquired by the analysis temperature setting unit 106. The grain boundary energy γ per unit length of all grain boundaries u set by the unit 105 is read from the graph or the like stored in the grain boundary energy (γ) storage unit 108 as described above. The grain boundary energy (γ) setting unit 109 sets (stores) the read grain boundary energy γ per unit length in the RAM or the hard disk.

The mobility storage unit 110 analyzes the mobility Mi [cm ² / (V · sec)], the absolute value of the difference Δξ of the orientations ξ of two crystal grains A adjacent to each other via the grain boundary u, and the analysis. A graph, a numerical string, an expression, or a combination thereof showing the relationship with the temperature θ (t) is stored. In the following description, these graphs, numeric strings, formulas, or combinations thereof are referred to as graphs.
For example, the mobility Mi at the grain boundary u1 shown in FIG. 3C is acquired by the absolute value of the difference Δξ between the orientation ξ1 of the crystal grain A1 and the orientation ξ2 of the crystal grain A2, and the analysis temperature setting unit 106. 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. The mobility storage unit 110 is configured using, for example, a RAM or a hard disk.

  The mobility setting unit 111 is controlled by the grain boundary setting unit 105 based on the orientation ξ of the crystal grain A set by the orientation setting unit 107 and the analysis temperature θ (t) acquired by the analysis temperature setting unit 106. The mobility Mi of all the set grain boundaries u is read 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 the hard disk.

  For example, the analysis time setting unit 112 acquires the analysis completion time T [sec] based on the operation of the operation device 300 by the user, and sets (stores) it in the RAM or the hard disk. Then, the analysis time setting unit 112 monitors the time t until the analysis completion time T elapses.

  The analysis point discriminating unit 113 sequentially designates all points (double points, triple points, and fixed points) i set by the point setting unit 103 as calculation target points without overlapping. The analysis point determination unit 113 determines whether or not the designated point i is a fixed point. If the specified point i is not a fixed point, the analysis point determination unit 113 further determines whether it is a double point or a triple point. .

The double-point driving force calculation unit 114 calculates the driving force Fi (t) generated at the double point when the analysis point determination unit 113 determines that the point i to be calculated is a double point.
FIG. 4 is a diagram illustrating an example of a method for calculating the driving force Fi (t) generated at the double point. In FIG. 4, the case where the driving force Fi (t) generated at the double point i is calculated will be described as an example.

  In FIG. 4, let Ri (t) [m] be the radius of curvature of the arc 41 defined by the double point i and the two points i−1 and i + 1 adjacent to the double point. The magnitude (absolute value) of grain boundary energy γ per unit length of grain boundary u to which double point i belongs is assumed to be γi. Then, the magnitude of the driving force Fi (t) generated at the double point i is expressed by the following equation (1). The direction of the driving force Fi (t) generated at the double point i is a direction from the double point i toward the curvature center O.

This equation (1) is derived as follows.
First, two vectors having the same size (absolute value) as the grain boundary vector γi of the grain boundary u to which the double point i belongs, and having a direction from the double point i to the points i−1 and i + 1. Assume that the vector sum of fi1 and fi2 is the driving force Fr generated at the double point i (see FIG. 4). Then, the magnitude of the driving force Fr generated at the double point i is expressed by the following equation (2).

Here, l is the length [m] of the arc 41 from the double point i to the point i-1 (or point i + 1). Α is an angle [°] formed by a straight line connecting the double point i and the center of curvature O and a straight line connecting the point i−1 (or point i + 1) and the center of curvature O.
The driving force generated at the double point i may be defined as in the equation (2). However, if it is defined in this way, the driving force generated at the double point i is changed from the double point i to the point i−1. It depends on the length l of the arc 41 up to (or point i + 1). That is, the driving force generated at the double point i depends on the number of double points i set for one grain boundary u. For example, as shown in FIG. 3C, when three double points i2 to i4 are set for the grain boundary u1, and when five double points are set for the grain boundary u1, The driving force generated at the double point i is different.

  Therefore, the right side of the equation (2) is set to the length l so that the driving force generated at the double point i does not depend on the length l of the arc 41 from the double point i to the point i-1 (or point i + 1). The value divided by is defined as the magnitude of the driving force Fi (t) generated at the double point i (see equation (1)).

  As described above, in order to obtain the driving force Fi (t) generated at the double point i using the equation (1), the double-point driving force calculation unit 114 calculates the double point i to be calculated and its double point. Information on two points i−1 and i + 1 adjacent to i is read from the point setting unit 103. Next, the double-point driving force calculation unit 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. The double-point driving force calculation unit 114 acquires the grain boundary energy γi per unit length of the grain boundary u to which the double point i to be calculated belongs from the grain boundary energy (γ) 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 generate a driving force Fi (t ) Is calculated. The double-point driving force calculation unit 114 calculates a direction from the double point i to be calculated toward the curvature center O, and determines the direction of the driving force Fi (t) generated at the double point i.

Returning to FIG. 2, when the analysis point discriminating unit 113 determines that the point i to be calculated is a triple point, the triple-point driving force calculation unit 115 generates the driving force Fi ( t) is calculated.
FIG. 5 is a diagram illustrating an example of a method for calculating the driving force Fi (t) generated at the triple point. In FIG. 5, a case where the driving force Fi (t) generated at the triple point i is calculated will be described as an example. In FIG. 5, three points adjacent to the triple point i are represented by “1”, “2”, and “3”, respectively.

  First, the triple-point driving force calculation unit 115 reads out information about 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 point driving force calculation unit 115 calculates a unit vector having a direction from the triple point i to be calculated toward the points 1, 2, and 3. Further, the triple point driving force calculation unit 115 calculates the size (absolute value) of the grain boundary energy γi1, γi2, γi3 per unit length at the grain boundary u to which the points 1, 2, and 3 belong, and the grain boundary energy ( γ) Obtained from the setting unit 109.

  The triple-point driving force calculation unit 115 calculates the magnitude (absolute value) of the grain boundary energy γi1, γi2, and γi3 per unit length and the direction from the triple point i to be calculated toward points 1, 2, and 3. Is substituted for the following equation (3) to calculate the driving force Fi (t) generated at the triple point i to be calculated.

In equation (3), 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 energy at the grain boundary u to which the points 1, 2, 3 belong has the same magnitude as the magnitude (absolute value) of grain boundary energy γi1, γi2, γi3, and , A drive in which a vector sum of three vectors Di1 (t), Di2 (t), Di3 (t) having a direction from a triple point i to be calculated toward a point adjacent to the triple point i occurs at the triple point i Calculated as force Fi (t).

  Returning to FIG. 2, the position calculation unit 116 calculates a change in position of the double point i and the triple point i over time. First, an example of a method for calculating the change in position of the double point i with the passage of 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 double point i to be calculated). Further, the position calculation unit 116 acquires the mobility Mi of the grain boundary u to which the double point i to be calculated belongs from the mobility setting unit 111. Then, the position calculation unit 116 determines the mobility Mi of the grain boundary u to which the double point i to be calculated belongs and a vector indicating the driving force Fi (t) of the double point i to be calculated as the following (4). Substituting into the equation, a vector indicating the velocity vi (t) of the double point i to be calculated is calculated.

  Thereafter, the position calculation unit 116 acquires “a vector indicating the current position ri (t) of the double point i to be calculated” set in the point setting unit 103. Then, the position calculation unit 116 calculates a vector indicating the speed vi (t) of the double point i to be calculated, a vector indicating the current position ri (t) of the double point i to be calculated, and a time Δt as follows: When Δt [sec] has elapsed from the current time t, a vector indicating the position ri (t + Δt) where the double point i to be calculated exists is calculated. In the present embodiment, in this way, the change in the position with the passage of time of the double point i to be calculated is calculated. 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.

  Then, the position calculation unit 116 outputs a vector indicating the position ri (t + Δt) where the double point i to be calculated exists to the point setting unit 103. In this way, as described above, the point setting unit 103 sets a vector indicating the current position ri (t) of the double point i to be calculated.

Next, an example of a method for calculating a change in the position of the triple point i over time 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.

  The position calculating unit 116 calculates the mobility Mi of the triple point i to be calculated using the mobility Mi1 to Mi3 of the three grain boundaries u to which the triple point i to be calculated belongs. Specifically, the position calculation unit 116 calculates a unit vector (dij (t) / | dij (t) |) having a direction from the triple point i to be calculated toward the points 1, 2, and 3, and the triple point to be calculated. The mobility Mi1 to Mi3 of the three grain boundaries u to which i belongs are substituted into the following equation (6) to calculate the mobility Mi of the triple point i to be calculated.

In equation (6), 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 point driving force calculation unit 115 (a vector indicating the driving force Fi (t) generated at the triple point i to be calculated). To do. Then, the position calculation unit 116 described above the mobility Mi of the grain boundary u to which the calculation target triple point i belongs and the vector indicating the driving force Fi (t) of the calculation target triple point i (4). Substituting into the equation, a vector indicating the velocity vi (t) of the triple point i to be calculated is calculated.

  Thereafter, the position calculation unit 116 acquires “a 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 obtains 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. Substituting into the equation (5), when Δt [sec] has elapsed from the current time t, a vector indicating the position ri (t + Δt) where the triple point i to be calculated exists is calculated. In the present embodiment, in this way, the change in position with the passage of time of the triple point i to be calculated is calculated. As described above, the time Δt defines the timing (interval) for calculating the position of the point i, and is determined in advance according to the type of the electromagnetic steel sheet to be analyzed, the analysis conditions, the analysis accuracy, and the like. It has been.

  Then, the position calculation unit 116 outputs a vector indicating the position ri (t + Δt) where the triple point i to be calculated exists to the point setting unit 103. In this way, as described above, the point setting unit 103 sets a vector indicating the current position ri (t) of the triple point i to be calculated.

  The analysis time setting unit 112 determines whether or not the position calculation unit 116 has calculated the position ri (t + Δt) after the analysis completion time T has elapsed or after the analysis completion time T has elapsed. By determining, it is determined whether or not the analysis is completed until the analysis completion time T.

  When the analysis time setting unit 112 determines that the analysis is completed until 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 displays an image indicating how the state of the crystal grains A changes during the time t from 0 (zero) to T [sec].

  When the user designates an inhibitor k (k1 to k4), which is an inclusion, with respect to the crystal grain image 31 displayed by the crystal image display unit 102 using the operation device 300, the inhibitor setting unit 118 performs a crystal image acquisition unit. Based on the crystal grain image signal acquired in 101, a region of the designated inhibitor k is detected. The inhibitor setting unit 118 approximates the detected area of the inhibitor k with a circle, calculates coordinate information indicating the center position bk of the inhibitor k, and information related to the radius ck, and sets the calculated information in the RAM or the hard disk. .

FIG. 6 is a diagram illustrating an example of an inhibitor setting method.
In FIG. 6, the broken line portion indicates the detected inhibitor k region. In this case, the inhibitor setting unit 118 approximates the detection area indicated by the broken line with a circle as shown in FIG. 6, and calculates coordinate information indicating the center position bk of the inhibitor k and information related to the radius ck. . Here, unlike the grain boundary point, the inhibitor k set by the inhibitor setting unit 118 does not change its position with time.

  The line change processing unit 119 determines whether each line p set by the line setting unit 104 passes through the inhibitor k set by the inhibitor setting unit 118, and when the line p passes through the inhibitor k Then, the process of changing the line p is performed.

