Computer programs for material analysis

Abstract

To provide a material analysis method and a computer program for material analysis that can reproduce a state in which a plurality of structures are nonuniformly mixed to model it, and can be used for material analysis.SOLUTION: After performing an initial selection step of selecting a randomly selected point within a set area as a center point, an area expansion step is repeated, which randomly selects a new center point within a predetermined limit range from the already selected center point, arranges a predetermined compartmentalized diagram at the center point, and sets an area surrounded by the compartmentalized diagrams as a first-type structure. While repeating the area expansion step, if the step in which the total area of the first-type structure being set when completing a certain area expansion step only increases less than a predetermined threshold value as compared with the total area of the first-type structure that was set when completing the previous area expansion step continues for a predetermined number of times, a randomly selected point in the set area is set as a new center point, and then the repetition of the area expansion step is continued.SELECTED DRAWING: Figure 1

Description

[Technical field]

[0001] The present invention relates to a material analysis method and a computer program for material analysis, and more particularly to a method and a computer program for creating a model that simulates a material structure and analyzing the characteristics of the material structure. [Background technology]

[0002] Inspections are conducted to evaluate the state of the material structure, utilizing phenomena such as ultrasonic scattering. Analysis is then conducted to associate the results of the inspection with the state of the material structure. When the material structure is highly uniform, analysis can be performed by setting uniform physical properties for the entire material structure.

[0003] However, when the material structure has a non-uniform spatial distribution and the non-uniformity is reflected in the inspection results, it is important to perform an analysis that takes the non-uniformity into account in order to accurately interpret the inspection results. For example, a method may be used in which the expected material structure is reproduced as a model, and then a simulation is performed on the reproduced model structure, reproducing the inspection process. The results of the simulation can then be compared with the results obtained in the actual inspection to estimate the state of the actual material structure.

[0004] As one method for preparing a model that reproduces a material structure having a non-uniform spatial distribution for the purpose of using it in a simulation that simulates an inspection process, a method can be mentioned in which structure images are collected by microscope observation or the like for a number of samples with different degrees of non-uniformity, and the structure images are appropriately subjected to image processing to create a model image. Another method is also used to artificially create a model image that simulates a material structure. For example, a method has been developed in which a model image that simulates a structure consisting of a number of crystal grains is created around points randomly arranged in a two-dimensional space using Voronoi division. In addition, as a method that further develops such a method, for example, Patent Document 1 discloses a method in which multiple mother points are randomly arranged within a set area, and multiple mapping points are arranged for each of these points by a predetermined mapping function within a two-dimensional area, and then Voronoi division is performed. In this way, it is said that by creating mapping points, a two-dimensional model can be generated in which the average crystal grain size and the degree of variation in crystal grain size distribution can be arbitrarily determined. [Prior art documents] [Patent documents]

[0005] [Patent Document 1] JP 2006-284457 A Summary of the Invention [Problem to be solved by the invention]

[0006] The above methods are known as methods for creating model images that reproduce non-uniform material structures, but when using a method that performs image processing on a structure image obtained by actual measurement, it is not possible to obtain a model image for a material structure that is difficult to prepare as an actual sample. Therefore, it is difficult to prepare model images that correspond to various material structures and use them for analysis.

[0007] On the other hand, by using a method of artificially creating a model image that simulates the material structure, various material structures can be prepared and used as the subject of analysis and examination. However, even when creating an artificial model image, it is often difficult to faithfully reproduce the heterogeneous structure that exists in the actual material and to freely change the degree of heterogeneity. For example, a method of simply randomly arranging points in a two-dimensional space and then performing Voronoi division cannot sufficiently form a heterogeneous distribution of the crystal structure. In order to sufficiently reproduce the heterogeneity, it is necessary to appropriately introduce a process such as a calculation to incorporate the heterogeneity into the model according to the form of the heterogeneity to be reproduced. In the case of the method of Patent Document 1, the creation of the mapping points using the mapping function corresponds to such a process, and by going through the creation of the mapping points, it is possible to reproduce the heterogeneity of the crystal grain size according to the form of the specific mapping function. However, the model published in Patent Document 1 reproduces the heterogeneous spatial distribution of the crystal grain size depending on the position in the material structure, and the method of Patent Document 1 may not be appropriate as a method for reproducing the heterogeneity of the material structure that takes another form. For example, in a situation where multiple types of tissues that contain different crystal phases and therefore exhibit different physical properties are spatially mixed, it is difficult to form a model that reproduces the heterogeneous distribution of these multiple types of tissues and further to make it possible to change the degree of that heterogeneity using the method disclosed in Patent Document 1.

[0008] The problem to be solved by the present invention is to provide a materials analysis method and a computer program for materials analysis that are capable of reproducing and modeling a state in which a plurality of structures are mixed in a non-uniform manner and that can be used for analyzing materials. [Means for solving the problem]

[0009] In order to solve the above problems, the material analysis method of the present invention creates a model simulating a material structure including mutually different first and second type structures, and analyzes the characteristics of the material structure. The material analysis method includes an initial selection step of selecting a point randomly selected within a set region as a center point, followed by a region expansion step of randomly selecting a new center point within a predetermined limited range from the already selected center point, arranging a predetermined partition figure at the center point, and setting the region surrounded by the partition figure as the first type structure. If the region expansion step is repeated a predetermined number of times, the total area of ​​the first type structure set upon completion of a certain region expansion step increases by only a predetermined threshold value or less compared to the total area of ​​the first type structure set upon completion of the previous region expansion step. Then, the randomly selected point within the set region is set as a new center point, and the repetition of the region expansion step is continued. When the total area of ​​the first type structure reaches a predetermined value, the repetition of the region expansion step is terminated, and finally, the region not set as the first type structure is set as the second type structure, thereby obtaining a model simulating the material structure.

