实际分形体维数计算中的RSC问题

在理论上解释了材料断裂表面维数计算中出现的ＲＳＣ问题，提出了建立实际分形体的分维谱Ｄ分析，并且讨论了这种分维谱分析对实际分形体结构研究的重要意义。     

固体薄膜材料裂纹分形结构维数计算中的不确定性研究

讨论了固体薄膜材料裂纹分形研究中出现的一类分维不确定性问题，指出实际分形体的近似分形结构是其产生的根本原因，并在数学上给予了证明，材料断裂行为中的多度域似分形结构维数测量、计算中也存在分维不确定性问题，文中也进行了讨论。     

基于数学形态学的分形维数计算及在轴承故障诊断中的应用

滚动轴承故障信号是一种典型的非线性信号,分形几何为描述轴承故障信号的特性提供了一个有力的分析工具。基于数学形态学的分形维数是在Minkowski-Boulingand维数基础上拓展的一种采用形态学操作计算分形维数的新方法。本文较详细的阐述了基于数学形态学的分维数计算方法,对比分析了与传统计盒维数方法的区别与联系,并对实际的滚动轴承正常、滚动体故障、内圈故障和外圈故障信号进行了分析,结果表明,基于数学形态学的分维数计算方法具有计算速度快,估计准确稳定的特点,为准确判断滚动轴承故障状态提供了一种快速有效的新方法。     

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。     

氢致裂纹慢扩展区断裂表面的分维研究

用垂直剖面法测量了一种含氢高强度钢在静弯矩作用下由裂纹慢扩展形成的断裂表面不同部位的分维 D,发现 D 随断裂表面塑性成分的增加而增加。在平面应变条件下,裂纹慢扩展形成断裂表面的过程是一个增维过程,当分维达到某一临界值时,裂纹失稳扩展。     

整体式载体的分形研究

整体式Al2O3载体结构实测结果表明,虽然不同组分、不同条件下形成的块体具有不同的结构,但孔隙尺寸均满足分形标度律,是一种分形.本文构造了整体式载体分形体,提出了整体式载体的一种分形模型--蜂窝分形体,导出了关联表面积和体积增量的分形表达式,并分析了表面分维数的几何意义.本文在测得载体孔径分布的基础上,利用该模型的表面积与体积增量分形表达式,从压汞法的实验数据,研究了整体式载体分维数:实验得到的比表面积、体积增量及样品制备条件、孔隙尺寸等性能与分维数的关系,与模型提出的结论符合得很好,此方法对优化制备条件与块状载体的性能有重要意义.     

高温蠕变中的金相分维变化

对经高温持久强度试验的试样，沿其轴线拍摄一系列金相照片，用周积法测算出各自的维数，得出维数沿轴向的分布规律。从中发现，蠕变程度越严重的区域，其分形维数越小，在断裂的地方达到最小。在工程上，可以利用其分维最小值与平台区的分维来判断炉管的安全性。     

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。     

数字图像单个像元分形维数的特征与计算方法

通过分形理论把空间结构信息引入遥感分类中,必须解决分形维数计算的问题,为此提出了一种通过相邻像元间灰度值大小的变化计算数字图像单个像元分形维数的算法。选定计算窗口值 L 后,运用所编程序对 TM 遥感数据进行运算,并得到所需分维值数据。发现所得分维值随窗口值 L 增大而减小;大窗口值的分维值图像较抽象,但建议窗口值不超过 61;小窗口值的分维值图像较清晰,但窗口值不能小于 5。     

分形在梯度功能材料中的应用

对材料科学中的分形图形提取过程进行了研究，探索出一条行之有效的分形图形提取流程，用ＶｉｓｕａｌＣ＋＋可视化编程语言设计了分形维数计算程序，提取了Ｍｏ／β′－Ｓｉａｌｏｎ与Ｔａ／β′－Ｓｉａｌｏｎ系梯度功能材料界面的分形，并利用分维计算程序对其分殂维数进行了计算，实验证实Ｍｏ／β′－Ｓｉａｌｏｎ与Ｔａ／β′－Ｓｉａｌｏｎ系ＦＧＭ界面存在扩散，且烧结过程为扩散控制。分形维数计算结果与实验吻合。     

Multirange Fractals in Materials: Applications to Fracture and Mechanical Alloying under Ball Milling

