JP5009222B2 - Method and apparatus for predicting deformation characteristics of polycrystalline material, program and recording medium - Google Patents

Description

  The present invention relates to a method and apparatus for predicting deformation characteristics of a polycrystalline material such as steel, aluminum, and magnesium, and a program and a recording medium.

Usually, metal materials such as steel, aluminum, and magnesium used as so-called structural materials are polycrystalline bodies composed of several component crystals called crystal grains.
On the other hand, the macroscopic mechanical properties such as tensile strength, yield stress, elongation, work hardening rate, and anisotropy of the material have a microscopic crystal structure, that is, individual crystal phase, crystal grain size, shape, crystal Influenced by orientation and distribution form. Therefore, the microscopic crystal structure described above is directly and indirectly measured using, for example, an optical microscope, an X-ray diffraction method, a backscattered electron diffraction (EBSD) method using a scanning electron microscope, and the like. To investigate the relationship with various mechanical properties.

Specifically, Patent Document 1 discloses a technique for reconstructing a crystal structure from measurement of crystal orientation by an EBSD method or the like.
In Patent Document 2, images before and after deformation of a crystal grain to be measured on a sample surface are acquired, a slip line angle and a crystal orientation on the sample surface are obtained, and predetermined values are obtained from the vertical and horizontal dimensions, area, slip line angle and crystal orientation of the grain boundary. A technique for calculating a three-dimensional strain tensor and plastic spin is disclosed.
In Patent Document 3, the deviation in crystal orientation of a plurality of measurement locations in each crystal grain of a sample in which plastic deformation occurs is measured to determine a two-dimensional change in orientation between a reference point and surrounding points, and plastic deformation In addition, a technique for specifying which deformation mode is fatigue damage, creep damage, or creep fatigue is disclosed.
Non-Patent Document 1 reports a technique in which a polycrystalline structure is discretized (mesh division) for each crystal grain and deformation analysis is performed by a finite element method.

JP 2003-121394 A JP 2004-317482 A JP-A-9-325125 Matsui et al .: Applied Mechanics Papers Vol. 5, pp. 175-183 (2002) EBSD Reader by TSL Solutions Inc. Matrix finite element method O.C.Zienkiwitz Baifukan

However, the conventional technique cannot predict macroscopic deformation characteristics directly for polycrystalline materials based on microscopic structure observation.
Specifically, in the method of Patent Document 1 described above, information such as crystal grain geometry, spatial distribution, orientation distribution, and the like can be obtained, but changes due to plastic deformation, that is, macroscopic mechanical characteristics of the polycrystalline material are directly related. Cannot be associated with.
In the technique of Patent Document 2, it is possible to measure macroscopically nonuniform deformation for each crystal grain at a relatively small deformation amount, but it can be directly correlated with the macroscopic deformation characteristics of the polycrystalline material. Can not. Further, in order to trace the behavior under large deformation such as destruction of the polycrystalline material, the local crystal grain deformation becomes very large, and it becomes difficult to associate (mapping) before and after the deformation. Furthermore, the observation of the crystal structure takes a long time from the preparation of the sample to the measurement, and the measurement at a plurality of stages of deformation requires a great deal of cost and time.

Moreover, since the technique of Patent Document 3 is a post-evaluation method for specifying a deformation mode from a microscopic structure of a polycrystalline material after plastic deformation, the mechanical properties are predicted from the initial structure of the polycrystalline material before deformation. It is not possible.
In the method of Non-Patent Document 1, if appropriate modeling is performed, the deformation behavior of a polycrystalline material can be predicted. However, it is very troublesome to discretize a complex polycrystalline structure (mesh division). In addition, there is a concern that the prediction results lack accuracy.

  The present invention uses crystal information of a polycrystalline material that has not undergone plastic deformation to quickly and reliably determine the uneven deformation state of the microstructure when the polycrystalline material has undergone macroscopic deformation. An object of the present invention is to provide a method and apparatus for predicting deformation characteristics of a polycrystalline material, a program, and a recording medium capable of predicting and accurately obtaining mechanical characteristics at the time of plastic deformation of the polycrystalline material.

  The deformation characteristic prediction method of the present invention is a method for predicting deformation characteristics of a polycrystalline material using crystal information of each measurement point obtained for a sample made of a polycrystalline material, and inputs the crystal information of each measurement point. Using the crystal information of the input measurement points, dividing the elements so as to correspond to the measurement points on a one-to-one basis, creating a discretization model, And performing a deformation analysis under a predetermined boundary condition.

