Nondestructive Evaluation of Corrosion by Fractal Geometry

Abstract

Fractal geometry is finding its application in the nondestructive evaluation (NDE) of corrosion by characterizing the corrosion surface with fractal dimensions. It was found that corrosion surfaces can be well described by multifractals. Two algorithms were used to obtain the fractal dimensions of a corroded aluminum alloy surface, one being box-counting and another being coherent light scattering. Fractal dimensions were related with the damage caused by corrosion and fatigue.     

垂直截面法测量的断口分形维数与7475 Al 合金超塑性的关系

本文利用垂直截面法测量了7475Al 合金在不同温度、不同应变速率及不同晶粒尺寸条件下超塑拉伸变形时断裂表面的分形维数。结果表明:断裂表面的分形维数越高,合金超塑拉伸破断时的延伸率越大。     

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。     

粉末NBR-PVC共混型热塑性弹性体断裂面的分形维数

本文利用扫描电镜对粉末NBR-PVC共混型热塑性弹性体拉伸断面形貌进行了观察与分析;基于断面小岛周长-面积关系,测定了试样的断口分形维数,考察了NBR含量、拉伸断面分形维数、力学性能(拉伸强度、断裂伸长率、邵氏硬度)之间的关系。结果表明,NBR-PVC弹性体拉伸断面的分形维数随着NBR含量的增加而增加,当NBR含量超过29份后其分形维数呈下降趋势;分形维数与材料的拉伸强度、断裂伸长率和邵氏硬度变化关系一致。     

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。     

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。     

超级分形管分形维数的上限与下限

超级分形管在结构和几何上都具有很强的自相似性,因此,通过选择一个特殊的覆盖单元——一个管就可以基于数格子法计算它的分形维数,推导出基于各级的拓扑结构分别为Zigzag和armchair的超级分形管的分形维数公式。虽然只有有限级的超级分形管在工程是可用的,但其结果为设计新型的超级分形天线、超级分形格栅以及分形电路中的电子器件提供了思路和启发。     

受腐蚀钢筋混凝土构件破坏过程的分形行为

本文根据试验资料，分析了受腐蚀钢筋混凝土构件在荷载作用下开裂及裂纹的演化、分布特性，证明了受腐蚀钢筋混凝土构件表面裂缝具有分形特征。利用分形几何学研究受腐蚀钢筋混凝土构件开裂及破坏过程,讨论了受腐蚀钢筋混凝土构件表面裂缝的分维数与构件中混凝土及钢筋的腐蚀损伤程度之间的关系及其延性系数降低量之间的关系。研究表明该分维数可作为构件受腐蚀程度的衡量指标,并可用来评估不同腐蚀程度钢筋混凝土构件的力学性能，从而为受腐蚀钢筋混凝土构件的剩余寿命评价提供了一个新的途径,为受腐蚀钢筋混凝土结构的承载力研究建立了一定的理论基础。     

基于分形理论的岩石冲击破坏分形分析

利用大直径分离式霍普金森压杆试验系统,对绢云母石英片岩和砂岩进行冲击压缩试验, 采用不同等级标准筛对岩石冲击破碎后试块进行筛分统计,运用分形几何理论,计算出冲击荷载作用下两种岩石破碎块度分布的分形维数,研究冲击速度对块度分维影响,分析两种岩石动态抗压强度随块度分维的变化关系。试验结果表明,绢云母石英片岩块度分维大部分集中在1.9~2.4之间,砂岩集中在2.5~3.0之间;两种岩石分形维数随冲击速度的升高呈上升趋势,近似线性正比关系;绢云母石英片岩动态抗压强度与块度分维无明显函数关系,砂岩动态抗压强度随块度分维的增大呈增加趋势。采用分形维数对岩石试件在冲击破碎过程中动态抗压强度的变化进行定量描述,为探索岩石动态破碎分形特征与冲击力学性能之间的内在规律,开辟新的研究途径。     

钛酸钾晶须增韧尼龙66及其断面分形研究

钛酸钾晶须用弹性体表面改性后实现了对尼龙66的有效增韧,改性剂 氧树脂用量为晶须的1．5％（质量）时,复合体系的冲击强度比纯尼66提高132％,同时弯曲,拉伸强度分别提高55％和48％,采用显微图像灰度法,对晶须增韧尼龙进行了基于断面小岛周长－面积关系的分形研究,考察了小岛选取对断面分维数测量结果的影响,研究表明,测得的分维数随选取小岛的面积阈值增加而增大,面积阈值达500η^2(η为侧量码尺）后,分维数趋于稳定,晶须增韧尼龙的力学强度与材料断面分维数之间的变化规律一致,对于从材断断裂机制与断面形貌进行了解释。     

光学表面的分形结构和表征算法

根据光学表面在微观结构上呈现出的统计自相似性，利用与尺度无关的分形模型描述了光学表面的结构特征，采用结构函数法对分形维数进行计算，分析了抛光表面的分形特点。在此基础上，提出了采用一阶自回归分形模型对抛光表面进行模拟的新方法，分析了界定尺度、模型参数对分形特征和分形维数的影响规律。     

Fractal research on AFM images of polycrystalline aluminum surface with adsorption film of SDS inhibitor

