Crack analysis method, program, material design support method and material design method

Abstract

To provide a crack analysis method, a program, a material design support method and a material design method, which can simply and objectively analyze cracks on a crystal interface.SOLUTION: A crack analysis method for analyzing a crack on a crystal interface of atomic simulation includes: an atomic model preparation step of preparing an atomic model including a crystal interface; a deformation step of deforming the atomic model; a first calculation step of Voronoi-dividing the atomic model before and after the deformation in the deformation step, and calculating a Voronoi volume and a frequency of the Voronoi volume; and an analysis step of analyzing cracks on the crystal interface on the basis of a relation between the Voronoi volume and the frequency of the Voronoi volume.SELECTED DRAWING: Figure 1

Description

[Technical Field]

[0001] The present disclosure relates to a crack analysis method, a program, a material design support method, and a material design method. [Background technology]

[0002] In analyzing the fracture process of materials, it is considered particularly effective to analyze cracks that occur on crystal interfaces. For example, atomic simulations are being used to analyze fracture phenomena that originate at crystal interfaces.

[0003] In analyses using atomistic simulations, deformations are applied to crystal interface models to simulate fracture phenomena that originate at the crystal interface, i.e., the initiation and growth processes of cracks. To understand the properties of crystal interfaces, it is important to understand not only global information about the atomic model, such as the stress and strain required for fracture, but also local information, such as the initiation and growth behavior of nano-level cracks that occur on the crystal interface.

[0004] Recent academic research using atomic simulations has suggested that nano-level cracks form on crystal interfaces just before the crystal interfaces break. Here, nano-level cracks can be treated as large clusters of atomic vacancies. The space in atomic simulations includes the bulk portion (parent phase), crystal interfaces, and nano-level cracks, which can be distinguished as follows: The bulk portion is crystalline and has the highest density. The crystal interfaces are regions with lower density than the bulk portion. Nano-level cracks are regions with even lower density than the crystal interfaces and are the cause of fracture.

[0005] Here, a crystal interface is a planar lattice defect that disrupts the crystal structure. Disruption of the crystal structure includes the crystal structure being discontinuous. Because of this, the density of a crystal interface is lower than that of the bulk portion of an atomic model, and so the crystal interface has characteristics similar to nano-level cracks. When nano-level cracks occur on a crystal interface, different types of defects coexist in the same location, which presents a challenge in that analysis becomes complicated.

[0006] For example, Patent Document 1 discloses a method for generating a crystal interface model (an atomic model including a crystal interface). Patent Document 2 discloses a method for analyzing defect positions in an atomic model. Patent Document 2 also describes classifying divided cells by determining particle density and defects using a Voronoi polyhedron that represents the area occupied by particles. [Prior art documents] [Patent documents]

[0007] [Patent Document 1] Japanese Patent Application Laid-Open No. 2005-11328 [Patent Document 2] Japanese Patent Application Publication No. 6-302665 Summary of the Invention [Problem to be solved by the invention]

[0008] In the past, crack detection was often performed by visually visually visualizing a crystal interface model using coordinate data, but this method of detecting cracks lacked objectivity.

[0009] For example, by generating a crystal interface model using the method of Patent Document 1 and then applying deformation to the generated crystal interface model, it is possible to simulate fracture originating at a crystal interface. However, even if the classification method of Patent Document 2 is applied to this simulation, it is difficult to distinguish between nano-level cracks that occur on the crystal interface and the crystal interface. This is because, as mentioned above, crystal interfaces have similar characteristics to nano-level cracks, but Patent Document 2 does not consider how to accurately distinguish between them.

[0010] In view of the above circumstances, an object of the present disclosure is to provide a crack analysis method, a program, a materials design support method, and a materials design method that are capable of easily and objectively analyzing cracks on crystal interfaces. [Means for solving the problem]

[0011] (1) A crack analysis method according to an embodiment of the present disclosure includes: A crack analysis method for analyzing a crack on a crystal interface by atomic simulation, comprising: an atomic model preparation step of preparing an atomic model including a crystal interface; a deformation step of deforming the atomic model; a first calculation step of performing Voronoi division on the atomic model before and after the deformation in the deformation step, and calculating a Voronoi volume and a frequency of the Voronoi volume; and an analysis step of analyzing cracks on the crystal interface based on the relationship between the Voronoi volume and the frequency of the Voronoi volume.

[0012] (2) As one embodiment of the present disclosure, in (1), The analysis step performs peak separation on a waveform obtained by plotting the frequency of the Voronoi volume against the Voronoi volume, and determines that a peak having a Voronoi volume exceeding the Voronoi volume of the crystal interface is due to a crack on the crystal interface.

[0013] (3) As an embodiment of the present disclosure, in (1) or (2), a visualization step of visualizing the atomic model before and after the deformation in the deformation step; an extraction step of extracting information about defects in the visualized atomic model; The method further includes a second calculation step of quantifying the cracks and calculating quantitative values ​​based on the relationship between the defect information and the analyzed crack information on the crystal interface.

