晶粒组织的三维模型构建与定量表征研究

发布时间：2018-04-29 14:10

  本文选题：晶粒组织 + 三维重建　； 参考：《北京科技大学》2017年博士论文

【摘要】：在多晶材料研究中,晶粒尺寸和形态的控制是一个基本问题,晶粒组织的观测与表征则是上述工作的基础。近年来,在三维层次上进行晶粒组织的表征与分析逐渐成为研究的热点,同时也使一些影响研究深入开展的不完善之处凸显出来,如晶粒(尤其是实际晶粒)样本数量不足、晶粒的某些特征表征不完善等。为了深入研究晶粒组织的相关问题,本研究从构建大样本量纯铁实际晶粒组织与仿真晶粒组织的三维模型入手,以晶粒拓扑学的完备表征、晶粒尺寸参量的定量测量为重点,对晶粒组织的特征与演变规律进行了分析。通过系列截面法三维重建和三维仿真技术构建了四种大样本量的数字化晶粒组织模型。结合系列截面图像采集与图像处理技术,完成了常规的和含显著有别于多晶体平均特征的"特异"晶粒的两种纯铁晶粒组织的三维重建。常规纯铁晶粒组织中含完整晶粒16 254颗,含"特异"晶粒的组织中包含25417颗常规晶粒和5颗"特异"晶粒(128～669面)。利用三维Monte Carlo仿真方法构建了基于Potts模型的晶粒长大组织的体素化模型,包含仿真晶粒150 428颗。实现了数字化的三维Poisson-Voronoi随机组织的构建,包含晶粒150 000颗。从图论角度出发,提出了用矩阵表征晶粒的全部拓扑学信息的方法,可以实现三维个体晶粒所有可能拓扑构型的数学表达。利用晶粒拓扑指数实现了晶粒拓扑性质的定量化,发现代数连通度是晶粒拓扑构型稳定性的表征。基于这一研究结果发现,晶粒长大组织具有向面数稍小的常见稳定构型择优分布的倾向;Monte Carlo仿真组织倾向于小的晶面边数分散度和大的构型代数连通度;在特定面族中,晶粒构型分布出现倾向于稳定方向的峰值。利用矩阵实现了晶粒构型演变的代数化算法,应用该算法计算了4～14面晶粒的拓扑构型,发现了多种前人没有发现的晶面二次相邻构型,并在三维纯铁晶粒组织中新观测到7种该类型的构型,根据此类构型特点提出了基于晶面曲率驱动的构型演变机制。提出并评估了多种基于不同数学原理的测量三维晶粒几何参量的方法并应用于实际测量中。分析了本研究中构建的四种晶粒组织的统计分布特征,发现纯铁晶粒组织和Monte Carlo仿真组织在各项特征的分布上更具有稳定倾向性;纯铁晶粒组织相关参数的分布均较Monte Carlo仿真组织分散。在形态参量上,Monte Carlo仿真组织的圆球度高且分布集中。以数量分数作为统计指标时,"特异"晶粒对分布曲线没有明显影响,但对分布统计参量有影响。利用体积分数作为统计指标时,"特异"晶粒对分布曲线影响显著。与组织总体平均值相比,"特异"晶粒紧邻晶粒的平均面数稍小,体积稍大,圆球度稍好;"特异"晶粒晶面的平均边数稍大,分布更分散。四种晶粒组织在晶粒尺寸参量之间的关系上和拓扑-尺寸关系上均具有一致的规律性,在尺寸-形态关系上有区别。含"特异"晶粒的组织中晶粒半径或面数与平均宽度的关系同不含"特异"晶粒的组织有区别,"特异"晶粒在几何性质上的特殊性体现在尺寸增大后曲率变化明显,呈现出明显的凹晶粒特征。利用大样本量纯铁晶粒组织实现了三维晶粒广义Aboav-Weaire关系的验证,发现三维晶粒的接触亲和度比二维更趋于随机,证实了维度效应对组织的影响,发现样品边界效应严重影响晶粒拓扑相关性,同时证明了大样本量晶粒的重要性。利用晶粒实测数据实证了晶粒总棱长与半径的平方关系,其原因在于不同面数分组的晶粒总棱长与半径的线性关系的斜率随面数线性变化。利用Monte Carlo仿真组织晶粒数据验证了 MacPherson-Srolovitz方程,发现Monte Carlo仿真组织的晶粒体积变化率同其尺寸与形态参量间有分段线性现象,分段界限的晶粒面数约为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..

【学位授予单位】：北京科技大学
【学位级别】：博士
【学位授予年份】：2017
【分类号】：TB303
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本文编号：1820269