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。     

The effect of crack propagation mechanism on the fractal dimension of fracture surfaces in steels

The paper reports on the results of a fractal analysis of fracture surfaces of Ni–Cr steel in two different states of heat treatment simulating embrittlement. The change in the fractal dimension of the fracture surface demonstrates a wavy character and dispersion depending on the microstructural state of the tested steel. The results of the fractal analysis in the crack growth direction and across the entire crack front were used as the basis for a reconstruction of the geometry of the fracture surface, providing a new geometric tool for fractographic analysis. The competing effects of transgranular and intergranular brittle fracture may lead to increased roughness of the fracture surface and its fractal dimension. The threshold value of the fractal dimension of the sections perpendicular to the fracture surface, indicating the transition from transgranular to intergranular fracture, is 1.12.     

Identification of modes of fracture in a 2618-T6 aluminum alloy using stereophotogrammetry

The identification and the development of a quantification technique of the modes of fracture in fatigue fracture surfaces of a 2618-T6 aluminum alloy were developed during this research. Fatigue tests at room and high temperature (230 °C) were carried out to be able to compare the microscopic fractographic features developed by this material under these testing conditions. The overall observations by scanning electron microscopy (SEM) of the fracture surfaces showed a mixture of transgranular and ductile intergranular fracture. The ductile intergranular fracture contribution appears to be more significant at room temperature than at 230 °C. A quantitative methodology was developed to identify and to measure the contribution of these microscopic fractographic features. The technique consisted of a combination of stereophotogrammetry and image analysis. Stereo-pairs were randomly taken along the crack paths and were then analyzed using the profile module of MeX software. The analysis involved the 3-D surface reconstruction, the trace of primary profile lines in both vertical and horizontal directions within the stereo-pair area, the measurements of the contribution of the modes of fracture in each profile, and finally, the calculation of the average contribution in each stereo-pair. The technique results confirmed a higher contribution of ductile intergranular fracture at room temperature than at 230 °C. Moreover, there was no indication of a direct relationship between this contribution and the strain amplitudes range applied during the fatigue testing.     

Correlation of microcrack fracture size with fatigue cycling on non-crimp fabric/RTM6 composite in the uniaxial fatigue test

Quantitative fractographic studies have become an important field to understand the fracture process. Future trends pointed out quantitative fractographic analysis as an important tool for a better comprehension of the damage and currently it had been focused on studies about geometric attributes of the fracture topographic surface and microstructure features. This research aimed a quantitative analysis of the cusp aspects generated in an axial fatigue test by carrying out fractographic measurements in order to know their influence on the fatigue test parameters, e.g. stress level, number of cycles, frequency, and stress ratio. Fatigue tests in tension–tension mode were undertaken in different stress levels, consequently leading to different number of cycles. Quasi-isotropic laminates were fatigue tested until the fracture, which was observed in SEM, and the hackle patterns were measured in the public domain program called Image J. The response of the laminate obeyed a cusp size pattern according to a number of cycles until the fracture was reached.     

D6AC钢冲击断口形貌的分形研究

本文利用扫描电镜对含Mn$夹杂物和含ZrN夹杂物的D6AC钢的冲击断口形貌进行了观察与分析;利用数字图象法测定了试样的断口分形维数,揭示了冲击断口形貌和冲击韧性与夹杂物含量之间的内在联系,探讨了材料冲击断口形貌与分形维数的关系,拓宽了分形几何学在材料领域的应用范围.     

The fractal geometry of Si3N4 wear and fracture surfaces

Good mechanical properties and chemical stability at high temperatures make silicon nitride a good candidate as an advanced engine material. Much research has been done to characterize the mechanical strength and resistance of crack propagation in this material. In this paper, we use fractal analysis to study the geometry of Si3N4 fracture and wear surfaces. We found that the geometries of the failure surfaces as characterized by the fractal dimensional increment, D*, under different failure stress states are similar for the same brittle material, but different for different brittle materials. The similar D* in an identical brittle material implies that the failure process in the material is the same regardless of loading mode, i.e., mode I or mixed-mode stress. The fractal technique is shown to be useful for correlating the fractal dimension to the material properties and fracture-surface topography. This revised version was published online in November 2006 with corrections to the Cover Date.     

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.     

Fracture toughness of maraging steel from Charpy “V” notch specimens

Compact tension (CT) and Charpy V notch (CVN) (impact and three-point bend) specimens of 18 Ni 1800 MPa maraging steel (parent metal and weldment) were used to determine plane strain fracture toughness (K _IC) and CVN impact energy (CVNIE), respectively. Using an empirical equation,K _IC-CVNIE correlation is attempted which could be advantageously utilized for routine quality control of inward material to effect savings in cost and time. Investigations reveal betterK _IC-CVNIE correlation for tests using the precracked CVN specimens. Scanning electron microscopic (SEM) observations reveal good correlation between fractographic features and fracture toughness.     