We propose a new method of fractal analysis of the phase images obtained by the atomic-force microscopy (AFM) to study the properties of molecular adsorption films of corrosion inhibitors on the coarse polycrystalline surface, which can hardly be distinguished by using AFM height images due to the roughness of the surface. The system of polycrystalline aluminum and SDS (Sodium Dodecyl Sulfate) inhibitor is chosen as the research object. The electrochemical measurements of aluminum electrodes precoated with SDS films are carried out in HCl solutions, and the results show that the inhibition efficiency increases with the concentration of SDS in the prefilming solution and then remains nearly constant as the CMC (critical micelle concentration) of SDS is exceeded. The fractal analysis of the AFM images of prefilmed aluminum surfaces obtained in SDS solutions is performed and demonstrates that, as the SDS concentration increases, no obvious changes are observed for the fractal dimensions of height images, whereas the phase images present regular changes in the values of fractal dimensions, thus displaying the consistent alteration rule as revealed by electrochemical tests. The results prove the feasibility of the fractal analysis of AFM phase images in characterizing the adsorption behavior of the corrosion inhibitor on polycrystalline coarse surfaces.     

异步轧制Pb-Ca-Sn-Al合金晶界节点分形分析

为了确定晶界节点分形维数是否存在,以低碳钢冷轧薄板标样为研究对象,在MATLAB软件平台上自行开发了晶界分形维数计算程序,采用标准分形图形-koch曲线检验了自开发分形程序的准确性,利用该程序计算了3种标准下(不同晶粒延伸度)不同晶粒度级别的金相图片晶界节点分形维数,并研究了不同工艺条件下Pb-Ca-Sn-Al合金晶界节点的分形维数.结果表明:自开发的分形计算程序准确;晶界节点的分形维数存在;不同工艺条件Pb-Ca-Sn-Al合金晶界节点的分形维数与工艺参数之间存在定量联系.在一定范围内,随着压下率、异速比、退火温度的增加,晶界节点的分形维数随之增加;随退火时间的增加,Pb-Ca-Sn-Al合金晶界节点分形维数先上升后下降;退火张力增加,晶界节点分形维数下降.     

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。     

基于分形的表面形貌特征描述与评定参数的研究

运用Ｗｅｉｅｒｓｔｒａｓ－Ｍａｎｄｅｌｂｒｏｔ函数对表面形貌进行描述，并利用结构函数求出表面形貌的分形维数和形貌系数。研究了分形参数与表面支承长度率曲线的关系。理论分析和实验结果表明：支承长度率曲线主要与分形维数有关，而形貌系数对该曲线的影响较小。用分形理论研究表面形貌时，分形维数是主要的评定参数，它能提供表面接触承载能力的单值定量的评估，从而比支承长度率曲线更简洁而实用。     

Fractal dimensions for fatigue fracture surfaces performed on micro- and meso-scale levels

A methodology was developed to use digital photograph fracture for calculating the integral fractal dimension and spectrum fractal dimensions for two perpendicular directions. The fractal dimension value, which was discovered by the variation of the pixel size up until the fractal dimension became unchangeable, i.e., where d _\min,d _\max are the borders of the scale level used. The effectiveness of the methodology performed showed the basis of the fracture surface analyses for Al-based alloys BS L65 and 2024 T351 (analogous to Al alloy D16T), specimens of which were tested by pull-push with imitation fretting corrosion damage of the sur- face and with four-point bending after the laser peening, respectively.     

Fractal dimensions for fatigue fracture surfaces performed on micro- and meso-scale levels

A methodology was developed to use digital photograph fracture for calculating the integral fractal dimension and spectrum fractal dimensions for two perpendicular directions. The fractal dimension value, which was discovered by the variation of the pixel size up until the fractal dimension became unchangeable, i.e., where d _\min,d _\max are the borders of the scale level used. The effectiveness of the methodology performed showed the basis of the fracture surface analyses for Al-based alloys BS L65 and 2024 T351 (analogous to Al alloy D16T), specimens of which were tested by pull-push with imitation fretting corrosion damage of the sur- face and with four-point bending after the laser peening, respectively.     

Analysis of the fractal dimension of grain boundaries of AA7050 aluminum alloys and its relationship to fracture toughness

Quantitative analysis of the grain boundaries in partially recrystallized microstructures of heat-treated 7050 aluminum alloys has been performed. Fractal dimensions of the extracted grain boundaries were calculated by box-counting method. Five different types of tear-tested materials rolled in different processes each at two orientations of 0° and 90° were studied. Efforts were made to connect the fractal dimensions of grain boundaries in the crack propagation direction to the fracture toughness (unit propagation energy, UPE, in tear test). The results show that there is a linear correlation between UPE and the fractal dimensions of the grain boundaries along the crack propagation direction for both 0° and 90° samples. The dependence corresponds well with the observation of transition from intergranular fracture to transgranular fracture with the increase of UPE. Quantitative analysis has also been performed on the micrographs to estimate the degree of recrystallization and the grain size in crack growth direction. No correlation between the fraction of recrystallized grains and the UPE could be detected.     

形变氮化20钢冲击断口的分形研究

利用垂直截面法测量了２０钢经不同形变和氮化复合处理后冲击断裂表面的分形维数。结果表明，材料的冲击功ＡＫ和沿裂纹扩展方向剖面Ｋｏｃｈ曲线的分形维数ＤＦ均随形变量的增加而增大。分形维数ＤＦ与ｌｎＡＫ之间呈正变化的线性关系，且满足关系式：ｌｎＡＫ＝６．３１３ＤＦ－４．９５１。