Fractal analysis of granular ore media based on computed tomography image processing

The cross-sectional images of nine groups of ore samples were obtained by X-ray computed tomography(CT)scanner. Based on CT image analysis,the fractal dimensions of solid matrix,pore space and matrix/pore interface of each sample were measured by using box counting method.The correlation of the three fractal dimensions with particle size,porosity,and seepage coefficient was investigated.The results show that for all images of these samples,the matrix phase has the highest dimension, followed by the pore ...     

金属断裂表面的分形(Fractal)与断裂韧性

本文借助于图象分析技术使用Slit island方法研究了两种高强度钢不同热处理制度和不同试验温度条件下平面应变断裂表面的分形维数.结果表明,断裂表面是一种分形结构,断裂韧性K_(IC)值的对数随分形维数D_F增加成单调下降的直线关系.这种关系反映了不同热处理制度所引起的材料微观结构变化和不同试验温度所引起的断裂机制变化,D_F可以做为金属断裂韧性的一种度量。最后,用临界裂纹扩展力与不规则断裂表面真实面积之间的关系对结果进行了理论分析.     

热变形Ti-15-3合金再结晶晶粒的分形分析

根据分形几何学理论,分析热变形Ti-15-3合金固溶处理后的再结晶组织。分别采用小岛法和盒维数法计算出晶粒的分形维数,并探讨分形维数、晶粒尺寸与变形条件之间的关系。结果表明：再结晶晶粒形态具有自相似性,表现出典型的分形特征;且随着变形程度、变形速率的增加和变形温度的降低,再结晶晶粒尺寸减小,分维增大。分形理论的应用为非规则热变形组织的定量研究提供了一种新的方法。     

Effect of pouring temperature on fractal dimension of primary phase morphology in semi-solid A356 alloy

The fractal dimensions of primary phase morphology in semi-solid A356 alloy prepared by low superheat pouring and slightly electromagnetic stirring were calculated, and the effect of pouring temperature on fractal dimension of primary phase morphology in semi-solid A356 alloy was researched. The results indicate that it is feasible to prepare semisolid A356 alloy slurry by low superheat pouring and slightly electromagnetic stirring, and there is an important effect of pouring temperature on the morphology and the grain size of the primary phase in semi-solid A356 alloy, in which the reduction of pouring temperature can obviously improve grain size and shape factor of primary phase in semi-solid A356 alloy under the condition of a certain stirring power. The primary phase morphology of semi-solid A356 alloy prepared by low superheat pouring and slightly electromagnetic stirring can be characterized by fractal dimension, and the primary phase morphology obtained by the different processing parameters has the different fractal dimensions. Solidification of semi-solid alloy is a course of change in fractal dimension.     

材料断口分形维数测量方法研究进展

通过对材料断口定量研究重要性的描述引入分形理论。首先，从分形定义、分形特征图形和分形计算原理3个方面对分形理论进行阐述；其次，介绍小岛法、垂直截面法、计盒维数法等3种分形维数的基本测量方法及其改进方法；最后，对分形实验中可能出现的变量进行简要分析。本研究提出测量分形维数实验时优先考虑计盒维数法，以及在分形实验前需要控制断口参数、拍摄方案、拍摄数据处理方式等实验变量。     

凝固微观组织的多层次模拟

通过引入溶质再分配、溶质扩散、界面能各向异性和界面曲率,构建了描述合金凝固微观组织形态演变的元胞自动机模型.在介观和微观尺度上的模拟结果表明,该模型可有效地解决微观组织形成的多尺度问题.模拟结果清晰地再现了与实测结果相一致的枝晶形态和生长现象.根据分形理论采用分维定量比较了模拟结果和实验结果,两者的计盒维数分别为1.703和1.694,阐述了分维定量表征枝晶形貌的物理含义.模拟结果表明熔体过冷度和树枝晶的计盒维数呈近似抛物线关系.     

不同工艺参数下超音速等离子喷涂层界面结合行为及其分形特性∗

随着研究不断深入，分形几何可以用来描述涂层的表面形貌和复杂性，分形维数可实现形貌结构的定性描述向定量表征转变。为研究超音速等离子喷涂层界面结合行为与其分形维数之间的关系，采用对比试验研究喷涂距离、喷涂电流等工艺参数对涂层结合界面形貌和结合强度的影响，并引入分形理论对界面结合行为进行定量表征，进而探究结合界面形貌、结合强度、分形维数三者的对应关系。结果表明：相比于喷涂电流，喷涂距离对分形维数的影响更为显著。当喷涂距离为 80 mm 和 100 mm 时，随着喷涂电流从 400 A 增大到 500 A，分形维数呈先减小后增大趋势，最小为 1.115 0；当喷涂距离为 120 mm 时，粒子在等离子焰流中的飞行时间增长，随电流增大，涂层界面分形维数则先增大后减小。界面分形维数与涂层结合强度之间存在着正相关的对应关系。当分形维数在一定范围内呈增大趋势时，涂层 / 基体结合界面处孔隙减少、结合强度增大。 因此，涂层 / 基体结合行为的分形特性研究对评价涂层质量具有重要意义。     

