粉体颗粒群粒度分布分形维与流动性及流动助剂影响关系研究

粉体颗粒粒度分布分形维能很好地表征颗粒群粒度分布情况,对表征颗粒流动性具有重要意义.通过建立便于用数字显微和图像处理计算颗粒粒度分布分形维数值的数学模型,采用图像处理技术得到粉体颗粒粒度分布分形维数值,探讨流动性表征参数休止角、崩溃角和差角与粒度分布分形维数值间的关系,确认颗粒粒度分布分形维数值可用于表征粉体流动性,形成了可靠和简洁的粉体流动性能测定新方法.并就流动助剂对粉体流动性能的改进与分形维数值关系做了初步探讨,得出了分形维数值可作为掺杂流动助剂量的指导参数的结论.     

基于分形损失理论的粗糙节理岩体中应力波波速研究

从损伤力学的基本理论出发,推导了应力波在节理岩石中传播波速的解析解,建立了节理面图像分形维数与波速间的关系。为了从数值角度探讨节理面图像维数对波速的影响规律,基于图像每一像素颜色可表示为一个三维空间矢量的基本假定,构建了节理面图像的粗糙“颜色表面”模型,计算了该“颜色表面”的分形维数,此维数即为节理面图像维数,并通过实例验证了该法的可行性。在此基础上,通过数值方法探讨了波速随图像维数的变化规律,研究显示：随着节理面图像维数增大,节理面粗糙程度的增加,应力波波速相应减小,且在不同的图像维数区间里,波速减小的速率也有所不同     

分形维数在判断海洋锋强度中的应用

提出一种用计算维数值预报海洋锋强度的方法。给出了用分形维数描述海洋锋强度的理论依据,介绍了分形维数的计算方法及现有的海洋锋强度的判断方法。应用网格法,以HOOM海洋锋模型和我国东海黑潮锋区的三维声速场数据为例,计算了三维声速场中不同深度、时间的声速等值线的分形维数,得出HOOM模型海洋锋声速场分维值在1.07和1.60之间,我国东海黑潮锋区分维值在1.04和1.30之间,无锋时声速等值线分维接近于1;分形维数可以表征海洋锋强度,维数值随锋强度的变化而变化的结论。     

用投影轮廓分维中位维表征颗粒群粗糙度的研究

为了表征颗粒群粗糙度,本文中构建了单颗粒投影轮廓分维数学模型,并以高精度数字光学显微系统为基础,测算了5种颗粒样品的单颗粒投影轮廓分维。结果表明,5种颗粒样品的单颗粒投影轮廓分维均值从小到大依次为:柴油汽车排气管沉积颗粒、碳黑颗粒、粉煤灰颗粒、石灰性褐土颗粒、河流沉积土壤颗粒。首次提出了"中位维"的概念以表征颗粒群粗糙度,计算了颗粒样品的中位维,其大小排序与投影轮廓分维均值一致,验证了将"中位维"作为表征颗粒群粗糙度的合理性。     

多孔颗粒材料内孔表面分维测算及与保水性能的关系

为考察多孔颗粒材料内孔表面分形特征及与其保水性能的关系,构建了多孔颗粒物内孔表面分维测算数学模型,并基于高精度扫描电子显微镜系统测算了4种多孔颗粒样品的内孔表面分维,测量了材料保水性能。结果表明:多孔颗粒的内孔表面的分维值介于2.088 2~2.193 5之间,且分形拟合曲线相关系数大于0.98,强的相关性说明内孔表面具有显著的分形特征。进一步研究发现,多孔颗粒材料保水性能与其内孔表面分维呈负相关。     

颗粒表面分维与其形状指数关系研究

构建了颗粒物表面分维测算模型,研究了颗粒投影轮廓大小与形状指数F的关系。研究表明:颗粒投影轮廓大小与形状指数F具有良好的线性相关性。文中还利用所构建的颗粒物表面分维模型测量了6种碳黑颗粒的表面分维,初步研究了颗粒物表面分维与形状指数F之间的关系,分析结果发现:随着颗粒表面分维的增加,其形状指数F也相应增加,二者具有良好的相关关系。因此,表面分维与形状指数F均可作为颗粒物形状的定量表征,且二者具有良好的相关性。     

大气颗粒物显微轮廓分形与源解析

为监测大气颗粒物的来源,根据静电吸附原理设计大气颗粒收集装置采集大气颗粒物,通过光学显微放大技术和图像分析方法,得到源颗粒的轮廓分形维数值,结合采样点周边的实际情况,分析和对比各源颗粒的轮廓分形维数值,确定颗粒部分来源;并采用偏光显微镜观察各源颗粒的偏光特征,协同确定大气颗粒的具体来源。结果表明,大气颗粒具有分形特征,其很多特性均与其分形特征有关;采用大气颗粒的轮廓曲线分形维数值作为降尘颗粒来源的辨析参数是可行的,轮廓曲线的分形维数值能很好地表达颗粒的结构形态,特定颗粒源的分形维数值具有一定的范围;将轮廓曲线的分形维数值与各源颗粒的偏光特征相结合,对颗粒来源的辨识准确率在90%以上。     

