JP2004317482A - Method of analyzing three-dimensional plastic deformation - Google Patents

Abstract

<P>PROBLEM TO BE SOLVED: To provide a three-dimensional plastic deformation analyzing method including a three-dimensional plastic strain analyzing method for evaluating highly precisely a plastic deformation of a crystal grain. <P>SOLUTION: This three-dimensional plastic deformation analyzing method is effective for evaluating the deformation of a micro material having the reduced number of crystal grains, and effective for evaluating strength of an electronic device and a micro machine, since the plastic deformation is accurately evaluated based on both "a plastic strain" and "plastic rotation" by acquiring images before and after the deformation on a sample surface of the measured crystal grain, by finding a sliding line angle and a crystal direction on the surface of the measured crystal grain, by calculating six components of three three-dimensional vertical strain components ε<SB>x</SB>, ε<SB>y</SB>, ε<SB>z</SB>and three shearing strain components γ<SB>xy</SB>, γ<SB>yz</SB>, γ<SB>zx</SB>, by a prescribed calculation expression, based on longitudinal and lateral dimensions and an area of a grain boundary, the sliding line angle and the crystal direction, by finding a rotational amount (angle change) of a crystal based on a difference between the crystal directions before and after the deformation, and by calculating three plastic rotation components ω<SB>x</SB>, ω<SB>y</SB>, ω<SB>z</SB>by a prescribed calculation expression. The plastic deformation strain is integrally evaluated three-dimensionally even in the micro material having the reduced number of crystal grains to analyze accurately the plastic deformation as the material. <P>COPYRIGHT: (C)2005,JPO&NCIPI

Description

  The present invention relates to a three-dimensional plastic deformation analysis method including a three-dimensional plastic strain analysis method for evaluating three-dimensional plastic strain from two-dimensional observation data of crystal grains present on a sample surface. Plastic deformation is considered to be composed of plastic strain and plastic rotation.

  Generally, the deformation behavior of a polycrystalline metal material widely used as an industrial material is extremely complicated. This is because its plastic deformation is mainly constituted by a combination of non-uniform deformations occurring in individual crystal grains. Analytical or experimental studies have been conducted on the non-uniform deformation of grains, and individual grains exhibit different deformation behavior depending on the orientation, and they are bonded to each other via grain boundaries. It has been found that the deformation of the whole polycrystal is caused by the deformation, so that the deformation becomes non-uniform. Therefore, when discussing the plastic deformation behavior of a polycrystal, a method for accurately evaluating the deformation of individual crystal grains is required. In particular, the constituent materials of miniaturized electronic devices and micromachines are composed of a large number of micro-dimensional materials (fine wires and thin films). In these micro-dimensional materials, the number of crystal grains contained in the material is small, It is possible to accurately evaluate the deformation of the entire material from the evaluation of the deformation of the crystal grains.

  Conventionally, plastic deformation of crystal grains has been performed by observing the structure of the surface, and recent techniques applicable to the evaluation of strain of crystal grains include a backscattered electron beam diffraction (EBS) method and image processing. In the former EBSD method, a test piece is set in a scanning electron microscope (SEM), and the crystal orientation is determined from a diffraction image (Kikuchi line) of an electron beam obtained from the sample surface. If so, the azimuth can be easily measured. With the improvement of computer processing capability in recent years, even in polycrystalline metal materials, if about 100 crystal grains are present in a target area of about several mm, their orientation is evaluated within a practical time. You can do it. On the other hand, in the latter image processing, with the recent advances in image information processing technology, digital images captured in a computer are processed using various filters, and high-speed recognition of the size and shape of objects, statistical processing of them, etc. It is possible.

  Using the above-described evaluation method, the present inventors report on deformation of crystal grains (see Non-Patent Documents 1 and 2 below) and observe and evaluate plastic deformation of crystal grains in a two-dimensional plane (see the following patent documents). Reference 1 and Patent Reference 2) have been made.

Shimizu et al. Transactions of the Japan Society of Mechanical Engineers, "Free Surface Roughness and Grain Deformation Associated with Compressive Plastic Deformation of Polycrystalline Iron" (60,578.P201-208.1994) Shimizu et al. Transactions of the Japan Society of Mechanical Engineers, "3D Evaluation of Roughness of Free Surface of Aluminum Plate in Various Plastic Strain Paths" (67, 663, P1760-1767.2001) JP-A-7-294436 (paragraph 10) JP-A-9-325125 (paragraph 11)

  However, any of these observations of plastic deformation of crystal grains by observation of the microstructure of the sample surface does not reach the evaluation range in a two-dimensional plane, and has not led to a three-dimensional deformation analysis. In particular, in the case of a micro-dimensional material, the deformation of the entire sample may be greatly affected by the crystal grains, and it is necessary to perform the deformation analysis of the crystal grains with a high degree of three-dimensional accuracy.

  Accordingly, the present inventors have solved the above-mentioned problem of the conventional observation of plastic deformation of crystal grains, and have proposed a three-dimensional plastic strain analysis method including a three-dimensional plastic strain analysis method that enables the evaluation of plastic deformation of crystal grains with higher accuracy. An object of the present invention is to provide a deformation analysis method.

For this reason, the present invention provides a three-dimensional plastic strain analysis method for evaluating three-dimensional plastic strain from two-dimensional observation data of crystal grains present on a sample surface, and acquires images of a measured crystal grain before and after deformation on the sample surface. Then, the grain boundaries of the crystal grain to be measured are specified, the vertical and horizontal dimensions and area thereof are obtained by the number of pixels by image processing, the slip line angle and the crystal orientation on the surface of the crystal grain to be measured are obtained, and the vertical and horizontal dimensions of the grain boundary are obtained. The three components of three-dimensional vertical strain (ε _x , ε _y , ε _z ) and three components of shear strain (γ _xy , γ _yz , γ _zx ) are calculated from the area, the slip line angle and the crystal orientation by a predetermined calculation formula. It is characterized in that three-dimensional plastic strain in the crystal is evaluated by calculating the components. Further, the present invention is characterized in that the vertical and horizontal dimensions and area are obtained by an image using an optical microscope. Further, the invention is characterized in that the slip line angle is obtained by a scanning electron microscope. Further, the present invention is characterized in that the crystal orientation is determined by a backscattered electron diffraction (EBSD) method to specify a crystal slip plane. Further, the present invention acquires an image before and after deformation on the surface of the crystal grain to be measured, specifies a grain boundary of the crystal grain to be measured, and determines the vertical and horizontal dimensions and area of the crystal grain by the number of pixels by image processing. An image rotated by 45 ° is obtained before and after the deformation, and the vertical strain components (ε _x , ε _y ) are obtained by a predetermined calculation formula, and the shear strain γxy is obtained by another predetermined calculation formula. The present invention also provides a method for determining the amount of rotation (angle change) of a crystal from the difference between the crystal orientation before and after deformation determined by the backscattered electron diffraction (EBSD) method in the three-dimensional plastic strain analysis method, and calculating the plasticity by a predetermined calculation formula. By calculating the three rotation components (ω _x , ω _y , ω _z ), the three components of the three-dimensional plastic deformation are evaluated by adding the three components of the three-dimensional plastic rotation to the six components in the three-dimensional plastic strain. It is characterized by being evaluated. Further, the invention is characterized in that a three-dimensional plastic rotation is obtained from the rotation amount of each crystal. Further, the present invention is characterized in that the plastic strain and the plastic rotation of each of the crystals are simultaneously determined and compared with each other. Further, the present invention is characterized in that the angle of the crystal surface after deformation is evaluated from the plastic strain and plastic rotation of each crystal, and these are used as means for solving the problem.

