Three-dimensional Grain and Grain Boundary Morphology and Size Distribution of 316L Stainless Steel

Abstract:

Three-dimensional characterization of grains and grain boundaries is significant to study the microstructure of polycrystalline materials, and is the key to advance the subject of three-dimensional materials science (3DMS). In this work, the technique of serial sectioning by mechanical polishing coupled with 3D electron backscatter diffraction (3D-EBSD) mapping was used to measure the microstructure of a 316L stainless steel in 3D. Volume of the collected 3D-EBSD microstructure is 600 μm×600 μm×257.5 μm, which is quite large to study the 3D microstructure of structural materials with conventional grain size (20~60 μm). Dream3D and in-house developed Matlab programs were used to process the 3D-EBSD data, and subsequently ParaView was used to visualize the grains and grain boundaries in 3D. Combined usage of these tools and in-house programs make the possibility that not only 3D grains but also 3D grain boundaries can be studied in both morphology and quantification. In total, 1840 grains and 9177 grain boundaries are included in the measured 3D-EBSD microstructure. The 3D morphological characteristics and size distributions of grains and grain boundaries in the 316L stainless steel were investigated, including 3D grain size, grain surface area, boundary quantity per grain, grain boundary size and the average boundary size per grain, as well as relationships between these morphological parameters were discussed. Results showed that distributions of all of these morphological parameters of 3D grains and grain boundaries in the polycrystalline 316L stainless steel can be well represented by log-normal distribution, and all relationships of these parameters versus grain size can be well represented by power function. Additionally, the 3D morphologies of most grains in the 316L stainless steel deviate from the ideal equiaxed grains, having complex shapes due to existing of twins, such as semi-sphere shaped, plate shaped and some very complex grains. In many ways, the larger grains have more complex morphology with greater number of faces, larger surface area and larger deviation from equiaxed grains.

Key words316L stainless steel ; 3D-EBSD ; 3D microstructure ; 3D grain ; 3D grain boundary
Tingguang LIU1,2, Shuang XIA2, Qin BAI2, Bangxin ZHOU2
1 National Center for Materials Service Safety, University of Science and Technology Beijing, Beijing 100083, China
2 School of Materials Science and Engineering, Shanghai University, Shanghai 200072, China