Fractal dimension of metallic fracture surface

In this study, a complete method of determination of the fractal dimension for fracture surfaces of ferrous alloys has been proposed. This dimension is determined for the vertical profile obtained by the profile technique cross-section. The image of the profile, seen through the microscope coupled with a camera, is recorded in a computer, where numerical processing is performed. For calculation of the same fractal dimension, the fd3 program has been used, which is available through the Internet. The essential element of the method is optimisation concerning microscopic magnification (scale of a length), resolution of the recorded image and selection of the grey level threshold at binarization. The tests for the stability of discretization, which enable minimization of the error of the measurement, have also been carried out. These tests consist in checking the difference in fractal dimensions for the same profile obtained in two different methods of contouring as well as the difference between capacitive, informative and correlative dimensions. In both cases, too big difference suggests that the determined dimension is not reliable. This method allows determination of the fractal dimension with an absolute accuracy of 0.05 in non-dimensional units. The method has been employed in many studies. In this paper the following tests have been presented: a “fractal map” of the fracture surface was made, an influence of the mechanical notch radius in a compact specimen on the fractal dimension of the fracture surface, an influence of the distortion rate on the fractal dimension, an effect of fatigue crack propagation rate on the fractal dimension and influence of the stress-intensity factor on the fractal dimension of the fracture surface. The following materials were examined: Armco iron, P355N steel and 41Cr4 steel in different states after the heat treatment. The measurements have been made for the specimens of the compact type. There was considered an influence of location of the place of measurement on the fractal dimension being determined. The dimension was determined on the profiles lying longwise and crosswise the crack propagation direction. It has been found that the fractal dimension of the fracture surface does not depend on a place of measurement. This suggests, among other things, that a distinction between the places, which were created under conditions of the plane stress, and the places, which were created under conditions of the plane strain state, cannot be made with the help of the fractal dimension. When testing an influence of the radius of the mechanical tip notch on the fractal dimension of a fracture surface, this dimension was determined in the places located at different distances from the tip of the mechanical notch. With respect to the radii up to 1.0 mm, no significant differences in fractal dimensions have been found. The fractal dimensions of the fracture surface for all examined materials were practically the same and they ranged from 2.02 to 2.10. However in some ranges of da/dN rate the dimension was changing inversely proportional to da/dN. Obtained results confirm that fractal dimension do not depend on the investigated material.     

大气降尘轮廓投影分形与来源辨识

选取燃煤锅炉、道路扬尘、汽车燃油不完全燃烧产生的颗粒、土壤颗粒等4种颗粒,利用数字显微和图像处理技术,求取降尘颗粒轮廓投影曲线的分形维数,并根据实际采样情况,求取降尘部分源颗粒的轮廓投影曲线分形维数,根据分形维数间的关系对比分析后判断降尘颗粒的来源。结果表明:将大气降尘轮廓投影曲线分形维数值作为降尘颗粒来源的辨析参数是可行的,将轮廓投影曲线的分形维数值和投影轮廓的其他几何特征参数相互结合可以得到很好的判断结果。     

矿用钢丝的表面腐蚀形貌及分形研究

钢丝绳中钢丝锈蚀是造成矿用提升钢丝绳失效的主要形式之一,以矿用钢丝为研究对象,在模拟矿井淋水的碱性腐蚀介质下开展长时间的腐蚀试验,观察腐蚀形貌并探讨钢丝的腐蚀规律,基于分形理论计算腐蚀形貌的分形维数。结果表明,分形维数值可以描述钢丝腐蚀过程中表面形貌的复杂程度;腐蚀表面与分形维数密切相关,腐蚀越严重,表面形貌越复杂,分形维数越大;浸泡初期以点蚀为主,失重速率变化较快,分形维数先升高达到一个峰值随后减小;浸泡后期以均匀腐蚀为主,失重速率变化趋于平缓,分形维数逐渐增大。     

分形维数与D6AC钢的韧性

本文研究了超高强度钢Ｄ６Ａｃ的断裂韧性、冲击韧性和拉伸面缩率与断口分形维数的关系。分别用二次电子线扫描和数字图象法测定断裂韧性试样的断口分形维数，得出试样的韧性与分形维数Ｄｓｅ、Ｄ_Ｈ和Ｄ_Ｌ成正比关系，即韧性随分形维数增大而增加。试样断口的粗糙度由夹杂物引起的差异小于金相组织不同引起的差异时，使用数字图象法测得的分形维数与韧性的线性关系优于二次电子线扫描的结果。     

Fractal dimension of Apollonian packing of spherical particles

Three-dimensional Apollonian packing with random distribution of initially prepacked spheres is investigated. The computer simulation model with specially designed changing range genetic algorithm was developed to estimate the fractal dimensions of Apollonian packing of spherical particles. The fractal dimensions corresponding to the packing degree and porosity were calculated for a large range of spherical particles (in the order of millions). The result obtained provides an experimental proof of a lower bound of the fractal dimension analytically found by [3] (Aste, Phys. Rev. E, 1996; 53: 2571).     