[0010] Here, the partition figure may have an anisotropic shape that is long in one direction. In this case, the partition figure may be an ellipse. In addition, in each round of the region expanding step, the partition figure may be positioned after a rotation angle of the partition figure is randomly selected.

[0011] In each round of the region expanding step, at least one of the area and the shape of the partition figure may be randomly selected from a plurality of preset candidates, and the partition figure may be arranged. In addition, as the analysis of the characteristics, an ultrasonic propagation analysis may be performed on the obtained model.

[0012] A computer program for material analysis according to the present invention causes a computer to execute the material analysis method. Effect of the Invention

[0013] In the material analysis method and the computer program for material analysis according to the above invention, after the initial selection step, in the region expansion step, a predetermined partition figure is arranged with a point set in the set region as a center point, and the operation of setting it as the first type tissue is repeated while randomly selecting a new center point within a predetermined limited range from the already selected center point. This makes it possible to reproduce a state in which the region consisting of the first type tissue is unevenly gathered. Furthermore, if the state in which the total area of ​​the first type tissue increases only to a predetermined threshold or less even after the region expansion step is repeated, a center point is selected again randomly from the entire set region, making it possible to reproduce a state in which multiple regions in which the first type tissue is unevenly gathered are distributed. After setting the region occupied by the first type tissue in this way, the region not occupied by the first type tissue is set as the second type tissue, and thus a model that reproduces a state in which the first type tissue and the second type tissue are spatially unevenly mixed can be obtained. In this case, the degree of non-uniformity can be freely changed by changing parameters related to model creation, such as the size of the limited range within which the next center point is set relative to the center point already set in the region expansion process, and the predetermined number of repetitions used to determine whether to reselect a center point from the entire set region when repeating the region expansion process.

[0014] Here, if the partition figure has an anisotropic shape that is long in one direction, such as an ellipse, and if the rotation angle of the partition figure is selected randomly, or if at least one of the area and shape of the partition figure is selected randomly from a number of pre-set candidates, it is easy to faithfully reproduce the state of a material in which different structures are mixed unevenly, such as a material structure in which two crystal phases are mixed.

[0015] In addition, when performing ultrasonic propagation analysis on the obtained model as an analysis of the characteristics, an inspection using ultrasonic waves is an inspection method that sensitively reflects the non-uniformity of the distribution of the material structure, and by performing ultrasonic propagation analysis on the structure reproduced in the model, it is possible to conduct a detailed study on the correlation between the non-uniformity of the material structure and the behavior of ultrasonic waves. By comparing the results of the ultrasonic propagation analysis using the model with the results of the actual ultrasonic inspection, it is possible to accurately estimate the state of the structure in the actual sample. [Brief description of the drawings]

[0016] [Figure 1] FIG. 4 is a flow diagram illustrating the creation of a model image in the material analysis method according to one embodiment of the present invention. [Diagram 2] FIG. 11 is a schematic diagram illustrating a process for creating a model image. [Diagram 3] 11 is an image showing the relationship between the limit distance L and the obtained model image. [Figure 4] 11 is an image showing the relationship between the number of judgments n and the obtained model image. [Diagram 5] This figure shows the correspondence between the SEM image of the actual material structure, the obtained model image, and the results of ultrasonic propagation analysis. (a) shows the case where the structure is highly uniform, and (b) shows the case where the structure is non-uniform. [Figure 6] FIG. 13 is a diagram showing a plurality of model images grouped according to non-uniformity evaluation values. [Figure 7] 13 is a diagram showing the results of ultrasound propagation analysis performed on a plurality of model images, in which the horizontal axis indicates the non-uniformity evaluation value and the vertical axis indicates the ultrasound scattering intensity. [Figure 8] The figure shows the results of ultrasonic testing and evaluation of the heterogeneity of the structure of multiple alloy samples. For each sample, the horizontal axis shows the heterogeneity evaluation value, and the vertical axis shows the distribution range of the ultrasonic scattering intensity for each measurement position. DETAILED DESCRIPTION OF THE PREFERRED EMBODIMENTS

[0017] Hereinafter, a material analysis method and a computer program for material analysis according to an embodiment of the present invention will be described with reference to the drawings. The material analysis method according to an embodiment of the present invention creates a model image that reproduces a material structure in which a plurality of structures are mixed, and then performs an analysis of the characteristics of the material structure, such as an ultrasonic propagation analysis, on the obtained model image. The computer program for material analysis according to an embodiment of the present invention causes a computer to execute the above-mentioned material analysis method. Hereinafter, a material analysis method according to one embodiment of the present invention will be described in detail.

[0018] [Creating a model statue] First, a method for creating a model image that reproduces a material structure in the material analysis method according to the present embodiment will be described. Fig. 1 shows a flow diagram of each step for creating a model image. Fig. 2 shows a schematic diagram of each step in creating a model image. The model image can be created simply by calculation using a computer, and a computer having a program according to one embodiment of the present invention stored therein may be used.