According to the present invention, in a three-dimensional plastic strain analysis method for evaluating three-dimensional plastic strain from two-dimensional observation data of crystal grains present on the sample surface, obtain images of the measured crystal grains before and after deformation on the sample surface. Then, the grain boundaries of the crystal grain to be measured are specified, the vertical and horizontal dimensions and area thereof are obtained by the number of pixels by image processing, the slip line angle and the crystal orientation on the surface of the crystal grain to be measured are obtained, and the vertical and horizontal dimensions of the grain boundary are obtained. The three components of three-dimensional vertical strain (ε _x , ε _y , ε _z ) and three components of shear strain (γ _xy , γ _yz , γ _zx ) are calculated from the area, the slip line angle and the crystal orientation by a predetermined calculation formula. By calculating the components, the three-dimensional plastic strain in the crystal is evaluated.Thus, even for a small material with a small number of crystal grains, the plastic deformation strain can be comprehensively evaluated in three dimensions, and the Analysis of accurate plastic deformation has become possible.

  In addition, by acquiring the vertical and horizontal dimensions and area by using an image with an optical microscope, it is possible to easily specify the grain boundaries of the crystal grains to be measured using an existing microscope that is relatively widely used. Further, by acquiring the slip line angle with a scanning electron microscope, it is possible to easily acquire the angle of the slip line in the crystal grain with respect to the load axis for three-dimensionally evaluating the strain of the crystal grain. Furthermore, the crystal orientation is determined by the backscattered electron diffraction (EBSD) method, and the crystal slip plane is specified. By using this together with the image processing, the strain of each crystal grain present in the polycrystalline metal material is determined. It is possible to obtain the three-dimensionally.

Images of the crystal grains to be measured before and after deformation on the sample surface are obtained, the grain boundaries of the crystal grains to be measured are specified, and their vertical and horizontal dimensions and area are obtained by image processing using the number of pixels. ° The rotated image is acquired before and after the deformation, and the vertical strain components (ε _x , ε _y ) are obtained by a predetermined calculation formula, and γ _{xy is obtained} by another predetermined calculation formula, thereby further improving the accuracy. , Six strain components necessary for three-dimensional display can be obtained.

Further, the amount of rotation (angle change) of the crystal is determined from the difference between the crystal orientation before and after the deformation obtained by the backscattered electron diffraction (EBSD) method in the three-dimensional plastic strain analysis method. (Ω _x , ω _y , ω _z ) to evaluate the three-dimensional plastic deformation in the crystal by adding the three components of the three-dimensional plastic rotation to the six components of the three-dimensional plastic strain. Thus, it is possible to examine both the "strain", which is a shape change, which constitutes the plastic deformation of the crystal grains, and the "rigid rotation (plastic rotation)" of the crystal grains caused by the plastic deformation. Plastic deformation can be evaluated more accurately.

  Furthermore, by obtaining a three-dimensional plastic rotation from the rotation amount of each crystal, especially in the case of a small material having a small number of crystal grains, the evaluation of the plastic deformation of each crystal grain by the above-described method is used to evaluate the deformation of the entire material. Can be used. Further, according to the present invention, the plastic strain and the plastic rotation of each of the crystals are simultaneously obtained, and by comparing them, the inclination of the crystal grain after the plastic deformation can be obtained. Furthermore, by evaluating the angle of the crystal surface after deformation from the plastic strain and plastic rotation of each crystal, it is possible to easily predict the undulation of crystal grains on the material surface after deformation.

<Three-dimensional plastic strain analysis method>
Hereinafter, an embodiment of a three-dimensional plastic deformation analysis method including a three-dimensional plastic strain analysis and a plastic rotation analysis of the present invention will be described with reference to the drawings. First, a three-dimensional plastic strain analysis method will be described, since plastic deformation is considered to consist of plastic strain and plastic rotation. As shown in FIG. 1, in a three-dimensional plastic strain analysis method for evaluating three-dimensional plastic strain from two-dimensional observation data of crystal grains present on a sample surface, images of a measured crystal grain before and after deformation on the sample surface are acquired. Then, the grain boundary of the crystal grain to be measured is specified, the vertical and horizontal dimensions and area thereof are obtained by the number of pixels by image processing, the slip line angle and the crystal orientation on the surface of the crystal grain to be measured are obtained, and the vertical and horizontal dimensions of the grain boundary are obtained. From the dimensions, the area, the slip line angle and the crystal orientation, the three-dimensional vertical strain three components (ε _x , ε _y , ε _z ) and the shear strain three components (γ _xy , γ _yz , γ _zx ) are calculated by a predetermined formula. It is characterized in that three-dimensional plastic strain in a crystal is evaluated by calculating six components.

Hereinafter, the principle of the present invention and advantages based on experimental results will be described in detail. First, in the present invention, by effectively combining the two techniques of the backscattered electron beam diffraction method and the image processing described above, each of the elements that change with the tension of the polycrystalline copper, which usually stays in two-dimensional evaluation, is changed. A method for three-dimensionally evaluating the plastic strain of crystal grains is proposed and experimentally verified. <Experiment and observation method>
The tensile test was carried out using a flat test piece of polycrystalline copper shown in FIG. The test material was an industrial pure copper rolled plate (purity 99.5%, plate thickness 1.00 mm), and the rolling direction was the longitudinal direction of the test piece. In the present invention, before the tensile test, first, the surface of the test piece was mirror-finished by mechanical polishing using # 2000 Emily paper and diamond paste having a particle size of 1 μm. Next, vacuum annealing (annealing temperature: 600 ° C., holding time: 1 h, furnace cooling) is performed, and further, after removing an oxide film on the surface of the test piece by electrolytic polishing, chemical corrosion is performed so that crystal grain boundaries can be identified. I made it.

  In the present invention, a square area of 500 μm × 500 μm was set at the center of the parallel part of the test piece shown in FIG. 2, and the deformation and the crystal orientation of the crystal grains existing in the area were measured. The tensile test was performed using a 200 kg sample tensile tester manufactured by Hitachi. The tensile test was interrupted at each stage where the macroscopic strain ε of the test piece was 0.03, 0.07 and 0.10, and various observations were made after unloading. Was carried out. In addition, the macroscopic load strain of the test piece was evaluated in advance by indenting an indentation in the center of the test piece using a microhardness tester (MVK-H0 manufactured by Akashi) and changing the interval. Indentations were made at six points in the longitudinal direction of the test piece at intervals of 500 μm, and four points at 500 μm intervals in the direction perpendicular to the longitudinal direction.

<Observation of crystal grains and measurement of crystal orientation>
In the present invention, two types of microscopes were used for observing the crystal grains present on the surface of the test piece. First, an optical microscope was used to evaluate the two-dimensional strain of each crystal grain. An image of the specimen surface observed by an optical microscope was taken into a computer, and the image was binarized. Thereafter, a Hilditch thinning process was performed to make the width of the grain boundary line one pixel, and the shape and the like of each crystal grain were evaluated from the final image. A method for evaluating distortion from an image will be described later. Next, the angle of the slip line in the crystal grain with respect to the load axis (slip line angle) was measured from an image taken using a scanning electron microscope. The slip line angle is necessary when three-dimensionally evaluating the strain of the crystal grain. Details will be described later. On the other hand, the crystal orientation analysis was performed by the EBSD method using a Link Opal system manufactured by Oxford Corporation installed in an S-3500N scanning electron microscope manufactured by Hitachi. Details of the measurement method have already been reported in a separate report. It has been confirmed that the crystal grain boundaries obtained from the above-mentioned optical microscope images are consistent with the EBSD results.

