材料断裂形貌分维的测量及计算机模拟

材料断裂形貌如断口表面、断裂裂等均被认为具有分形结构而被称为实际分形体,论述了这类实际分形体维数的实验测量、计算方法和分维测量、计算中出现的分维不性问题,指出生分维不确定性的原因,并且通过计算机模拟演示了一些实际测量因素对测量和计算实际分形体维数的影响。     

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。     

分形理论及其在高分子材料研究中的应用

本文介绍了分形、分维的基本概念，评述了分形在高分子材料研究方面的一些应用。     

动态界面裂纹扩展行为的分形描述

本文以无限弹性体中具有自相似分形几何结构的含裂纹界面研究对象，借助分形几何概念对分形界面裂纹的动态扩展行为即对界面裂尖应力场，界面裂纹扩展速度，加速度，裂尖复合应力强度因子，动态能量释放率，双材料不匹配参数，界面裂纹的分维以及它们之间的关系进行描述，给出了界面裂纹扩展行为的分形动力学模式。     

超细粉末团聚体分形结构的小角散射测量及分维表征

通过小角散射实验对多种超细粉末的团聚体结构进行了研究，发现分形形态是粉末团聚体的普遍特征。提出了用新的团聚参数分维来表征粉末的聚集程度。分析并讨论了分维与团聚状态、工艺条件和粉末性能的相互关系。     

材料断口分形研究现状及发展前景

讨论了分形几何应用于断裂研究的几个基本问题,主要包括断面的分形特征与分形测量,分维与断裂韧性的关系以及金属断裂的多种分形模型.进一步阐述了分形理论在金属断裂方面的应用前景.     

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。     

粉体粒度分布的分形特征

应用分形几何理论，研究了粉体的粒度分布特征，发现在双对数坐标下，许多材料粒径的重量积百分含量与粒长之间呈直线关系。表明其粒度分布具有分形结构，分维可作为粒度分布特征的一个序参量，它反映了粉体颗粒的粗细程度和集中、均匀特性。     

多孔材料孔结构分形维数的研究现状

分形表征是多孔材料孔结构表征中的一种新兴的方法。通过构造分形几何模型，阐述了多孔材料孔结构分形表征中不同类型的分形维数。分析了现阶段研究中存在的问题，探讨了分形表征在多孔材料孔结构表征中未来的发展趋势。     

嘉陵江流域形态及流量过程分维研究

本文运用分形有关的基本理论和方法初步探讨了嘉陵江流域形态特征的分形性和分维值变化，并对控制站的日流量过程的分维进行了计算和对比分析，以利将分形理论和分维值用于水文计算和预报的进一步研究。     

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.     

Ag-TCNQ分形生长现象研究

利用溶液化学反应法，在Ag-TCNQ过饱和度较大的条件下，发现了Ag-TCNQ的分形生长现象。研究表明，Ag膜厚度和与溶液反应的时间对样品的形貌有影响。Ag膜薄生成的样品稀疏，分形维数小；反之样品致密，分形维数大。反应完全时样品最致密，分形维数最大。SEM研究表明，这些分形生长主要是堆垛分形，分支堆积有序，表现出材料良好的自组织性。     

Fractal processing of AFM images of rough ZnO films

Fractal image processing has been applied to characterize the surface roughness of ZnO films as measured by atomic force microscopy. The simple fractal analysis suggests that the fractal dimension D can be used to describe the change of the whole grain morphology along the growth direction. Multifractal analysis shows that the scaling range is close to three orders of magnitude, which is larger than that of a simple fractal and most empirical fractals. The width of the multifractal spectrum can be used to characterize the roughness of the film surface quantitatively and the shape of multifractal spectrum can describe the ratio between the number of the lowest valleys and the highest peaks statistically.     

基于分形的航天器故障预报

提出了一种基于分形的航天器故障预报新方法,并给出具体预报公式。由于故障发生前都蕴含前兆因子,这些因子可导致测量信号分形维数的变化,根据这些变化可进行故障预报,该方法理论明确,参数简单,克服了传统故障预报方法易丢失故障信息的缺点。     

分形理论应用于包装材料性能研究的进展

目的 分形现象广泛存在于包装材料性能等方面,目前尚无系统性的描述,有必要总结分形理论应用于包装材料性能的研究进展,为采用分形方法研究包装材料性能提供参考.方法 从分形特征的提取、分形维数的计算方法等方面,综述应用于金属合金和陶瓷等无机材料、高分子聚合物和复合材料等的分形分析方法.通过包装材料的分形维数模型,分析包装材料的分形特征参数与其性能之间的关系.结果 利用分形分析方法,可以定性和定量表征大量不同种类包装材料的分形特征、微观结构和力学等性能.结论 利用分形理论研究包装材料性能的方法具有普遍性,包装材料性能与分形维数的关系将是分形理论在包装材料性能研究方面的重要发展趋势之一.     

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     

Application of the Fractal Approach to Determination of the Poisson Coefficient of Polymeric Systems

Within the framework of the combination of the classical elasticity theory with the concepts of the scale invariance of the polymer structure, the dependence of the Poisson coefficient on the dimension of the fractal cluster has been found. It has been shown that the Poisson coefficient of polymers is related to the value of relative deformation. The range of permissible values of the fractal dimension of materials for the cases of uniaxial tension and compression has been determined.     

薄壁圆盘裂纹的应变分形特征及诊断识别研究

运用有限元方法对裂纹圆盘进行动态特性分析,获得振型和应变响应。应用多重分形理论计算和分析裂纹圆盘应变响应的广义维数和敏感维数。把应变广义分形维数、敏感维数作为圆盘裂纹状态的特征量,对圆盘的裂纹诊断与识别进行定性及定量研究。通过计算得到圆盘裂纹的应变广义维数相关系数,用广义维数相关系数法对圆盘裂纹长度进行定量识别。通过对实例的识别分析,考查了裂纹长度的识别精度及广义维数相关系数法对裂纹长度的定量识别的实用性。