Microstructure analysis occupies an important position in the study of materials science and is a bridge to build the relationship between the structure and properties of materials. However, most of the current microscopic analysis techniques can only observe and analyze the two-dimensional (2D) cross-section of the material and cannot obtain comprehensive three-dimensional (3D) microstructure information [1], which may bring uncertainties to the research results. Sex. For example, the grain shape should be similar to the polyhedron, but it is shown as a polygon in the 2D cross-section. The exact grain size and the number of crystal interfaces cannot be obtained. For example, if the grain boundary network connectivity problem is interrupted, the connectivity of the random grain boundary network is interrupted. The use of grain boundary engineering techniques [2,3,4] to improve the grain boundary related performance of the material [5], 2D simulation study [6] obtained the special grain boundary ratio threshold when the random grain boundary network connectivity is interrupted It is about 0.5, and the result of the 3D simulation study [7] is about 0.8. In addition, the exact research on trifurcation angle and quadrangular angle can only be carried out in 3D space. The 3D microscopic characterization technology is a major challenge to further promote the development of materials science.
In recent years, with the progress of experimental technology and computer technology, 3D characterization and research of material microstructures has become possible, and the concept of 3D material science (3DMS) has been proposed [1]. The traditional method of 3D microstructure preparation is “mechanical polishing to prepare continuous section and metallographic microscope (3D-OM)” [8], but this method can only obtain 3D topography information; 3D microstructure orientation analysis is currently the study It is important to be able to obtain grain, grain boundary, phase, and other orientation-related information, such as grain orientation, grain boundary re-site lattice characteristics (CSL), etc., through orientation analysis. Commonly used 3D orientation imaging techniques are continuous section methods combined with electron backscatter diffraction (3D-EBSD) [9,10,11,12,13,14] and three-dimensional X-ray diffraction imaging (3D-XRD) [15, 16,17,18,19]. In general, continuous cross sections are prepared using a focused ion beam (FIB) called the “FIB-EBSD” technique [9, 10, 11]. This method has developed an automatic 3D microstructure acquisition method that can automatically work for several days, but The disadvantage of the method is that the observation area is very small, the size in any direction is difficult to exceed 100 μm, while the grain size of ordinary metal structure materials is 40 to 100 μm; another method is to use mechanical polishing to prepare a continuous section, combined with EBSD The acquisition of orientation information [12,13,14] has the disadvantages of low automation, heavy workload, and poor polishing control accuracy. However, the observation area is almost unlimited, enabling large-scale 3D analysis. 3D-XRD techniques include high energy diffraction imaging (HEDM) [15,16,17], diffraction contrast tomography (DCT) [18] and variable aperture X-ray imaging (DAXM) [19]. The advantage is that 3D information can be obtained without destroying the sample, but it requires the use of high-energy ray and other complex and valuable equipment.
The current major 3D microstructure research results obtained are knowledge of 3D grains. First, the 3D grain morphology can be equivalent to a polyhedron, the 3D grain size distribution obeys the lognormal distribution [8, 20, 21], and the average crystal grain number of the grains is 12 to 14 [8, 20~23 ]. In addition, Lind et al. [15] comparatively studied the size of 3D grain clusters (twinned regions) processed by grain boundary engineering and common pure Cu, indicating that the grain clusters in grain boundary engineering process materials are significantly larger than those of common materials. Marrow et al. [24] studied the 3D morphology of intergranular stress corrosion cracking; Zaefferer et al. [10] studied the 3D phase structure and crystal orientation of carbon steel and other materials. However, there are few reports on the 3D grain boundary, such as grain boundary morphology, grain boundary size, and poor grain boundary orientation.
This work uses mechanical polishing to prepare continuous section combined with EBSD technology to collect large-size 3D microstructures of 316L stainless steel, analyze the 3D grain and 3D grain boundary morphology characteristics and their size distribution, and establish the quantification between grain and grain boundary. relationship.
1 Experimental method
The materials used in this study were normal 316L stainless steel, chemical composition (mass fraction, %): Cr 16.26, Ni 10.10, Mo 2.08, C 0.028, Si 0.47, Mn 1.03, P 0.044, S 0.005, Fe balance. The initial state of 316L stainless steel is rapidly quenched by 50% hot rolling at 1000°C; it is then annealed, and then quenched by rapid water quenching at 1000°C for 0.5 h to obtain a fully recrystallized state of the experimental material. The size is cut using a wire saw. It is a 15 mm x 10 mm x 20 mm sample.
The 3D microstructure of 316L stainless steel was collected using “continuous cross-section combined with electron backscatter diffraction (EBSD) technology”. The flow was as follows:
(1) Preparation of continuous section by mechanical polishing: The polished surface is a 10 mm x 20 mm surface of the specimen, using a 40-7920 type polishing cloth and a 40-6377-064 type Al2O3 suspension at a fixed pressure load (about 15 N) and Grind and turn for 20 min at 100 r/min, and the pressure should be evenly applied to the sample to ensure that the grinding layer does not tilt, and finally obtain a polished polished surface with no strain layer, and EBSD acquisition can be directly performed. The amount (sample thickness reduction) is about 2.5 μm. After the following three steps were performed, the surface of the sample was polished again using the same method. This was repeated, and it was called a continuous section method.
(2) Grinding amount measurement: After each polishing, the thickness of the sample is measured with a micrometer with a measuring accuracy of 1 μm to obtain the thickness of each grinding layer. The desired grinding amount is 2.5 μm.
(3) Positioning of the collection area: Mark the area of interest on the polished surface with a micro-hardness indentation, as shown in Fig. 1a. The depth of the indentation needs to be guaranteed not to disappear after each polishing and then pressed in the original position after each polishing. New indentation.
(4) EBSD acquisition: After each polishing, orientation information of the region of interest was acquired using EBSD configured on a CamScan Apollo 300 Field Emission Scanning Electron Microscope (FESEM). The acquisition region size was 600 μm × 600 μm in steps of 2.5 Μm. To ensure that the specimen is not rotated and tilted relative to each FESEM, the relative position of the specimen in FESEM (such as working distance, etc.) must be consistent.
Repeat the above steps to obtain 101 layers of 2D EBSD data. The expected thickness of each layer is 2.5 μm, the actual measured value is 1 to 5 μm, the most is 2 to 3 μm, the average thickness is 2.55 μm, and the reconstructed 3D The microstructure size is 600 μm×600 μm×257.5 μm.
3D-EBSD data processing is another key point and difficulty in 3D microstructure characterization. In this work, a variety of software and self-programming programs are used to perform 3D microstructure analysis. First use Dream3D [23,25~27] to perform 3D reconstruction on acquired 2D continuous section EBSD data, then use ParaView[28] for 3D visualization, which can display overall 3D organization, cross-section organization, grain boundary network, 3D grain and 3D grain boundary. In the process of 3D reconstruction using Dream3D, different crystal grains can be identified, and the information such as the size, crystal orientation, shape parameters, number of adjacent crystal grains, and the like of each crystal grain can be obtained and output; in addition, multiple programs are written using Matlab. The program can calculate the surface area, grain boundary area, etc. of each crystal grain, and identify the twin boundaries among them, thereby realizing the analysis and size distribution of the 3D grain and grain boundary characteristics.
2 experimental results
2.1 3D-EBSD Reconstruction
In this work, 3D-EBSD images were constructed using the lapping process. Although the precision of the layer spacing control was low (2.5±1) μm), the grain size relative to that of ordinary austenitic stainless steels (such as the average grain size of 316L stainless steel used in this work) With a grain size of 31 μm, the control accuracy is relatively high. This method can be used to construct large-size 3D microstructures, and statistically analyze the morphology and size of 3D grains and grain boundaries.
Figure 1b is a 3D-EBSD micrograph of the reconstructed 316L stainless steel, size 600 μm × 600 μm × 257.5 μm, corresponding in the Z-direction (thickness direction) crystal direction in the standard inverse pole figure (IPF) color code The color is colored for each crystal grain; FIG. 1c is a cross-sectional view of 3 vertical directions (XYZ) arbitrarily selected from FIG. 1b; FIG. 1d is a grain boundary network diagram of a partial region, and is based on the orientation difference angle for each grain boundary Coloring, the grain boundary network is a honeycomb structure. The 3D microstructure contains 1840 grains (including 891 grains cut by the outer surface), and the average grain size (equivalent sphere diameter) is 28.4 μm; there are 9177 grain boundaries, and the average grain boundary area is 637.1 μm 2 . Figure 1e shows the 101D 2D EBSD microstructure. It can be seen that the 316L stainless steel contains a large number of twin boundaries (Σ3 boundary, 54%).
20180615071834 97739 - Three-dimensional Grain and Grain Boundary Morphology and Size Distribution of 316L Stainless Steel