<Evaluation method of plastic strain of crystal grains>
The vertical and shear strains in the material surface and the vertical strain in the depth direction will be described. Generally, assuming that the strain in the material is a minute strain, the strain at an arbitrary location is defined by six components of ε _x , ε _y , ε _z , γ _xy , γ _yz , and γ _zx . In the present invention, the vertical strain and shear strain ε _x , ε _y , γ _xy within the material surface and ε _z , the vertical strain in the direction perpendicular to the surface (depth direction), are subjected to image processing of crystal grains. Determined from the results. The remaining shear strains in the depth direction, γ _yz and γ _zx, were separately determined by taking into account the constraints on the plastic deformation of the crystal grains. FIG. 3 shows a scanning electron microscope image after a typical crystal grain deformation within the measurement range. However, in the drawing, the crystal grain boundaries are shown by thin lines for easy understanding. As can be seen from the figure, a slip line appears in each crystal grain almost uniformly throughout the crystal grain, and the direction of the slip line is almost the same. This indicates that the deformation of the crystal grains is caused by the slip deformation of a single slip system.

In the present invention, the following assumptions are made regarding the plastic deformation of each crystal grain.
(1) Plastic deformation of each crystal grain occurs uniformly within the crystal grain.
(2) The plastic deformation of each crystal grain is incompressible, and the volume does not change before and after the deformation.
(3) The slip surface of the slip deformation generated in each crystal grain has the same orientation, and no multiple slip occurs.
In the present invention, first, based on the assumptions (1) and (2), strains ε _x , ε _y , and γ _xy are obtained as follows. As shown in FIG. 4, an xyz coordinate system including a load axis direction (x axis), a direction perpendicular to the load axis direction (y axis), and a z axis perpendicular to both directions, and an xyz coordinate system (hereinafter referred to as xyz coordinate system) , Xy coordinate system), an x'y'z coordinate system (hereinafter referred to as an x'-y 'coordinate system) rotated by 45 ° around the z-axis is considered. It is the strain of each axial x-y coordinate system epsilon _x and ε _{y, x'-y} 'strain in which epsilon _x and epsilon _y direction of each axis of the coordinate system determined by the following equation.

式（１）〜（４）の各項は以下で与えられる画像に関する情報量である。
Ｎｘ￣＝Ｎｔ／ｌｙ：ｘ軸方向の平均画素数
Ｎｙ￣＝Ｎｔ／ｌｘ：ｙ軸方向の平均画素数
Ｎｘ’￣＝Ｎｔ／ｌｙ’：ｘ’軸方向の平均画素数
Ｎｙ’￣＝Ｎｔ／ｌｘ’：ｙ’軸方向の平均画素数
ここで、Ｎｔ ：結晶粒内の総画素数
ｌｘ ：ｘ軸方向の最大長さ
ｌｙ ：ｙ軸方向の最大長さ
ｌｘ’：ｘ’軸方向の最大長さ
ｌｙ’：ｙ’軸方向の最大長さ
ただし、添字に０が付いている項は、各量の変形前の量であり、例えば、Ｎｘ￣（ただし、Ｎｘ￣はＮｘの算術平均を表しており、バーＮｘのことで、数式以外の文章では便宜的にＮｘ￣で表している。以下の同様の表記についても同じ）の場合は、Ｎt0￣／ｌyoとなる。また、ｌｘ、ｌｙ、ｌｘ’、ｌｙ’は、画素の大きさを基準長さとする無次元化長さとする。ｌｘが３画素分の長さであればｌｘ＝３となる。

Each term of the expressions (1) to (4) is the information amount regarding the image given below.
Nx￣ = Nt / ly: average number of pixels in the x-axis direction
Ny￣ = Nt / lx: average number of pixels in the y-axis direction
Nx′￣ = Nt / ly ′: average number of pixels in the x′-axis direction
Ny′￣ = Nt / lx ′: average number of pixels in the y′-axis direction
Here, Nt: total number of pixels in a crystal grain
lx: Maximum length in x-axis direction
ly: maximum length in the y-axis direction
lx ': Maximum length in x' axis direction
ly ′: the maximum length in the y′-axis direction. However, the term with 0 added to the subscript is the quantity of each quantity before deformation. For example, Nx￣ (where Nx￣ is the arithmetic mean of Nx In the case of a sentence other than a mathematical expression, it is expressed as Nx￣ for convenience, and the same applies to the following notation.), Nt0￣ / lyo. In addition, lx, ly, lx ′, and ly ′ are dimensionless lengths having the pixel size as a reference length. If lx is three pixels long, lx = 3.

Next, the flow of the procedure of the three-dimensional plastic strain analysis method of the present invention will be described with reference to FIG. (1) The sample is compared between the initial state and the state after deformation (such as a tensile test). The observation surface of the sample is in a state where the crystal grain boundaries can be identified. (2) Obtain an image by observing the surface with an optical microscope or an electron microscope, determine crystal grains to be measured, perform grain boundary extraction and binarization image processing. The same processing is performed on images obtained by rotating the same crystal grains before and after deformation by 45 ° in the same plane. (3) With respect to the deformed target crystal grain, a slip line angle and a crystal orientation on the crystal grain surface are determined by a scanning electron microscope and backscattered electron diffraction. From the above (1) and (2), three components of vertical strain (ε _x , ε _y , ε _z ) and a shear strain component (γ _xy ) are calculated. From (3) and (4), the shear strain components (γ _yz , γ _zx ) are calculated.

An image of a crystal grain to be measured is acquired by an optical microscope, a grain boundary is specified, and dimensions before and after deformation and the number of pixels entering the crystal grain boundary are obtained by image processing. Assuming that the number of pixels entering the crystal grain and the lengths in the x-axis and y-axis directions are Nt0, lx0, and ly0 before deformation and Nt, lx, and ly after deformation, ε _x and ε _y are obtained by the above equations (1). (2). In this concept, as a first step, deformation in the surface of a crystal grain is captured. At this time, the area on the surface does not change (the number of pixels; Nt0 does not change), and the vertical and horizontal lengths change. In the second step, the area change (Nt, lx, ly) on the surface is grasped assuming that the volume of the crystal grain before and after plastic deformation does not change. It is considered that the depth dimension has changed by the area change. Since similarity deformation and volume conservation are assumed, each term is multiplied by ２.

Next, the vertical strain component ε _z is determined based on the law of volume conservation in plastic deformation. Then, the slip plane in the crystal grain is identified. The slip surface of the crystal grain surface is identified by a scanning electron microscope. The crystal orientation is measured by the backscattered electron diffraction (EBSD) method, and the active slip surface is identified from these. The slip line angles θ and ξ (described later) are obtained. Next, the shear strain components γ _xy , γ _yz , and γ _zx are determined. Perform more accurate calculation of γ _xy . Data obtained by rotating the strain evaluation of the crystal grain orientation by 45 ° is acquired. The calculation formula is the same, and (ε _x , ε _y ) is obtained, and then γ _xy is obtained.