[0014] (4) A program according to an embodiment of the present disclosure includes: In order to analyze a crack on a crystal interface by atomic simulation, a computer that executes the atomic simulation is an atomic model preparation step of preparing an atomic model including a crystal interface; a deformation step of deforming the atomic model; a first calculation step of performing Voronoi division on the atomic model before and after the deformation in the deformation step, and calculating a Voronoi volume and a frequency of the Voronoi volume; and an analysis step of analyzing cracks on the crystal interface based on the relationship between the Voronoi volume and the frequency of the Voronoi volume.

[0015] (5) A materials design method according to an embodiment of the present disclosure includes: (3) A step of calculating the size of the crack at the time of fracture initiation using the quantitative value calculated by the crack analysis method; and outputting a material design guideline based on the calculated crack size at the time of fracture initiation.

[0016] (6) A material design method according to an embodiment of the present disclosure includes: (5) Design the material according to the design guidelines for the material output by the material design support method.

[0017] (7) As an embodiment of the present disclosure, in any one of (1) to (3), The atomic simulation uses a force field that utilizes machine learning, and the force field is generated using training data that incorporates data on the atomic structure in the precursor stage of crack generation. [Effects of the Invention]

[0018] According to the present disclosure, it is possible to provide a crack analysis method, a program, a materials design support method, and a materials design method that are capable of easily and objectively analyzing cracks on crystal interfaces. [Brief explanation of the drawings]

[0019] [Figure 1] FIG. 1 is a flowchart showing processing steps of a crack analysis method according to an embodiment of the present disclosure. [Figure 2] FIG. 2 is a diagram showing an example of the configuration of a crack analysis device. [Figure 3] FIG. 3 is a diagram illustrating the visualization results of an atomic model including a crystal interface. [Figure 4] FIG. 4 shows an example of a stress-strain diagram when tensile deformation is applied. [Figure 5] FIG. 5 illustrates the atomic model at maximum load, fracture initiation, and post-fracture. [Figure 6] FIG. 6 is a diagram illustrating the results of displaying the maximum load, fracture initiation, and post-fracture atomic models using Voronoi polyhedrons. [Figure 7] FIG. 7 is a diagram illustrating the Voronoi volumes of the atomic model before tension, at the maximum load, and after fracture, and the frequency distribution of the Voronoi volumes. [Figure 8] FIG. 8 is a diagram illustrating the distribution of samples with a frequency of 50 or less from before tension to when fracture begins. [Figure 9] FIG. 9 is a diagram illustrating the frequency distribution of the maximum load, the frequency of fracture initiation, and the frequency after fracture when the frequency is 40 or less and the Voronoi volume is 60 Å 3 or less. DETAILED DESCRIPTION OF THE INVENTION

[0020] Hereinafter, a crack analysis method, a program, a material design support method, and a material design method according to embodiments of the present disclosure will be described with reference to the drawings.

[0021] The present inventors have investigated methods for analyzing cracks on crystal interfaces using atomic simulations, and have focused on Voronoi tessellation, which is used in defect location analysis methods (see Patent Document 2). Voronoi tessellation makes it possible to identify the location of individual atomic vacancies in the bulk (parent phase) or precipitates in an atomic model. However, when a deformation is applied to a crystal interface model to simulate a fracture phenomenon originating at a crystal interface, simply applying Voronoi tessellation to the atomic model makes it impossible to distinguish between nano-level cracks that occur on the crystal interface and the crystal interface itself.

[0022] After further intensive research, the present inventors have found that a simple and objective analysis of cracks is possible by using the relationship between the Voronoi volume and the frequency of the Voronoi volume obtained by applying Voronoi tessellation to an atomic model before and after deforming a crystal interface model. The crack analysis method generally includes at least an atomic model preparation step, a deformation step, a first calculation step, and an analysis step. The atomic model preparation step is a step of preparing an atomic model including a crystal interface to be used in an atomic simulation for analyzing cracks on a crystal interface. The deformation step is a step of deforming the prepared atomic model. The first calculation step is a step of applying Voronoi tessellation to the atomic model before and after deformation in the deformation step, and calculating the Voronoi volume and the frequency of the Voronoi volume. The analysis step is a step of analyzing cracks on a crystal interface based on the relationship between the calculated Voronoi volume and the frequency of the Voronoi volume.

[0023] The crack analysis method according to this embodiment further includes a visualization step, an extraction step, and a second calculation step. The visualization step is a step of visualizing the atomic model before and after the deformation due to the deformation step. The extraction step is a step of extracting information about defects in the visualized atomic model. The second calculation step is a step of quantifying the crack and calculating a quantitative value based on the relationship between the extracted defect information and information about the crack on the analyzed crystal interface. Each step is performed using an atomic simulation. Below, the atomic simulation in which the crack analysis method according to this embodiment is performed, the device that performs the atomic simulation, each step, etc. will be described.