Fig.1
Reconstructed 3D-EBSD microstructures of a 316L stainless steel sample
(a) schematic of specimen and mark for EBSD mapping
(b) the bulk microstructure that colored by using the standard inverse-pole-figure (IPF) color code of direction Z
(c) cross-section map in X-Y-Z directions
(d) visualization of a part of the measured 3D grain boundary network (The grain boundaries were colored according to the angle of misorientation) 
(e) the 2D EBSD microstructure of slice 101
2.2 3D Morphology of Grains
Fig. 2a shows the 3D morphology of a typical grain. The grain is colored according to the misorientation of grain boundaries, and the single crystal interface has a unique color. The grain size (equivalent sphere diameter, the same below) is 89.7 μm, and there are 27 crystal interfaces, and the crystal grain is adjacent to 27 crystal grains. Figure 2 also shows the 3D features of the 4 grain boundaries on the grain, all of which are surfaces with an area of 1556.6 μm 2 (Figure 2b), 1107.5 μm 2 (Figure 2c), 1753.3 μm 2 (Figure 2d), 1764.1 μm 2 (Figure 2e). The edges of these four grain boundaries are jagged, and the curvature of some positions is very large. From the viewpoint of interface energy, this is not very realistic, which may be caused by the lower resolution of 3D data acquisition, and 3D reconstruction using Dream3D. In the process, only the crystal interface was smoothed, and the grain boundary edge morphology was not processed (the current software does not yet have this function) [23,25,26].
20180615072039 53874 - Three-dimensional Grain and Grain Boundary Morphology and Size Distribution of 316L Stainless Steel