Equations (1) to (4) will be described with reference to the schematic diagram relating to crystal grain deformation shown in FIG. FIG. 5A shows crystal grains before deformation, and FIG. 5B shows crystal grains after deformation. In the present invention, as shown in the figure, the slip deformation is a deformation in the xy plane from FIG. 5A to FIG. 5B and a vertical deformation in the z-axis direction from FIG. 5B to FIG. It is considered in two stages c). Here, γ _yz and γ _zx, which are shear strains in the vertical direction with respect to the test piece surface, are not considered, but all other components can be separated into these two stages. The deformation shown in FIGS. 5 (a) to 5 (b) is a deformation assuming that there is no strain ε _{z in} a direction perpendicular to the surface of the test piece. Be composed. Now, since it is assumed that ε _z = 0 in the deformation from FIG. 5A to FIG. 5B, the area of the crystal grains on the surface of the test piece (the hatched portion in the drawing) is under deformation. It is immutable. Therefore, when the aspect ratio (the ratio of the length in the x-axis direction to the length in the y-axis direction) is changed, the change is twice the rate of change in the length in the x-axis (or y-axis) direction. Therefore, 1/2 of the change in the aspect ratio is the vertical strain in each axial direction, and this corresponds to the first term of the equations (1) to (4). Here, even if the same amount is obtained between FIG. 5 (a) and FIG. 5 (c), which is the final crystal grain shape after deformation, here, the aspect ratio (the length in the x-axis direction and the y-axis direction) is obtained. 5 (a) to FIG. 5 (b), since the change of the ratio of the height is calculated.

  Next, the deformations shown in FIGS. 5B to 5C will be considered. In this deformation, the shape of the crystal grains on the surface of the test piece does not change, but the size changes. Now, according to the assumption (2) regarding the deformation described in the paragraph (paragraph 0014), since the volume conservation law is established in each crystal grain, the area change rate of the crystal grain on the surface (Nt−Nto) / Nto is calculated by the crystal. This corresponds to εz which is a vertical strain in the depth direction of the grains. Furthermore, since it is assumed that the shape of the crystal grains is not changed in the transformation from FIG. 5B to FIG. 5C, (Nt−Nt0) / Nt0 is multiplied by 、. This is the vertical strain in each of the x and y axis directions at this deformation stage. As described above, a method of obtaining the strain in the direction perpendicular to the area change rate from the rate of change of the area has been conventionally proposed when obtaining the vertical strain in the depth direction of the crystal grain.

以上、ひずみε_x 、ε_y 、ε_z 、γ_xyを求める手法について説明してきたが、その妥当性については、数値的に作成した種々の形状の結晶粒に関して確認している。本手法の特徴の一つとして、ひずみの計算に変位の測定結果を用いていないことが挙げられる。通常は、ひずみを評価する領域内、あるいは、その近傍に基準点を設け、そこから各点の変位を測り、その変位の変化に基いてひずみを計算するが、本発明では、ひずみの算出にそのような基準点の設定が不要であるため、画像処理を用いてひずみを計算する場合には便利である。 Shear strain gamma _xy is the strain in the x-axis direction epsilon _x of the test piece in the surface, by the following equation using the strain epsilon _{x 'axial'} x in the coordinate system 'y-axis direction of the strain epsilon _y, and x'-y Desired.

The method of _obtaining the strains ε _x , ε _y , ε _z , and γ _xy has been described above, and the validity has been confirmed for crystal grains of various shapes created numerically. One of the features of this method is that it does not use displacement measurement results for strain calculation. Normally, a reference point is provided in or near the area where strain is evaluated, the displacement of each point is measured therefrom, and the strain is calculated based on the change in the displacement. Since it is not necessary to set such a reference point, it is convenient when calculating distortion using image processing.

<Evaluation method of shear strain in depth direction>
It is not possible to calculate γ _yz and γ _zx , which are the shear strains of the crystal grains in the direction of the inside of the test piece only by changing the outer shape of the crystal grains on the material surface. Therefore, in the present invention, the slip plane of each crystal grain is specified using the angle θ of the slip line with respect to the load axis observed by the SEM and the result of the crystal orientation obtained by the EBSD method. Thereafter, γ _yz and γ _zx are calculated in consideration of the mechanical deformation constraint on the specified slip surface. The specific method is shown below.

<Determination of the slip surface>
It is generally known that {111} plane is an active slip plane in face-centered cubic lattice (fcc) metal. Therefore, when the orientation of a certain crystal grain is measured by the EBSD method, (111), (−111), (−1−11), and (1−11) of the crystal grain (where − is a negative value) The orientation of the four slip planes is clarified, and the angle between the line of intersection of each slip plane and the surface with the load axis, that is, the slip line angle can be determined at the same time. FIG. 6 schematically shows the geometric relationship between the load axis, the slip surface, and the slip line. In the present invention, four slip surface candidates are considered for all the crystal grains present in the measurement region, and the slip line angle θ, which is the intersection of each slip and the test piece surface, is calculated. Among the four slip surface candidates, those having the closest angle to the slip line observed by SEM were estimated as active slip surfaces. The difference between the actual slip line angle θ and the slip line angle estimated from the EBSD method was small, and was at most about 5 °. The three-dimensional azimuth of the active slip surface is clarified by the above process, and ξ, which is the angle in the depth direction of the active slip surface shown in FIG. 6, is obtained. Details of ξ will be described later.

<Restriction in plastic deformation of each crystal grain>
Now, as shown in FIG. 7, a case is considered where plastic deformation of a certain crystal grain is constituted by slips of a large number of slip surfaces in the same direction. In the figure, n is a unit normal vector of the active slip plane, and m is a unit vector in the slip line direction. M ′ is a unit direction vector related to the intersection of y = 0 and the slip surface. Therefore, m and m 'are both unit direction vectors perpendicular to n. Since it is assumed that the plastic deformation of the crystal grains is completely constituted by the slip deformation between the slip surfaces, the crystal grains undergo only shear deformation parallel to the slip surfaces, and ε which is the vertical strain in the n, m, and m ′ directions _n , ε _m , and ε _{m '} are all 0. Therefore, the following equation is established.

試験片表面内のせん断ひずみγｘｙは式（５）からも求められるので、両式から求めたγｘｙを比較することで仮定した変形が実際の塑性変形において生じているか否かを確認することができる。また、ε_x 、ε_y 、ε_z 、γ_xy、γ_yzおよびγ_zxの結晶粒の塑性ひずみの６成分が既知であれば、ひずみテンソル[ ε_ij ]の固有値、固有ベクトルから主ひずみと主ひずみ方向も三次元的に求められる。 Therefore, the shear strains γ _xy , γ _yz , and γ _zx of the crystal grains are expressed by the following equations using the slip line angles θ, ξ and the vertical strains ε _x , ε _y , ε _z in the x, y, and z directions. Required.

Since the shear strain γxy in the surface of the test piece is also obtained from the equation (5), it is possible to confirm whether or not the assumed deformation occurs in the actual plastic deformation by comparing γxy obtained from both equations. . If the six components of the plastic strain of the crystal grains of ε _x , ε _y , ε _z , γ _xy , γ _yz and γ _zx are known, the principal strain and the principal strain are obtained from the eigenvalues and eigenvectors of the strain tensor [ε _ij ]. The direction is also obtained three-dimensionally.

<Experimental results and discussion>
<Confirmation of assumed deformation mode of crystal grains>
As described above, in the present invention, it is assumed that the plastic deformation of each crystal grain is constituted by the slip of a large number of slip surfaces in the same direction, and the constraint in the depth direction is obtained by using the constraint condition expression regarding the deformation derived from the assumption. Shear strains γ _yz and γ _zx were determined. Here, since the shear strain γ _{xy on the} surface of the test piece is obtained from both the equations (5) and (9), if the two agree, the actual crystal grains are deformed in the assumed deformation mode. This will support that. FIG. 8 shows the result of comparison between the two. In the figure, the horizontal axis represents the shear strain obtained from equation (5) as γ _xy BMP, and the vertical axis represents the shear strain γ _xy obtained from equation (9). Note that the results are divided according to the range of 22.5 ° ≦ θ ≦ 67.5 ° and the ranges of θ <22.5 ° and 67.5 ° <θ, as can be seen from Expression (9). Since γ _xy includes terms of 1 / tan θ and tan θ, the error of γ _xy increases when θ is near 0 ° and 90 °.