FIG. 7 is a diagram illustrating an example of line change processing by the line change processing unit 119.
7A to 7A show an example of the line p before being processed by the line change processing unit 119. FIG. Moreover, the 1st process example with respect to each line p shown to FIG.7 (1a)-(6a) is shown to FIG.7 (1b)-(6b), and a 2nd process example is shown in FIG.7 (1c)-(6c). It shows.

  Specifically, the line change processing unit 119, as shown in FIG. 7 (1a), is a case where the line p passes through the inhibitor k and the end point (grain boundary point) of the line p is not in the inhibitor k. 7 (1b) or 7 (1c), a double point in is generated at an arbitrary position on the line p, and the line p is divided into two lines. Then, the line change processing unit 119 moves the generated double point in to the center position (bk) of the inhibitor k, and performs processing for setting this as the fixed point ik. In this case, the fixed point ik is an end point of the line p and a fixed double point constituting the line. In this case, as shown in FIG. 7 (1b) or FIG. 7 (1c), a fixed point ik is newly generated, and the line p has two lines p′1 and p′2 whose end points are the fixed point ik. It is divided into.

  Further, the line change processing unit 119 is a case where the line p passes through the inhibitor k, and one end point (grain boundary point) of the line p is in the inhibitor k (FIGS. 7 (2a) to (4a). In this case, the end point in the inhibitor k is moved to the central position (bk) of the inhibitor k, and this is moved to the fixed point ik (FIG. 7 (2b) to (4b) or FIG. 7 (2c) to (4c). ) Is performed as a fixed point ik). In this case, the line p is changed to a line having the fixed point ik as one end point.

  Further, the line change processing unit 119 is a case where the line p passes through the inhibitor k, and both end points (grain boundary points) of the line p are in the inhibitor k (FIGS. 7 (5a) and (6a). In the case shown in FIG. 7, a process of eliminating the line p in the inhibitor k is performed (FIG. 7 (5b) and (6b), or FIG. 7 (5c) and (6c)). Further, the line change processing unit 119 uses two fixed points ik (FIG. 7 (5b) and FIG. 7 (6b)) that are located at the center position (bk) of the inhibitor k as two points in the inhibitor k. 7 (5c) and (6c) as fixed points ik), and processing for constructing a line having each end point of the line p and each end point constituting the line and the fixed point ik as end points is performed.

  That is, when the line p set by the line setting unit 104 passes through the inhibitor k, the line change processing unit 119 generates a fixed point ik having the center position bk as a fixed position in the inhibitor k, and the fixed point A line changing process with the point ik as an end point is performed.

  Then, the line change processing unit 119 performs various reset processes for the point setting unit 103 and the line setting unit 104 according to point changes (including disappearance and occurrence) and line changes (including disappearance and occurrence). To do.

  The grain boundary energy (E) calculation unit 121 is centered on the coordinate information of the fixed point ik, information indicating the position of each other point constituting the fixed point ik and the line p, and the fixed point ik to be processed. Information on the inhibitor k at the position bk is acquired, and the grain boundary energy γ per unit length of the grain boundary u to which the fixed point ik belongs is acquired from the grain boundary energy (γ) setting unit 109, and these acquired information Based on the above, the grain boundary energy Ei of the grain boundary u to which the fixed point ik belongs is calculated (calculated). That is, the grain boundary energy (E) calculation unit 121 includes the grain boundary energy γ per unit length of the grain boundary u to which the fixed point ik belongs, the other point constituting the line with the fixed point ik and the fixed point ik. Is used (the length of each line) to calculate (calculate) the grain boundary energy (first grain boundary energy) Ei of the grain boundary u to which the fixed point ik belongs.

  Here, “the grain boundary u to which the fixed point ik belongs” is defined as the grain boundary u between the fixed point ik and the point (grain boundary point) i constituting the line. In the grain boundary energy Ei calculation process by the grain boundary energy (E) calculation unit 121, the grain boundary is not included in the inhibitor k (not including the surface (boundary) of the inhibitor k) having the fixed point ik as the center position bk. Calculation (calculation) is performed on the assumption that u does not exist.

  Specifically, with reference to FIG. 8 and FIG. 9, a method for calculating the grain boundary energy Ei when the fixed point ik is a double point (fixed double point) and a triple point (fixed triple point) will be described below. Explained.

  First, as shown in FIG. 8, when the fixed point ik is a double point, lines px and py are connected between the fixed point ik and the points ix and iy that are grain boundary points adjacent to the fixed point ik. Is formed. Here, since the grain boundary u does not exist in the inhibitor k, the effective length used in the calculation of the grain boundary energy Ei is the length of each line px and py and the radius ck of the inhibitor k. Lx and Ly are obtained by subtracting the length.

Further, since the fixed point ik is a double point, the portion of the effective length Lx in the line px and the portion of the effective length Ly in the line py belong to the same grain boundary u. Therefore, for example, the grain boundary energy Ei shown in FIG. 8 when the fixed point ik is a double point is calculated by the following equation (7).
Ei = (grain boundary energy γ per unit length of grain boundary u of Lx (Ly) portion)
× (Lx + Ly) (7)

  Subsequently, as shown in FIG. 9, when the fixed point ik is a triple point, a line is formed between the fixed point ik and the points ix, iy and iz which are grain boundary points adjacent to the fixed point ik. px, py and pz are formed. Here, since the grain boundary u does not exist in the inhibitor k, the effective length used in calculating the grain boundary energy Ei is the radius of the inhibitor k from the lengths of the lines px, py, and pz. Lx, Ly, and Lz are obtained by subtracting the length of ck.

Further, since the fixed point ik is a triple point, the portion of the effective length Lx in the line px, the portion of the effective length Ly in the line py, and the portion of the effective length Lz in the line pz are different from each other. Belongs to the field u. Therefore, for example, the grain boundary energy Ei when the fixed point ik shown in FIG. 9 is a triple point is calculated by the following equation (8).
Ei = (grain boundary energy γ per unit length of grain boundary u of Lx portion) × Lx
+ (Grain boundary energy γ per unit length of grain boundary u of Ly portion) × Ly
+ (Grain boundary energy γ per unit length of grain boundary u of Lz portion) × Lz
... (8)

  Further, the grain boundary energy (E) calculation unit 121 is a position in a region excluding the inside of the inhibitor k when the fixed point i is released from the fixed position (center position bk of the inhibitor k), and the grain boundary energy E is the minimum. The grain boundary energy (second grain boundary energy) Ei ′ at the position (equilibrium position) is calculated (calculated). At this time, in the calculation process of the grain boundary energy Ei ′ by the grain boundary energy (E) calculation unit 121, in the inhibitor k having the fixed point i as the center position bk (not including the surface (boundary) of the inhibitor k), Calculation (calculation) is performed on the assumption that the grain boundary u does not exist and the other inhibitor k does not exist.

  Specifically, using FIG. 8 and FIG. 9, the calculation method of the grain boundary energy Ei ′ when the fixed point i is a double point (fixed double point) and a triple point (fixed triple point), This will be described below.

  First, as shown in FIG. 8, when the fixed point ik is a double point, as described above, the portion of the effective length Lx in the line px and the portion of the effective length Ly in the line py are the same. Since it belongs to the grain boundary u, the equilibrium position is an arbitrary position on a line (virtual line) pxy connecting the point ix and the point iy with the shortest distance. Here, as an example, the equilibrium position is described as the position of w on the line pxy. Further, the grain boundary energy γ per unit length of the grain boundary u in the line pxy is the grain boundary energy γ per unit length of the portion of the effective length Lx in the line px (effective length Ly in the line py). .

Therefore, for example, the grain boundary energy Ei ′ at the equilibrium position w shown in FIG. 8 is calculated by the following equation (9).
Ei ′ = (grain boundary energy γ per unit length of grain boundary u of Lx (Ly) portion)
× (Lwx + Lwy)
= (Grain boundary energy γ per unit length of grain boundary u of Lx (Ly) portion)
× Lxy (9)

  Although not applicable in the example shown in FIG. 8, when the line pxy passes through the inhibitor k, the length obtained by subtracting the length of the line pxy through the inhibitor k from the length of the line pxy (Lxy). This is multiplied by the grain boundary energy γ per unit length.

  Subsequently, as shown in FIG. 9, when the fixed point ik is a triple point, the effective length Lx portion in the line px, the effective length Ly portion in the line py, and the effective length in the line pz. The portions of Lz belong to different grain boundaries u. Here, as an example, the case where the equilibrium position is the position w shown in FIG. 9 will be described.

  In this case, a line (virtual line) pwx that connects the point ix and the equilibrium position w, a line (virtual line) pwy that connects the point iy and the equilibrium position w, and a line (virtual line) that connects the point iz and the equilibrium position w ) To form pwz. At this time, the effective length used for the calculation of the grain boundary energy Ei ′ includes the length Lwx of the line pwx, the length Lwy of the line pwy, and the length Lk in the inhibitor k from the length Lwz of the line pwz. The subtracted length (Lwz-Lk) is obtained.

  Further, the grain boundary energy γ per unit length of the grain boundary u in the line pwx becomes the grain boundary energy γ per unit length of the portion of the effective length Lx in the line px. Similarly, the grain boundary energy γ per unit length of the grain boundary u in the line pwy is the grain boundary energy γ per unit length of the portion of the effective length Ly in the line py. Further, the grain boundary energy γ per unit length of the grain boundary u in the portion excluding the inside of the inhibitor k in the line pwz becomes the grain boundary energy γ per unit length in the portion of the effective length Lz in the line pz.

Therefore, for example, the grain boundary energy Ei ′ when the fixed point ik shown in FIG. 9 is a triple point is calculated by the following equation (10).
Ei ′ = (grain boundary energy γ per unit length of grain boundary u of Lx portion) × Lwx
+ (Grain boundary energy γ per unit length of grain boundary u of Ly portion) × Lwy
+ (Grain boundary energy γ per unit length of grain boundary u in Lz portion)
× (Lwz-Lk) (10)

  Returning to FIG. 2, the fixed point processing unit 120 compares the grain boundary energy Ei obtained by the grain boundary energy (E) calculation unit 121 with the grain boundary energy Ei ′, and the grain boundary energy Ei ′ is the grain boundary energy. When it is less than Ei (Ei ′ <Ei), a process of canceling the fixed point ik is performed.

  Specifically, the fixed point processing unit 120 moves the fixed point i to the surface (boundary) of the inhibitor k when the grain boundary energy Ei ′ is less than the grain boundary energy Ei (Ei ′ <Ei), The process of releasing the fixation and setting the normal point ik is performed. Here, in the present embodiment, as shown in FIG. 8 when the fixed point i is a double point and as shown in FIG. 9 when the fixed point i is a triple point, the fixed point i is positioned at the normal point im. Shall be moved to

Specifically, in the present embodiment, among the regions defined by the lines shown in FIGS. 8 and 9, the boundary of the inhibitor k in the region between the line px and the line py where the equilibrium position w exists. The normal point im is moved to the position of the intersection (point im) with the line segment pm that bisects the angle (2β) between the line px and the line py.
The point after movement of the fixed point i is not limited to the position of the point im. For example, the position of the point on the boundary of the inhibitor k where the grain boundary energy Ei ′ is minimized. It is applicable even if it is a form to move to. The calculation method of the grain boundary energy Ei ′ in this case is calculated by the above-described equation (9) when the fixed point i is a double point, and is described above when the fixed point i is a triple point ( 10) Calculated by the equation.

  Then, the fixed point processing unit 120 causes the point setting unit 103 to perform resetting according to the change of the fixed point i.