Fig.2 3D visualizations of a typical grain (a) from the 316L stainless steel and four boundaries (b~e) on the grain (The grains or boundaries were colored according to the angle of grain boundary misorientations)

In addition to the crystal interface, edges and vertices are the other two topographical features of 3D grains. The crystal interface is shown as a line in the 2D cross-section, and the edge is the intersection of the 3 lines in the 2D cross-section. The vertex of the 3D grain cannot be observed in the 2D cross-section. In addition, the edges of the crystal grains correspond to the triple junctions [7, 8] and consist of three crystal grains that are adjacent to each other; the apex of the grains corresponds to a quadruple junction [7, 8]. Four crystal grains next to each other.
2.3 3D grain size distribution
The grain size is one of the important parameters of the microstructure of the polycrystalline material and is an important factor influencing the material properties. However, in the 2D study, only the cross-sectional area of each grain on the 2D cross section can be obtained, and the true 3D grain size cannot be obtained. This work uses 3D-EBSD technology to measure the crystal orientation of each 3D pixel in 316L stainless steel. In the process of 3D reconstruction using Dream3D software, the connected area with an orientation difference within 15° is identified as 1 grain; in addition, 3D During the reconstitution process, the minimum size threshold of the crystal grain is set to 9 pixels. Grains smaller than 9 pixels are phagocytized by the surrounding crystal grains, thereby obtaining a 3D grain microstructure, and the crystal orientation and volume of each crystal grain. And other parameters.
20180615072344 65260 - Three-dimensional Grain and Grain Boundary Morphology and Size Distribution of 316L Stainless Steel

Fig.3 Grain size distribution for the 3D-EBSD microstructure of 316L and its log-normal fitting curve (y0, A and w—constants, d—grain diameter, c—the median value in the log-normal distribution)

There are a total of 1840 grains in the 3D-EBSD microstructure, and the grain size distribution is shown in FIG. 3 , and the larger the size, the smaller the number of grains. It is generally believed that the grain size (d) distribution follows the lognormal distribution function f(d) [8,23,29]:
20180615072456 95127 - Three-dimensional Grain and Grain Boundary Morphology and Size Distribution of 316L Stainless Steel
In the formula, w is the scale, and c is the median value of the lognormal distribution. However, the use of equation (1) to perform a poor fitting effect on the grain size distribution of the 3D microstructure measured in this work may be due to the fact that 316L stainless steel contains many twins, and the morphology and size of twins and equiaxed crystals The deviation is large, and Equation (1) is a fitting function derived from the equiaxed crystal material. Correct the formula (1) to get the lognormal distribution function:
20180615072509 45140 - Three-dimensional Grain and Grain Boundary Morphology and Size Distribution of 316L Stainless Steel
Where y0 is the position parameter and A is the concentration parameter. Equation (2) has a good effect on the grain size distribution fitting, as shown in the fitting curve in Figure 3, where y0 is small and can be ignored; but A is larger and is a general fitting function (Equation (1) ) The main difference compared.
2.4 3D grain morphology distribution
Grain size has a significant effect on material properties, but the effect of this effect is not grain size but grain size density. The crystal lattice imperfections at the grain boundaries cause dislocation packing, impurity atom segregation, and precipitation of the second phase, as well as a fast path for the destruction of materials such as corrosion [3, 18]. Therefore, grain boundary density and material properties There is a direct relationship between the two, and there is an indirect relationship between grain size and material properties. However, for a generally equiaxed material, the grain boundary density in the material is inversely proportional to the grain size, and a direct relationship between material properties and grain size can be established. For example, the Hall-Petch formula describes the material strength and grain size. The quantitative relationship between. In addition, since the grain boundary area (or length) is difficult to measure, and the grain size measurement is relatively simple, it also makes the grain size and density of the amorphous layer more important during the research. However, the Hall-Petch formula cannot accurately describe the quantitative relationship between strength and grain size. One of the main reasons is that the grain boundary density of the material is not only related to the grain size, but also related to the grain morphology, such as a spherical crystal. The surface area of the granules and the grain size conform to the sphere area formula, and the specific surface area is the smallest, while the specific surface area of the complex morphological grains is relatively large.
Figure 4 shows the grain surface area distribution of the 316L stainless steel 3D microstructure, and the relationship between surface area and grain size. Compared with the grain size distribution (Figure 3), they all obey the lognormal distribution, but the grain surface area distribution is more inhomogeneous and the fitting parameters y0, A, and w are all greater. Due to the presence of many twins in 316L stainless steel, the twins were identified as different grains during 3D-EBSD reconstitution, resulting in some very complex grain morphology and large surface area of the grains, as shown in Figure 4a. The number and surface area of the 6 grains with the largest surface area. The 3D morphology of the second largest crystal grain g101 (grain number) is shown in Fig. 5a. The crystal grain surface area is 1.90 × 105 μm 2 and the crystal grain size is 151.5 μm. Adjacent to 126 crystal grains, the crystal grain shape The appearance is very complicated and should be caused by twinning crystals. For example, Figure 5b shows the crystal grains at the point where the arrows point. The grain shape is sheet-shaped, and the upper and lower surfaces are basically parallel and are two parallel twinning boundaries; Figure 5c The crystal grains in the other empty area indicated by the arrow can be cut into a sheet-shaped portion and a square-shaped portion from the top view. The upper and lower surfaces of the sheet-shaped portion are relatively flat grain boundaries (twinned grain boundaries). Although the morphology of crystal grain g101 is very complicated, it is formed by combining some simple morphologies such as flakes and blocks. This feature is a result of continuous twin formation during grain growth (multiplex twinning process) [30] ).
20180615072644 10726 - Three-dimensional Grain and Grain Boundary Morphology and Size Distribution of 316L Stainless Steel