  The deformation characteristic prediction apparatus of the present invention is a deformation characteristic prediction apparatus of a polycrystalline material using crystal information of each measurement point obtained for a sample made of a polycrystalline material, and uses the crystal information of each measurement point. Means for dividing the elements so as to correspond to the respective measurement points on a one-to-one basis and creating a discretized model; and means for performing deformation analysis under a predetermined boundary condition using the discretized model. Including.

  The program of the present invention includes a step of inputting the crystal information of each measurement point when performing a method for predicting deformation characteristics of a polycrystalline material using crystal information of each measurement point obtained for a sample made of a polycrystalline material. Using the crystal information of each of the input measurement points, dividing the elements so as to correspond to the measurement points on a one-to-one basis, creating a discretization model, and using the discretization model, And causing the computer to execute a step of performing deformation analysis under a predetermined boundary condition.

  According to the present invention, by using the crystal information of a polycrystalline material that has not undergone plastic deformation, a non-uniform deformation state of the microstructure when the polycrystalline material is subjected to macroscopic deformation can be quickly and easily performed. It is possible to reliably predict and accurately obtain the mechanical properties of the polycrystalline material during plastic deformation.

  In the present invention, the fact that crystal information for each measurement point (pixel) of a sample made of a polycrystalline material is obtained by the EBSD method or the like is used for creating, for example, a finite element when creating a discretized model. That is, using the crystal information for each pixel obtained from the EBSD method, etc., parameters (material parameters) of the stress-strain relational expression (constitutive model) are set, and element division is performed in a one-to-one correspondence with each pixel To create a discretized model. Then, deformation analysis of the sample is performed under a predetermined boundary condition using the obtained discretized model.

Hereinafter, specific embodiments to which the present invention is applied will be described in detail with reference to the drawings.
FIG. 1 is a block diagram showing a schematic configuration of the deformation characteristic prediction apparatus according to the present embodiment.
The deformation characteristic prediction apparatus 20 predicts the deformation characteristics of a polycrystalline material using crystal information of each pixel obtained by the EBSD method for a sample made of a polycrystalline material that has not undergone plastic deformation.

The deformation characteristic prediction device 20 includes a memory 1 that stores input data from the EBSD device 10, a finite element creation unit 2 that creates a finite element mesh (element) in the finite element method, and an element that sets material properties of each element. A material property setting unit 3, a deformation analysis unit 4 that performs deformation analysis by a finite element method, and a display unit 5 that displays state quantities obtained as a result of the deformation analysis as an image are configured.
Here, the finite element creation unit 2, the element material property setting unit 3, and the deformation analysis unit 4 are realized as functions of a central processing unit (CPU) of a computer, for example.

Hereinafter, the deformation characteristic prediction method will be described together with various functions of the deformation characteristic prediction apparatus 20.
FIG. 2 is a flowchart showing the deformation characteristic prediction method according to this embodiment in the order of steps.
In this embodiment, prior to predicting the shape characteristics of a sample made of a variable polycrystalline material, the sample is analyzed using the EBSD device 10 to obtain crystal information.

The EBSD device includes a scanning electron microscope (SEM) and analyzes a sample by the EBSD method.
An example of the orientation mapping image obtained by the EBSD device is shown in FIG. Here, the orientation of each pixel is colored according to the color key of the reverse pole figure, but in the example shown, it is displayed as a density difference. Normally, the characteristics are based on the distribution of primary information such as crystal information obtained by the EBSD method, specifically XY coordinate values, image quality (IQ) values, reliability indices (CI values), fit values, phase information, etc. Quantification, for example, crystal orientation distribution, average grain size, volume fraction of crystal phase, and the like are calculated and evaluated as characteristic values of the sample (see Non-Patent Document 2).

  In the present embodiment, a sample made of a polycrystalline material is analyzed by the EBSD device 10. In the numerical file indicating the analysis result, for example, crystal information is displayed as shown in FIG. Here, numerical values of items (1) to (10) are shown for each pixel as crystal information. Specifically, each item includes (1) to (3) crystal direction (for example, Euler angle), (4) to (5) XY coordinate value, (6) image quality (IQ) value, and (7) reliability index. (CI value), (8) fit value, and (9) to (11) phase information.