Research on fractal characteristics of primary phase morphology in semi-solid A356 alloy

Semi-solid slurry of A356 alloy was prepared by low superheat pouring and slightly electromagnetic stirring, and the fractal characteristics of morphology in semi-solid primary phase was researched. The fractal dimensions of primary phase morphology in the semi-solid A356 alloy were calculated by the program written to calculate the fractal dimensions of box-counting in the image of solid phase morphology in semi-solid metal slurry. The results indicated that the morphology of primary phase in semi-solid A356 prepared by low superheat pouring and slightly electromagnetic stirring is characterized by fractal dimension, and the primary phase morphology obtained by the different processing parameters has different fractal dimensions. The morphology of primary phase at the different position of ingot has different fractal dimensions, which reflected the effect of solidified conditions at different positions in the same ingot on the morphology of semi-solid primary phase. Solidification of semi-solid alloy is a course of change in fractal dimension.     

Cross-scale characteristics of backfill material using NMR and fractal theory

This paper analyzed the pore structure, quantified the pore fractal dimension, calculated the grading index (GI) of mixed aggregate, and studied the relationship among GI, pore structure, and strength to describe the cross-scale characteristics of backfill, which is made from stone powder and cemented tailing. A series of experiments were conducted on stone powder cement tailings backfill (SPCTB). The GI formulas for mixed aggregates, containing stone powder and tailings, were derived based on the Füller theory. The nuclear magnetic resonance (NMR) fractal dimensions of backfills were derived using fractal geometry principles. Compared to the mesopore and macropore fractal dimensions, the correlation between micropore fractal dimension and macro-properties in terms of NMR porosity, pore structure complexity, uniaxial compression strength (UCS), and GI is the most significant. Macropore fractal dimension is generally correlated with UCS and GI and the other properties such as the shape of mixed aggregates also have an impact on fractal dimension. However, mesopore fractal dimension has no obvious relationship with macro-properties. Finally, the relationship between GI and UCS was studied, which contributed to improving backfill’s strength and optimizing gradation.     

A study on transition of iron from active into passive state

An investigation was carried out on the transition of an iron electrode from active to passive state in a sulphuric acid solution. It was found that the active-passive transition was an auto-catalytic process in which a pre-passive film grew on the electrode surface. The growing pre-passive film had a fractal edge whose dimension was affected by the applied passivating potential and the presence of chlorides in the solution. Applying a more positive passivating potential led to a faster active-passive transition and resulted in a more irregular pre-passive film. If chlorides were introduced into the sulphuric acid solution, the active-passive transition became more rapid and the pre-passive film more irregular. Apart from the influence on the growth of the pre-passive film, the presence of chlorides in the passivating solution was found to deteriorate the stability of the final passive film. All these phenomena can be understood if the passivating iron electrode is regarded as a dissipative system. To explain these results, a fractal pre-film model is proposed in this paper.     

Fractal analysis of fracture in aluminum alloy 01450T

The fractal dimensions of rupture surfaces of specimens of aluminum alloy 01450T tested for cyclic and static tension are evaluated. The relationship between the fatigue curve and the fractal dimension as a function of stress is established. The dependence of the maximum coefficient of stress intensity on the fractal dimension is determined.Translated from Metallovedenie i Termicheskaya Obrabotka Metallov, No. 8, pp. 20–25, August, 1995.     

Fractal phenomena in powder injection molding process

1　INTRODUCTIONGenerally ,Thefilling processofpowderinjec tionmolding(PIM )isanalyzedbyrheologicaltheory .Rheologicalmodelismadeupofbasicconservatione quations(mass ,momentum ,energyconservatione quations)thatmustbesatisfiedbymeltfeedstockinPIM ,constitutiveequationthatisusedtodescribetheprocessing parametersofmaterials ,andcorre spondingrestrictiveconditions .Itisagroupofpartialdifferentialequationsandisalsoanonlineardynamicssystemofmanyinfluentialfactors .Thevariationofmaterialthermo…     

锆-4合金低周疲劳断口裂纹扩展能量及分形特征研究

对锆-4合金低周疲劳裂纹扩展过程进行了探索性的研究。通过分析锆-4合金低周疲劳断口在裂纹扩展方向上能量及分形维数变化趋势，发现锆-4合金动态裂纹扩展中扩展期由3个阶段组成，每一阶段的能量和分形维数都不同。A-B段的能量最小，归一化值为0-0．0156，A-B段的分形维数居中，在工工方向均值为2．2796，标准差为0．0277，在LH方向均值为2．4516，标准差为0．0592。D-E段能量远大于A-B段，归一化值为0．8754～0．9652，但分形维数最小，LL方向均值为2．2214，标准差为0．0131，LH方向均值为2．3477，标准差为0．0550。F-H（或G-H）段能量最大，归一化值达到1，同时分形维数也达到最大，LL方向均值为2．3414，标准差为0．0704，LH方向均值为2．5398，标准差为0．0263。虽后，根据二次电子成像原理以及锆-4合金低周疲劳断口的形貌特征对此现象进行了初步分析。     