Fig.4 Statistic of grain surface area for the 3D microstructure and the log-normal fitting curve (The 6 grains with surface area larger than 1.1×105 μm2 are shown separately) (a), relationship between the grain surface area and the grain size and its power function fitting curve, and the curve of sphere surface area to diameter (b)

Figure 4b is the statistics of the grain surface area (Sg) versus the grain size (d). The fitted curve (solid line in Figure 4b) shows a power function between them:
20180615072732 58057 - Three-dimensional Grain and Grain Boundary Morphology and Size Distribution of 316L Stainless Steel
In the formula, a, b, and n are all fitting parameters.
In general, equiaxed grains are regarded as convex polyhedrons, which can be equivalent to spheres. The relationship between grain surface area and crystal grain size should be close to the spherical surface area formula. However, the grain morphology and the like of 316L stainless steel used in this work are equivalent. The axis crystals deviate greatly, as shown in FIG. 5 . The dashed line in Figure 4b shows the relationship between the sphere surface area and the sphere diameter. Compared to the fitted curve (solid line) of the relationship between the surface area of the crystallite and the grain size, the small crystal is close to a sphere, and the larger the size, the greater the deviation from the sphere. The more complex the appearance.
20180615072912 98448 - Three-dimensional Grain and Grain Boundary Morphology and Size Distribution of 316L Stainless Steel

Fig.5 A morphologically complex large grain g101 in the 3D microstructure of 316L (a) and two relative small grains g1211 (b) and g1026 (c) that are neighbors of the large grain

The number of crystal interfaces is another morphological feature of the crystal grains. Figure 6 shows the statistics of the number of crystal interfaces for each grain in the measured 3D microstructure. Note that the grains cut by the outer surface are also counted, and the cross section is counted as a crystal interface of the grain. It can be seen from the crystal grain number distribution of the crystal grains that the number of crystal grain interfaces of most crystal grains is 1 to 30, but there are a few crystal grain crystal surface numbers exceeding 30, for example, the crystal grains shown in FIG. 5a have 126 crystal grains. The interface is the grain with the largest number of crystal interfaces in the microstructure, and is also the grain with the most complex morphology. The fitted curve in Figure 6a shows that the crystal grain number distribution of the grains also obeys the lognormal distribution. Figure 6b shows the relationship between the number of crystal grain boundaries and the grain size. The larger the grain size, the more the number of crystal grain boundaries tends to be, but the distribution is more dispersed. The fitting curve shows that the relationship between the number of crystal grain boundaries and the grain size also conforms to the power function distribution.