Therefore, when the angle θ is close to both angles, γ _xy was calculated using the angle θ ′ evaluated based on the xy coordinate system described above. The accuracy is improved in the same way for γ _yz that will appear in the following _sections . As can be seen from the figure, the values of γ _xy calculated from both equations (5) and (9) are in good agreement, indicating that the assumed deformation mode is realized for almost all crystal grains. I can say. Note that, among the plotted results, those having relatively low correlation (relative error of 5 ° or more) are indicated by ●, but these were often small crystal grains. This is presumably because the smaller the crystal grains, the more the deformation is not uniform, and the deformation by the single slip system assumed in this analysis is not strictly established.

Therefore, in the following sections, only the data indicated by a circle having a high correlation with respect to γ _xy was adopted. FIG. 8 shows only an example in which ε = 0.07 as an example. However, data having a low correlation with other load strains are almost small crystal grains. Of the 150 crystal grains present in the observation region, after applying each load strain, the number of crystal grains in which a slip line was clearly observed was 123 at ε = 0.03, 123 at ε = 0.07, It was 121 when ε = 0.10. By the extraction of γ _xy and γ _{x′y ′} , finally, the remaining strain of 103 crystal grains at ε = 0.03, 97 at ε = 0.07, and 91 at ε = 0.10. Evaluation was possible.

<Distribution of each plastic strain component of crystal grains>
FIG. 9 shows changes in six components of plastic strain of crystal grains. The bars in the vertical direction for each strain in the drawing indicate the maximum value and the minimum value of the strain for the crystal grain for which the strain could be evaluated, that is, the range of the strain variation. Also, among the crystal grains whose strain could be evaluated up to ε = 0.10, ten typical crystal grains are shown by broken lines so that the change of the strain component in the same crystal grain can be understood. As can be seen from the figure, the average value of the strain ε _x in the load axis direction (x-axis direction) shows a linear increase while the value of each crystal grain increases and decreases as the strain increases. In the vertical strain ε _z in the depth direction, the average value shows a linear decrease while the value of each crystal grain increases and decreases. On the other hand, the average value of the strain ε _{y in} the direction perpendicular to the load axis in the surface of the test piece is almost zero. Therefore, it can be said that the crystal grains elongated in the direction of the load axis maintain a certain volume mainly by shrinking in the depth direction. Next, looking at the changes in the shear strain components γ _xy , γ _yz , and γ _zx shown in FIGS. 9D, _9E , and _9F , the values of the respective shear strains increase with an increase in the load strain. And some that decrease are mixed in, and some that repeatedly increase and decrease exist. However, the average value is almost zero and constant.

<Principal strain of crystal grain and distribution of principal strain direction>
FIG. 10 shows the change in the maximum principal strain of each crystal grain. However, as in FIG. 9, the bars in the vertical direction indicate the maximum value and the minimum value of the strain, and ten typical crystal grains are connected by broken lines. Similarly to the vertical strain ε _{x in} the load axis direction shown in FIG. 9A, the maximum principal strain increases almost linearly with an increase in the macroscopic load strain. FIG. 11 shows a three-dimensional distribution in the principal strain direction. Here, the circles in the figure indicate the positions of the tips of the unit vectors on the xyz coordinate system, and the right halves of (a), (b), and (c) in the figures are the projection points on the xy plane, and the left half. The half shows the projection point on the yz plane. It can be seen that on any of the xy plane and the yz plane, the principal strain direction tends to be in the direction of the load axis as the macroscopic load strain increases.

  FIGS. 12 and 13 show the change in the principal strain direction in more detail. The distribution of angles θxy and θzx that the principal strain direction component makes with the load axis in the surface of the test piece (xy plane) and the depth direction of the test piece (zx plane) is shown. Both results show that the principal strain direction is directed to the load axis direction with the increase in macroscopic load strain, but the principal strain direction is directed to the load axis direction in the specimen surface and in the specimen depth direction. There is a difference in the tendency, and it can be seen that the principal strain direction tends to quickly shift toward the load axis direction on a plane perpendicular to the surface. This is probably because one of the crystal grains existing on the free surface is the material surface, and there is a difference between the constraint between adjacent crystal grains and the deformation constraint in the depth direction in the deformation on the test piece surface.

<Conclusion>
The present invention proposes a method for three-dimensionally obtaining the strain of each crystal grain present in a polycrystalline metal material by using a backscattered electron diffraction (EBSD) method and image processing together, and also proposes a number of the proposed methods. Applied for tensile of crystalline copper. The results obtained can be summarized as follows. (1) Six components of plastic strain of each crystal grain ε _x , ε _y , ε _z , γ _xy , γ _yz , γ _zx (x is the load axis direction, xy plane is the test piece surface, z is the test piece surface In the normal direction), the four components of ε _x , ε _y , ε _z , and γ _xy are based on the image information of the crystal grains, and the other two components γ _yz and γ _zx are single-slid with the orientation information of the crystal grains It is obtained by considering the constraints of plastic deformation by the system.

(2) ε _x , ε _y , ε _z , and γ _xy are obtained by changing the length ratio of each crystal grain in the x and y directions and rotating the x and y axes by 45 ° about the z axis. In addition to the change in the ratio of lengths with respect to the x 'and y' axes, which are directions, the change was obtained from the change in the total number of pixels of each crystal grain.
(3) γ _yz and γ _zx are obtained by assuming that the plastic deformation of each crystal grain is caused by the slip of a large number of slip surfaces in the same direction, and the angle of the slip surface with respect to the load axis and the strain obtained in (2). I asked. The active slip plane of copper used in the present invention (one of the four {ll} planes) was determined by observation of slip lines with a scanning electron microscope and EBSD method.

  (4) As a result of three-dimensionally evaluating the strain of each crystal grain in tension of polycrystalline copper using the above-described method, the strain of each crystal grain varies greatly, but on average, the expected macroscopic strain is obtained. This is consistent with the tendency of the mechanical strain to increase or decrease. Also, with the increase of the macroscopic strain of the test piece, the direction of the maximum principal strain tends to gather in the direction of the tensile load axis, and the tendency is more in the zx plane (test piece surface) than in the xy plane (test piece surface). (The plane perpendicular to the surface) was stronger. This is presumably because one of the crystal grains existing on the surface of the test piece is a free surface, and there is a difference in the state of deformation constraint between adjacent crystal grains in the surface of the test piece and in a plane perpendicular thereto.

<3D plastic rotation analysis method>
In the present invention, the rigid rotation component (plastic rotation) of crystal grains necessary for accurately describing plastic deformation was evaluated, and the relationship between plastic rotation and plastic strain in each crystal grain was examined. In addition, regarding the validity of the evaluation method and results, using a surface shape measurement microscope, separately, whether the measured surface inclination angle of each crystal grain shows a good correspondence with the result predicted from plastic strain and plastic rotation or not It was examined by.