  Next, an example of processing operations performed by the crystal grain analysis apparatus 100 will be described with reference to the flowcharts of FIGS. 10-1 to 10-4. 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, whereby the processing of the flowchart shown in FIG.

  First, in step S1 of FIG. 10A, the crystal image acquisition unit 101 includes an image signal (crystal image signal) of an inhibitor existing between the crystal grain A of the electromagnetic steel sheet and the crystal grain A of the electromagnetic steel sheet, and the image signal. And a signal indicating the orientation ξ of each crystal grain A included in the. When a crystal grain image signal and a signal indicating the orientation ξ of each crystal grain A included in the image signal are input, the process proceeds to step S2.

  In 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 causes the display device 200 to display 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. . Here, after the analysis temperature θ (t) and the analysis completion time T are sequentially input, the user can designate the point (double point or triple point) i while referring to the crystal grain image 31. A case will be described as an example.

  Next, in step S <b> 3, the analysis temperature setting unit 106 stands by until the analysis temperature θ (t) of the electromagnetic steel sheet to be analyzed (crystal grain A) is input based on the operation of the operation device 300 by the user. And if analysis temperature (theta) (t) of the electromagnetic steel plate (crystal grain A) of analysis object is input, it will progress to step S4.

  In step S4, the analysis temperature setting unit 106 sets the input analysis temperature θ (t) of the analysis target electrical steel sheet (crystal grain A) in the RAM or the hard disk. In the flowcharts of FIGS. 10-1 to 10-4, 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 S5, the analysis time setting unit 112 stands by until an analysis completion time T is input based on the operation of the operation device 300 by the user. When the analysis completion time T is input, the process proceeds to step S6.

  In step S6, the analysis time setting unit 112 sets the input analysis completion time T in the RAM or the hard disk.

  Next, in step S <b> 7, the point setting unit 103 waits until a point (double point or triple point) i is designated for the crystal grain image 31 displayed by the crystal image display unit 102. When the point (double point or triple point) i is designated, the process proceeds to step S8.

  In step S8, the point setting unit 103 calculates a vector indicating the position ri (t) of the point i determined to be specified in step S7, and sets the calculated value in the RAM or the hard disk.

  Next, in step S <b> 9, the point setting unit 103 determines whether or not an instruction to end the work specifying the point (double point or triple point) i has been made based on the operation of the operation device 300 by the user. If the result of this determination is that there has been no instruction to end the work specifying the point i, the process returns to step S7, and the point (double point or triple point) i already specified and another point (double point or triple point). ) Wait until i is specified.

  On the other hand, as a result of the determination in step S9, when an instruction to end the work specifying the point i is made, the process proceeds to step S10. In step S10, the point setting unit 103 calculates the number NI of points (double points or triple points) i determined to have been designated in step S7 (that is, the number of times the process in step S7 has been performed) NI, and the RAM Or set to hard disk.

  Next, in step S <b> 11 of FIG. 10B, the inhibitor setting unit 118 waits until an inhibitor k is designated for the crystal grain image 31 displayed by the crystal image display unit 102. When the inhibitor k is designated, the process proceeds to step S12.

  In step S12, the inhibitor setting unit 118 detects the region of the inhibitor k determined to be specified in step S11 based on the crystal grain image signal acquired in step S1, and approximates this detection region with a circle. Then, coordinate information indicating the center position bk of the inhibitor k and information related to the radius ck are calculated and set in the RAM or the hard disk.

  Next, in step S <b> 13, the inhibitor setting unit 118 determines whether or not an instruction to end the work specifying the inhibitor k has been made based on the operation of the operation device 300 by the user. If the result of this determination is that there is no instruction to end the work specifying the inhibitor k, the process returns to step S11 and waits until another inhibitor k already specified is specified.

  On the other hand, as a result of the determination in step S13, if an instruction to end the work specifying the inhibitor k is given, the process proceeds to step S14. In step S14, the inhibitor setting unit 118 calculates the number NK of the inhibitor setting units 118 determined to have been specified in step S11 (that is, the number of times the processing in step S11 has been performed) NK, and sets the calculated value in the RAM or the hard disk. .

Next, in step S15, the line setting unit 104 specifies a line specified by two points i adjacent to each other on the same grain boundary u among the points (double points or triple points) i set in step S8. p and its number NP are set in the RAM or hard disk. Note that the line p is set in step S15 without considering the presence of the inhibitor k. Specifically, the line setting unit 104 defines the line p by two points i that specify the line p. For example, the line p1 shown in FIG. 3C is defined as the following equation (11).
p1 = {i1, i2} (11)

Next, in step S16, the grain boundary setting unit 105 determines the grain boundary u specified by the lines p connected to each other with the triple point i set in step S8 as both ends among the lines p set in step S15. Are set in the RAM or hard disk. Specifically, the grain boundary setting unit 105 defines the grain boundary u by a plurality of lines p that specify the grain boundary u. For example, the grain boundary u1 shown in FIG. 3C is defined as the following equation (12).
u1 = {p1, p2, p3, p4} (12)

  Next, in step S <b> 17, the orientation setting unit 107 determines the crystal grain image 31 based on the “signal indicating the orientation ξ of each crystal grain A included in the crystal grain image 31” determined to have been input in step S <b> 1. The orientation ξ of all the included crystal grains A is set in the RAM or hard disk.

  Next, in step S18, the grain boundary energy (γ) setting unit 109 sets the grain boundary based on the orientation ξ of the crystal grain A set in step S17 and the analysis temperature θ (t) set in step S4. The grain boundary energy γ per unit length of all grain boundaries u set in step S16 is read from the graph or the like stored in the field energy (γ) storage unit 108. The grain boundary energy (γ) setting unit 109 sets the read grain boundary energy γ per unit length in the RAM or the hard disk.

  Next, in step S19, the mobility setting unit 111 stores the mobility based on the orientation ξ of the crystal grain A set in step S17 and the analysis temperature θ (t) set in step S4. The mobility Mi of all the grain boundaries u set in step S16 is read from the graph or the like stored in the unit 110. Then, the mobility setting unit 111 sets the read mobility Mi in the RAM or the hard disk.

  Next, in step S20 of FIG. 10-3, the analysis time setting unit 112 sets the time t to 0 (zero).

  If the analysis time t is set to 0 by the analysis time setting unit 112, then in step S21, the line change processing unit 119 sets the variable p indicating the line to be processed to 1. At this time, the line change processing unit 119 acquires information regarding the line p set in step S21 from the line setting unit 104.

  Next, in step S22, the line change processing unit 119 sets ΔNI indicating the number of points to be increased or decreased to 0 (zero), and sets ΔNP indicating the number of lines to be increased or decreased to 0 (zero).

  Next, in step S23, the line change processing unit 119 sets a variable k indicating the inhibitor to be processed to 1. At this time, the line change processing unit 119 obtains information related to the inhibitor k set in step S23 (coordinate information indicating the center position bk of the inhibitor k and information related to the radius ck) from the inhibitor setting unit 118.

  Here, in the following description, it demonstrates with the schematic diagram shown in FIG.

  In step S24, the line change processing unit 119 determines whether or not the line p passes through the inhibitor k based on the information regarding the line p acquired in step S21 and the information regarding the inhibitor k acquired in step S23. At this time, it is determined that the surface (boundary) of the inhibitor k is not within the inhibitor k. If the result of this determination is that the line p is not within the inhibitor k (if it does not fall under (1a) to (6a) in FIG. 7), the process proceeds to step S34.

  On the other hand, if the result of determination in step S24 is that the line p passes through the inhibitor k, the process proceeds to step S25. In step S25, the line change processing unit 119 determines whether or not the end point of the line p is within the inhibitor k.

  As a result of the determination in step S25, when the end point of the line p is not in the inhibitor k (in the case shown in FIG. 7 (1a)), the process proceeds to step S26. In step S26, the line change processing unit 119 generates a double point (double point in shown in FIG. 7 (1b) or FIG. 7 (1c)) at an arbitrary position on the line p. As a result, the line p is divided into two lines.

  Next, in step S27, the line change processing unit 119 sets the double point generated on the line p in step S26 (the double point in shown in FIG. 7 (1b) or FIG. 7 (1c)) to the center position of the inhibitor k. It is moved to (bk), and this is set as a fixed point ik (fixed point ik shown in FIG. 7 (1b) or FIG. 7 (1c)). In this case, the fixed point ik is an end point of the line p and a fixed double point constituting the line. As a result, a fixed point ik is newly generated, and the number of points is increased by one. In addition, since the line p is divided into two lines (lines p′1 and p′2 shown in FIG. 7 (1b) or FIG. 7 (1c), respectively), the number of lines increases by one. In this case, the line change processing unit 119 also relates to information about the newly generated fixed point ik (for example, information indicating that the point is a fixed point and its coordinate information), and about the newly set line. Information (for example, information indicating that a line is set between each end point of the line p and the fixed point ik) is stored in the RAM or the hard disk.

  Next, in step S28, the line change processing unit 119 increases the number of points and the number of lines by 1 in the processing of steps S26 and S27, so that the currently set ΔNI indicating the number of points to be increased or decreased is set. 1 is added to change the ΔNI, and 1 is added to the currently set ΔNP indicating the number of lines to be increased or decreased to change the ΔNP.

  On the other hand, if the result of determination in step S25 is that the end point of the line p is within the inhibitor k (as shown in FIGS. 7 (2a) to (6a)), the process proceeds to step S29. In step S29, the line change processing unit 119 determines whether or not both end points of the line p are in the inhibitor k.

  As a result of the determination in step S29, when both end points of the line p are not within the inhibitor k, that is, when only one of the end points of the line p is within the inhibitor k (when shown in FIGS. 7 (2a) to (4a)). In step S30, the process proceeds to step S30. In step S30, the line change processing unit 119 moves the end point in the inhibitor k to the center position (bk) of the inhibitor k, and moves this to the fixed point ik (FIG. 7 (2b) to (4b) or FIG. (2c) to (4c) as fixed points ik). In the case shown in FIG. 7 (3a), since the end point in the inhibitor k is at the center position (bk) of the inhibitor k, the movement process is not performed. In this case, since the number of points and the number of lines do not increase or decrease, ΔNI indicating the number of points to be increased or decreased and ΔNP indicating the number of lines to be increased or decreased are not changed. In this case, the line change processing unit 119 stores information indicating that the end point in the inhibitor k has been changed to the fixed point ik in the RAM or the hard disk.

  On the other hand, as a result of the determination in step S29, if both end points of the line p are within the inhibitor k (as shown in FIGS. 7 (5a) and (6a)), the process proceeds to step S31. In step S31, the line change processing unit 119 eliminates the line p in the inhibitor k (FIG. 7 (5b) and (6b) or FIG. 7 (5c) and (6c)). This reduces the number of lines by one.

  Next, in step S32, the line change processing unit 119 moves two points in the inhibitor k to the center position (bk) of the inhibitor k (this example is the first processing example), One fixed point ik (fixed point ik shown in FIGS. 7 (5b) and 7 (6b)) is assumed. In the case shown in FIG. 7 (6a), since one end point in the inhibitor k is at the center position (bk) of the inhibitor k, the movement process is not performed on the one end point. The number of points is reduced by one by the process of step S32. Also, in this case, the line change processing unit 119 stores information indicating that the two end points in the line p have been changed to one fixed point ik and information indicating that the line p has been deleted from the RAM or the hard disk. To remember.

  Next, in step S33, the line change processing unit 119 reduces the number of points and the number of lines by 1 in the processing of steps S31 and S32, respectively, so that ΔNI indicating the currently set number of points to be increased or decreased is set. 1 is subtracted to change the ΔNI, and 1 is subtracted from the currently set ΔNP indicating the number of lines to be increased or decreased to change the ΔNP.