[0019] In the following, we will deal with the case of creating a model that two-dimensionally reproduces a material structure in which a first type structure and a second type structure that are different from each other are mixed. A situation in which two types of structures are spatially non-uniformly mixed like this is observed, for example, in a metal material that can generate two crystal phases, when a region where one crystal phase is aggregated and a region where another crystal phase is aggregated are generated together.

[0020] (1) Parameter settings First, in step S1, parameters are set as a preparation for creating a model image. Here, a setting region R for creating a model is prepared, and various parameters used for creating the model image are set.

[0021] A square or rectangular two-dimensional matrix may be prepared as the set region R. Each element (pixel) constituting the matrix is ​​made selectable as an area occupied by the first or second type of structure. The size of the set region R may be selected so that it contains a sufficient number of areas consisting of the first and second types of structure in the material structure to be reproduced by the model image in order to accurately analyze the material properties. Hereinafter, the number of elements in the x direction of the set region R is denoted as h, and the number of elements in the y direction is denoted as w.

[0022] The various parameters that should be set to create a model image include the following: The meaning of each parameter will be explained later when each parameter is used, but in step S1, the numerical values ​​to be substituted for each parameter are determined and stored in the computer's memory.

[0023] The parameters to be set are as follows: ·Limited distance L (2L <h,2L<w) Ellipse major axis a · Ellipse minor axis b(b <a) Area change threshold A Threshold judgment count n ·Target area S

[0024] (2) Initial selection process Next, the repetition number i is set to 0, and an initial selection step is performed in step S2. In the initial selection step, a random number is used to randomly select coordinates within the set region R, and an initial center point C0 is set.

[0025] (3) Region expansion process After the initial selection step in step S2 is completed, the region expansion step in steps S3 to S9 is repeatedly executed. In the region expansion step, the center point C i Select the center point C i A specified partition figure is placed in the area.

[0026] In the region selection process, first, the number of repetitions i is incremented by one (i+=1), and then in step S3, the center point C i The coordinates of the center point C are determined. i is the already set center point C i-1 In other words, the center point C i-1 A new center point C is set within the square area of ​​±L in the x and y directions. i Randomly set the coordinates of the center point C i In setting the boundary condition, a periodic boundary condition is applied. In other words, the set region R is assumed to be continuous in the x and y directions with periods of h and w, respectively. Then, the initial center point C i-1 Since the center point C is close to one of the edges of the set region R, i However, if the portion of the pattern extends beyond the edge of the set region R, the portion that extends beyond the edge opposite the edge is positioned inside the set region R.

[0027] Next, in step S4, the shape and angle of the partition figure to be placed are determined. In this example, the partition figure is an ellipse. In step S4, the shape and angle of the ellipse E to be placed in the area expansion step are determined based on the major axis, minor axis and rotation angle of the ellipse. i Determine the specific shape and angle of the ellipse E. i The major axis of the ellipse E is chosen to be a or a+1 (the unit is the number of elements; hereafter, the same applies to quantities expressing length and area unless otherwise specified). i Select b or b+1 as the minor axis of the ellipse E. The selection is performed randomly using random numbers, independently for the major axis and the minor axis. i The rotation angle of is randomly selected from the range 0 to 360 degrees.

[0028] Next, in step S5, the center point C i Ellipse E to i That is, the center point C set in step S2 is i The ellipse E having the minor axis and major axis selected in step S4 isi is rotated by the rotation angle determined in step S4 and placed. Then, the placed ellipse E i The region surrounded by the ellipse E in step S5 is designated as a region in which the first type of tissue exists. i The periodic boundary conditions are also applied in the configuration of

[0029] In step S5, ellipse E i When the arrangement of the first type textures is completed, in steps S6 and S7, it is determined whether or not to continue repeating the region expanding process. First, in step S6, the total area T i That is, the total area of ​​the first type tissue set through all the region expansion steps up to that time is calculated. At this time, the region where multiple partition figures (ellipses) are overlapped is also included only once as the area of ​​the first type tissue.

[0030] In step S6, the total area T i In addition, the area increase ΔT of the first type tissue is used in the subsequent step S8. i Also calculate the area increase ΔT i is the total area T of the first type of tissue set at the end of the region expansion process. i is the total area T i-1 It shows the amount of increase with respect to ΔT i =T i -T i-1 As a result, the area increase ΔT i Calculate the calculated total area T i and area increase ΔT i The value of is stored in the computer's memory.

[0031] In step S7, the end determination is performed. That is, the total area T i It is determined whether the total area T of the first type tissue calculated in step S6 reaches the preset target area S. iIf it has reached the target area S (T i ≧S; Yes in step S7), it is determined that the first type of tissue with a sufficient area has been set, the repetition of the region expansion process is terminated, and the process proceeds to step S10. In step S10, after setting the regions that have not been finally set as the first type of tissue as the second type of tissue, the distribution image of the tissues created in the set region R is saved as a model image. The value of the target area S may be set as the area of the first type of tissue in the material tissue to be reproduced by the model image with reference to a microscopic image or the like of the actual material.

[0032] On the other hand, if the total area T of the first type of tissue i has not reached the target area S (T i <S; No in step S7), it is determined that the first type of tissue with a sufficient area has not yet been set. Then, in the next steps S8 and S9, after re-setting the center point C i according to the conditions, the iteration count i is incremented by 1 (i += 1), the process returns to step S3, and the repetition of the region expansion process is continued.