<Experimental method>
The test material was an industrial pure copper rolled plate (purity: 99.5%, plate thickness: 1.0 mm). As shown in FIG. This was mechanically polished, and the surface of the test piece was mirror-finished, vacuum annealing (annealing temperature: 873 K, holding time: 1 h, furnace cooling) and electrolytic polishing were performed. Oxide film and fine polishing scratches were removed. Furthermore, chemical corrosion was performed so that the grain boundaries could be distinguished. The tensile test was performed using a 200 kg sample tensile tester manufactured by Hitachi, and the tensile test was interrupted at two stages of macroscopic strain ε of the test piece of 0.03 and 0.07, and various measurements were performed after unloading. The measurement was performed on a square area of 500 μm × 500 μm at the center of the parallel part of the test piece. In this report, only the results when the macroscopic strain is 0.03 are shown due to space limitations. However, even when the macroscopic strain is 0.07, almost the same results are obtained in the distribution of the plastic strain and the plastic rotation. Was done. The macroscopic strain of the test piece was evaluated from the change in the distance between the indentations before the deformation, by using a micro hardness tester MVK-H0 manufactured by Akaashi to strike six indentations at 500 μm intervals in the longitudinal direction.

  In the evaluation of strain and rotation used in the present invention, images of crystal orientation and crystal grains before and after deformation of each crystal grain are required. First, the crystal orientation was measured by the EBSD method using an Oxford Link Opal system installed in a Hitachi S-3500N scanning electron microscope. The measurement of the crystal orientation by the EBSD method is performed at about 10,000 points at intervals of 5 μm by automatic scanning of an electron beam, and the analysis accuracy of the crystal orientation evaluated from the diffraction diagram has an allowable error of 0.1 [deg]. Next, the image acquisition of the crystal grain was performed using the surface shape measurement microscope VF-7500 made by KEYENCE. At that time, the image capturing magnification was 2500 times, and the image resolution was 28.364 pixels / cm. As will be described later, a total of 191 crystal grains were present in the measurement area. However, in the present invention, a crystal grain whose distortion number can be measured with high accuracy has a pixel number of 10000 or more as an evaluation target. .

Furthermore, in the present invention, in order to confirm that the obtained plastic strain and plastic rotation of each crystal grain are appropriate, the tilt angle of the crystal grain surface expected from the strain and rotation was compared with the tilt angle measured separately. . For measuring the inclination angle of the surface of the test piece, the same surface shape measuring microscope as that used for acquiring the image of the crystal grains was used, and the surface was measured at intervals of 10 μm in the x-axis and y-axis directions of the test piece coordinates shown in FIG. Shape measurement was performed. Next, from the relative displacement in the z-axis direction within the same crystal grain, the expression of the approximate plane of the crystal grain surface is obtained by the least square method, and the inclination angles θ _x and θ _y in the x-axis and y-axis directions with respect to this approximate plane are determined. I got it.

<Plastic deformation of crystal grains>
<Plastic strain and plastic rotation>
FIG. 15 shows a model relating to plastic deformation of crystal grains. The x'y'z 'and x "y" z "coordinate systems shown in the figure are crystal coordinate systems before and after deformation, and the xyz coordinate system is a macroscopic test piece coordinate system. Considering the case where the amount is very small, plastic deformation is generally represented by the displacement gradient tensor ∇ _j u _i, which as possible Te separated into further strain tensor epsilon _ij and the rotation tensor omega _{ij.
∇ j u i = ε ij +} ω ij
Here, ε _ij is a symmetric tensor component of the displacement gradient tensor, and ω _ij is an anti-symmetric tensor component. Therefore, ε _ij is represented by six independent components, and ω _ij is represented by three independent components. Here, when each component of ε _ij and ω _ij is represented by a general engineering notation, (ε _x , ε _y , ε _z , γ _xy / 2, γ _yz / 2, γ _zx / 2) and (ω _x , ω _y , ω _z ), and if all these nine components are obtained for each crystal grain, the plastic deformation is completely described three-dimensionally. In the present invention, the former six components are referred to as “plastic strain”, and the latter three components are referred to as “plastic rotation”.

  In general, microdeformation in continuum mechanics can be represented by “strain”, which indicates a change in the outer shape (degree of distortion) of the forest material, and “rotation”, which indicates the rigid rotation of the forest material without changing the outer shape, for example, copper. When applied to the plastic deformation of fcc metal materials such as the above, as shown in FIG. 15, the plastic deformation is caused by "plastic strain" constituted by shear deformation between slip surfaces in crystal grains and slip between slip surfaces. In other words, the crystal grains are entirely rotated without causing “plastic rotation”. Regarding the former, a new strain evaluation method for three-dimensionally identifying the active slip surface by observation of the test piece surface and the EBSD method is proposed, and the evaluation can be performed by that. On the other hand, although the latter can be evaluated almost directly from the crystal orientation measurement results by the EBSD method, the plastic rotation of each crystal grain has not yet been studied in detail, and the plastic strain The correlation between each component of の and each component of plastic rotation is not discussed. In the present invention, both plastic strain and plastic rotation are evaluated for a large number of crystal grains present in the observation region, and the relationship between them is considered.

<Evaluation method for plastic strain>
The three-dimensional plastic strain (ε _x , ε _y , ε _z , γ _xy , γ _yz , γ _zx ) of the crystal grain is calculated based on the assumption in paragraph 0019 above regarding the plastic deformation of the crystal grain. That is,
(1) The plastic deformation of each crystal grain is incompressible, and no volume change occurs before and after the deformation. (2) The plastic deformation of each crystal grain is caused by slip deformation and occurs uniformly within the crystal grain. (3) The slip surface of the slip deformation generated in each crystal grain has the same orientation, and multiple slips on a plurality of slip surfaces do not occur.
When the above assumption is satisfied, the vertical distortion component can be calculated from the above equations (1) and (2) and the following equation.
ε _z = (N _t −N _t0 ) / N _t0
Here, N _x ￣ and N _yで are the average number of pixels of the crystal grains in the x-axis and y-axis directions, respectively, and N _t is the total number of pixels. However, the term with 0 added to the subscript is the quantity before deformation. These amounts can all be obtained by image processing of the observation results of the test piece surface.

On the other hand, in addition to the above-described vertical strains ε _x and ε _y , the shear strain γ _xy in the surface of the test piece is obtained by calculating the vertical strain ε ₄₅ in a coordinate system obtained by rotating the z-axis of the xyz coordinate system by 45 ° counterclockwise. The vertical strain in the three directions can be calculated using the following equation.
γ _xy = −ε _x −ε _y + ε ₄₅
Further, the shear strains in the inward direction of the test piece, γ _yz and γ _zx , identify the active slip surface three-dimensionally by the EBSD method and the observation result of the slip line on the test piece surface, and the equations (10) and (11) Can be calculated using
Note that θ and ζ in the equations are the angles of the active slip surface.

<Evaluation method of plastic rotation>
The x'y'z 'and x "y" z "coordinate systems shown in Fig. 15 are crystal coordinate systems before and after deformation, and can be directly obtained from the results of crystal orientation measurement by the EBSD method. undeformed x'y'z a crystal coordinate system 'coordinate system as a reference coordinate system, the basic vector e _x', plastic rotation from the rotation angle before and after deformation of e y _'and e _z' ω _x, ω _y and evaluating the omega _z. FIG. 16 crystal coordinate system x'y'z 'and x "y" z "and the relationship of plastic rotation of each crystal grain. First, referring to FIG. 16 (a), the considered angles of z "of the axial unit vector e _z". In the figure, γ is the angle formed by ez _″ with the z ″ axis, γ ₁ is the angle formed by the orthogonal projection of ez _″ onto the z′x ′ plane, and γ ₂ is the y formed by ez _″ . This is the angle that the orthographic projection on the 'z' plane makes with the z 'axis. Now, since a small plastic deformation is assumed, γ, γ ₁ and γ ₂ are very small, and the gradients of displacement ∂ux _′ / ∂z ′, ∂uy _′ / ∂z ′ and ∂uz _′. / ∂z ′ is represented by the following equation (12).