  When the process of step S28, step S30, or step S33 ends, the process proceeds to step S34. In step S34, the line change processing unit 119 determines whether or not the variable k indicating the inhibitor to be processed is smaller than the number NK set in step S14. As a result of the determination, if the variable k indicating the inhibitor to be processed is smaller than the number NK set in step S14, it is determined that all the inhibitors k set in step S14 have not been processed, and the process proceeds to step S35. move on.

  In step S35, the line change processing unit 119 adds 1 to the variable k indicating the inhibitor to be processed, and changes the inhibitor k to be processed. At this time, the line change processing unit 119 acquires, from the inhibitor setting unit 118, information related to the inhibitor k set in step S35 (coordinate information indicating the center position bk of the inhibitor k and information related to the radius ck). And the process after step S24 is performed again with respect to the changed inhibitor k.

  On the other hand, as a result of the determination in step S34, when the variable k indicating the inhibitor to be processed is equal to or larger than the number NK set in step S14, it is determined that all the inhibitors k set in step S14 have been processed, Proceed to step S36.

  In step S36, the line change processing unit 119 determines whether or not the variable p indicating the processing target line is smaller than the number NP set in step S15. If the variable p indicating the processing target line is smaller than the number NP set in step S15 as a result of this determination, it is determined that all the lines p set in step S15 have not been processed, and the process proceeds to step S37. move on.

  In step S37, the line change processing unit 119 adds 1 to the variable p indicating the processing target line to change the processing target line p. At this time, the line change processing unit 119 acquires information regarding the line p set in step S <b> 37 from the line setting unit 104. And the process after step S23 is performed again with respect to the changed line p.

  On the other hand, as a result of the determination in step S36, when the variable p indicating the processing target line is equal to or greater than the number NP set in step S15, it is determined that all the lines p set in step S15 have been processed, Proceed to step S38.

  In step S38, the line change processing unit 119 outputs ΔNI information indicating the number of points that are currently set to increase or decrease to the point setting unit 103, and sets the number NI of points that are currently set. Then, ΔNI indicating the number of output increasing / decreasing points is added, and the number of points NI is reset. Further, the line change processing unit 119 outputs ΔNP information indicating the currently set increase / decrease line to the line setting unit 104, and outputs the output increase / decrease line to the number NP of lines set in step S15. Is added to reset the number of lines NP.

  Next, in step S39, the line change processing unit 119 causes the point setting unit 103 and the line setting unit 104 to change points (including disappearance and occurrence) and change lines (including disappearance and occurrence). Various resetting processes are performed.

  Specifically, the line change processing unit 119 outputs to the point setting unit 103 information related to the change (including disappearance and generation) of the points generated in the processes in steps S21 to S38, and the point i in step S8. Let's reset. At this time, for the generated fixed point ik, the point setting unit 103 sets coordinate information indicating the position of the point in the RAM or the hard disk together with information indicating that the point is a fixed point.

  Further, the line change processing unit 119 outputs to the line setting unit 104 information related to the line change (including disappearance and generation) that has occurred in steps S21 to S38. Make settings. At this time, the line change processing unit 119 may cause the line setting unit 104 to reset the line based on the point i reset by the point setting unit 103.

  Further, the grain boundary setting unit 105 resets the grain boundary u in step S <b> 16 triggered by the resetting of the point i in the point setting unit 103 and the resetting of the line p in the line setting unit 104. Further, the grain boundary energy (γ) setting unit 109 resets the grain boundary energy γ per unit length in step S18 when the grain boundary u is reset by the grain boundary setting unit 105. Further, the mobility setting unit 111 resets the mobility Mi in step S19 when the grain boundary u is reset by the grain boundary setting unit 105.

  Next, in step S40 of FIG. 10-4, the analysis point determination unit 113 sets a variable i indicating a calculation target point to 1. Thereby, the point i to be calculated is set.

  Next, in step S41, the analysis point determination unit 113 determines whether or not the point i to be calculated is a fixed point (ik). As a result of the determination, if the point i to be calculated is not a fixed point (ik), the process proceeds to step S42.

  Next, in step S42, the analysis point determination unit 113 determines whether the point i to be calculated is a double point. As a result of the determination, if the point i to be calculated is a double point, the process proceeds to step S43.

  In step S43, double-point driving force / position calculation processing by the double-point driving force calculation unit 114 and the position calculation unit 116 is performed. Here, the detailed processing operation of step S43 will be described with reference to FIG.

  In step S43 of FIG. 10-4, first, in step S431 of FIG. 11, the double-point driving force calculation unit 114 calculates the double point i to be calculated and two points i-1, i + 1 adjacent to the double point. Is read from the point setting unit 103. Then, the double-point driving force calculation unit 114 calculates the center of curvature O and the radius of curvature Ri (t) of the arc 41 defined by the double point i and the two points i−1 and i + 1 adjacent to the double point i. To do.

  Next, in step S432, the double-point driving force calculation unit 114 determines the grain boundary energy γi per unit length of the grain boundary u to which the double point i to be calculated belongs from the grain boundary energy (γ) setting unit 109. read out.

  Next, in step S433, the double-point driving force calculation unit 114 calculates the radius of curvature Ri (t) calculated in step S431 and the grain boundary energy γi per unit length read in step S432 by the equation (1). And the magnitude of the driving force Fi (t) generated at the double point i is calculated.

  The double-point driving force calculation unit 114 reads a vector indicating the current position ri (t) of the double point i to be calculated from the point setting unit 103. Then, the double-point driving force calculation unit 114 calculates the curvature from the double point i to be calculated from the vector indicating the current position ri (t) of the double point i to be calculated and the curvature center O calculated in step S431. The direction toward the center O is calculated, and the direction of the driving force Fi (t) generated at the double point i is determined. Thereby, a vector indicating the driving force Fi (t) generated at the double point i is obtained.

  Next, in step S434, the position calculation unit 116 reads out the mobility Mi corresponding to the grain boundary u to which the double point i to be calculated belongs from the mobility setting unit 111.

  Next, in step S435, the position calculation unit 116 receives a vector indicating the current position ri (t) of the double point i to be calculated from the point setting unit 103.

  Next, in step S436, the position calculation unit 116 firstly calculates the “vector indicating the driving force Fi (t) generated at the double point i to be calculated” obtained in step S433 and the “calculation” obtained in step S434. The mobility Mi of the grain boundary u to which the target double point i belongs is substituted into the equation (4) to calculate a vector indicating the speed vi (t) of the target double point i.

  Then, the position calculation unit 116 calculates a vector indicating the speed vi (t) of the double point i to be calculated, a vector indicating the current position ri (t) of the double point i to be calculated, and a time Δt as follows: When Δt [sec] has elapsed from the current time t, a vector indicating the position ri (t + Δt) where the double point i to be calculated exists is calculated.

  By performing the processing from step S431 to step S436, the double-point driving force / position calculation processing shown in step S43 of FIG. 10-4 is performed.

  On the other hand, if the result of determination in step S42 is that the point i to be calculated is not a double point but a triple point, the process proceeds to step S44.

  In step S44, triple point driving force / position calculation processing by the triple point driving force calculation unit 115 and the position calculation unit 116 is performed. Here, the detailed processing operation of this step S44 is demonstrated using FIG.

  In step S44 of FIG. 10-4, first, in step S441 of FIG. 12, the triple point driving force calculation unit 115 calculates the grain boundary energy per unit length at the three grain boundaries u to which the triple point i to be calculated belongs. The magnitudes (absolute values) of γi1, γi2, and γi3 are read from the grain boundary energy (γ) setting unit 109. Further, the triple-point driving force calculation unit 115 reads the triple point i to be calculated and information on the three points 1, 2, and 3 adjacent to the triple point i from the point setting unit 103. Then, the triple point driving force calculation unit 115 calculates a unit vector having a direction from the triple point i to be calculated toward the points 1, 2, and 3.

  Next, in step S442, the triple point driving force calculation unit 115 reads the “magnitudes of grain boundary energy γi1, γi2, γi3 per unit length” read out in step S441 and “calculation target” calculated in step S441. The unit vector having a direction from the triple point i to points 1, 2, and 3 ”is substituted into the equation (3) to calculate a vector indicating the driving force Fi (t) generated at the triple point i to be calculated. To do.

  Next, in step S443, the position calculation unit 116 reads the mobilities Mi1 to Mi3 corresponding to the three grain boundaries u to which the triple point i to be calculated belongs from the mobility setting unit 111.

  Next, in step S444, the position calculation unit 116 moves to the points 1, 2, and 3 from the mobility Mi1 to Mi3 of the three grain boundaries u to which the triple point i to be calculated belongs, and from the triple point i to be calculated. A unit vector (dij (t) / | dij (t) |) having a direction is substituted into the equation (6) to calculate the mobility Mi of the triple point i to be calculated. The unit vector having the direction from the triple point i to be calculated toward the points 1, 2, and 3 can be the one calculated in step S441.

  Next, in step S445, the position calculation unit 116 receives a vector indicating the current position ri (t) of the triple point i to be calculated from the point setting unit 103.

  Next, in step S446, the position calculation unit 116 firstly calculates the “vector indicating the driving force Fi (t) generated at the triple point i to be calculated” obtained in step S442 and the “calculation” obtained in step S444. By substituting “the mobility Mi of the target triple point i” into the equation (4), a vector indicating the velocity vi (t) of the target triple point i is calculated.

  Then, the position calculation unit 116 calculates a vector indicating the velocity vi (t) of the triple point i to be calculated, a vector indicating the current position ri (t) of the triple point i to be calculated, and a time Δt ( 5) By substituting into the equation, when Δt [sec] has elapsed from the current time t, a vector indicating the position ri (t + Δt) where the triple point i to be calculated exists is calculated.

  Through the processing from step S441 to step S446 described above, the triple point driving force / position calculation processing shown in step S44 of FIG. 10-4 is performed.

  On the other hand, if the result of determination in step S41 is that the point i to be calculated is a fixed point (ik), the process proceeds to step S45.

  In step S45, the fixed point processing unit 120 indicates the coordinate information of the fixed point i determined by the analysis point determining unit 113 and the positions of the other points constituting the fixed point i and the line p. Information is read from the point setting unit 103. Further, the fixed point processing unit 120 reads information about the inhibitor k having the processing target fixed point i as the center position bk (coordinate information indicating the center position bk and information related to the radius ck) from the inhibitor setting unit 118.

  Next, in step S46, the grain boundary energy (E) calculation unit 121 acquires the information read in step S45, and calculates the grain boundary energy γ per unit length of the grain boundary u to which the fixed point i belongs. Read from the grain boundary energy (γ) setting unit 109. Then, the grain boundary energy (E) calculation unit 121 includes the grain boundary energy γ per unit length of the grain boundary u to which the fixed point i belongs, and the other points constituting the line between the fixed point i and the fixed point i. Is used (the length of each line) to calculate (calculate) the grain boundary energy Ei of the grain boundary u to which the fixed point i belongs. In the calculation process of the grain boundary energy Ei in step S46, the calculation is performed assuming that the grain boundary u does not exist in the inhibitor k (not including the surface (boundary) of the inhibitor k) having the fixed point i as the center position bk. (Calculation) is performed.