[0033] In step S8, it is determined whether the area increase amount ΔT i calculated in step S6 is less than or equal to a preset area change threshold A. Here, if it is determined that the area increase amount ΔT i is less than or equal to the area change threshold A (ΔT i ≦A), the values of the area increase amounts ΔT (ΔT i-1 , ΔT i-2 , …) calculated in the past region expansion processes stored in the memory are referred to. Then, it is checked whether the number of times when the area increase amount ΔT is less than or equal to the area change threshold A (ΔT ≦ A) continues for a preset threshold determination count n. If the number of times when ΔT ≦ A has continued for n times (Yes in step S8), it is determined that the total area of the first type of tissue will not increase effectively even if the region expansion process is repeated as it is, and the process proceeds to step S9, and the center point C iOn the other hand, if the state where ΔT≦A does not continue over n region expansion steps (No in step S8), that is, if it is determined that the total area of ​​the first type of texture is effectively increased by repeating the region expansion steps, step S9 is omitted and the already set center point C i While keeping it as it is, set i+=1 and return to step S3.

[0034] Here, if the state of ΔT≦A continues in the past n region expansion processes, the total area T i The total area T of the first type of tissue at the time when the nth previous region growing process was completed i-n The increase ΔTn compared to the area change threshold A is also below (ΔTn=T i -T i-n Therefore, instead of calculating the area increase amount ΔT for each time in step S6 and referring to the area increase amount ΔT for the past n times in step S8, the total area T i and the total area T n times ago i-n In this case, if the increase amount ΔTn of the total area from the nth time before is equal to or less than the area change threshold A, the process proceeds to step S9. i On the other hand, if the increase amount ΔTn exceeds the area change threshold A, step S9 is omitted, i+=1 is set, and the process returns to step S3. In this way, while repeating the region expansion process, the total area T i However, the judgment condition in step S8 is whether the total area of ​​the first type tissue, which was set when the previous region expansion step (the region expansion step m times ago), was increased by only the area change threshold A or less, continues for a predetermined number of repetitions n, and if so, step S9 is executed. There is no particular limit to how many previous region expansion steps the total area of ​​the first type tissue is compared with, and as long as m≦n, the comparison can be arbitrarily made to any region expansion step m times ago.

[0035] Regardless of how m is set, the area change threshold A may be set to zero. In that case, the total area T i In addition, the number of repeated judgments n may be set to 1. In that case, the area increase amount ΔT from the previous region expansion step is simply determined. i is equal to or less than the area change threshold A. The determination in step S8 may be made based on the area itself of the region set as the first type tissue, or may be made based on the area ratio between the region set as the first type tissue and the region that is not set as the first type tissue and will become the second type tissue.

[0036] Step S9 is a step of calculating the total area T of the first type of tissue in step S8. i This is a step that is executed when it is determined that the center point C i In step S8, even if the region expansion process is performed n times, the total area T i The result is that the ellipse E i The center point C where the first type of tissue was set by the arrangement of i In the vicinity of i+1 ,C i+2 ,…) to create an ellipse (E i+1 ,E i+2 This means that even if the arrangement of the first type tissues is continued, no further effective increase in the total area of ​​the first type tissues can be expected. Therefore, the center point C i A new center point C is added to the area away from i (In Fig. 2, C' i Step S9 is a process for setting the center point C i Instead of selecting within the range of ±L from the center point C, select random coordinates from the entire set region R again in the same way as in the initial selection step in step S2, and select a new center point C iAt this time, the new center point C is set without distinguishing between the areas already selected as the first tissue and those not selected. i Configure the settings.

[0037] In this way, in step S8, the total area T i Depending on the degree of increase, the center point C i Keep it as it is (No in step S8), or add a new center point C i After resetting (Yes in step S8→step S9), the next (i+1) region growing process is started. That is, the number of repetitions i is incremented by one (i+=1), and the process returns to step S3, where the center point C i Within the range of ±L in the x and y directions, i+1 Set the new center point C in step S3. i+1 In selecting the new center point C, it is not distinguished whether the selected point is inside or outside the region designated as occupied by the first type of tissue in the previous region growing step. i+1 The technique of randomly selecting within a given bounded range is known as a random walk.

[0038] In step S3, a new center point C i+1 When is selected, in step S4, the ellipse E i+1 After creating the center point C i+1 With ellipse E at its center i+1 Place the ellipse E i+1 The area surrounded by the ellipse E is designated as the area where the first type tissue exists. At this time, the area already designated as the first type tissue is left designated as the first type tissue, while the area that has not been designated as the first type tissue is designated as the first type tissue. i+1 The area enclosed by the arrows will be added and designated as a new first-type tissue.

[0039] In this way, in steps S3 to S5, the center point that has already been set, that is, the center point C i-1 For the center point C, the new center point C is located within the range set by the limit distance L. i Then, an ellipse E with a specified shape and rotation angle is set at the center point. i The region expanding step is repeated while expanding the region occupied by the first type tissue by placing the first type tissue.

[0040] (4) Obtained model image Through the above steps, a model image that reproduces the material structure is obtained. The model image contains a mixture of two types of structure: the first type and the second type.

[0041] When repeating the region expansion process, after a center point is set in one region expansion process and a partition figure such as an ellipse is placed, the center point for placing the partition figure in the next region expansion process is selected within a limited range defined by a predetermined limit distance L from the already set center point. In other words, the distance between the already set center point and the next set center point is limited by the limited range, and the next set center point is located near the already set center point. Therefore, the region set as the first type tissue by placing a partition figure at the center point also exists near the region already set as the first type tissue. As a result, in the obtained model image, the region occupied by the first type tissue is not distributed uniformly throughout the set region R, but is concentrated in some places and distributed unevenly.