晶粒度的分形特征研究

测量了标准图谱中铁素体晶粒度图形有分形维数。考察了晶粒度与分维之间的关系。结果表明,金属晶粒可用分形维数定量描述。在１～８级晶粒度内,随着晶粒度级别的提高,分维数值逐渐增大,其中以１～５级内增大得最为显著。     

Fractal Description of the Shearing-Surface of Tools

In this paper, the basic methods are introduced to calculate the fractal dimensions of the shearing surface of some tools. The fractal dimension of the shearing surface of experimental sampling is obtained and the fractal characteristics are also discussed. We can apply the fractal method to identify types of tools used by burglars and to do the job of individual recognition. New theories and methods are provided to measure and process the shearing surface profile of tools.     

Relationship between Fracture Toughness and Fractal Dimension of Fracture Surface of Steel

The relationship between fracture toughness and fractal dimension of fracture surface was analysed based on a united fractal model of microscopic fracture modes. It was indicated that fracture toughness is a multivariant function of yield strength, microstructural length, fractal dimension of fracture surface and volume fraction of inclusions, other than a monovariant function of fractal dimension of fracture surface. This new fractal model of fracture toughness was verified to fit well with a set of experimental data of a ultrahigh strength steel with equal microstructure and grain size but different volume fraction of inclusion.     

复合评定法在三维粗糙表面评定中的应用

提出一种将双树复小波与分形理论相结合的复合评定方法。即利用双树复小波近似的平移不变性和方 向性好等优点,将信号分解成更为细腻的低频和高频信号,同时根据多尺度下信号分形维数的不变性,利用图像灰 度值自相关求得高低频信号的分形维数,通过计算高低频信号分形维数之间的差值（即分形维数距)来确定双树复 小波的分解尺度。仿真结果表明复合评定法可以较好地提取基准面,且分形维数距确定分解层数的准确性通过均 方根*Sq值得到了验证;两个实例均说明,复合评定法可以很好地提取具有分形特征的纳米级三维粗糙表面基准或 波纹度,为实际工程表面评定提供了可靠的理论基础。     

Statistical Analysis of Reinforcement Characterization in SiC Particle Reinforced Al Matrix Composites

The characterization of reinforcement in 15% SiC particles reinforced Al matrix composites processed by powder metallurgy route was studied by statistical method. During the analysis, a new approach for the estimation of the characterization of reinforcement was presented. The mathematic software MATLAB was used to calculate the area and perimeter of reinforcement, in which the image processing technique was applied. Based on the calculation, the fractal dimension, shape factor, reinforcement size distribut...     

Optical free-path-length distribution in a fractal aggregate and its effect on enhanced backscattering

A free-path-length distribution function (FPDF) of multiply backscattered light is theoretically derived for a fractal aggregate of particles. An effective mean-free path-length l(D) is newly introduced as a measure of randomness analogous with a homogeneously random medium. We confirm the validity of the FPDF by demonstrating agreement between the dimensions designed for a particle distribution generated by a random walk based on the derived FPDF and estimated by the radius of gyration method. The FPDF is applied to Monte Carlo simulations for copolarized multiply backscattered light from the fractal aggregate of particles. It is shown that a copolarized intensity peak of enhanced backscattering in the far field decreases in accordance with theta(2-D) and has an angular width of lambda/l(D). This spatial feature of the backscattering enhancement corresponds to that of the copolarized intensity peak produced from a homogeneously random medium with a dimension of D = 3. As a result, the validity of the model for the fractal structure of particle aggregates and the applicability of the derived FPDF are confirmed by the numerical results.     

Determination and interpretation of fractal properties of the sandstone pore system

A knowledge of fractal properties of the pore system is extremely useful with regard to the interrelationships between moisture transport and pore structure. The fractal dimension characterises the egree of resolutiondependence of a property. Given a completely interlaced pore system such as that of sandstone, the fractal dimension of the pore volume, or the porosity, quantifies the cross-sectional variability of the pore channels and is thus of great relevance with regard to transport processes. The fractal dimension of the pore surface describes the surface roughness. A newly-developed measuing technique is presented for the simultaneous determination of fractal dimensions of porosity and pore surface and for establishing fraction radii distributions in order to derive relevant parameters for moisture transport.