[0024] (Atomic Simulation) Atomic simulation is a numerical calculation method that enables direct handling of discrete atoms, as typified by first-principles calculations or molecular dynamics calculations. In the materials field, general-purpose software capable of performing atomic simulations has been developed, allowing various boundary conditions, etc., to be freely selected and set in atomic simulations. Free software capable of performing atomic simulations, such as Quantum Espresso and LAMMPS, has been released. Therefore, the crack analysis method according to this embodiment can be performed using software capable of performing atomic simulations. Furthermore, the device (crack analysis device) that performs the crack analysis method according to this embodiment may be a device on which such software can be installed, such as a computer. For example, a commercially available general-purpose computer may be used. The computer includes, for example, a storage device such as a memory and a hard disk drive, an arithmetic unit (processor), and an input / output device. The atomic simulation (processing of the crack analysis method) may be performed by the processor. Furthermore, data (e.g., atomic model information) and programs required for processing the crack analysis method may be stored in the storage device. Furthermore, instructions for executing the crack analysis method and output of results (e.g., the design guidelines described below) may be performed by the input / output device. The computer may be a computer with high processing power, such as a supercomputer, a quantum computer, etc. The program may cause a computer that performs atomic simulations to execute each step in order to analyze cracks on a crystal interface.

[0025] Software capable of performing atomic simulations may be selected that has the functionality to generate an atomic model by determining the types of atoms, positions of atoms, and modeling cell size required as initial information for calculations without requiring the user to do any effort (by using the minimum necessary settings).

[0026] (Atomic model preparation process) The atomic model preparation step is a step of preparing an atomic model including a crystal interface, which is used in an atomic simulation for analyzing cracks on a crystal interface, as described above. The atomic model including a crystal interface may be generated by any known method, and is not limited to any particular method. For example, the method disclosed in Patent Document 1 can be used. Here, the prepared atomic model is preferably an atomic model that excludes disturbance factors. For example, to improve the accuracy of peak separation described below, it is preferable to prepare an atomic model consisting only of a bulk portion and a crystal interface. In the case of a bicrystal model having a bulk portion and a crystal interface, as in this embodiment, lattice defects are introduced in the bulk portion or the crystal interface. Examples of lattice defects include substitutional elements, interstitial elements, precipitates, dislocations, dislocation sources, atomic vacancies, and atomic vacancy clusters. Analysis of atomic models containing lattice defects is generally complex, but can be performed by understanding the properties of the lattice defects. Here, the bulk portion may not be a pure metal but may be a crystal containing multiple elements (e.g., carbide and iron). It is also preferable to use a perfect crystal for the bulk portion.

[0027] (Deformation process) The deformation step is a step of deforming the prepared atomic model as described above. The deformation of the atomic model is performed by applying at least one of tension, compression, and shear deformation to the atomic model quasi-statically or dynamically using an atomic simulation. Here, in this embodiment, the time of fracture due to deformation is determined as the time when the stress for deformation reaches less than 20% of the maximum stress (see "After Break" in FIG. 4). Furthermore, in this embodiment, the stress for deformation is determined as the average stress for the entire atomic model.

[0028] Here, the deformation of the atomic model may be performed using a function of software capable of executing atomic simulation. As a specific example, LAMMPS can execute deformation of the atomic model using the "fix deform" command.

[0029] In the deformation process, it is preferable that the change over time when at least one of tension, compression, and shear deformation is applied to the atomic model can be output so as to capture each moment. Also, it is preferable that the format of the output data, etc., be determined in advance and information on the changing atomic model be automatically extracted systematically. Based on the automatically extracted and stored atomic model information, it becomes possible to grasp the details of the change over time of the atomic model.

[0030] (1st calculation step) As described above, the first calculation step is a step of subjecting the atomic model before and after deformation in the deformation step to Voronoi division, and calculating the Voronoi volume and the frequency of the Voronoi volume.

[0031] Here, the Voronoi volume is the volume of a Voronoi polyhedron that can be obtained by Voronoi tessellation. Voronoi tessellation is an analytical method in which multiple kernel points are placed at any position in a metric space, and regions are divided based on which kernel points other points in the same metric space are closer to. In an atomic model, it is possible to calculate the Voronoi volume of each atom by analyzing the points in the metric space of the Voronoi tessellation in correspondence with atomic coordinates. Furthermore, by statistically processing the Voronoi volume of an atomic model, it is possible to calculate the frequency of the Voronoi volume (i.e., to find the frequency distribution of the Voronoi volume).

[0032] Here, the calculation of the Voronoi volume may be performed using a function provided by software capable of performing atomic simulations. As a specific example, LAMMPS can calculate the Voronoi volume using the "compute voronoi / atom" command. Also, Ovito, a general-purpose software capable of visualizing atomic models, can perform Voronoi division by executing the GUI operation "Voronoi analysis."

[0033] (Analysis process) The analysis step is a step of analyzing cracks on the crystal interface based on the relationship between the calculated Voronoi volume and the frequency of the Voronoi volume, as described above.