Similarly, displacement gradients of the basic vector ε _{x ′} shown in FIG. 16B and the unit vector ε _{y ′} shown in FIG. 16C are expressed by the following equations (13) and (14).

さらに、本発明では、全ての結晶粒に関する塑性回転を同じ試験片座標系で評価するために、上式で求めた各結晶粒の結晶座標系を基準とする塑性回転（ε_x'，ε_y'，ε_z'）を、座標変換マトリックスを用いて試験片座標系ｘｙｚに関する塑性回転（ε_x ，ε_y ，ε_z ）に変換した。 Using the angles γ ₁ , γ ₂ , α ₁ , α ₂ , β ₁ , and β ₂ defined above, the plastic rotation in the x′y′z ′ coordinate system (ε _{x ′} , ε _{y ′} , ε _{z ′} ) Is obtained by the following equation (15).

Further, in the present invention, in order to evaluate the plastic rotation of all the crystal grains in the same specimen coordinate system, the plastic rotation (ε _{x ′} , ε _y) based on the crystal coordinate system of each crystal grain obtained by the above equation is used. _', epsilon _z' a), was converted plastic rotated about the test piece coordinate system xyz using the coordinate transformation matrix (ε _x, ε _y, the epsilon _z).

Next, the flow of the procedure of the three-dimensional plastic deformation analysis method of the present invention, which is composed of three-dimensional plastic strain analysis and three-dimensional plastic rotation analysis, will be described with reference to FIG. (1) The sample is compared between the initial state and the state after deformation (such as a tensile test). The observation surface of the sample is in a state where the crystal grain boundaries can be identified. (2) Obtain an image by observing the surface with an optical microscope or an electron microscope, determine crystal grains to be measured, perform grain boundary extraction and binarization image processing. The same processing is performed on images obtained by rotating the same crystal grains before and after deformation by 45 ° in the same plane. (3) With respect to the deformed target crystal grain, a slip line angle and a crystal orientation on the crystal grain surface are determined by a scanning electron microscope and backscattered electron diffraction. From the above (1) and (2), three components of vertical strain (ε _x , ε _y , ε _z ) and a shear strain component (γ _xy ) are calculated. From (3) and (4), the shear strain components (γ _yz , γ _zx ) are calculated, and the rotation three components (ω _x , ω _y , ω _z ) are calculated by calculating the change in crystal orientation angle.

<Experimental results and discussion>
<Distribution of grain boundaries and twin boundaries>
FIG. 17A shows an optical microscope image before deformation of the entire 500 μm × 500 μm square area which is the measurement range. However, in the figure, the crystal grain boundaries and twin boundaries of the crystal grains to be measured this time are complemented by thin lines for easy understanding. As can be seen from the figure, the shape of the crystal grains is relatively simple, but the portion surrounded by the twin boundaries has a linear and elongated shape. FIG. 17 (b) shows an optical microscope image of typical crystal grains after a plastic deformation of macroscopic strain ε = 0.03 is given by tension. In the crystal grains a and c, the slip lines are uniform and appear almost over the entire surface of the crystal grains. On the other hand, in the crystal grain b, a slip line cannot be clearly observed even after deformation. The boundary between crystal grains b and c can be determined as a twin boundary in the crystal orientation distribution diagram described in the next section, but the directions of slip lines in both crystal grains are different from each other. In the present invention, based on the above observation results, the twin boundaries were treated in the same manner as ordinary crystal grain boundaries, and the portion surrounded by any one of the boundaries was evaluated as strain, etc., as one crystal grain.

<Crystal orientation map>
FIG. 18 shows a crystal orientation distribution diagram in the normal direction of the specimen surface and in the load axis direction before the deformation (initial state) and after the tensile plastic deformation of macroscopic strain ε = 0.03. The shades of the crystal orientation distribution map correspond to the shades of the inverse pole figure shown in the figure. As can be seen from the figure, the orientation is substantially constant within the same crystal grain before and after the deformation, and the boundary portion having a different orientation coincides with the crystal grain boundary obtained in FIG. Although not so large, a change in the orientation of the crystal grains is also observed.

<Relationship between plastic strain of crystal grains and plastic rotation>
FIGS. 19 and 20 show the relationship between the three-dimensional plastic strain of the crystal grains and the plastic rotation after applying the tensile plastic deformation of macroscopic strain ε = 0.03. 19 shows the relationship between the vertical strain component and rotation, and FIG. 20 shows the relationship between the shear strain component and rotation. Here, in the data in both figures, the slip line can be clearly observed, and the depth angle of the identified active slip surface is in the range of π / 8 ≦ | ζ | ≦ 3π / 8. Here, the reason why the value of the angle ζ is limited is that when the angle ζ takes a value of 0 or a value near π / 2, as is clear from the equations (10) and (11), a slight This is because the error appears as a large difference between the evaluation values of γ _yz and γ _zx . There are 125 crystal grains having a surface prime number of l0000 or more in the observation area shown in FIG. 17 (a), and those satisfying the above-mentioned criteria regarding the slip line and the slip plane angle are: There are 105, and only the results for these are shown in FIG.

As can be seen from FIG. For each crystal grain, the components of vertical strain and plastic rotation vary greatly, but there is no clear correlation between the two. The average values of the vertical strains ε _x , ε _y , ε _z were 0.026, −0.008, and −0.018, respectively. Because it does not cover all crystal grains in the region, although there are some differences, the average value of epsilon _x indicates a value close to 0.03 which is the strain macroscopic tensile plastic. The average values of the plastic rotation components ω _x , ω _y , ω _z were 0.008, 0.001, and 0.006, respectively, which were almost zero. As in FIG. 19, no clear correlation is seen between the components of the shear strain and the plastic rotation shown in FIG. From this figure, the mutually complementary relationship between γ and ω is such that the change in the outer shape angle of the object caused by the shear deformation predicted from the conventional simple single-crystal plastic deformation model is compensated by the rigid body rotation. It can be seen that this is not always the case with plastic deformation. Further, when the average values of the shear strains γ _xy , γ _yz and γ _zx of the crystal grains were respectively obtained, they were 0.001, 0.001 and 0.003, respectively, which were almost 0, and were almost 0. The result almost coincides with the macroscopic deformation state.

<Surface inclination angle of crystal grains>
As schematically shown in FIG. 21, under the small deformation, if the six components of the strain and the three components of the rotation in the target area are determined, the displacement gradient in the area can be obtained. In the crystal grains present on the surface of the test piece studied in the present invention, the components of strain and rotation evaluated in the previous section, θ _x and θ _y , which are the surface tilt angles of the x- and y-axis directions of each crystal grain surface Γ _zx / 2−ω _y and γ _yz / 2 + ω _x . In the present invention, both the surface inclination angles obtained from the plastic strain and the plastic rotation were compared with θ _x and θ _y separately measured using a surface shape measurement microscope. The relationship between the surface inclination angle theta _x and γ _zx / 2-ω _y in FIG. 22, respectively the relationship between the surface inclination angle theta _y and γ _yz / 2 + ω _x in FIG. Since the surface of each crystal grain is approximated to one plane, the correlation is not so good. However, γ _zx / 2−ω _y and θ _x and γ _yz / 2 + ω _x and θ _y have a substantially equal relationship. You can see that. This indicates that the evaluation result is appropriate if the method for evaluating plastic strain and plastic rotation of crystal grains used in the present invention is Δ.