In this embodiment, first, crystal information of each pixel is input as an input process.
Specifically, the deformation characteristic prediction apparatus 20 sequentially reads the numerical values of the crystal information of the items (1) to (10) for each pixel as basic information together with basic information such as the number of pixels, and stores it in the memory 1 (step S1). ).

Subsequently, as a modeling process, using the crystal information for each pixel, the element is divided so as to correspond to each pixel on a one-to-one basis, thereby creating a discretized model.
Specifically, the finite element creation unit 2 uses the XY coordinates of each pixel stored in the memory 1 as the node coordinates, for example, as shown in FIG. 5, a list of node numbers (triangles in FIG. 5) constituting the elements. Create the number of the three nodes that make up the element). A distortion-displacement relationship matrix is created for each element from the node number list and the XY coordinates of the nodes (step S2). Here, when the pixels are arranged at regular intervals of equal intervals, for example, in the example of FIG. 5, all the elements are congruent equilateral triangles, and the load of creating a finite element mesh is remarkably reduced. .

Next, the element material property setting unit 3 determines the material property of the element, that is, the parameter (material parameter) of the stress-strain relational expression (constitutive model) based on the crystal information of the pixel corresponding to each node constituting the element. ) Is set (step S3).
Specifically, from the crystal information of the pixel corresponding to each node constituting the element, the crystal orientation and the crystal phase of the element are determined by, for example, averaging, and for each crystal phase obtained in advance. A discretization model is created by associating with a stress-strain relationship matrix.

Subsequently, as a deformation analysis step, a deformation analysis of the sample is performed under a predetermined boundary condition using a discretized model.
Specifically, if the strain-displacement relationship matrix and the stress-strain relationship matrix for each element are determined, the deformation analysis unit 4 follows the procedure of a normal finite element method shown in Non-Patent Document 3, for example. The displacement and reaction force of each node and the distortion and stress of each element are calculated through the creation of the above, the assembly of the entire stiffness matrix, the processing of boundary conditions, and the solution of simultaneous equations (step S4).
Here, for example, when considering only the elastic deformation of each crystal phase, it is only necessary to calculate the number of crystal phases in the stress-strain relationship matrix and the element stiffness matrix, and the load of the finite element analysis is remarkably reduced.

Subsequently, as an output process, a state quantity obtained as a result of the deformation analysis is displayed.
Specifically, the display unit 5 displays various information according to the purpose from the calculated state quantities, here, displacement of each node, reaction force, and distortion and stress of each element. As the display format, the display unit 5 is exemplified here as an image display device. However, instead of the image display, or together with the image display, for example, each data may be displayed in a table form.

For example, a macroscopic stress-strain relationship can be predicted from the relationship between the nodal displacement of the boundary side and the reaction force. Further, for example, by displaying the displacement and stress distribution, it is possible to specify in advance the portion of the microscopic tissue that is expected to be the starting point of the fracture.
All of the above steps can be automatically processed, and the user can predict the deformation characteristics of the sample on the spot while observing the microscopic tissue with a scanning electron microscope.

  As described above, according to the present embodiment, the microscopic information when the polycrystalline material is subjected to macroscopic deformation using the crystal information of the polycrystalline material not subjected to plastic deformation obtained by the EBSD method or the like. The uneven deformation state of the structure can be predicted quickly and reliably by a simple method, and the mechanical characteristics at the time of plastic deformation of the polycrystalline material can be accurately obtained.

  In the present embodiment, the case where the crystal information obtained by the EBSD method or the like is used for a sample that is a polycrystalline material has been described, but the present invention is not limited to this. For example, instead of performing the EBSD method, an image of an optical microscope or an electron microscope may be captured in a bitmap format. In this case, for example, using the obtained bit information such as the color and shading of each measurement point as crystal information, the bit information for each measurement point is associated with the finite element mesh, and the discretization as described above is performed. Create a model.

(Other embodiments to which the present invention is applied)
Functions such as each component (excluding the memory 1 and the display unit 5) constituting the deformation characteristic prediction apparatus according to the present embodiment described above can be realized by operating a program stored in a RAM or ROM of a computer. Similarly, each step (steps S1 to S5 in FIG. 2) of the deformation characteristic prediction method can be realized by operating a program stored in a RAM, a ROM, or the like of the computer. This program and a computer-readable storage medium storing the program are included in the present invention.