[0042] Therefore, the obtained model image can well reproduce the state in which two different types of structures are distributed spatially non-uniformly. An example of a material that forms such a non-uniform structure is a metal structure in which a region where crystal grains of one crystal phase are aggregated and a region where crystal grains of another crystal phase are aggregated are spatially non-uniformly mixed. In this case, each of the partition figures such as an ellipse arranged at each center point corresponds to a region where multiple crystal grains are aggregated, rather than to each individual crystal grain. This is different from the case of Patent Document 1, in which the regions set for each mapping point correspond to one crystal grain each.

[0043] Furthermore, in the method according to the present embodiment, when the increase ΔT in the total area of ​​the first type structure is equal to or less than the predetermined area change threshold A for a predetermined number of consecutive determinations (n ​​times) during the region expansion step, a new center point is randomly selected from the entire set region R without being restricted to the restricted region of ±L from the already set center point. This makes it possible to avoid a situation in which the area of ​​the first type structure does not increase effectively even if the region expansion step is repeated, causing the model creation process to not proceed smoothly. In addition, it is possible to suitably reproduce the state of an actual material structure in which a large number of regions in which the first type structure is distributed in a concentrated manner are distributed at a certain distance from each other.

[0044] In the embodiment described above, the limit range in which the next center point can be set with respect to a certain center point is defined by a square with a limit distance L, but the shape of the limit range can be set arbitrarily, for example, as a circle having a predetermined radius. The shape of the partition figure to be placed at the center point is not limited to an ellipse, and any shape may be selected so as to reproduce the assumed material structure well. However, by adopting a figure having an anisotropic shape that is long along one direction, such as an ellipse, as the partition figure, rather than adopting a highly isotropic figure such as a circle, it is possible to reproduce well a metal structure in which regions in which different crystal phases are gathered are mixed unevenly. In particular, an ellipse is a shape that is easy to set in a two-dimensional matrix and is easy to handle in creating a model image.

[0045] The area and detailed shape of the partition figure may be fixed to one type, but as in the embodiment described above, where the major axis of the ellipse is selected from a or a+1, and the minor axis is selected from b or b+1, multiple options with at least one different area and shape may be prepared as partition figures. Then, in each region expansion step, a random selection is made from these options to determine the shape and area of ​​the partition figure to be placed. In this way, a metal structure in which regions in which different crystal phases are aggregated are unevenly mixed can be reproduced well.

[0046] Furthermore, when the partition figure is an anisotropic shape such as an ellipse, it is preferable to randomly select the rotation angle of the set figure and then arrange the partition figure as in the embodiment described above. By doing so, it is possible to avoid a situation in which the partition figure having an anisotropic shape is arranged oriented in a specific direction, which generates an unnecessary anisotropy in the model image and makes it impossible to reproduce the structure of the actual material.

[0047] In the method according to the present embodiment, the state of the structure in the model image, such as the degree of non-uniformity in the distribution of the structure, can be changed by changing the set values ​​of various parameters used to create the model image. Specific values ​​to be used as each parameter can be determined so that the material structure actually assumed can be reproduced well. Furthermore, by changing the values ​​of each parameter based on these values, structures having different states can be prepared as model images, and phenomena caused by differences in the state of the material structure can be considered in the analysis of characteristics, etc.

[0048] The degree of heterogeneity of the tissue distribution can be varied by changing the limit distance L that defines the limit range for setting the next center point relative to the already set center point and the number of judgments n for judging the change in the total area of ​​the first type tissue, among other parameters. As shown in the examples below, the larger the limit distance L and the number of judgments n are, up to a certain extent, the higher the heterogeneity of the obtained tissue.

[0049] [Analysis of characteristics using model images] Next, a method for analyzing the characteristics of a material using the model image obtained above will be described. Here, the characteristics exhibited by a material having a structure represented by the model image obtained above are evaluated by simulation. For example, it is possible to estimate what values ​​can be obtained as macroscopic physical quantities (physical properties) corresponding to the microscopic structure represented in the model image, and what test results and measurement results can be obtained when a specified test or measurement is performed on a material having such a structure.

[0050] In order to estimate the characteristics of a material using a model image, it is necessary to set physical properties for each of the first and second types of tissues included in the model image. In other words, referring to actual measurements and database values, the regions set as the first and second types of tissues in the model image are made to correspond to regions occupied by actual substances, and predetermined physical properties are set. Here, the physical properties to be set may be selected to have an effect on the material properties of interest. For example, when performing an ultrasonic propagation analysis to analyze behavior of a material in response to ultrasonic waves, the response behavior to ultrasonic waves, such as scattering factors, may be set as the physical properties of the first and second types of tissues.

[0051] Next, a simulation is performed on the model image in which the physical properties are set for each structure, and the distribution of microscopic physical properties is converted into the properties of the material as a whole. In this simulation, a known simulation method that can analyze the target phenomenon, such as mechanical analysis or electromagnetic analysis, using a calculation method such as the finite element method may be applied. For example, when the behavior of the material against ultrasonic waves is treated as a material property, a known ultrasonic propagation analysis may be used. The computer program according to the embodiment of the present invention may be configured as an integrated program that continuously performs the creation of the model image described above and the simulation for the characteristic analysis of the created model image, or may be configured as a separate program that can perform them independently. In the latter case, a known program may be used as it is as a program that performs the simulation for the characteristic analysis.