Using fractal structure to describe nickel crystal morphology

The morphology of nickel crystals can be quantified using measurements of fractal structure. In the study described in this article, fractal dimensions of cross sections of 16 nickel samples were determined, and the numerical analysis indicates that the more rugged surfaces are characterized by higher fractal dimensions although the relationship between morphology and fractal dimension is relatively weak. However, the data also show that fractal dimension is a better predictor of morphology than apparent density, which is the measurement currently used. The nickel samples were also subjected to an avalanching disc technique that has the potential to separate out the differences in flow in the different types of nickel powder. The differences in flow between powders were ascribed to the similar gross morphologies of the particles, and the presence of shattered individual particles in the mix. For more information, contact A.E. Lewis, University of Cape Town, Precipitation and Crystallisation Research Facility, Department of Chemical Engineering, Rondebosch, 7701, South Africa; +27-21-650-4091; fax +27-21-689-7479; e-mail alison@chemeng.uct.ac.za.     

粗糙度和尖峰高度对粗糙铜晶圆表面化学反应动力学参数的影响

根据液固化学反应特性和欧几里得有效面积公式,建立了适用于粗糙晶圆表面的化学反应动力学方程,得到了不同晶圆表面的化学反应速率常数和化学机械平坦化(CMP)前后晶圆质量差。根据晶圆表面不同位置的lg(RMS height)lgx拟合直线斜率和截距的平均值,得到了每个晶圆表面的分形维数与尺度系数,进一步得到了铜膜化学反应分级数。通过分析晶圆表面分形维数对化学反应动力学参数的影响,可以得出： 当表面分形维数为2.917时,铜膜的化学反应分级数为1,此时铜膜的络合反应过程中的所有瞬时反应数量达到最小值。最后的验证试验表明： 晶圆表面分形维数越大,CMP后尖峰消除量越大,即铜膜表面化学反应速率越快;晶圆表面分形维数越小,CMP后粗糙度下降越明显,即铜膜表面化学反应均匀性越好。     

超声强化和温度对铝酸钠溶液种分过程的影响

运用分形动力学的方法考察了超声强化和温度对铝酸钠溶液种分过程的影响。通过SEM图象观察发现低频超声强化相在种分过程中晶种表面有大量次生晶核的生成 ;较低温度下 (5 0℃ )能明显加速铝酸钠溶液晶种分解 ;升高温度 (6 0℃ )虽然对铝酸钠溶液的种分热力学平衡不利 ,但由于温度升高 ,晶种表面活性增大 ,因而可以增大种分反应的谱维数 ,前期能够加快铝酸钠溶液晶种分解反应速率。实验表明超声强化在较低温度下强化效果较好 ,而升高温度较超声强化对种分影响更为显著     

FRACTAL ANALYSES OF DIRECTIONAL SOLIDIFICATION BEHAVIOR OF A Ni-BASE SUPERALLOY

The morphology of solid/liquid interface of a directionally solidification process is describedby means of fractal analysis,and the relations among the fractal dimension of the solid/liq-uid interface,solidification rate,dendrite arm space and the phosphorus content of the test al-loys have been given.It was found that the increase of the solidification rate and the phos-phorus content of the test alloy will lead to a increase,following the regularity of exponentialfunction,in the fractal dimension of solid/liquid interface.Furthermore,by combining thefractal theory and the thermodynamic principle with the measured results,it has been provedthat the fractal dimension is not only a kind of simple geometrical parameter used in des-cribing irregular geometry,but also a state function depending the change of solidificationparameters and chemical compositions.     

高温合金定向凝固行为的分形分析

采用分形理论定量地描述了定向凝固过程中固-液界面的形态,给出了固-液界面的分形维数与凝固速度、枝晶间距和试验合金中磷含量之间的关系发现随着凝固速率和合金中磷含量增大,固-液界面的分形线数呈指数规律增加。而且,结合分形理论和热力学理论论证了分形维数不仅仅是单纯描述不规则图形的几何参量,而且是一个依赖于凝固参数、化学成分变化的态函数     

定向凝固高温合金晶界形貌的分形描述SCIEI

用分形分析的方法定量描述了定向凝固高温合金的树枝晶晶界形貌。结果表明，随着凝固速率的提高，晶界分形维数均增大。还讨论了凝固合金系统熵与晶界分形维数之间的关系。     

基于空间维和信息维的疲劳断口定量分析

定性描述4种典型的疲劳断口形貌。采用计盒法获得断口空间维和信息维大小,对数坐标系下,覆盒数目和覆盒尺度数据线性拟合优度均大于0.99,空间维和信息维结果可信;4种不同断口空间维大小在2.40~2.47之间,信息维数据在1.69~1.76之间;综合两种分维结果可定量评价断口的不规则性和复杂性。