Three-dimensional Modeling And Quantitative Characterization Of Grain Structure

The characterization of grain structures is of great importance in that the controlling of the grain size and morphology is a key problem in three-dimensional materials science.While there have been many theories and simulations formulated to predict the evolution of the microstructures,there still exist some problems such as lack of the grain(especially real grain)samples and uncomplete characterization of the grain topological and geometrical characteristics.In this thesis,with the construction of three-dimension model of large sample size grain structure,the complete topology of grains is described in a new way and the feature of grain size is measured directly.These results are compared to current theories of three-dimensional(3-D)grain growth.Serial sectioning was used to measure two kinds of 3-D microstructures of pure iron,i.e.,grain-growth structures with and without "exceptional big" grains(EBGs),respectively.A total of 25417(include 5 EBGs with 128-669 faces)and 16254 pure iron grains were measured in the structures with and without EBGs,respectively.Poisson-Voronoi structures and Potts model-Monte Carlo structures were also employed in this work,with 150 000 Poisson-Voronoi random grains and 150 428 Monte Carlo simulated grains within the simulation datasets.A new,efficient method based on a series of matrices is introduced to completely describe the detailed topology of individual grains and their topology evolution in 3-D grain structures.The grain topological indices are used to represent the topological characteristic of grains.It is found that the algebraic connectivity is a very important parameter to describe the grain stability.This topological index serves as a new convenient differentiator of different cellular structures.Noticeable topological bias among pure iron grains,Monte Carlo grains and other type of grains is observed in terms of the most frequent grain forms.The grain growth microstructure favors topological forms with large algebraic connectivity relative to the Poisson-Voronoi structure.In a certain face class,the distribution of grain topological forms tends to reach a stable peak.With such matrix description,the topological grain forms for 4-14 faced grains were predicted.A lot of new band-face grain forms which have never been reported bef-ore being first found.And,28 grains that belong to 7 kinds of-new forms were found in the pure iron grain microstructure.A new evolution mechanism is proposed based on the curvature driven according to the features of band-face forms.The geometry features of individual grains are directly measured by developing various methods based on different mathematical algorithms.Some difference in the statistical distributions of various parameters among different structures is observed.It shows that grain growth microstructure has higher stability than random structure and the distribution of related parameters of pure iron is more dispersed than that of Monte Carlo structure.The sphericity distribution of Monte Carlo simulated grains is concentrated and its peak value is high enough.For quantity fraction,the exceptional big grains have no obvious effect on the distribution curves but affect the statiscal values seriously.Meanwhile,those grains affect the distribution curves strongly when volume fraction is considered.Their neighbors also have some characteristics on average which is different from the mean values of neighboring grains in the system,such as smaller average faces,bigger average volume and better sphericity.The relationships of various geometrical sizes or topology-size are all consistent,and the size-shape relationships are distinct.The relationship of mean width and radius(or face number)is different between grain structure with and without EBGs.The particularity of the EBGs is shown in the characteristic of concave surface which has obvious change of curvature.It is observed that the generalized Aboav-Weaire relation is verified by experimental data for the first time.The expected trends of high affinity for contact between few-and many-faced or edged grains and avoidance of contact between grains in similar face or edge classes are also observed.However,this correlation appears relatively stronger in genuine 2D system than in 2D cross-sectional and 3D system.This result indicates that the increase in dimension has dampening effect on the contact affinity of curvature-driven grain-growth structure.The total edge length and radius of grains showed a square relationship statistically.However,for a given face class,they showed linear relationship.And,the slope increased linearly with the increase of the value of face class.The MacPherson-Srolovitz relation,a theory of grain growth,has also gotten support from the Monte Carlo simulation data.A slightly difference in the trend of grain growth rate is observed between many-faced grains(F>22)and the others.