[0052] If the material properties can be estimated using the model image, the estimated results can be used to consider the correlation between the state of the material structure and the properties, compare the results with actual measurements, and estimate the state of the material structure based on the actual measurements. As an example, by creating many model images with different states while changing parameters, performing simulations on the properties of each model image, and comparing the simulation results, it is possible to consider how the state of the material structure, such as the degree of non-uniformity, and its properties correlate. As another example, it is sufficient to create many model images with different states, and estimate the results obtained when performing a specified inspection or measurement on the material structure reproduced by each model image by simulation. Then, the results obtained by the inspection or measurement of the actual sample can be compared with the simulation results, and an analysis is performed to determine which of the many models the results are closest to, thereby estimating the state of the structure of the actual sample.

[0053] Here, as an example, the correlation between the heterogeneity of a material and the behavior of ultrasonic waves incident on the material will be described. When ultrasonic waves are incident on a material containing crystal grains, the ultrasonic waves are backscattered at the grain boundaries. The larger the crystal grain size, the larger the scattered energy at this time. When a first type of structure consisting of a collection of crystal grains with a large grain size and a second type of structure consisting of a collection of crystal grains with a small grain size exist in a material, the ultrasonic waves incident on the first type of structure are scattered more strongly than the ultrasonic waves incident on the second type of structure. When the first type of structure and the second type of structure are mixed in a material, the total scattered components are given as the sum of the ultrasonic components scattered on the first type of structure and the second type of structure. Therefore, the scattered energy of the ultrasonic waves changes depending on the ratio of the first type of structure and the second type of structure present in the path through which the ultrasonic waves are incident and pass (the path determined by the incident position and incident angle). Specifically, the greater the ratio of the first type of structure in the path, the greater the scattered energy of the ultrasonic waves.

[0054] Here, we consider preparing a large number of individual specimens as actual samples or model images, or setting various ultrasonic passage paths for one individual specimen, detecting the scattered components of the incident ultrasonic waves, and recording the scattered energy properly normalized by the path length. When the first type tissue and the second type tissue are mixed, but the area of ​​the area occupied by each tissue is small and the two types of tissue are mixed with high uniformity (see Fig. 5(a)), the ratio of the probability of scattering by the first type tissue and the probability of scattering by the second type tissue in the path through which the ultrasonic waves are incident and pass should not change significantly for each individual specimen and each path. Therefore, the scattered energy should not change so diversely for each individual specimen and each path. On the other hand, when the first type tissue and the second type tissue each occupy a large area of ​​continuous area and the two types of tissue are distributed unevenly (see Fig. 5(b)), the ratio of the probability of scattering by the first type tissue and the probability of scattering by the second type tissue in the path through which the ultrasonic waves are incident and pass may change significantly for each individual specimen and each path. This is because the specific distribution of the two types of tissues varies greatly from individual to individual and from path to path, and in this case, the scattered energy of the ultrasound should vary widely over a wide energy range.

[0055] In this way, the degree of variation in the scattered energy of the ultrasound is an index of the degree of uniformity of the distribution of the two types of tissues, and the higher the uniformity of the tissue, the smaller the variation (distribution width) of the scattered energy. Therefore, by comparing the degree of variation in the scattered energy when an ultrasonic test is performed on an actual sample and when an ultrasonic propagation analysis is performed on a model image, the degree of uniformity of the tissue in the sample can be estimated. It is not necessarily easy to prepare various samples with different degrees of uniformity of the tissue as actual samples, but with model images, tissues with various degrees of uniformity can be freely prepared. Therefore, if the correspondence between the degree of uniformity of the tissue and the magnitude of the variation in the scattered energy is estimated in detail using the model image and constructed as a database, the degree of uniformity of the tissue in the sample can be estimated by comparing the magnitude of the variation in the scattered energy obtained by ultrasonic measurement of the actual sample. EXAMPLES

[0056] Examples of the present invention are shown below. Note that the present invention is not limited to these examples. Here, reproduction of a material structure having non-uniformity using a model image was confirmed, and ultrasonic propagation analysis was performed on the model image to examine the variation in scattering intensity.

[0057] [1] Relationship between model image creation parameters and uniformity of material structure First, we confirmed how the uniformity of the material structure in the obtained model image changes when the limit distance L and the number of threshold judgments n, which are representative parameters used when creating the model image, are changed.

[0058] (Test Method) According to the material analysis method according to the present embodiment described above in detail, a model image including a first type structure and a second type structure was created.

[0059] The following parameters were used to create the model image: The limit distance L and the number of threshold judgments n were varied. ·Setting area R: h (x direction) = 1mm (1000 elements) w (y direction) = 8 mm (8000 elements) · Ellipse minor axis a=1 element · Ellipse major axis b=3 elements Area change threshold A=0 ·Target area S=5,600,000 elements

[0060] (Test Results) Figure 3 shows a model image obtained when the number of threshold judgments n is fixed at 1 and the limit distance L is changed as shown in the figure. Figure 4 shows a model image obtained when the number of threshold judgments n is changed as shown in the figure. In the model images shown in Figures 3 and 4 and in the subsequent figures, the first type tissue is displayed in white and the second type tissue is displayed in black.