[0034] Lattice defects in crystalline materials generally include atomic vacancies, atomic vacancy clusters, dislocations, grain boundaries, and precipitates. Here, atomic vacancies are defects resulting from the absence of a single atom that constitutes the bulk of an atomic model. Atomic vacancy clusters are formed by the aggregation of multiple atomic vacancies. The aggregation, shape, and size of atomic vacancy clusters are arbitrary. Nano-level cracks that arise from deformation of an atomic model represent the presence of one or more localized spaces with lower density compared to the density of the crystal interface of the atomic model. Nano-level cracks can be treated as large atomic vacancy clusters. Furthermore, vacuum regions defined in an atomic model can be treated as atomic vacancy clusters that are much larger than nano-level cracks. To distinguish between vacuum regions and nano-level cracks, the size of a nano-level crack is defined as less than 20% of the area of ​​the xy plane (plane parallel to the interface) of the atomic model. Here, the atomic model is composed of finite values ​​arbitrarily set in the x, y, and z directions and has a finite surface area.

[0035] Here, typical cracks in real materials are shown in atomistic simulations as voids after fracture in Figure 5. In contrast, nano-level cracks are damage at the interface. Vacuum regions are regions that can be arbitrarily set by users of atomic simulations.

[0036] In this embodiment, the analysis process performs peak separation on the waveform obtained by plotting the frequency of the Voronoi volume against the Voronoi volume, and determines that a peak having a Voronoi volume that exceeds the Voronoi volume of the crystal interface is due to a crack on the crystal interface.

[0037] First, to extract cracks present on crystal interfaces, it is necessary to distinguish between the bulk portion and the crystal interface in the atomic model before cracks occur. In this embodiment, the bulk portion and the crystal interface are distinguished based on the difference between the average volume of atoms constituting the bulk portion and the average volume of atoms constituting the crystal interface. To achieve this distinction, Voronoi tessellation of the atomic model, plotting the Voronoi volume and the frequency distribution of the Voronoi volume, and peak separation based on a normal distribution are performed. As a result of the peak separation process, two peaks are mainly detected. Here, considering that the crystal interface is a lattice defect, the average volume of the crystal interface is larger than the average volume of the bulk portion. Therefore, for the peak with the smaller Voronoi volume value (the first peak) and the peak with the larger Voronoi volume value (the second peak), the Voronoi volume value of the first peak can be treated as the average volume of the bulk portion, and the Voronoi volume value of the second peak can be treated as the average volume of the crystal interface.

[0038] When the atomic model includes lattice defects (lattice defects other than those at crystal interfaces) in addition to the bulk and crystal interfaces, the peaks of the bulk, crystal interfaces, and lattice defects can be easily distinguished by understanding the properties of the lattice defects (e.g., the magnitude relationship of the average volume) before peak separation. Furthermore, the Voronoi volume value of each peak can be made to correspond to the average volume of the bulk, crystal interfaces, and lattice defects, respectively.

[0039] As a specific example, when the lattice defect is a substitutional element, analysis may be performed without distinguishing the substitutional element from the bulk element. In contrast, when the lattice defect is an interstitial element, analysis is performed by distinguishing the interstitial element from the bulk element. When an atomic model including an interstitial element is subjected to Voronoi tessellation, a peak appears in the Voronoi volume for the atomic points of the interstitial element and the atomic points of the bulk element, resulting in a Voronoi volume that is significantly smaller than the average Voronoi volume of the bulk element. This is undesirable for crack evaluation. Therefore, it is preferable to perform Voronoi tessellation without including the interstitial element in the target to obtain a frequency distribution (frequency distribution).

[0040] In the analysis step, Voronoi tessellation is performed on the atomic model deformed in the deformation step. As a result of the deformation (over time), peaks are detected that have Voronoi volume values ​​that did not exist before the deformation step (exceeding the Voronoi volume value before the deformation step). When such changes over time were examined by outputting information on the atomic model and visualizing the state of the atomic model, it was found that the detected peaks correspond to cracks on the crystal interfaces. In other words, when Voronoi tessellation is performed over time on the atomic model in the deformation step, the point at which a peak appears with a Voronoi volume value that exceeds the Voronoi volume value of the crystal interface can be determined to be the point at which a crack has occurred. Furthermore, it can be determined that this peak is due to a crack on the crystal interface.

[0041] (Visualization process) The visualization step is a step of visualizing the atomic model before and after the deformation in the deformation step, as described above. The atomic model may be visualized by reading information about the atomic model before and after the deformation into software such as Vesta, Ovito, and Atomeye.

[0042] For example, Atomeye can be used to visualize atomic models using the center symmetry parameter (CSP). CSP is a method for quantifying local symmetry based on the relative positions of the atom in question and its surrounding atoms. If the structure has a crystalline structure, CSP will be zero. CSP is an index that indicates that the larger the value, the greater the local disorder.

[0043] Furthermore, the atomic model may be visualized by subjecting the atomic model to Voronoi division and visualizing the resulting Voronoi polyhedron. Here, the Voronoi polyhedron has information on its center of gravity. Therefore, it is possible to visualize the center of gravity of the Voronoi polyhedron as a three-dimensional point, and color each point according to its Voronoi volume.

[0044] (extraction process) The extraction process is a process of extracting information about defects in the visualized atomic model, as described above. The defect information may include the number, shape, and representative length of cracks obtained by visualizing the atomic model. Here, cracks have various shapes. Therefore, a representative length that is an approximately calculated value such as a circle equivalent diameter or a Feret diameter may be used.