A new model of multirange fractals is proposed to explain the experimental results observed on the fractal dimensions of the fractured surfaces in materials. A new expIanation to the WilIiford's multifractal curve on the relationship of fractal dimension with fracture properties in materials has been given. It shows the importance of fractorizing out the effect of fractal structure from other physical causes and separating the appropriate range of scale from multirange fractals.Mechanical alloying process under ball milling as a non-equilibrium dynamical system has been also analyzed     

分形概念及材料研究中的若干分形现象

本文叙述了分形及其在材料科学中的某些应用。主要内容有三方面:(1)规则和不规则分形的概念以及求分形维数的各种方法;(2)无序和分形,包括自然和物理现象中的分形,质量分形和表面分形、聚集体生长过程的模拟;(3)应用分形的例子,其中包括粉体生长过程和分形,离子束作用下薄膜相变中的分形现象,断裂面的定量观察。     

单轴多级循环加载岩石声发射分形特性试验研究

通过对三种岩石试样进行单轴循环加载试验,获得岩石试样加载过程中声发射事件率、能量率和空间位置分布数据。运用相空间重构理论直接从时间序列上通过G-P算法求得事件率和能量率关联分维,根据柱覆盖法求解得到声发射事件源空间分布关联分维。研究结果表明,声发射事件率、能量率和空间分布都具有分形特性,且声发射源空间分布分形特性最为显著。相空间的选取对关联维数有一定影响,相空间取值为4时能够较好地计算关联维数。将不同加卸载循环声发射源空间分布的变化趋势和声发射源空间分布关联维数变化趋势进行对比发现,声发射关联维数能够很好地反映岩石内部损伤破坏的发展。在等压加卸载条件下,声发射源空间分布关联维数显著突增。随着加卸载循环应力的增加,关联维数总体呈下降趋势,在达到较高应力时,关联维数则在较小区间内波动或下降趋势变得极其缓慢。该特点可以作为矿山地压微震监测预警的参考依据。     

金属断裂表面分形维数与组织、性能之间的关系

借助分形研究了拉伸条件下,分形维数 D_F 与拉伸性能之间的关系,讨论了显微组织对分形维数的影响,并把冲击韧性与分形维数之间的关系和拉伸性能与分形维数之间的关系进行了比较。实验结果表明,拉伸性能与分形维数只存在定性关系。延伸率与分形维数成正比,强度σ_b、σ_s与分形维数成反比,显微组织对分形维数有重要影响。断裂方式对分形维数、断裂性质以及两者的对应关系也有重要影响。     

Fraunhofer Diffraction by Koch Fractals: The Dimensionality

Abstract

Some properties concerning the fractal dimension of generalized Koch fractals and their Fraunhofer diffraction patterns are investigated as a continuation of the previous paper by Uozumi et al. The methods are discussed for evaluating the fractal dimension of object fractals from the intensity distribution of their diffraction patterns. Experimental results are shown to demonstrate some properties in this context. The fractal dimension of fractal areas in the Fraunhofer diffraction patterns is also considered.     

无机膜的分形性

介绍了无机膜的分形性和物体的三种重要分形．在溶胶－凝胶（Ｓｏｌ－Ｇｅｌ）制无机膜的工艺中，胶粒通过生长聚集方式成膜，它受质量分形规律控制，可以通过测定质量分形维数，利用ＤＬＡ、ＤＬＣＡ、ＲＬＣＡ等数学模型定量描述Ｓｏｌ－Ｇｅｌ膜生长的形态构造及对孔结构的影响．同样，在注浆及浸涂工艺制微孔基质膜工艺中，粉体以桥接堆积，存在孔结构分形，可通过测定孔分形维数定量描述这种在三维空间下高度复杂的孔结构．     

Multirange Fractal Analysis on the Negative Correlation between Fractal Dimension of Fractured Surface and Toughness of Materials

Applying the concept of multirange fractals, a new explanation to the Williford's multifractal curve on the relationship of fractal dimension with fracture properties in materials has been given. It 5hows the importance of factorizing out the effect of fractal structure from other physical causes and separating the appropriate range of scale from multirange fractals     

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.     

基于分形的结构损伤检测方法

将分形维数用于结构损伤检测。研究结果表明,结构不同状态下的振动信号的分形维数有明显的不同,可以将分形维数作为结构损伤检测的特征量,为结构的损伤检测技术提供了一个新的分析方法。