[0061] First, let us consider the results of FIG. 3 in which the number of threshold judgments n is fixed and the limiting distance L is changed. In the region where the limiting distance L is small, such as L=1, the first type tissue and the second type tissue each form a small region and are mixed in a highly uniformly dispersed state. Up to about L=31, the larger the limiting distance L, the larger the region occupied by the first type tissue and the second type tissue, and the lower the uniformity of the tissue. This is because, when the limiting distance L is increased, it becomes possible to set the next center point in a wide range around the already set center point when repeating the region expansion process, and the first type tissue formed by arranging the partition figure at each center point tends to occupy a wide continuous range. However, at L=41, the uniformity of the tissue appears to be lower than at L=31, and even when the limiting distance L is further increased beyond L=41, the degree of uniformity of the tissue in the model image is almost unchanged compared to the state of L=41. This is because if the limit distance L is set too large, when the region expansion process is repeated, the next center point is likely to be set at a position far away from the already set center point, approaching a situation where center points are randomly placed throughout the set region. As a result, the region occupied by the first type texture is more likely to be formed discretely.

[0062] Next, the results of FIG. 4, in which the limit distance L is fixed and the number of threshold judgments n is changed, are examined. In the region where the number of threshold judgments n is small, such as n=1, the first type tissue and the second type tissue are mixed in a state of being dispersed with high uniformity. Up to about n=31, the larger the number of threshold judgments n, the larger the region occupied by the first type tissue and the second type tissue, respectively, and the non-uniformity in the distribution of the first type tissue and the second type tissue increases. This is because, as the number of threshold judgments n increases, the process of arranging a new first type tissue in the vicinity of the region already occupied by the first type tissue is repeated many times in the region expansion step, and the region occupied by the first type tissue in the vicinity of the region already occupied by the first type tissue is likely to become large. However, even if the number of threshold judgments n is further increased from n=31, the degree of uniformity of the tissue in the model image hardly changes. This is because, even if the process of arranging the first type tissue in the vicinity of the region already occupied by the first type tissue is repeated a certain number of times, the total area of ​​the first type tissue is unlikely to increase effectively.

[0063] As described above, it was found that the uniformity of tissue distribution in the model image created can be varied by changing the limit distance L and the number of threshold judgments n, among the parameters used when creating the model image. Up to a certain point, the uniformity of tissue distribution can be improved by increasing the values ​​of both the limit distance L and the number of threshold judgments n.

[0064] [2] Comparison of model image and actual material structure Next, the created model image was compared with the actual material structure to confirm whether the model image could reproduce the changes in uniformity in the actual material structure.

[0065] (Test Method) As an actual sample, an alloy sample containing multiple phases was prepared. In this case, after casting the alloy material, two types of samples with different degrees of structural homogeneity were produced by changing the forging ratio during forging. Then, the cross sections of the two types of samples were observed with a scanning electron microscope (SEM) to obtain structural observation images.

[0066] As in the above test [1], model images containing the first and second types of structures were created. Here, parameters including the limit distance L and the number of threshold judgments n were adjusted so as to reproduce as closely as possible the SEM images of the two types of materials obtained above. Furthermore, ultrasonic propagation analysis was performed on each of the two models obtained. In the ultrasonic analysis, the element size was set to 0.001 mm, which corresponds to less than 1 / 16 of the wavelength. The time step was 4 × 10 -11 seconds, which corresponds to less than 1 / 3 of the time it takes for a longitudinal wave to propagate through the element size.

[0067] (Test Results) Figure 5 shows the SEM microstructure images, the corresponding model images, and the results of ultrasonic propagation analysis for two types of samples. (a) shows the case where the microstructure is highly uniform, and (b) shows the case where the microstructure is non-uniform.

[0068] Comparing the microstructural observation images of the actual alloy with the model images in Figures 5(a) and (b), we find that in both cases, the size and shape of the regions occupied by the first and second types of structures are very similar between the microstructural observation images and the model images, and it can be said that the degree of uniformity shown in the microstructural observation images is well reproduced by the model images.

[0069] Next, in the results of the ultrasonic propagation analysis, we focus on the backscattered components shown in the squares in the figure. Compared to the homogeneous structure in (a), a larger scattering intensity (amplitude) is observed in the heterogeneous structure in (b). This is interpreted as being because the more heterogeneous the structure, the more likely it is that the ultrasonic waves will pass through many areas where phases that give a large scattering intensity are concentrated and distributed, and thus the ultrasonic waves will progress. In addition, compared to the homogeneous structure in (a), the beat of the backscattered waves is larger in the heterogeneous structure in (b). This is interpreted as being because the heterogeneity of the structure causes the ultrasonic waves to pass through paths with a variety of different distribution ratios of the two types of structure, and the distribution width of the scattering intensity becomes larger. These trends are consistent with the trends obtained by ultrasonic measurements of the alloy samples that give each microstructure observation image.

[0070] [3] Relationship between tissue homogeneity and variation in ultrasound scattering intensity Next, we performed ultrasound propagation analysis on several model images with different degrees of tissue uniformity, and investigated the relationship between tissue uniformity and the variation in scattering intensity.

[0071] (Test Method) Similar to the above tests [1] and [2], model images containing the first and second types of structures were created. In this case, the degree of uniformity was varied over a wide range by adjusting each parameter. However, the area ratio of the first and second types of structures was kept constant for all model images.