[0045] (Second calculation process) The second calculation step is a step of quantifying the cracks and calculating quantitative values ​​based on the relationship between the extracted defect information and the analyzed crack information on the crystal interface, as described above. For example, the cracks can be identified based on the number of cracks obtained as defect information in the extraction step and the number or area of ​​cracks on the crystal interface obtained from peaks having Voronoi volume values ​​exceeding the Voronoi volume value of the crystal interface detected in the analysis step. In addition, for example, the volume of the identified cracks can be calculated.

[0046] Here, the analysis using Voronoi division (Voronoi analysis) is preferably performed on all states of the continuous atomic model output from the atomic simulation. Furthermore, by appropriately utilizing the functions of software capable of executing the atomic simulation, a graphic user interface may be created that visualizes, for example, a portion selected from the frequency distribution data as a graph. Such a graphic user interface can reduce the number of steps required for analysis and improve work efficiency.

[0047] FIG. 1 is a flowchart showing processing steps of a crack analysis method according to this embodiment. The crack analysis device may execute each step in the processing order shown in FIG. 1. That is, the atomic model preparation step, deformation step, first calculation step, analysis step, visualization step, extraction step, and second calculation step may be executed in this order. Here, the visualization step, extraction step, or second calculation step may be omitted. FIG. 2 is a diagram showing an example configuration of a crack analysis device. In the example of FIG. 2, the crack analysis device is configured by a computer including an arithmetic unit, a storage device, and an input / output device. By executing a program, the arithmetic unit functions as an atomic model preparation unit, deformation unit, first calculation unit, analysis unit, visualization unit, extraction unit, and second calculation unit. Here, the atomic model preparation unit executes the atomic model preparation step. The deformation unit executes the deformation step. The first calculation unit executes the first calculation step. The analysis unit executes the analysis step. The visualization unit executes the visualization step. The extraction unit executes the extraction step. The second calculation unit executes the second calculation step. Here, the visualization unit, extraction unit, or second calculation unit may be omitted.

[0048] The crack analysis method described above can also be applied to materials design support methods or materials design methods. Atomic simulations can simultaneously handle multiple elements by selecting an appropriate force field. The crack analysis method described above can quantitatively evaluate the effect of elements on the average volume of crystal interfaces or on the formation of cracks at interfaces. For example, it is possible to perform relative comparisons between multiple materials. In other words, the crack analysis method described above can be incorporated into materials development through digital transformation using data science and can be applied to materials design and its support. When applied to materials design support, it is important to vary multiple conditions and capture changes in trends, rather than performing a single calculation. This method can evaluate not only the atomic model (e.g., the type and concentration of elements segregated at grain boundaries), but also, for example, the tensile speed and tensile temperature depending on the deformation section (deformation process). In other words, it is possible to evaluate whether the addition of elements increases or decreases the crack growth rate depending on the deformation section (deformation process). By varying multiple conditions and evaluating changes in trends using this method, it is possible to streamline and support materials design.

[0049] Here, quantitative evaluation can be performed as follows. The average volume can be evaluated based on the change in the Voronoi mean volume of the interface before and after the addition of an element. It is also important to track changes over time in the crack shape. For example, the crack shape can be evaluated based on whether the addition of an element increases or decreases the crack growth rate. Based on such evaluation, elements or concentrations that accelerate or decrease the crack growth rate can be identified, and thermodynamic calculations can be used to predict holding temperatures favorable for grain boundary segregation. The identified elements that accelerate or decrease the crack growth rate can be output as material design guidelines. In this way, a material design method can be performed that includes the steps of calculating the crack size at fracture initiation using the quantitative values ​​calculated by the above-described crack analysis method, and outputting material design guidelines based on the calculated crack size at fracture initiation. Furthermore, a material design method can be performed in which a material is designed according to the material design guidelines output by the material design method.

[0050] In recent years, the development of force fields utilizing machine learning has been actively pursued. Neural networks, deep learning, and the like can be used as machine learning techniques. For example, force fields designed to be universally applicable to all elements, or force fields specialized for specific purposes, such as CHGNet (Crystal Hamiltonian Graph Neural Network) or MACE-MP, have been generated by machine learning. The quality of a force field generated by machine learning (machine learning force field) varies depending on, for example, the force field elements being trained. The above-described method disclosed herein can identify the location of crack initiation and obtain the atomic structure of a precursor stage of crack initiation. By using data on the atomic structure of a precursor stage of crack initiation (specifically, data obtained by analyzing the atomic structure of the precursor stage using first-principles calculations) as training data for the machine learning force field, phenomena related to crack initiation can be handled with high accuracy. In other words, machine learning force fields can be used in atomic simulations. By using a machine learning force field generated using training data incorporating accumulated past data on the atomic structure of a precursor stage of crack initiation, the calculation accuracy of atomic simulations of phenomena related to crack initiation can be improved. Here, when analyzing the atomic structure of a precursor stage using first-principles calculations, the computational load of first-principles calculations is very high, and therefore there is a substantial limit to the number of atoms that can be handled. Therefore, it is necessary to appropriately extract atoms in the precursor stage where a crack will occur and atoms nearby them. In the method disclosed herein, for example, by performing Voronoi analysis, it is possible to appropriately and efficiently extract atoms in the precursor stage where a crack will occur and atoms nearby them. In other words, although it is not essential to incorporate data on the atomic structure of a precursor stage where a crack will occur into the training data, incorporating data on the atomic structure of a precursor stage where a crack will occur can improve the calculation accuracy of the atomic simulation.