  Here, when the fixed point i (ik) is a double point, for example, as shown in FIG. 8, between the fixed point ik and the points ix and iy adjacent to the fixed point ik, the line px and py is formed. In addition, since the fixed point i (ik) is a double point, the portion of the effective length Lx in the line px and the portion of the effective length Ly in the line py belong to the same grain boundary u. . Therefore, the grain boundary energy Ei when the fixed point i (ik) is a double point is calculated by, for example, the above-described equation (7) in the case shown in FIG.

  On the other hand, when the fixed point i (ik) is a triple point, for example, as shown in FIG. 9, a line px is connected between the fixed point ik and points ix, iy, and iz adjacent to the fixed point ik. , Py and pz are formed. Since the fixed point i (ik) is a triple point, the portion of the effective length Lx in the line px, the portion of the effective length Ly in the line py, and the portion of the effective length Lz in the line pz are respectively , They belong to different grain boundaries u. Therefore, the grain boundary energy Ei when the fixed point i (ik) is a triple point is calculated by, for example, the above-described equation (8) in the case shown in FIG.

  Next, in step S47, the grain boundary energy (E) calculation unit 121 determines that the fixed point i is released from the fixed position (the center position bk of the inhibitor k) and is the position of the region excluding the inside of the inhibitor k. The grain boundary energy Ei ′ when the field energy E is at the minimum position (equilibrium position) is calculated (calculated). At this time, in the calculation process of the grain boundary energy Ei ′ in step S47, the grain boundary u does not exist in the inhibitor k (not including the surface (boundary) of the inhibitor k) having the fixed point i as the center position bk. In addition, calculation (calculation) is performed on the assumption that no other inhibitor k exists.

  Here, when the fixed point i (ik) is a double point, for example, the portion of the effective length Lx in the line px and the portion of the effective length Ly in the line py in FIG. Therefore, the equilibrium position W is an arbitrary position on a line (virtual line) pxy connecting the point ix and the point iy with the shortest distance. Further, the grain boundary energy γ per unit length of the grain boundary u in the line pxy is the grain boundary energy γ per unit length of the portion of the effective length Lx in the line px (effective length Ly in the line py). . Therefore, the grain boundary energy Ei ′ when the fixed point i (ik) is a double point is calculated by, for example, the above-described equation (9) in the case shown in FIG.

  Although not applicable in the example shown in FIG. 8, when the line pxy passes through the inhibitor k, the length obtained by subtracting the length of the line pxy through the inhibitor k from the length of the line pxy (Lxy). This is multiplied by the grain boundary energy γ per unit length.

  On the other hand, when the fixed point i (ik) is a triple point, for example, a portion of the effective length Lx in the line px, a portion of the effective length Ly in the line py, and an effective length in the line pz in FIG. The portions of Lz belong to different grain boundaries u.

  Here, for example, when the equilibrium position is the position w shown in FIG. 9, a line (virtual line) pwx connecting the point ix and the equilibrium position w and a line (virtual line) connecting the point iy and the equilibrium position w are shown. A line (virtual line) pwz connecting pwy, the point iz, and the equilibrium position w is formed. At this time, the effective length used for the calculation of the grain boundary energy Ei ′ includes the length Lwx of the line pwx, the length Lwy of the line pwy, and the length Lk in the inhibitor k from the length Lwz of the line pwz. The subtracted length (Lwz-Lk) is obtained.

  In the case shown in FIG. 9, the grain boundary energy γ per unit length of the grain boundary u in the line pwx is the grain boundary energy γ per unit length in the portion of the effective length Lx in the line px. Similarly, the grain boundary energy γ per unit length of the grain boundary u in the line pwy is the grain boundary energy γ per unit length of the portion of the effective length Ly in the line py. Further, the grain boundary energy γ per unit length of the grain boundary u in the portion excluding the inside of the inhibitor k in the line pwz becomes the grain boundary energy γ per unit length in the portion of the effective length Lz in the line pz. Therefore, the grain boundary energy Ei ′ when the fixed point i (ik) is a triple point is calculated by, for example, the above-described equation (10) in the case shown in FIG.

  Next, in step S48, the fixed point processing unit 120 compares the grain boundary energy Ei calculated in step S46 with the grain boundary energy Ei ′ calculated in step S47. It is determined whether or not the energy is less than Ei (Ei ′ <Ei).

  As a result of the determination in step S48, if the grain boundary energy Ei ′ is less than the grain boundary energy Ei, the process proceeds to step S49. In step S49, the fixed point processing unit 120 moves the fixed point i to the surface (boundary) of the inhibitor k, releases the fixation, and sets the normal point i. Here, in the present embodiment, as described above, when the fixed point i is a double point, as shown in FIG. 8, and when the fixed point i is a triple point, as shown in FIG. It is assumed to be moved to the position of point im.

  When the process of step S49 is completed, or when it is determined in step S48 that the grain boundary energy Ei ′ is not less than the grain boundary energy Ei, the process proceeds to step S50.

  In step S50, the analysis point determination unit 113 determines whether or not the variable i indicating the calculation target point is smaller than the number of points NI currently set by the point setting unit 103. If the variable i indicating the point to be calculated is smaller than the number of points NI currently set by the point setting unit 103 as a result of this determination, processing is performed for all points i currently set by the point setting unit 103. It is determined that the process has not been performed, and the process proceeds to step S51.

  In step S51, the analysis point determination unit 113 adds 1 to the variable i indicating the point to be calculated, and changes the point i to be calculated. And the process after step S41 is performed again with respect to the changed point i.

  On the other hand, if it is determined in step S50 that the variable i indicating the point to be calculated is greater than or equal to the number of points NI currently set by the point setting unit 103, the point setting unit 103 sets the current value. It is determined that all points i have been processed, and the process proceeds to step S52.

  In step S52, the fixed point processing unit 120 causes the point setting unit 103 to perform resetting in accordance with the change of the point i in step S49. At the same time, the position calculation unit 116 outputs a vector indicating the position ri (t + Δt) where the point i calculated in step S43 or step S44 exists to the point setting unit 103. Thereby, the vector indicating the current position ri (t) of the point i is reset in the point setting unit 103.

  The line setting unit 104 resets the line p when the point i is reset by the point setting unit 103. Further, the grain boundary setting unit 105 resets the grain boundary u in response to resetting of the point i in the point setting unit 103 and resetting of the line p in the line setting unit 104. Furthermore, the resetting in the grain boundary energy (γ) setting unit 109 and the mobility setting unit 111 is also performed in response to the resetting of the grain boundary u in the grain boundary setting unit 105.

  Next, in step S53, the analysis time setting unit 112 determines whether or not the time t is greater than the analysis completion time T set in step S6. That is, it is determined whether or not the analysis completion time T has elapsed. If the result of this determination is that the time t is not greater than the analysis completion time T set in step S6 (if the analysis completion time T has not elapsed), the routine proceeds to step 54. In step S54, the analysis time setting unit 112 updates the time t by adding the time Δt to the currently set time t. Then, it returns to step S21 and performs the process after step S21 again. In step S53, the processing from step S21 to step S53 is repeatedly performed until it is determined that the time t is greater than the analysis completion time T set in step S6 (when the analysis completion time T has elapsed). .

  On the other hand, if the result of determination in step S53 is that the time t is greater than the analysis completion time T set in step S6 (when the analysis completion time T has elapsed), the process proceeds to step S55. In step S55, the analysis image display unit 117 sets 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 S43 or step S44. In the meantime, an image showing how the state of the crystal grains A changes is displayed on the display device 200. Then, the series of flowcharts of FIGS.

  When the analysis temperature θ (t) input in step S3 depends on time, for example, after step S54, the analysis temperature θ (t + Δt) at time t + Δt set in step S54 is read and the analysis temperature θ After resetting the grain boundary energy γ and the mobility Mi per unit length at (t + Δt), the processing after step S21 may be performed.

-Modification of the first embodiment-
FIG. 13 is a flowchart illustrating an example of a processing operation performed by the crystal grain analysis apparatus, showing a modification of the first embodiment of the present invention. In the flowchart shown in FIG. 13, the same steps as those shown in FIG. 10-3 are denoted by the same reference numerals, and detailed description thereof is omitted. Specifically, this modification implements a second processing example in the line change processing by the line change processing unit 119 shown in FIG. In the following description, description will be made with the schematic diagram shown in FIG.

  First, in this modification, the steps shown in FIGS. 10-1 to 10-2 are performed. Furthermore, it goes through each step shown to step S20-step S24 of FIG. 10-3.

  As a result of the determination in step S24, when the line p passes through the inhibitor k (for example, the case corresponding to FIGS. 7 (1a) to (6a)), the process proceeds to step S25. In step S25, the line change processing unit 119 determines whether or not the end point of the line p is within the inhibitor k.

  As a result of the determination in step S25, when the end point of the line p is not in the inhibitor k (in the case shown in FIG. 7 (1a)), the process proceeds to step S101. In step S101, the line change processing unit 119 generates a double point (double point in shown in FIG. 7 (1c)) at an arbitrary position in the inhibitor k on the line p. As a result, the line p is divided into two lines, and the number of lines increases by one, and the number of points also increases by one.

  Next, in step S102, the line change processing unit 119 increases the number of points and the number of lines by 1 in the processing of step S101, so that 1 is set to ΔNI indicating the currently set number of points to be increased or decreased. Addition is performed to change the ΔNI, and 1 is added to the currently set ΔNP indicating the number of lines to be increased or decreased to change the ΔNP.

  On the other hand, if the result of determination in step S25 is that the end point of the line p is within the inhibitor k (as shown in FIGS. 7 (2a) to (6a)), the process proceeds to step S29. In step S29, the line change processing unit 119 determines whether or not both end points of the line p are in the inhibitor k.

  As a result of the determination in step S29, when both end points of the line p are within the inhibitor k (in the case shown in FIGS. 7 (5a) and (6a)), the process proceeds to step S103. In step S103, the line change processing unit 119 moves one end point of the line p to the other end point to make it one point, and eliminates the line p in the inhibitor k (FIG. 7 (5c) and FIG. 7 (6c)). As a result, the number of points and the number of lines are reduced by one.

  Next, in step S104, the line change processing unit 119 decreases the number of points and the number of lines by 1 in the processing of step S103, so that 1 is set to ΔNI indicating the currently set number of points to be increased or decreased. The ΔNI is changed by subtraction, and 1 is subtracted from the currently set ΔNP indicating the number of lines to be increased or decreased to change the ΔNP.

  When the process of step S102 is completed, when the process of step S104 is completed, or when it is determined in step S29 that both end points of the line p are not within the inhibitor k (shown in FIGS. 7 (2a) to (4a)). In the case), the process proceeds to step S105. In step S105, the line change processing unit 119 moves the point in or the end point in the inhibitor k to the center position (bk) of the inhibitor k, and moves this to the fixed point ik (FIGS. 7 (1c) to (6c). The fixed point ik) shown in FIG. In the case shown in FIG. 7 (3c), since the end point in the inhibitor k is at the center position (bk) of the inhibitor k, the movement process is not performed.

  In step S105, the line change processing unit 119 receives information on point changes (including disappearance and occurrence) by the processes in steps S101 to S105, and information on line changes (including disappearance and occurrence). , Stored in RAM or hard disk.

  When the process of step S105 is completed, the process after step S34 shown in FIG. 10-3 is performed, and the flowchart in the modified example of the processing operation performed by the crystal grain analysis apparatus of the first embodiment is completed.

(Second Embodiment)
Hereinafter, a second embodiment of the present invention will be described.
In the first embodiment, as shown in FIG. 3B, double points i2 to i4, i6 to i10, i12 to i15, i17, i18, and triple points as grain boundary points with respect to the crystal grain A1. In the second embodiment, i1, i5, i11, and i16 are set. However, in the second embodiment, for simplification of processing, the grain boundary point is shown in FIG. Only the triple points i1, i5, i11, and i16 shown are set.