20180615073332 24728 - Three-dimensional Grain and Grain Boundary Morphology and Size Distribution of 316L Stainless Steel

Fig.6 Statistic of the quantity of boundaries (or faces) per grain (F) for the 3D microstructure and the log-normal fitting curve (a), relationship between the boundary quantity per grain and the grain size and its power function fitting curve (b)

2.5 3D grain boundary size distribution
Two crystal grains with different crystal orientations intersect, and a transitional region with disordered lattice arrangement at the junction is called a grain boundary. Therefore, the grain boundary is not only an interface, but is a region at the atomic scale. In the 3D-EBSD reconstruction process, consecutive regions with an orientation difference of less than 15° between adjacent pixels are identified as one grain, and a grain-free interface is reconstructed between the grain and the grain, ie, the 3D. – Grain boundaries in EBSD microstructures, although the thickness characteristics of the grain boundaries are lost, the morphology and orientation difference of grain boundaries can be studied. Figure 7 shows the grain boundary size (equivalent circle diameter) distribution in the 3D microstructure of the 316L stainless steel tested. There are a total of 9177 grain boundaries (including grain boundaries that are truncated by the outer surface). The arithmetic average of the grain boundary size is 21.1 μm, most of the grain boundary size is less than 50 μm, and the maximum grain boundary size is 202.6 μm. The fitting analysis of the grain boundary size distribution shows that the grain boundary size distribution and the grain size distribution are similar, and it also conforms to the lognormal distribution.
20180615073502 64731 - Three-dimensional Grain and Grain Boundary Morphology and Size Distribution of 316L Stainless Steel

Fig.7 Statistic of equivalent circle diameters of boundaries for the 3D microstructure and the log-normal fitting curve

Fig. 7 is an analysis of the grain boundary as an independent object. It is also necessary to analyze the grain boundaries and crystal grains together. Although the grain surface area distribution has been obtained in the previous text, each crystal grain has several grain boundaries, and the average grain boundary size of crystal grains is a characteristic parameter describing grain morphology. Figure 8a shows the average grain boundary size distribution for each grain in the measured 3D microstructure. The fitting analysis results show that it also conforms to the lognormal distribution, and compared with the distribution of other parameters (Figs. 3, 4, 6 and 7), the average grain boundary grain size distribution of the crystal grains is more uniform. Figure 8b shows the statistics of the relationship between the average grain boundary grain size and the grain size of the grains. The fitting analysis shows that they are also power functions.

20180615073624 94577 - Three-dimensional Grain and Grain Boundary Morphology and Size Distribution of 316L Stainless Steel

Fig.8 Statistic of the average boundary diameter per grain for the 3D microstructure and the log-normal fitting curve (a), relationship between the average boundary diameter per grain and the grain size and its power function fitting curve (b)

3 Analysis and discussion
The 3D grain and grain boundary morphology characteristics and the statistical distribution of various characteristic parameters are the first concerns of the 3D microstructure study of polycrystalline materials. Most of the previous 3D studies only analyzed the 3D grain size distribution [8, 20, 21], and almost no grain boundary related parameters were studied. The main reason is that 3D data collection is difficult, and 3D research itself is rare; followed by 3D data. When it is difficult to handle, it is difficult to abstract the grain boundaries and analyze them. This work used 3D-EBSD technology to collect large-size 3D microstructure data of 316L stainless steel. Combining Dream3D software [23,25,26] and Matlab self-writing program, it can not only analyze the 3D grain size, but also The 3D grain boundary morphology parameters (such as the surface area of crystal grains, the number of crystal grain interfaces and the average grain boundary size, and the grain boundary size (equivalent circle diameter)) were quantitatively analyzed, and were visualized using ParaView software. Get the above research results.
The results show that the grain size distribution, grain surface area distribution, crystal grain number distribution, average grain boundary size distribution and grain boundary size distribution of 3D microstructure of 316L stainless steel obey the lognormal distribution. Studies [8,20,21] have found that the 3D grain size conforms to the lognormal distribution function shown in equation (1). However, using formula (1) has a poor fitting effect on the geometrical parameters of grain and grain boundaries in this work, and the fitting effect obtained by using the modified fitting formula (2) is better. The fitting curve of each parameter is shown in Fig. 3, 4a, 6a, 7 and 8a. The parameter y0 in the fitting formula is approximately equal to 0. Therefore, the 3D grain and grain boundary feature parameters of 316L stainless steel (x) The distribution function can be expressed as:
20180615073728 59496 - Three-dimensional Grain and Grain Boundary Morphology and Size Distribution of 316L Stainless Steel