[0051] Furthermore, as a method for generating a force field using machine learning, a method has been considered in which new training data is added to an existing machine learning force field to efficiently generate a machine learning force field with improved functionality. Even in such a method for generating a machine learning force field, the selection of the new training data to be added is important. For example, by adding new data on the atomic structure of a precursor stage of crack generation based on an existing publicly available machine learning force field and the training data used to generate it, a machine learning force field that can improve the calculation accuracy of atomic simulations can be efficiently generated. The method of the present disclosure may also perform atomic simulations using a machine learning force field generated in this manner.

[0052] The effects of the present disclosure will be specifically described below based on examples, but the present disclosure is not limited to these examples.

[0053] Using LAMMPS as atomic simulation software, a machine learning force field capable of handling a binary Fe-H system was applied to create an atomic model (atomic model preparation step). In this example, an atomic model of pure iron with a body-centered cubic structure was divided into two and joined. The rotation axis during joining was set to the 112 axis of the body-centered cubic structure, and by rotating, a bicrystal model of pure iron (atomic model with symmetric twist grain boundaries) with a crystal misorientation of 44 degrees was created. In addition, the model size was adjusted so that periodic boundary conditions could be applied after rotation.

[0054] Dynamic structural relaxation of the atomic model was then performed using the LAMMPS functionality to obtain an atomic model with energetically reasonable crystal interfaces. The unit of operation for LAMMPS was selected as "metal." The timestep was set to the default value of 1.0 fs. Periodic boundary conditions were applied to all directions of the x, y, and z axes of the atomic model.

[0055] For dynamic structural relaxation, a hold of 30,000 steps at 1200 K was performed using the “fix npt” command of LAMMPS, followed by a hold of 20,000 steps at 300 K.

[0056] Next, a fracture simulation was performed on the prepared symmetric twist grain boundary of the above atomic model by applying tensile deformation (deformation step). In this example, the strain rate was set to 1.0 × 10 s at a temperature controlled state of 300 K using the "fix nvt" and "fix deform" commands of LAMMPS. 8 The tensile deformation was controlled at 1 / s. The constraint condition was used to prevent the cell size from changing in the direction perpendicular to the tensile direction. The deformation was continued until fracture occurred along the interface.

[0057] Furthermore, in the deformation step, atomic model information was output every 2000 steps so that it could be used in the first calculation step and the visualization step.

[0058] Figure 3 shows the results of visualizing an atomic model using Atomeye with the center symmetry parameter (CSP).

[0059] In this example, it was found that the symmetry is locally low at the 0% position as well as the 50% position on the z axis. Here, due to the characteristics of the periodic boundary conditions, the 0% and 100% positions are synonymous. Furthermore, the periodic boundary conditions are applied to all axes, x, y, and z. In the example in Figure 3, atoms with high CSP were confirmed at the 50% and 0% positions on the z axis. Therefore, it was found that crystal interfaces exist at these positions.

[0060] FIG. 4 shows a stress-strain diagram when tensile deformation is applied. Before fracture initiation, a maximum load is applied for tensile deformation, resulting in maximum stress. In this example, fracture initiation was determined as the step in which the stress reduction reaches 0.1 GPa or more in the step of outputting atomic model information (every 2000 steps as described above). Post-fracture is the point at which the stress first reaches 0.0 after the stress begins to decrease. Hereinafter, the points at maximum load, fracture initiation, and post-fracture may be simply referred to as maximum load, fracture initiation, and post-fracture.

[0061] Figure 5 shows an example of the atomic model of maximum load, fracture initiation, and post-fracture. Visualization using CSP is also performed in the example of Figure 5.

[0062] At the maximum load, no atomic vacancy clusters were observed on the crystal interface. However, as deformation progressed, atomic vacancy clusters, i.e., cracks, were observed at the onset of fracture. Furthermore, after fracture, it was confirmed that voids larger than the atomic vacancy clusters had formed, originating from the cracks. These large voids were atomic vacancy clusters exceeding 10% of the volume of the atomic model, and fracture was confirmed. Here, because a pure iron model was used in this example, due to the toughness of the metallic bond, brittle fracture did not occur along the crystal interface even after fracture, and some of the voids remained connected. However, since the stress-strain curve in Figure 4 confirmed that fracture had occurred, it was determined that fracture had occurred.

[0063] Furthermore, as can be seen from the visualized image in Figure 5, it is difficult to objectively evaluate whether or not cracks (atomic vacancy clusters) have formed by visual inspection alone. Furthermore, methods such as CPS, which perform analysis based on atomic coordinate data within an atomic model, cannot quantitatively calculate the size of cracks (atomic vacancy clusters).