  FIG. 14 is a diagram illustrating an example of a point (triple point i) set by the crystal grain analyzer according to the second embodiment, a line p, and a grain boundary u. In FIG. 14, the same points as those shown in FIG.

  FIG. 15 is a block diagram illustrating an example of a functional configuration of the crystal grain analysis apparatus according to the second embodiment. In FIG. 15, the same components as those shown in FIG. The crystal grain analysis apparatus 150 according to the second embodiment is obtained by omitting the double-point driving force calculation unit 114 from the crystal grain analysis apparatus 100 according to the first embodiment shown in FIG. In the second embodiment, since the processing content of the fixed point processing unit 120 shown in FIG. 2 is changed, the fixed point processing unit 151 is used in FIG.

  FIG. 16 is a flowchart for explaining an example of a processing operation performed by the crystal grain analysis apparatus according to the second embodiment.

  In the processing operation of the crystal grain analyzer 150 according to the second embodiment, first, each step shown in FIG. 10A, each step shown in FIG. 10B, and each step shown in FIG. It passes.

  At this time, in step S7 shown in FIG. 10A, the user designates the triple point i for the crystal grain image 31 shown in FIG. Specifically, in the example shown in FIG. 14, triple points i1, i5, i11, and i16 are designated for the crystal grain A1.

  In response to this, in step S8, the point setting unit 103 calculates a vector indicating the position ri (t) of the triple point i determined to have been specified in step S7, and sets it in the RAM or hard disk.

  Further, in step S15 of FIG. 10-2, the line setting unit 104 sets the line p specified by the triple point i set in step S8 and the number NP thereof in the RAM or the hard disk. Specifically, in the example shown in FIG. 14, four lines connecting the triple point i1 and the triple point i5, the triple point i5 and the triple point i11, the triple point i11 and the triple point i16, and the triple point i16 and the triple point i1, respectively. p1. p2, p3 and p4 are set.

  In step S16 of FIG. 10-2, the grain boundary setting unit 105 sets the grain boundary u specified by the line p connected to each other with the triple point i set in step S8 as both ends in the RAM or the hard disk. Is done. In the second embodiment, since only the triple point is set in step S8, the grain boundary u is set corresponding to the line p as shown in FIG.

  First, in step S201 in FIG. 16, the analysis point determination unit 113 sets a variable i indicating a calculation target point to 1. Thereby, the point i to be calculated is set. Here, the calculation target point i is not limited to the normal triple point i set in step S8, but also in steps S26 and S27 in FIG. 10-3 (or steps S101 and S105 in FIG. 13). Newly generated fixed double point (for example, the fixed point ik shown in FIGS. 7 (1b) and (1c)), for example, generated in step S30 of FIG. 10-3 (or steps S29 and S105 of FIG. 13). The fixed triple points (for example, the fixed points ik shown in FIGS. 7 (4b) and (4c)) are also included.

  Next, in step S202, for example, the fixed point processing unit 151 sets ΔNI ′ indicating the number of points to be decreased to 0 (zero).

  Next, in step S203, the analysis point determination unit 113 determines whether the point i to be calculated is a fixed point (ik). As a result of the determination, if the point i to be calculated is not a fixed point (ik), the process proceeds to step S204. If it is determined in step S203 that it is not a fixed point (ik), it is a normal triple point i as described in step S201.

  In step S204, triple point driving force / position calculation processing by the triple point driving force calculation unit 115 and the position calculation unit 116 is performed. Here, the processing in step S204 is the same as the processing in step S44 in FIG.

  On the other hand, as a result of the determination in step S203, if the point i to be calculated is a fixed point (ik), the process proceeds to step S205. The points determined to be the fixed point (ik) in step S203 include a double point fixed point and a triple point fixed point as described in step S201.

  In step S205, the fixed point processing unit 151 indicates the coordinate information of the fixed point i determined by the analysis point determining unit 113 and the positions of the other points constituting the fixed point i and the line p. Information is read from the point setting unit 103. Further, the fixed point processing unit 151 reads information about the inhibitor k having the processing target fixed point as the center position bk (coordinate information indicating the center position bk and information related to the radius ck) from the inhibitor setting unit 118.

  Next, in step S206, the grain boundary energy (E) calculation unit 121 acquires the information read in step S205, and calculates the grain boundary energy γ per unit length of the grain boundary u to which the fixed point i belongs. Read from the grain boundary energy (γ) setting unit 109. Then, the grain boundary energy (E) calculation unit 121 includes the grain boundary energy γ per unit length of the grain boundary u to which the fixed point i belongs, and the other points constituting the line between the fixed point i and the fixed point i. Is used (the length of each line) to calculate (calculate) the grain boundary energy Ei of the grain boundary u to which the fixed point i belongs. In the calculation process of Ei in step S206, calculation (calculation) is performed assuming that there is no grain boundary u in the inhibitor k (not including the surface (boundary) of the inhibitor k) having the fixed point i as the center position bk. I do. Here, a specific method for calculating the grain boundary energy Ei when the fixed point i is a double point and a triple point is the same as step S46 of FIG. 10-4 in the first embodiment. Therefore, the description is omitted.

  Next, in step S207, the grain boundary energy (E) calculation unit 121 determines that the fixed point i is released from the fixed position (the center position bk of the inhibitor k) and is the position of the region excluding the inside of the inhibitor k. The grain boundary energy Ei ′ when the field energy E is at the minimum position (equilibrium position) is calculated (calculated). At this time, in the calculation process of the grain boundary energy Ei ′ in step S207, the grain boundary u does not exist in the inhibitor k (not including the surface (boundary) of the inhibitor k) having the fixed point i as the center position bk. In addition, calculation (calculation) is performed on the assumption that no other inhibitor k exists. Here, a specific method for calculating the grain boundary energy Ei ′ when the fixed point i is a double point and a triple point is the same as step S47 of FIG. 10-4 in the first embodiment. Therefore, the description thereof is omitted.

  Next, in step S208, the fixed point processing unit 151 compares the grain boundary energy Ei calculated in step S206 with the grain boundary energy Ei ′ calculated in step S207, and the grain boundary energy Ei ′ is It is determined whether or not the energy is less than Ei (Ei ′ <Ei).

  As a result of the determination in step S208, if the grain boundary energy Ei ′ is less than the grain boundary energy Ei, the process proceeds to step S209. In step S209, for example, the fixed point processing unit 151 determines whether or not the fixed point i is a triple point.

  If the result of determination in step S209 is that the fixed point i is a triple point, the process proceeds to step S210. In step S210, the fixed point processing unit 151 moves the fixed point i to the surface (boundary) of the inhibitor k, releases the fixation, and sets the normal point i. Also in the second embodiment, as in the first embodiment, when the fixed point i is a triple point, the fixed point i is moved to the position of the normal point im as shown in FIG.

  On the other hand, as a result of the determination in step S209, if the fixed point i is not a triple point, that is, if the fixed point i is a double point, the process proceeds to step S211. In step S211, the fixed point processing unit 151 extinguishes two lines p connecting the fixed point i and the two points adjacent to the fixed point i, and sets two grain boundaries belonging to the fixed point i. Process to make it disappear. At this time, the fixed point processing unit 151 causes the line setting unit 104 to set the disappearance of the two lines p, and causes the grain boundary setting unit 105 to disappear the two grain boundaries belonging to the fixed point i.

  Next, in step S212, the fixed point processing unit 151 causes the line setting unit 104 to newly set a line p connecting two points adjacent to the fixed point i, and causes the grain boundary setting unit 105 to perform the fixing. A grain boundary u connecting two points adjacent to the point i is generated (set).

  Here, the resetting in the grain boundary energy (γ) setting unit 109 and the mobility setting unit 111 is also performed in response to the resetting of the grain boundary u in the grain boundary setting unit 105 in steps S211 and S212.

FIG. 17 is a diagram illustrating an example of the processing operation in steps S211 and S212 in FIG.
In the second embodiment, as shown in step S204, since the driving force / position calculation process is executed only for the triple point, first, in the process of step S211, the fixed point ik shown in FIG. The two lines px and py connecting the point ik and the two adjacent points ix and iy are eliminated, and the two grain boundaries ux and ui belonging to the fixed point ik are eliminated. In step S212, a line pxy connecting the two points ix and iy adjacent to the fixed point ik is set, and a grain boundary uxy connecting the two points ix and iy adjacent to the fixed point ik is generated ( Set).

  Next, in step S213, the fixed point processing unit 151 deletes one fixed point i in step S211. Therefore, the fixed point processing unit 151 subtracts 1 from the currently set ΔNI ′ indicating the number of points to be decreased. ΔNI ′ is changed.

  When the process of step S213 is completed, when the process of step S213 is completed, or when it is determined in step S208 that the grain boundary energy Ei ′ is not less than the grain boundary energy Ei, the process proceeds to step S214.

  In step S214, the analysis point determination unit 113 determines whether or not the variable i indicating the point to be calculated is smaller than the number of points NI currently set by the point setting unit 103. If the variable i indicating the point to be calculated is smaller than the number of points NI currently set by the point setting unit 103 as a result of this determination, processing is performed for all points i currently set by the point setting unit 103. It is determined that the process has not been performed, and the process proceeds to step S215.

  In step S215, the analysis point determination unit 113 adds 1 to the variable i indicating the calculation target point to change the calculation target point i. And the process after step S203 is performed again with respect to the changed point i.

  On the other hand, if it is determined in step S214 that the variable i indicating the calculation target point is greater than or equal to the number of points NI currently set by the point setting unit 103, the point setting unit 103 sets the current value. It is determined that all points i have been processed, and the process proceeds to step S216.

  In step S216, for example, the fixed point processing unit 151 outputs information of ΔNI ′ indicating the number of points that are currently set to the point setting unit 103, and the point of the currently set point is output. ΔNI ′ (ΔNI ′ is a negative value) indicating the number of output decreasing points is added to the number NI, and the number of points NI is reset.

  Next, in step S217, the fixed point processing unit 151 causes the point setting unit 103 to perform resetting according to the change of the point i in steps S210 and S211. At the same time, the position calculation unit 116 outputs a vector indicating the position ri (t + Δt) where the point i calculated in step S204 exists to the point setting unit 103. Thereby, the vector indicating the current position ri (t) of the point i is reset in the point setting unit 103.

  Then, the line setting unit 104 resets the line p, triggered by the resetting of the point i in the point setting unit 103. In the grain boundary setting unit 105, the grain boundary u is reset when the point i is reset by the point setting unit 103 and the line p is reset by the line setting unit 104. Furthermore, the resetting in the grain boundary energy (γ) setting unit 109 and the mobility setting unit 111 is also performed in response to the resetting of the grain boundary u in the grain boundary setting unit 105.

  Next, in step S218, the analysis time setting unit 112 determines whether or not the time t is greater than the analysis completion time T set in step S6. That is, it is determined whether or not the analysis completion time T has elapsed. If the result of this determination is that the time t is not greater than the analysis completion time T set in step S6 (if the analysis completion time T has not elapsed), the routine proceeds to step 219. In step S219, the analysis time setting unit 112 updates the time t by adding the time Δt to the currently set time t. Then, it returns to step S21 of FIG. 10-3 (or FIG. 13), and performs the process after step S21 again. Then, in step S218, until it is determined that the time t is longer than the analysis completion time T set in step S6 (when the analysis completion time T has elapsed), step S21 in FIG. 10-3 (or FIG. 13). To Step S39 and Steps S201 to S218 in FIG. 16 are repeated.