[0072] The degree of uniformity in each model image was quantitatively evaluated by the non-uniformity evaluation value. Specifically, the moving average in the x and y directions was calculated for the model image, and the coefficient of variation of the histogram of the intensity distribution in the obtained image was used as the non-uniformity evaluation value. When two types of tissues form small regions and are mixed with high uniformity, the moving average image contains many elements showing intermediate gradations (middle gray) between the first type of tissue and the second type of tissue, whereas when the two types of tissues are grouped together to form large regions and distributed non-uniformly, elements with a variety of gradations exist, ranging from the gradation corresponding to the first type of tissue (white) to the gradation corresponding to the second type of tissue (black). Therefore, the larger the non-uniformity evaluation value, the higher the non-uniformity of the tissue (lower the uniformity).

[0073] In addition, ultrasonic propagation analysis was performed on each model image in the same manner as in test [2]. The scattering intensity values ​​of the backscattered components obtained in the analysis were recorded.

[0074] To compare the results of the ultrasonic analysis using the model images, ultrasonic testing was also performed on actual alloy samples to evaluate the distribution of ultrasonic scattering intensity. Specifically, three types of samples with different degrees of microstructural uniformity were prepared in the same manner as in the above test [2]. Ultrasonic waves were then irradiated from multiple positions in the circumferential and vertical directions of each cylindrically processed sample, and the reflected waves were detected. The backscattered components contained in the reflected waves were extracted for each measurement position, and the scattering intensity was estimated. Additionally, SEM observations were performed on the cross sections of each sample, and the nonuniformity evaluation value was estimated for the SEM observation images in the same manner as for the model images above.

[0075] (Test Results) Figure 6 shows all the model images created, categorized into those with a heterogeneity evaluation value of 20 (20 or more and less than 21), those with a heterogeneity evaluation value of 21 (21 or more and less than 22), and those with a value of 24 or more. In each category, model images in which the first and second types of textures are mixed with the same degree of homogeneity are obtained, corresponding to the fact that similar heterogeneity evaluation values ​​were obtained.

[0076] Figure 7 shows the relationship between the heterogeneity evaluation value estimated from the images and the scattering intensity obtained by the ultrasonic propagation test for all model images, including the one shown in Figure 6. Figure 7 shows that the larger the heterogeneity evaluation value, the larger the scattering intensity tends to be, and the scattering intensity varies greatly between plot points with similar heterogeneity evaluation values, and the plot points are distributed over a wide energy range. These trends are consistent with those obtained for two model images with different microstructural uniformities in Figure 5, obtained in the test [2]. They also match the trends observed in ultrasonic measurements of actual alloy samples.

[0077] Furthermore, Fig. 8 shows the results of ultrasonic testing of actual alloy samples. Here, for three types of samples, the horizontal axis shows the heterogeneity evaluation value estimated from the SEM observation image, and the vertical axis shows the distribution range of the scattering intensity obtained for each measurement position by ultrasonic testing. The scattering intensity is displayed in arbitrary units. According to Fig. 8, the scattering intensity varies exponentially over a wider range as the heterogeneity evaluation value increases. This tendency is the same as the result of Fig. 7 obtained by ultrasonic propagation analysis of the model image. This supports the validity of the material analysis method in which ultrasonic propagation analysis is performed using the model image and the distribution width of the obtained scattering intensity is associated with the degree of heterogeneity of the structure. In an actual alloy sample, it is difficult to change the degree of heterogeneity finely and over a wide range as in the case of using a model image, but the analysis using the model image makes it possible to investigate the scattering behavior of ultrasonic waves in detail, assuming a structure with various heterogeneities.

[0078] Although the embodiments of the present invention have been described above, the present invention is not particularly limited to these embodiments and various modifications can be made. [Explanation of symbols]

[0079] C1,C i-1 ,C i ,C i+1 center point C' i Reset center point E1,E i-1 ,E i ,E i+1 Ellipse (compartment shape) R Setting area

Claims

1. A material analysis method comprising: creating a model simulating a material structure including a first type structure and a second type structure that are different from each other; and analyzing characteristics of the material structure, After performing an initial selection step of selecting a randomly selected point within the set region as a center point, a region expansion step is repeated in which a new center point is randomly selected within a predetermined limited range from the already selected center point, a predetermined partition pattern is placed at the new center point, and the region surrounded by the partition pattern is set as a first type tissue; When the total area of ​​the first type tissue set at the completion of a certain region expanding step is increased by a predetermined threshold or less compared to the total area of ​​the first type tissue set at the completion of the previous region expanding step for a predetermined number of consecutive times during the repetition of the region expanding step, a point randomly selected within the set region is set as a new center point, and the repetition of the region expanding step is continued; When a total area of ​​the first type structure reaches a preset value, the repetition of the region expansion step is terminated, and finally, a region that has not been set as a first type structure is set as a second type structure, thereby obtaining a model simulating the material structure.

2. The computer program for material analysis according to claim 1 , wherein the partition figure has an anisotropic shape that is long along one direction.

3. 3. The computer program for material analysis according to claim 2, wherein the partition figure is an ellipse.

4. 4. The computer program for material analysis according to claim 2, wherein in each of said region expanding steps, said partition figure is positioned after a rotation angle of said partition figure is randomly selected.

5. 5. The computer program for material analysis according to claim 1, wherein in each of the region expanding steps, at least one of an area and a shape of the partition figure is randomly selected from a plurality of preset candidates, and the partition figure is arranged.

6. 6. The computer program for material analysis according to claim 1, further comprising: performing an ultrasonic propagation analysis on the obtained model as the analysis of the characteristics.

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