[0064] Figure 6 shows the results of Voronoi tessellation performed using Ovito on the atomic model at maximum load, fracture initiation, and post-fracture, and displayed as Voronoi polyhedra. At maximum load, a region where the Voronoi polyhedra were slightly larger, i.e., a crystal interface, was observed. At fracture initiation, a cluster of Voronoi polyhedra larger than the Voronoi polyhedra on the crystal interface was observed. This cluster of large Voronoi polyhedra represents a single vacancy cluster, i.e., a crack. Additionally, in areas where vacancy clusters did not occur, continuous bonding was observed, confirming that no fracture had occurred. After fracture, elongated Voronoi polyhedra occupied most of the crystal interface. This indicates the formation of a crack and that the fracture occurred along the crystal interface.

[0065] The occurrence of cracks was evaluated from the frequency distribution of the Voronoi volume. In the Voronoi tessellation using Ovito, the Voronoi volume of each atomic point is displayed as a list and can be output as text data. A frequency distribution was obtained based on this data (first calculation step). In the first calculation step, known spreadsheet software may be used to obtain the frequency distribution. Here, the difference in Voronoi volume when creating the frequency distribution was set to 1 Å.

[0066] Figure 7 shows the Voronoi volume of the atomic model before tension, at maximum load, and after fracture, as well as the frequency distribution of the Voronoi volume. Looking at the overall picture of the frequency distribution, the frequency distribution before tension was 12 Å. 3 In addition to the presence of a broad peak (hereafter referred to as "peak 1") at 13 Å, 3 It was confirmed that the area around 13 Å was broad. 3 It is thought that a small peak (hereinafter referred to as the "second peak") is included in the vicinity. Here, "broad" means that the width is wide.

[0067] The crystal interface accounts for a few percent of the entire atomic model (see Figure 3). Furthermore, the atomic density is lower at the crystal interface compared to the bulk portion. This means that the Voronoi volume of the atoms that make up the crystal interface is larger than the Voronoi volume of the atoms that make up the bulk portion. It is thought that the information from the bulk portion dominates the first peak. Furthermore, since the sample was held at 300 K, the broadening of the peak is thought to be due to variations caused by thermal vibration. The second peak is thought to originate from the atoms that make up the crystal interface. In other words, the Voronoi volume corresponding to the first peak represents the average volume of the bulk portion. Furthermore, the Voronoi volume corresponding to the second peak represents the average volume of the crystal interface.

[0068] At the maximum load, it was confirmed that the first and second peaks shifted toward a larger Voronoi volume. The frequency of the first peak, i.e., the maximum number of atoms, decreased slightly. The frequency of the second peak, i.e., the maximum number of atoms, increased. The shift is thought to be due to the increased atomic spacing caused by the application of tensile deformation (elastic deformation). The change in the maximum number of peaks is thought to be due to the different degree of influence of elastic deformation between the bulk portion and the crystal interface.

[0069] After fracture, it was confirmed that the peak position, which had shifted at the maximum load, shifted again to the same position as the peak position before tension. It is thought that the resistance to deformation is lost upon fracture, returning to the same state as before tension when no stress was applied. 3 The large changes seen in the plot below are thought to be due to atomic disorder caused by plastic deformation of the fracture surface (see Figure 5).

[0070] Next, to analyze cracks, the researchers investigated the region with a Voronoi volume exceeding the average Voronoi volume of the crystal interface, which is the second peak. The number of Voronoi volumes exceeding the Voronoi volume of the second peak is small compared to the total number of atoms in the atomic model, making it difficult to grasp trends from the overall picture of the frequency distribution. Therefore, they focused on regions with a frequency of 20 or less.

[0071] As shown in the lower diagram of Figure 7, the post-fracture atomic model showed a broad region with a Voronoi volume larger than the Voronoi volumes of the first and second peaks, confirming the presence of a peak. Looking at the visualized post-fracture atomic model (Figure 6), this peak is thought to originate from a crack generated by the fracture.

[0072] In this way, by focusing on the frequency distribution of regions with larger Voronoi volumes than the first and second peaks, it is possible to determine whether or not atomic vacancy clusters, that is, cracks, have occurred on the crystal interface (analysis step).

[0073] Figure 8 shows the distribution of frequencies of less than 50 from before tension to the onset of fracture. When the plot for strain 0.00% is separated into two peaks, the Voronoi volume is 12.0 Å. 3 and 13.4Å 3 The peak is indicated by 12.0 Å. 3 The peak at 13.4 Å is in the bulk region. 3 The peak corresponds to the crystal interface. Comparing the plots for different strains, no significant changes were observed in the plots between strains of 0.00% and 9.46%. However, at 10.72% strain (see the right panel of Figure 4), which corresponds to the initiation of fracture, the shape of the plot clearly changed, with atoms with large Voronoi volumes appearing. This is thought to be a change corresponding to the formation of atomic vacancy clusters, i.e., cracks.