  On the other hand, if the result of determination in step S218 is that the time t is greater than the analysis completion time T set in step S6 (when the analysis completion time T has elapsed), the process proceeds to step S220. In step S220, the analysis image display unit 117 determines that the time t is from 0 (zero) to T [sec] based on the “vector of the position ri (t + Δt) of the point i” calculated in step S204. In addition, an image showing how the state of the crystal grains A changes is displayed on the display device 200. Then, the series of flowcharts of FIG. 10-1, FIG. 10-2, FIG. 10-3 (or FIG. 13), and FIG.

Next, an embodiment of a crystal grain analysis apparatus that performs the above processing operation will be described.
Here, the grain analysis apparatus 100 of the first embodiment is used as a crystal grain analysis apparatus, and a grain-oriented electrical steel sheet manufactured using an inhibitor as a metal material that is an object of crystal grain analysis is applied. A case will be described as an example.

  In the manufacturing process of the grain-oriented electrical steel sheet, high-temperature annealing (for example, peak temperature 1200 [° C.], about 20 hours) is performed as finish annealing. At this time, the grain size of the primary recrystallized crystal grains before performing the high-temperature finish annealing is, for example, about 20 μm to 30 μm, but the secondary recrystallization at the time when the high-temperature finish annealing is completed. The grain size of the crystal grains is about several centimeters. Thus, in the manufacturing process of a grain-oriented electrical steel sheet, it is necessary to enlarge the crystal grain after secondary recrystallization, and an inhibitor is used in order to realize this.

  Specifically, while the inhibitor is present between the crystal grains, the growth of the crystal grains is suppressed. For example, when the inhibitor disappears due to a high temperature during finish annealing, The crystal grains that have been suppressed to an enormous size grow at once, and crystal grains of the grain-oriented electrical steel sheet are formed.

  As described above, in the grain of the grain-oriented electrical steel sheet, the grain boundary movement is inhibited by the inhibitor, so that it is essential to perform the calculation while incorporating this effect. Therefore, in order to confirm the effect, the present invention was applied to actually simulate the growth of crystal grains by finish annealing.

  In this embodiment, in order to predetermine the growth state of crystal grains after finish annealing for each through coil in a grain-oriented electrical steel sheet, first, an actual crystal grain image 31 before finish annealing is observed to check the inhibitor. The crystal grain analysis apparatus 100 was operated by extracting one crystal grain from the crystal grain image 31 of each plate coil and making various settings for the crystal grain.

  FIG. 18 is a diagram showing the results of verifying the growth state of crystal grains for each through-plate coil in the grain-oriented electrical steel sheet, showing an example of the present invention. Here, in FIG. 18, the result of having verified about the 10 through-plate coils shown to AJ is shown. Specifically, FIG. 18 shows data on the grain size (experiment) of the crystal grain after actually performing the finish annealing on the crystal grain set in advance before the finish annealing, and the grain analysis apparatus according to the present invention. Data on the grain size of the crystal grain when the simulation is performed at 100 (application of the present invention), and the grain size of the crystal grain when the simulation of only the growth of the crystal grain is performed without considering the inhibitor (application of the present invention) Data) is shown.

  Moreover, in FIG. 18, the result of having verified about 10 through-plate coils shown to A-J as experimental data is shown, Moreover, as data of this invention application, and data without this invention application, The result of having verified about the two through-plate coils of the coils B and G is shown.

  First, when considering the simulation of the passing plate coil of the coil B, the experimental data is 1.3 cm, whereas the data not applied to the present invention is 1.7 cm, which is an error of 30% or more. Has occurred. On the other hand, in the data applied to the present invention, it is 1.4 cm, and the error is less than 10%.

  Further, when considering the through-plate coil of the simulated coil G, the experimental data is 1.2 cm, but the data without applying the present invention cannot maintain the crystal grains. (No secondary recrystallization). On the other hand, in the data applied to the present invention, it was 1.2 cm, and the growth of crystal grains could be simulated almost accurately.

  From the above verification results, it has been confirmed that, when the present invention is applied, the crystal grain growth state of the grain-oriented electrical steel sheet manufactured using the inhibitor can be simulated almost accurately.

  As described above, in each embodiment of the present invention, when a line having two end points of two grain boundary points adjacent to each other on the same grain boundary passes through the inhibitor, a fixed point is generated in the inhibitor. The line changing process with the fixed point as an end point is performed (see, for example, FIG. 7). Thereby, it is possible to simulate a state in which the grain boundary movement of the crystal grains A is inhibited (suppressed) by the inhibitor. Further, the first grain boundary energy Ei at the grain boundary to which the fixed point belongs and the fixed point are released from the fixed position and moved to the equilibrium position where the grain boundary energy is the minimum in the region excluding the inside of the inhibitor. The second grain boundary energy Ei ′ at the grain boundary is calculated, and when the second grain boundary energy Ei ′ is less than the first grain boundary energy Ei, a process of releasing the fixed point is performed. I am doing so. Thus, the transition from the state in which the grain boundary movement of the crystal grain A is suppressed by the inhibitor to the state in which the grain boundary movement of the crystal grain A resumes and the state of the grain boundary movement of the crystal grain A after the transition are simulated. Can do.

  According to the embodiment of the present invention, the state in which the grain boundary movement of the crystal grain A is suppressed by the inhibitor, and the transition to the state in which the grain boundary movement of the crystal grain A resumes from the suppressed state and after the transition. It is possible to simulate the state of the grain boundary movement of the crystal grain A, so that it is easier and more accurate to analyze how the crystal grain A changes over time through the inhibitor. it can.

  In the present embodiment, the case where the user designates the point i and the inhibitor k using the operation device 300 while viewing the crystal grain image 31 has been described as an example. However, this is not necessarily required. There is no. For example, the crystal grain analysis apparatus 100 (computer) may automatically specify the point i and the inhibitor k based on the crystal grain image signal obtained by the analysis by the EBSP method.

  In the embodiment of the present invention, the inhibitor setting unit 118 sets the inhibitor k by approximating the detected inhibitor k region with a circle as shown in FIG. The approximate shape may be changed according to the shape of the region. At this time, for example, when the inhibitor k is approximated to an ellipse, coordinate information indicating the center position (fixed position) of the ellipse, information on the length of the major axis of the ellipse, and the length of the minor axis of the ellipse Such information is calculated and the inhibitor k is set in the RAM or the hard disk. For example, when the inhibitor k is approximated to a polygon, for example, coordinate information indicating the center of gravity position as a fixed position and coordinate information indicating each vertex in the polygon are calculated, and the inhibitor k is stored in the RAM or the hard disk. Take the form set to.

In this embodiment, the grain boundary u is defined by the grain boundary setting unit 105. However, if the point i, the line p, and the crystal grain A are used, the grain boundary u is naturally determined. There is no need to define u.
In the present embodiment, the grain boundary energy (γ) setting unit 109 and the mobility setting unit 111 are based on the absolute value of the difference Δξ of the orientations ξ of two crystal grains A adjacent to each other via the grain boundary u. The grain boundary energy γ and the mobility Mi per unit length are set, but the unit is based on the difference Δξ of the orientations ξ of two crystal grains A adjacent to each other via the grain boundary u. You may make it set the grain boundary energy (gamma) per length and the mobility Mi.

  In this embodiment, the mobility Mi at the triple point i to be calculated is obtained using the equation (6). However, it is easy to correspond to the three grain boundaries u to which the triple point i to be calculated belongs. If the mobility Mi1 to Mi3 is used to determine the mobility Mi of the triple point i to be calculated, this need not necessarily be done. For example, you may make it obtain | require the mobility Mi in the triple point i of calculation object using the following (13) Formula.

  In the above-described embodiment, the magnetic steel sheet is described as an example of the metal material that is an example of the material analyzed by the crystal grain analysis device. However, the material analyzed by the crystal grain analysis device according to the present invention is Anything can be applied as long as it is manufactured using inclusions such as inhibitors. When the metal material analyzed by the crystal grain analyzer is different, the contents of the graph stored in the grain boundary energy (γ) storage unit 108 and the mobility storage unit 110 are input to the crystal grain analyzer. Depending on the material, the data will vary.

Of the embodiments of the present invention described above, the part executed by the CPU can be realized by the computer executing the program (computer program). Further, 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 also be applied as an embodiment of the present invention. . A program product such as a computer-readable recording medium in which the program is recorded can also be applied as an embodiment of the present invention. The above programs, computer-readable recording media, transmission media, and program products are included in the scope of the present invention.
In addition, the above-described embodiments are merely examples of implementation in carrying out the present invention, and the technical scope of the present invention should not be construed as being limited thereto. That is, the present invention can be implemented in various forms without departing from the technical idea or the main features thereof.

It is a figure which shows the 1st Embodiment of this invention and shows an example of the analysis method performed with a crystal grain analyzer. It is a block diagram which shows the 1st Embodiment of this invention and shows an example of a function structure of a crystal grain analyzer. It is a figure which shows the 1st Embodiment of this invention and shows an example of a crystal grain image, a double point, a triple point, a line, and a grain boundary. It is a figure which shows the 1st Embodiment of this invention and demonstrates an example of the calculation method of the driving force which arises in a double point. It is a figure which shows the 1st Embodiment of this invention and demonstrates an example of the calculation method of the driving force which arises in a triple point. It is a figure which shows the 1st Embodiment of this invention and demonstrates an example of the setting method of an inhibitor. It is a figure which shows the 1st Embodiment of this invention and demonstrates an example of the line change process by a line change process part. It is a figure which shows the 1st Embodiment of this invention and demonstrates an example of the calculation method of the grain boundary energy in case a fixed point is a fixed double point. It is a figure which shows the 1st Embodiment of this invention and demonstrates an example of the calculation method of the grain boundary energy in case a fixed point is a fixed triple point. 4 is a flowchart illustrating an example of a processing operation performed by the crystal grain analysis apparatus according to the first embodiment of this invention. It is a flowchart which shows the 1st Embodiment of this invention and follows FIG. 10-1. It is a flowchart which shows the 1st Embodiment of this invention and follows FIG. 10-2. It is a flowchart which shows the 1st Embodiment of this invention and follows FIG. 10-3. It is a flowchart which shows the 1st Embodiment of this invention and demonstrates an example of the detailed process operation of step S43 of FIG. 10-4. It is a flowchart which shows the 1st Embodiment of this invention and demonstrates an example of the detailed processing operation of FIG.10-4 step S44. It is a flowchart which shows the modification of the 1st Embodiment of this invention and demonstrates an example of the processing operation which a crystal grain analyzer performs. It is a figure which shows the 2nd Embodiment of this invention and shows an example of the point (triple point) set with a crystal grain analyzer, a line, and a grain boundary. It is a block diagram which shows the 2nd Embodiment of this invention and shows an example of a function structure of a crystal grain analyzer. It is a flowchart which shows the 2nd Embodiment of this invention and demonstrates an example of the processing operation which a crystal grain analyzer performs. It is a figure explaining an example of the processing operation of step S211 and S212 of FIG. It is a figure which shows the Example of this invention and shows the result of having verified the growth state of the crystal grain for every threading coil in a grain-oriented electrical steel sheet.