  Specifically, the program is recorded on a recording medium such as a CD-ROM or provided to a computer via various transmission media. As a recording medium for recording the program, besides a CD-ROM, a flexible disk, a hard disk, a magnetic tape, a magneto-optical disk, a nonvolatile memory card, or the like can be used. On the other hand, as the program transmission medium, a communication medium in a computer network system for propagating and supplying program information as a carrier wave can be used. Here, the computer network is a WAN such as a LAN or the Internet, a wireless communication network, or the like, and the communication medium is a wired line such as an optical fiber or a wireless line.

  Further, the program included in the present invention is not limited to the one in which the functions of the above-described embodiments are realized by the computer executing the supplied program. For example, such a program is also included in the present invention when the function of the above-described embodiment is realized in cooperation with an OS (operating system) or other application software running on the computer. Further, when all or part of the processing of the supplied program is performed by the function expansion board or function expansion unit of the computer and the functions of the above-described embodiment are realized, the program is also included in the present invention.

  For example, FIG. 6 is a schematic diagram illustrating an internal configuration of a personal user terminal device. In FIG. 6, reference numeral 1200 denotes a personal computer (PC) having a CPU 1201. The PC 1200 executes device control software stored in the ROM 1202 or the hard disk (HD) 1211 or supplied from the flexible disk drive (FD) 1212. The PC 1200 generally controls each device connected to the system bus 1204.

  By the program stored in the CPU 1201, the ROM 1202 or the hard disk (HD) 1211 of the PC 1200, the procedure of steps S1 to S5 in FIG.

  Reference numeral 1203 denotes a RAM which functions as a main memory, work area, and the like for the CPU 1201. A keyboard controller (KBC) 1205 controls instruction input from a keyboard (KB) 1209, a device (not shown), or the like.

  Reference numeral 1206 denotes a CRT controller (CRTC), which controls display on a CRT display (CRT) 1210. Reference numeral 1207 denotes a disk controller (DKC). The DKC 1207 controls access to a hard disk (HD) 1211 and a flexible disk (FD) 1212 that store a boot program, a plurality of applications, an editing file, a user file, a network management program, and the like. Here, the boot program is a startup program: a program for starting execution (operation) of hardware and software of a personal computer.

  Reference numeral 1208 denotes a network interface card (NIC) that exchanges data bidirectionally with a network printer, another network device, or another PC via the LAN 1220.

Based on the embodiment described above, an analysis example of deformation characteristics in which carbon steel is selected as a sample will be described.
FIG. 7 is a view showing a photograph of a secondary electron image of carbon steel as a sample.
This sample is a composite tissue material having a hard second phase. FIG. 8 shows the result of mapping the crystal phase by the EBSD method. In the conventional method, a statistic such as a volume fraction of the second phase and an average particle diameter of each phase is calculated from the mapping result and used as a material characteristic value.

In this embodiment, in FIG. 5, measurement is performed with a close-packed grid having a measurement pitch of 0.5 μm, and the measurement range is 100 μm × 100 μm (201 pixels × 232 pixels). Therefore, all elements are congruent equilateral triangles, and the displacement-strain relationship matrix is common to all elements.
Moreover, the equivalent stress (σ [MPa])-equivalent plastic strain (ε _ep [−]) relational expression in the plastic deformation of each phase was set as follows by a separate experiment.

First phase (soft phase): σ = 400 + 100 {1-exp (−10ε _ep )}
Second phase (hard phase): σ = 600 + 150 {1-exp (−10ε _ep )}

In the elastic region, as an isotropic elastic body, an elastic modulus E = 206 [GPa] and a Poisson's ratio ν = 0.3. FIG. 9 shows an example of the result of finite element analysis that gives a uniaxial tensile deformation with a macroscopic strain of 1% in the vertical direction of the paper after the above modeling. FIG. 9 shows the distribution of the equivalent plastic strain and shows how the strain concentrates around the hard phase. For example, it is possible to analyze in detail the microscopic tissue that is the starting point of destruction by measuring a region where distortion is concentrated in this display at a higher magnification.
An example of the equivalent stress strain corresponding to the distribution of the equivalent plastic strain in FIG. 9 is shown in FIG.

Further, FIG. 11 shows the relationship between displacement and reaction force obtained in the same manner as described above in this example. In FIG. 11, in the normal srtain (displacement (relative value)) on the horizontal axis, the end displacement / length (100 μm), and in the stress (reaction) on the vertical axis, the total of the end reaction / cross-sectional area (100 μm ² ). Respectively.