When A=1, it is formula (1). In the present study, the grain size distribution and crystal grain interface number distribution can also obtain better fitting results when parameter A is 1, but A is not equal to 1 when the best fitting result is obtained; it is related to the grain boundary area. The distribution includes the surface area distribution of crystal grains, the average grain boundary size distribution of crystal grains, and the grain boundary size distribution. The fitting effect when parameter A is 1 is relatively poor. Other distribution functions such as normal distribution, exponential distribution, Gauss distribution, Laplace distribution, etc. have also been tried. The fitting effect is not as good as the lognormal distribution, or only the distribution of individual morphological characteristic parameters can be described well. Therefore, the lognormal distribution (4) is a function that can more appropriately describe the distribution of the topological characteristic parameters of 3D grains and grain boundaries.
Both grain and grain boundary morphology parameters are affected by the recrystallization process, such as recrystallization nucleation density, grain boundary migration rate, twin formation probability, microstructure anisotropy factor, etc. Therefore, these parameters are There should be a certain statistical relationship. For example, assuming that the grains are all spherical, the surface area of the grains and the grain size should follow the spherical surface formula. The relationship between the surface area of the equiaxed grains and the grain size should be close to the spherical surface area formula. This work statistics the relationship between the grain surface area of 316L stainless steel, the number of crystal grain boundaries, the average grain boundary grain size of the grains, and the grain size. The results show that they all obey the power function relationship (Equation (3)). However, the statistical relationship between grain surface area and grain size is very different from the spherical surface area formula (Fig. 4b). The comparison shows that the bigger the grain size, the larger the difference between the grain shape and the spherical shape, and the more the number of grain boundaries. (Fig. 6b) shows that the larger the size of the grain, the more complex the morphology and the more deviating from the equiaxed grain, which is caused by twinning.
The stacking fault energy of 316L stainless steel is low, and twins are easily formed during recrystallization. The 2D EBSD results (Fig. 1e) show that about 50% of grain boundaries in the material are twin boundaries (length ratio). During grain growth, due to the formation of twins, the 3D grain morphology may be hemispherical, lamellar, or rectangular (3D-EBSD is recognized as a grain during the reconstruction process), even due to the occurrence of multiple defects. Crystals lead to very complex grain morphology [4, 15, 30], such as the grains shown in Figure 5a. There are obvious lamellar vacancies on the complex topography grains. If these vacancies are all complemented, the crystal grains are close to equiaxed crystals, and each missing part corresponds to one or more grains, such as Figure 5b and Crystals shown in c (g1211 and g1026). The crystal orientation (Euler angle) of the complex morphology grain g101 shown in FIG. 5a is 186.8°, 28.7°, and 203.2°, and the crystal orientations of the vacant crystal grains g1211 and g1026 are 297.1°, 28.6°, 63.1°, and 4.4°, respectively. , 21.0°, 329.1°, so that it can be calculated that the orientation difference between the crystal grains g101 and g1211 is 58.6° [111], the orientation difference between the crystal grains g101 and g1026 is 59.2° [111], both are twin orientations The relationship indicates that the morphology of some of the grains in 316L stainless steel caused by twinning has become very complicated.
4 Conclusion
(1) The 3D grain size distribution, grain surface area distribution, crystal grain boundary number distribution, and 3D grain boundary size distribution and grain grain average grain size distribution of 316L stainless steel all obey the lognormal distribution.
(2) The statistical relationship between the grain boundary area, the number of crystal interfaces, and the average grain boundary size and grain size of 3D grains in 316L stainless steel obeys the power function relationship.
(3) The distribution of 3D grain morphology and equiaxed grain distribution in 316L stainless steel is greatly deviated, mainly due to the presence of a large number of twins in 316L stainless steel, resulting in very complex grain morphology and larger crystal sizes. The more complex the grain morphology, the greater the number of crystal interfaces and even individual crystal grains with more than one hundred crystal interfaces.
The authors have declared that no competing interests exist.

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