Explanation of symbols

DESCRIPTION OF SYMBOLS 100 Crystal grain analyzer 101 Crystal image acquisition part 102 Crystal image display part 103 Point setting part 104 Line setting part 105 Grain boundary setting part 106 Analysis temperature setting part 107 Orientation setting part 108 Grain boundary energy ((gamma)) memory | storage part 109 Grain boundary energy (Γ) 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 117 analysis image Display unit 118 Inhibitor setting unit 119 Line change processing unit 120 Fixed point processing unit 121 Grain boundary energy (E) calculation unit 200 Display device 300 Operating device

Claims (16)

Image signal acquisition means for acquiring image signals of crystals in the metal material and inclusions included in the metal material;
Corresponding to both end points of the grain boundaries of the crystal grains included in the crystal, and corresponding to the midpoint of the grain boundaries of the crystal grains included in the crystal, and a triple point in contact with the three crystal grains including the crystal grains, And when a double point in contact with two crystal grains including the crystal grain is designated based on the image signal, a grain boundary point setting means for setting the designated triple point and double grain boundary point; ,
Line setting means for setting a line having two grain boundary points that are adjacent to each other on the same grain boundary, which is a grain boundary point set by the grain boundary point setting means,
When the inclusion is designated based on the image signal, inclusion setting means for setting the designated inclusion;
When the line set by the line setting means passes through the inclusion, a line change processing means for generating a fixed point in the inclusion and performing a line changing process with the fixed point as an end point;
The first grain boundary energy at the grain boundary to which the fixed point belongs, and the fixed point are released from the fixed position and moved to an equilibrium position where the grain boundary energy is at a position in a region excluding the inside of the inclusion. Grain boundary energy calculating means for calculating a second grain boundary energy at the grain boundary when
A crystal grain analysis apparatus comprising: a fixed point processing unit that performs processing for releasing the fixed point when the second grain boundary energy is less than the first grain boundary energy.   The fixed point processing means, when releasing the fixed point, is a boundary of the inclusion in a region between the lines where the equilibrium position exists among the regions defined by the lines having the fixed point as an end point. The crystal grain analysis apparatus according to claim 1, wherein the crystal grain analysis apparatus performs a process of moving as the grain boundary point to a position of an intersection with a line segment that bisects an angle between the lines. Image signal acquisition means for acquiring image signals of crystals in the metal material and inclusions included in the metal material;
When a triple point corresponding to both end points of a grain boundary of a crystal grain included in the crystal and in contact with three crystal grains including the crystal grain is specified based on the image signal, the specified triple point Grain boundary point setting means for setting the grain boundary point of
Line setting means for setting a line having two grain boundary points that are adjacent to each other on the same grain boundary, which is a grain boundary point set by the grain boundary point setting means,
When the inclusion is designated based on the image signal, inclusion setting means for setting the designated inclusion;
When the line set by the line setting means passes through the inclusion, a line change processing means for generating a fixed point in the inclusion and performing a line changing process with the fixed point as an end point;
The first grain boundary energy at the grain boundary to which the fixed point belongs, and the fixed point are released from the fixed position and moved to an equilibrium position where the grain boundary energy is at a position in a region excluding the inside of the inclusion. Grain boundary energy calculating means for calculating a second grain boundary energy at the grain boundary when
A crystal grain analysis apparatus comprising: a fixed point processing unit that performs processing for releasing the fixed point when the second grain boundary energy is less than the first grain boundary energy. The line change processing means generates, as the fixed point, a fixed double point that forms a line with two triple points, or a fixed triple point that forms a line with three triple points,
The fixed point processing means includes
When releasing the fixed double point as the fixed point, perform the process of eliminating the fixed double point,
When releasing the fixed triple point as the fixed point, among the areas defined by the lines having the fixed triple point as an end point, the boundary of the inclusion in the region between the lines where the equilibrium position exists The crystal grain analysis apparatus according to claim 3, wherein the crystal grain analysis apparatus performs a process of moving as the grain boundary point to a position of an intersection with a line segment that bisects an angle formed between the lines. Further comprising grain boundary energy setting means for setting grain boundary energy per unit length in the grain boundary to which the grain boundary point and the fixed point belong;
When calculating the first grain boundary energy, the grain boundary energy calculating means includes a length obtained by subtracting a length in the inclusion from a length of a line having the fixed point as an end point, and the fixed point belongs to 5. The crystal grain analysis apparatus according to claim 1, wherein the calculation is performed using grain boundary energy per unit length in the grain boundary.   When the grain boundary energy calculation means calculates the second grain boundary energy, a virtual line connecting the other end point of the line having the fixed point as an end point and the equilibrium position does not pass through the inclusions. Is calculated using the length of the virtual line and the grain boundary energy per unit length at the grain boundary to which the fixed point belongs, and the other end point of the line having the fixed point as an end point and the equilibrium position When the virtual line connecting the two passes through the inclusions, the length of the virtual line minus the length in the inclusions, and the grain boundary per unit length in the grain boundary to which the fixed point belongs 6. The crystal grain analysis apparatus according to claim 5, wherein calculation is performed using energy.   The line change processing means is a case where the line set by the line setting means passes through the inclusions, and any of the two grain boundary points constituting the line is the intervention. 7. The method according to claim 1, wherein a fixed double point that forms a line with the two grain boundary points is generated at the fixed position as the fixed point when the object is not in an object. The crystal grain analysis apparatus described.   The line change processing means is a case where the line set by the line setting means passes through the inclusions, and one of the two grain boundary points constituting the line is the interposition. The crystal grain analyzer according to any one of claims 1 to 6, wherein when it is in an object, the one grain boundary point is moved to the fixed position to generate the fixed point. .   The line change processing means is a case where the line set by the line setting means passes through the inclusions, and both grain boundary points of the two grain boundary points constituting the line are the intervention. The crystal grain analysis apparatus according to any one of claims 1 to 6, wherein when it is in an object, the two grain boundary points are generated at the fixed position as one fixed point. The driving force generated at the grain boundary point set by the grain boundary point setting means is the grain boundary energy per unit length set by the grain boundary energy setting means with respect to the grain boundary to which the grain boundary point belongs. Driving force calculating means for calculating using,
6. The crystal according to claim 5, further comprising position calculating means for calculating a change in position of the grain boundary point over time using the driving force calculated by the driving force calculating means. Grain analyzer. Grain boundary energy storage means for storing the relationship between the difference between the orientations of two crystal grains adjacent to each other via the grain boundary and the grain boundary energy per unit length;
Orientation acquisition means for acquiring the orientation of crystal grains included in the image signal,
The grain boundary energy setting means is an orientation of crystal grains acquired by the orientation acquisition means, and is per unit length corresponding to a difference in orientation between two crystal grains adjacent to each other via the grain boundaries. 6. The crystal grain analysis apparatus according to claim 5, wherein the grain boundary energy is determined and set from the relationship stored by the grain boundary energy storage means.   The crystal grain analyzer according to any one of claims 1 to 11, wherein the inclusion does not change its position with time and is an inhibitor. An image signal acquisition step of acquiring an image signal of a crystal in the metal material and inclusions included in the metal material;
Corresponding to both end points of the grain boundaries of the crystal grains included in the crystal, and corresponding to the midpoint of the grain boundaries of the crystal grains included in the crystal, and a triple point in contact with the three crystal grains including the crystal grains, And when a double point in contact with two crystal grains including the crystal grain is designated based on the image signal, a grain boundary point setting step for setting the designated triple point and double grain boundary point; ,
A line setting step for setting a line having two grain boundary points that are adjacent to each other on the same grain boundary at the grain boundary point set by the grain boundary point setting step;
When the inclusion is designated based on the image signal, an inclusion setting step for setting the designated inclusion;
When the line set by the line setting step passes through the inclusion, a fixed point is generated in the inclusion, and a line change processing step for changing the line with the fixed point as an end point; and
The first grain boundary energy at the grain boundary to which the fixed point belongs, and the fixed point are released from the fixed position and moved to an equilibrium position where the grain boundary energy is at a position in a region excluding the inside of the inclusion. A grain boundary energy calculating step for calculating a second grain boundary energy at the grain boundary when
A crystal grain analysis method comprising: a fixed point processing step of performing a process of releasing the fixed point when the second grain boundary energy is less than the first grain boundary energy. An image signal acquisition step of acquiring an image signal of a crystal in the metal material and inclusions included in the metal material;
When a triple point corresponding to both end points of a grain boundary of a crystal grain included in the crystal and in contact with three crystal grains including the crystal grain is specified based on the image signal, the specified triple point A grain boundary point setting step for setting the grain boundary point of
A line setting step for setting a line having two grain boundary points that are adjacent to each other on the same grain boundary at the grain boundary point set by the grain boundary point setting step;
When the inclusion is designated based on the image signal, an inclusion setting step for setting the designated inclusion;
When the line set by the line setting step passes through the inclusion, a fixed point is generated in the inclusion, and a line change processing step for changing the line with the fixed point as an end point; and
The first grain boundary energy at the grain boundary to which the fixed point belongs, and the fixed point are released from the fixed position and moved to an equilibrium position where the grain boundary energy is at a position in a region excluding the inside of the inclusion. A grain boundary energy calculating step for calculating a second grain boundary energy at the grain boundary when
A crystal grain analysis method comprising: a fixed point processing step of performing a process of releasing the fixed point when the second grain boundary energy is less than the first grain boundary energy. An image signal acquisition step of acquiring an image signal of a crystal in the metal material and inclusions included in the metal material;
Corresponding to both end points of the grain boundaries of the crystal grains included in the crystal, and corresponding to the midpoint of the grain boundaries of the crystal grains included in the crystal, and a triple point in contact with the three crystal grains including the crystal grains, And when a double point in contact with two crystal grains including the crystal grain is designated based on the image signal, a grain boundary point setting step for setting the designated triple point and double grain boundary point; ,
A line setting step for setting a line having two grain boundary points that are adjacent to each other on the same grain boundary at the grain boundary point set by the grain boundary point setting step;
When the inclusion is designated based on the image signal, an inclusion setting step for setting the designated inclusion;
When the line set by the line setting step passes through the inclusion, a fixed point is generated in the inclusion, and a line change processing step for changing the line with the fixed point as an end point; and
The first grain boundary energy at the grain boundary to which the fixed point belongs, and the fixed point are released from the fixed position and moved to an equilibrium position where the grain boundary energy is at a position in a region excluding the inside of the inclusion. A grain boundary energy calculating step for calculating a second grain boundary energy at the grain boundary when
When the second grain boundary energy is less than the first grain boundary energy, a computer program for causing a computer to execute a fixed point processing step of performing a process of releasing the fixed point. An image signal acquisition step of acquiring an image signal of a crystal in the metal material and inclusions included in the metal material;
When a triple point corresponding to both end points of a grain boundary of a crystal grain included in the crystal and in contact with three crystal grains including the crystal grain is specified based on the image signal, the specified triple point A grain boundary point setting step for setting the grain boundary point of
A line setting step for setting a line having two grain boundary points that are adjacent to each other on the same grain boundary at the grain boundary point set by the grain boundary point setting step;
When the inclusion is designated based on the image signal, an inclusion setting step for setting the designated inclusion;
When the line set by the line setting step passes through the inclusion, a fixed point is generated in the inclusion, and a line change processing step for changing the line with the fixed point as an end point; and
The first grain boundary energy at the grain boundary to which the fixed point belongs, and the fixed point are released from the fixed position and moved to an equilibrium position where the grain boundary energy is at a position in a region excluding the inside of the inclusion. A grain boundary energy calculating step for calculating a second grain boundary energy at the grain boundary when
When the second grain boundary energy is less than the first grain boundary energy, a computer program for causing a computer to execute a fixed point processing step of performing a process of releasing the fixed point.

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