本文選題：晶粒組織 + 三維重建　； 參考：《北京科技大學》2017年博士論文

【摘要】：在多晶材料研究中,晶粒尺寸和形態(tài)的控制是一個基本問題,晶粒組織的觀測與表征則是上述工作的基礎(chǔ)。近年來,在三維層次上進行晶粒組織的表征與分析逐漸成為研究的熱點,同時也使一些影響研究深入開展的不完善之處凸顯出來,如晶粒(尤其是實際晶粒)樣本數(shù)量不足、晶粒的某些特征表征不完善等。為了深入研究晶粒組織的相關(guān)問題,本研究從構(gòu)建大樣本量純鐵實際晶粒組織與仿真晶粒組織的三維模型入手,以晶粒拓撲學的完備表征、晶粒尺寸參量的定量測量為重點,對晶粒組織的特征與演變規(guī)律進行了分析。通過系列截面法三維重建和三維仿真技術(shù)構(gòu)建了四種大樣本量的數(shù)字化晶粒組織模型。結(jié)合系列截面圖像采集與圖像處理技術(shù),完成了常規(guī)的和含顯著有別于多晶體平均特征的"特異"晶粒的兩種純鐵晶粒組織的三維重建。常規(guī)純鐵晶粒組織中含完整晶粒16 254顆,含"特異"晶粒的組織中包含25417顆常規(guī)晶粒和5顆"特異"晶粒(128～669面)。利用三維Monte Carlo仿真方法構(gòu)建了基于Potts模型的晶粒長大組織的體素化模型,包含仿真晶粒150 428顆。實現(xiàn)了數(shù)字化的三維Poisson-Voronoi隨機組織的構(gòu)建,包含晶粒150 000顆。從圖論角度出發(fā),提出了用矩陣表征晶粒的全部拓撲學信息的方法,可以實現(xiàn)三維個體晶粒所有可能拓撲構(gòu)型的數(shù)學表達。利用晶粒拓撲指數(shù)實現(xiàn)了晶粒拓撲性質(zhì)的定量化,發(fā)現(xiàn)代數(shù)連通度是晶粒拓撲構(gòu)型穩(wěn)定性的表征。基于這一研究結(jié)果發(fā)現(xiàn),晶粒長大組織具有向面數(shù)稍小的常見穩(wěn)定構(gòu)型擇優(yōu)分布的傾向;Monte Carlo仿真組織傾向于小的晶面邊數(shù)分散度和大的構(gòu)型代數(shù)連通度;在特定面族中,晶粒構(gòu)型分布出現(xiàn)傾向于穩(wěn)定方向的峰值。利用矩陣實現(xiàn)了晶粒構(gòu)型演變的代數(shù)化算法,應用該算法計算了4～14面晶粒的拓撲構(gòu)型,發(fā)現(xiàn)了多種前人沒有發(fā)現(xiàn)的晶面二次相鄰構(gòu)型,并在三維純鐵晶粒組織中新觀測到7種該類型的構(gòu)型,根據(jù)此類構(gòu)型特點提出了基于晶面曲率驅(qū)動的構(gòu)型演變機制。提出并評估了多種基于不同數(shù)學原理的測量三維晶粒幾何參量的方法并應用于實際測量中。分析了本研究中構(gòu)建的四種晶粒組織的統(tǒng)計分布特征,發(fā)現(xiàn)純鐵晶粒組織和Monte Carlo仿真組織在各項特征的分布上更具有穩(wěn)定傾向性;純鐵晶粒組織相關(guān)參數(shù)的分布均較Monte Carlo仿真組織分散。在形態(tài)參量上,Monte Carlo仿真組織的圓球度高且分布集中。以數(shù)量分數(shù)作為統(tǒng)計指標時,"特異"晶粒對分布曲線沒有明顯影響,但對分布統(tǒng)計參量有影響。利用體積分數(shù)作為統(tǒng)計指標時,"特異"晶粒對分布曲線影響顯著。與組織總體平均值相比,"特異"晶粒緊鄰晶粒的平均面數(shù)稍小,體積稍大,圓球度稍好;"特異"晶粒晶面的平均邊數(shù)稍大,分布更分散。四種晶粒組織在晶粒尺寸參量之間的關(guān)系上和拓撲-尺寸關(guān)系上均具有一致的規(guī)律性,在尺寸-形態(tài)關(guān)系上有區(qū)別。含"特異"晶粒的組織中晶粒半徑或面數(shù)與平均寬度的關(guān)系同不含"特異"晶粒的組織有區(qū)別,"特異"晶粒在幾何性質(zhì)上的特殊性體現(xiàn)在尺寸增大后曲率變化明顯,呈現(xiàn)出明顯的凹晶粒特征。利用大樣本量純鐵晶粒組織實現(xiàn)了三維晶粒廣義Aboav-Weaire關(guān)系的驗證,發(fā)現(xiàn)三維晶粒的接觸親和度比二維更趨于隨機,證實了維度效應對組織的影響,發(fā)現(xiàn)樣品邊界效應嚴重影響晶粒拓撲相關(guān)性,同時證明了大樣本量晶粒的重要性。利用晶粒實測數(shù)據(jù)實證了晶�？偫忾L與半徑的平方關(guān)系,其原因在于不同面數(shù)分組的晶粒總棱長與半徑的線性關(guān)系的斜率隨面數(shù)線性變化。利用Monte Carlo仿真組織晶粒數(shù)據(jù)驗證了 MacPherson-Srolovitz方程,發(fā)現(xiàn)Monte Carlo仿真組織的晶粒體積變化率同其尺寸與形態(tài)參量間有分段線性現(xiàn)象,分段界限的晶粒面數(shù)約為22。
[Abstract]:In the study of polycrystalline materials, the control of grain size and morphology is a basic problem. The observation and characterization of grain structure are the basis of the above work. In recent years, the characterization and analysis of grain structure on the three dimensional level has gradually become a hot spot of research. At the same time, some of the imperfections which have been deeply carried out are highlighted. In order to study the related problems of grain structure, this study starts with the construction of the three-dimensional model of the actual grain structure and the simulation grain structure for the large sample quantity of pure iron, with the complete characterization of the grain topology and the quantitative measurement of the grain size parameters. The characteristics and evolution laws of grain structure are analyzed. Four large sample size digital grain organization models are constructed by series cross section method and three-dimensional simulation technology. The three-dimensional reconstruction of the grain structure of two kinds of pure iron. In conventional pure iron, there are 16254 intact grains and a "specific" grain containing 25417 conventional grains and 5 "specific" grains (128~669 surfaces). A voxel model of the grain growth structure based on the Potts model is constructed by using the three-dimensional Monte Carlo simulation method. The simulation grain consists of 150428 grains. The digital three-dimensional Poisson-Voronoi random structure is constructed, including 150000 grains of grain. From the point of view of graph theory, the method of using matrix to characterize all the topological information of grain is proposed, which can realize the mathematical expression of all possible extension forms of the three dimensional individual grain. It is found that the algebraic connectivity is the characterization of the stability of the topological structure of grain. Based on this