<Conclusion>
The present invention proposes a method for three-dimensionally obtaining the plastic rotation of each crystal grain present in a polycrystalline metal material using a backscattered electron beam diffraction (EBSD) method. Applied to the pull of The results obtained can be summarized as follows.
(1) A method for evaluating the plastic rotation (ω _x , ω _y , ω _z ) of crystal grains using the measurement results of the crystal orientation by the EBSD method was proposed. When combined with the above-described method of evaluating plastic strain ((ε _x , ε _y , ε _z , γ _xy , γ _yz , γ _zx )), all nine components necessary for expressing microdeformation of crystal grains are evaluated. It became possible.
(2) As a result of examining the relationship between the plastic strain of the crystal grains and the plastic rotation, no clear correlation was found between the two. This is because the complementary interaction between γ _ij and ω _k is such that the change in the outer shape angle of the object caused by the shear deformation predicted from the conventional simple single-crystal plastic deformation model is compensated for by the rigid body rotation. This shows that this is not necessarily true in plastic deformation of polycrystal.
(3) In order to examine the evaluation method of plastic strain and plastic rotation and the validity of the evaluation result, the surface inclination angle that can be estimated from the plastic strain and plastic rotation of each crystal grain was compared with a separately measured value. As a result, the correspondence between the two was good, and the validity of the proposed method was confirmed.

As described above, the embodiments of the present invention have been described. However, within the scope of the present invention, an image acquisition mode before and after deformation of crystal grains (an appropriate similar image acquisition mode other than an optical microscope may be adopted), Selection of the number of pixels at the time of image processing for obtaining the vertical and horizontal dimensions and area for specifying the grain boundaries of the crystal grains to be measured, the acquisition form of the slip line angle (appropriate similar equipment other than the scanning electron microscope can be adopted) ), The form of obtaining the crystal orientation for specifying the crystal slip plane (an appropriate similar method may be employed in addition to the method obtained by the backscattered electron diffraction method), the vertical strain components (ε _x , ε _y ), and the shear strain γ _The form of calculation for obtaining _xy , the form of obtaining the amount of rotation (angle change) of the crystal, and the form of calculating the three components of plastic rotation (ω _x , ω _y , ω _z ) can be appropriately selected. In addition, the format of the plastic deformation microscope (scanning electron microscope and, if necessary, the optical microscope) as a means for quantitatively grasping and visualizing the plastic deformation of the crystal grains, and the format of the crystal orientation analysis device and the image processing device are as follows. Can be selected as appropriate. In addition, the specifications of the experimental apparatus are illustrative, and should not be construed as limiting.

It is a flow figure about a procedure of a three-dimensional plastic strain analysis method of the present invention. It is a figure which shows the flat plate test piece of polycrystalline copper used for the same tensile test. FIG. 3 is a scanning electron microscope image after deformation of the crystal grain, showing a slip line in the crystal grain. FIG. 4 is a diagram related to a coordinate system when the test piece is rotated around the z-axis by 45 °. FIG. It is a schematic diagram of the geometric relationship between the load axis, the slip surface, and the slip line. FIG. 3 is a diagram showing a plastic deformation state of a crystal grain formed by a large number of slip surfaces. FIG. 7 is a diagram showing the result of comparing the actual deformation of crystal grains with the assumed deformation mode. FIG. 6 is a diagram showing changes in six components of plastic strain of crystal grains. FIG. 4 is a graph showing the change of the maximum principal strain of each crystal grain. It is a three-dimensional distribution diagram of the same principal strain direction. FIG. 4 is a detailed view of the change in the principal strain direction, which is a result diagram in the xy plane as a test piece. It is a result figure in the zx plane which is the same as the test piece depth direction. It is a flow figure about a procedure of a three-dimensional plastic deformation analysis method including a three-dimensional plastic strain analysis method of the present invention. FIG. 4 is a schematic diagram relating to crystal grain plastic deformation. FIG. 4 is a diagram showing the relationship between the crystal coordinate systems x′y′z ′ and x ″ y ″ z ″ and the plastic rotation of each crystal grain. FIG. 3B is an optical microscope image of the entire square area before deformation and an enlarged image after deformation. FIG. 3 is a crystal orientation distribution diagram of a test piece surface normal direction and a load axis direction after plastic deformation is applied. FIG. 4 is a diagram showing the relationship between vertical distortion components and rotation. FIG. 4 is a diagram showing the relationship between a shear strain component and rotation. FIG. 4 is a diagram showing the relationship between the inclination angle of the crystal grain surface and the test piece coordinate system. Same, it is a relationship diagram of the surface inclination angle theta _x and γ _zx / 2-ω _y. Same, it is a relationship diagram of the surface inclination angle theta _y and γ _yz / 2 + ω _x.

Claims (9)

In a three-dimensional plastic strain analysis method for evaluating three-dimensional plastic strain from two-dimensional observation data of crystal grains present on the sample surface, an image of the measured crystal grain before and after deformation on the sample surface is obtained, The vertical and horizontal dimensions and area of the grain boundary are determined by the number of pixels by image processing, and the slip line angle and crystal orientation on the surface of the crystal grain to be measured are determined, and the vertical and horizontal dimensions, area and slip line angle of the grain boundary are determined. By calculating the three components of three-dimensional vertical strain (ε _x , ε _y , ε _z ) and three components of shear strain (γ _xy , γ _yz , γ _zx ) from the crystal orientation and a predetermined calculation formula, A three-dimensional plastic strain analysis method characterized by evaluating three-dimensional plastic strain in a crystal. The three-dimensional plastic strain analysis method according to claim 1, wherein the vertical and horizontal dimensions and the area are obtained by an image using an optical microscope. The three-dimensional plastic strain analysis method according to claim 1, wherein the slip line angle is obtained by a scanning electron microscope. The three-dimensional plastic strain analysis method according to any one of claims 1 to 3, wherein the crystal orientation is determined by a backscattered electron beam diffraction (EBSD) method to specify a crystal slip plane. Obtain images before and after deformation of the crystal grain to be measured on the sample surface, specify the grain boundary of the crystal grain to be measured, and determine the vertical and horizontal dimensions and area by the number of pixels by image processing. The obtained image is obtained before and after the deformation, the vertical strain components (ε _x , ε _y ) are obtained by a predetermined calculation formula, and the shear strain γ _{xy is obtained} by another predetermined calculation formula. 4. The method for analyzing three-dimensional plastic strain according to any one of 4. A rotation amount (angle change) of the crystal is determined from a difference between before and after the deformation of the crystal orientation obtained by a backscattered electron diffraction (EBSD) method in the three-dimensional plastic strain analysis method according to claim 4 or 5, and a predetermined calculation is performed. By calculating the three components of plastic rotation (ω _x , ω _y , ω _z ) according to the formula, the three components of three-dimensional plastic rotation are evaluated by adding the three components of three-dimensional plastic rotation to the six components in three-dimensional plastic strain. A three-dimensional plastic deformation analysis method characterized by evaluating plastic deformation. The three-dimensional plastic deformation analysis method according to claim 6, wherein a three-dimensional plastic rotation is obtained from the rotation amount of each crystal. 8. The three-dimensional plastic deformation analysis method according to claim 6, wherein a plastic strain and a plastic rotation of each of the crystals are obtained simultaneously and compared with each other. The three-dimensional plastic deformation analysis method according to claim 6, wherein an angle of the crystal surface after the deformation is evaluated from the plastic strain and the plastic rotation of each crystal.

Images