[0074] Figure 9 shows the maximum load, the frequency of fracture initiation and post-fracture fracture is less than 40, and the Voronoi volume is 60 Å. 3 The frequency distribution is shown below. The change in strain from maximum load to post-fracture was approximately 0.3%. In the example in Figure 9, the plot changes suddenly. At the onset of fracture, several dozen atoms were formed in total with Voronoi volumes slightly larger than the maximum Voronoi volume at maximum load, but smaller than the maximum Voronoi volume after fracture. When the atomic model was visualized (visualization step) and analyzed as in Figure 6, it was found that only one atomic vacancy cluster was formed (extraction step). The change in Voronoi volume distribution is thought to be the size of the crack that occurred when the load changed from maximum load to the onset of fracture. The Voronoi volume where the change was most noticeable was 20 Å. 3 The difference area of ​​the above region is calculated by numerical integration to be 1284 Å. 3 This is considered to be the size of the crack at the time of fracture initiation. Furthermore, assuming that the crack is an ellipsoid with an aspect ratio of 10, the diameter was calculated to be 14.5 Å. In other words, the characteristic length of the crack was calculated to be 14.5 Å (second calculation step). In this way, quantitative evaluation of the crack is possible in a simple manner.

[0075] By comparing the changes in the frequency distribution with the visualized atomic model, the positional relationship within the crystal interface where the cracks have occurred can be identified by a similar analysis, even when multiple atomic vacancies exist. Furthermore, by determining the ratio (relative size) of the size of each crack in the visualized model, it becomes possible to easily approximate the size of each crack.

[0076] As described above, the crack analysis method, program, materials design support method, and materials design method according to the present embodiment can easily and objectively analyze cracks on crystal interfaces through the above steps. That is, in atomic simulations that have conventionally been used mainly for understanding phenomena through model visualization, performing the above-described processing of deformation of the atomic model makes it possible to accurately determine whether or not cracks have occurred and to quantitatively analyze the cracks.

[0077] Although the embodiments of the present disclosure have been described based on the drawings and examples, it should be noted that those skilled in the art would easily be able to make various modifications or alterations based on the present disclosure. Therefore, it should be noted that these modifications and alterations are included within the scope of the present disclosure. For example, the functions included in each component or step can be rearranged so as not to cause logical inconsistencies, and multiple components or steps can be combined or divided into one. The embodiments of the present disclosure can also be realized as a storage medium on which a program executed by a processor included in an apparatus is recorded. It should be understood that these are also included within the scope of the present disclosure.

[0078] Here, the device (e.g., a computer) that executes the above-described method or program may not be a single device, but may be composed of multiple devices located in multiple locations and capable of transmitting and receiving data to and from each other via a network. In other words, multiple devices connected via a network may function as a whole as a device that executes the above-described method or program. Therefore, for example, the device that executes the above-described method or program may be composed of a single computer as a hardware configuration, or may be composed of multiple computers connected via a network. When composed of multiple computers, a shared memory accessible by each computer may be used to share data or programs.

Claims

1. A crack analysis method for analyzing a crack on a crystal interface by atomic simulation, comprising: an atomic model preparation step of preparing an atomic model including a crystal interface; a deformation step of deforming the atomic model; a first calculation step of performing Voronoi division on the atomic model before and after the deformation in the deformation step, and calculating a Voronoi volume and a frequency of the Voronoi volume; and analyzing the crack on the crystal interface based on the relationship between the Voronoi volume and the frequency of the Voronoi volume.

2. 2. The crack analysis method according to claim 1, wherein the analysis step performs peak separation on a waveform obtained by plotting the frequency of the Voronoi volume against the Voronoi volume, and determines that a peak having a Voronoi volume exceeding the Voronoi volume of the crystal interface is due to a crack on the crystal interface.

3. a visualization step of visualizing the atomic model before and after the deformation in the deformation step; an extraction step of extracting information about defects in the visualized atomic model; A crack analysis method as described in claim 1 or 2, further comprising a second calculation step of quantifying the crack and calculating a quantitative value based on the relationship between information about the defect and information about the crack on the analyzed crystal interface.

4. In order to analyze a crack on a crystal interface by atomic simulation, a computer that executes the atomic simulation is an atomic model preparation step of preparing an atomic model including a crystal interface; a deformation step of deforming the atomic model; a first calculation step of performing Voronoi division on the atomic model before and after the deformation in the deformation step, and calculating a Voronoi volume and a frequency of the Voronoi volume; an analysis step of analyzing cracks on the crystal interface based on the relationship between the Voronoi volume and the frequency of the Voronoi volume.

5. Calculating the size of the crack at the time of fracture initiation using the quantitative value calculated by the crack analysis method according to claim 3; and outputting a material design guideline based on the calculated crack size at the time of fracture initiation.

6. A material design method, comprising the step of designing the material in accordance with the design guidelines for the material output by the material design support method according to claim 5.

7. A crack analysis method as described in claim 1 or 2, wherein the atomic simulation uses a force field utilizing machine learning, and the force field is generated using learning data incorporating data on atomic structures in a precursor stage of crack generation.

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