  In this example, the case where a specific part where non-uniform deformation occurs and strain concentrates is identified by modeling the work hardening characteristics of a two-phase structure having a hard second phase. The invention is not limited to this form. For example, by appropriately assigning arbitrary deformation characteristics to individual pixels, the deformation characteristics of various polycrystalline materials can be predicted in situ.

It is a block diagram which shows schematic structure of the deformation characteristic prediction apparatus by this embodiment. It is a flowchart which shows the deformation | transformation characteristic prediction method by this embodiment in order of a step. It is a figure which shows an example of the orientation mapping image obtained by the EBSD method. It is a figure which shows an example of the numerical value file obtained by the EBSD method. It is a schematic diagram which shows an example of the finite element mesh by a finite element method. It is a schematic diagram which shows the internal structure of a personal user terminal device. It is a figure which shows the photograph of the secondary electron image of the carbon steel which is a sample. In a present Example, it is a figure which shows the result of having mapped the crystal phase by EBSD method. It is a figure which shows an example of the result of having performed the finite element analysis in a present Example. It is a figure which shows an example of the equivalent stress distortion corresponding to distribution of equivalent plastic distortion. It is a characteristic view which shows the relationship between the displacement and reaction force in a present Example.

Explanation of symbols

DESCRIPTION OF SYMBOLS 1 Memory 2 Finite element creation part 3 Element material characteristic setting part 4 Deformation analysis part 5 Display part 10 EBSD apparatus 20 Deformation characteristic prediction apparatus

Claims (16)

A method for predicting deformation characteristics of a polycrystalline material using crystal information at each measurement point obtained for a sample made of the polycrystalline material,
Inputting the crystal information of each measurement point;
Using the crystal information of the input measurement points to divide the elements in a one-to-one correspondence with the measurement points, and creating a discretization model;
Performing a deformation analysis under a predetermined boundary condition using the discretized model. A method for predicting deformation characteristics of a polycrystalline material.   2. The method for predicting deformation characteristics of a polycrystalline material according to claim 1, wherein the crystal information of each measurement point obtained by a backscattered electron diffraction method is used for the sample.   The method for predicting deformation characteristics of a polycrystalline material according to claim 1 or 2, further comprising a step of displaying a state quantity obtained as a result of the deformation analysis.   The method for predicting deformation characteristics of a polycrystalline material according to any one of claims 1 to 3, wherein each of the measurement points has a regular period at regular intervals.   The method for predicting deformation characteristics of a polycrystalline material according to claim 1, wherein the deformation analysis is performed by a finite element analysis method. A device for predicting deformation characteristics of a polycrystalline material using crystal information of each measurement point obtained for a sample made of the polycrystalline material,
Means for dividing the element so as to correspond to each measurement point on a one-to-one basis using the crystal information of each measurement point, and creating a discretized model;
Means for performing deformation analysis under a predetermined boundary condition using the discretized model.   The apparatus for predicting deformation characteristics of a polycrystalline material according to claim 6, wherein the crystal information of each measurement point obtained by a backscattered electron diffraction method is used for the sample.   The apparatus for predicting deformation characteristics of a polycrystalline material according to claim 6 or 7, further comprising means for displaying a state quantity obtained as a result of the deformation analysis.   9. The polycrystalline material deformation characteristic prediction apparatus according to claim 6, wherein each of the measurement points has a regular period of equal intervals.   The deformation characteristic prediction apparatus for a polycrystalline material according to any one of claims 6 to 9, wherein the deformation analysis is performed by a finite element analysis method. When performing a method for predicting deformation characteristics of a polycrystalline material using crystal information at each measurement point obtained for a sample made of the polycrystalline material,
Inputting the crystal information of each measurement point;
Using the crystal information of the input measurement points to divide the elements in a one-to-one correspondence with the measurement points, and creating a discretization model;
A program for causing a computer to execute a deformation analysis under a predetermined boundary condition using the discretization model.   The program according to claim 11, wherein the crystal information of each measurement point obtained by a backscattered electron diffraction method is used for the sample.   The program according to claim 11 or 12, further causing the computer to execute a step of displaying a state quantity obtained as a result of the deformation analysis.   The program according to any one of claims 11 to 13, wherein each of the measurement points has a regular cycle at equal intervals.   The program according to any one of claims 11 to 14, wherein the deformation analysis is performed by a finite element analysis method.   The computer-readable recording medium which recorded the program of any one of Claims 11-15.