study, it is found that the grain growth structure has the tendency to select the preferred distribution of the common stable configurations with smaller number of directions, and the Monte Carlo simulation organization tends to the small degree of dispersion of the crystal surface and the large configuration algebra connection. Degree; in a specific family, the distribution of grain configuration appears to be a peak in the direction of stability. An algebraic algorithm for the evolution of grain configuration is realized by using the matrix. The topological configuration of 4~14 surface grains is calculated with this algorithm, and a variety of two adjacent structures of the crystal surface have been found, and a new observation of 7 in the three-dimensional pure iron grain structure has been found. According to the characteristics of this type, the configuration evolution mechanism based on the crystal surface curvature is proposed. A variety of methods based on different mathematical principles are proposed and applied to the actual measurement. The statistical distribution characteristics of four kinds of grain structures in this study are analyzed. The distribution of iron grain structure and Monte Carlo simulation tissue is more stable in the distribution of various characteristics; the distribution of grain structure related parameters of pure iron is more dispersed than that of Monte Carlo simulation tissue. On the morphological parameters, the sphere of Monte Carlo simulation organization is high and distributed. When the number fraction is used as the statistical index, the "specific" grain is divided. The distribution curve has no obvious influence, but it has an influence on the distribution statistical parameters. When the volume fraction is used as the statistical index, the "specific" grain has a significant influence on the distribution curve. Compared with the overall mean value of the tissue, the average number of the "specific" grain adjacent to the grain is slightly smaller, the volume is larger, the ball degree is slightly better, and the average edge number of the "specific" grain surface is slightly larger. The relationship between the grain size and the relationship between the grain size parameters and the relationship between the size parameters of the grain size and the topological size relation have the same regularity. There is a difference between the size and the shape relation. The relation between the grain radius or the surface number in the tissues containing the "specific" grain is different from the average width of the four grain tissues, and the specific grain is in geometry. The characteristics of the nature are manifested in the obvious change of the curvature after the size enlargement and the obvious concave grain characteristics. Using the large sample amount of pure iron grain to verify the generalized Aboav-Weaire relation of the three dimensional grain, it is found that the contact affinity of the three-dimensional grain is more random than the two dimension, and the effect of the dimension effect on the tissue is confirmed. The boundary effect of the grain seriously affects the topological correlation of grain. At the same time, the importance of the large sample size grain is proved. The square relation between the length of grain length and the radius of the grain is proved by using the measured data of grain. The reason is that the oblique rate of the linear relationship between the length of grain length and the radius of the different surface numbers is linearly changed with the number of the surface. The Monte Carlo simulation is used. The MacPherson-Srolovitz equation is verified by the grain data of the tissue. It is found that the grain volume change rate of the Monte Carlo simulation organization has a piecewise linear phenomenon between the size and the morphological parameter, and the number of the grain surface of the segmented boundary is about 22..

【學位授予單位】：北京科技大學
【學位級別】：博士
【學位授予年份】：2017
【分類號】：TB303
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本文編號：1820269