SiC填充PP/FA复合材料拉伸强度及分形特征

目的定量研究不同含量碳化硅晶须(SiC)对聚丙烯(PP)/粉煤灰(FA)复合材料拉伸强度以及拉伸断口复杂程度的影响。方法以聚丙烯为基体,马来酸酐接枝聚丙烯(PP-g-MAH)为相容剂,FA和SiC为填料,采用熔融共混法制备PP/FA/SiC复合材料。利用电子万能试验机测试复合材料的拉伸强度,同时采用扫描电镜对拉伸断口进行形貌分析,并基于分形原理,利用差分盒维计数法计算复合材料拉伸断面的分形维数,分析研究复合材料拉伸断面的分形维数与其拉伸强度间的关系。结果复合材料的拉伸断面分形维数在1.24~1.90之间,相关系数均大于0.9,说明其具有统计意义上的自相似和较强的相关性。结论复合材料拉伸强度的对数与其断面的分形维数呈线性函数关系。     

Three-dimensional fractal analysis of fracture surfaces in titanium–iron particulate reinforced hydroxyapatite composites: relationship between fracture toughness and fractal dimension

Fractal dimension has been considered as a measure of fracture surface roughness of materials. Three-dimensional (3D) surface analysis is anticipated to provide a better evaluation of fracture surface toughness and fractal dimension. The objective of this study was to quantify the fracture surfaces and identify a potential relationship between fracture toughness and fractal dimension in a new type of core–shell titanium–iron particulate reinforced hydroxyapatite matrix composites using SEM stereoscopy coupled with a 3D surface analysis. The obtained results showed that both fracture surface roughness and fractal dimension increased with increasing amount of core–shell Ti–Fe reinforcing particles. The fractal dimension was observed to be a direct measure of fracture surface roughness. The fracture toughness of the composites increased linearly with the square root of fractal dimensional increment (i.e., followed the Mecholsky–Mackin equation well) due to the presence of Ti–Fe particles along with the effect of porosity in brittle materials. The 3D fractal analysis was suggested to be a proper tool for quantifying the fracture surfaces and linking the microstructural parameter to fracture toughness.     

Characterization of grain-boundary configuration and fracture surface roughness by fractal geometry and creep-rupture properties of metallic materials

Grain-boundary configuration in heat-treated specimens and fracture surface roughness in creep-ruptured specimens of several kinds of metallic material were quantitatively evaluated on the basis of fractal geometry. Correlations between the fractal dimension of grain boundary, that of fracture surface profile, the creep-rupture properties and the fracture mechanisms of the alloys are discussed. In heat-resistant alloys, the fractal dimension of a nominally serrated grain boundary was always larger than that of a straight grain boundary in the same alloy. The relative importance of the ruggedness of grain boundaries was estimated by the fractal dimension difference between these two grain boundaries. There was a quantitative relationship between the increase of the fractal dimension of the grain boundary and the improvement of rupture ductility and rupture strength owing to grain-boundary serration in the alloy. A similar correlation was also found between the increase in the fractal dimension of the fracture surface profile and the improvement of the creep-rupture properties, since in some cases the fractal dimension of the fracture surface profile was correlated with that of the grain boundary. Both grain boundary and fracture surface profile were assumed to exhibit a fractal nature between one grain boundary length (upper bound) and an interatomic spacing (lower bound). In carbon steels with ferrite-pearlite structure, according to the increase in pearlite volume fraction, the rupture ductility decreased and the fracture mechanism changed from transgranular fracture in pure iron and low-carbon steels to intergranular fracture at ferrite-pearlite grain boundaries in medium-carbon steels, and further to intergranular fracture at pearlite grain boundaries in high-carbon steels. The correspondence between the fractal dimension of the grain boundary and that of the fracture surface was confirmed in ruptured specimens of ferrite-pearlite steels when the grain boundary was the fracture path.     

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。     

A Fractal Study on Brittle-Ductile Transition forTi-24Al-11Nb Alloy

The mechanical behaviours of Ti-24Al-11Nb alloy in the brittle-ductile transition (BOT) have been investigated by using three-point bending tests. The temperature dependence of the fractal dimensions and fractal characterization of fracture surfaces are presented. The probable mechanism controlling BDT of intermetallic alloys are proposed according to fractal geometry.Additionally. it is found that there is a positive relationship between the fractal dimension and fracture toughness in BDT for Ti-24Al-11Nb alloy     

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。     

水泥断口表面形貌的分形维数定量表征研究

利用分形几何学理论定量表征了几种水泥断口表面的微观形貌特征,并且考察了断口表面分形维数与其抗压强度的关系.结果表明,水泥断口的表面分形维数介于2～3之间,且线性回归分析的相关系数均大于0.98,强的相关性表明实验所选用的水泥断口具有明显的分形特征;水泥的抗压强度与其断口表面分形维数值呈正相关关系.     

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.     

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.     

The fractal dimension of grain-boundary fracture in high-temperature creep of heat-resistant alloys

The fractal dimension of the grain-boundary fracture in high-temperature creep was estimated by the vertical section method on several creep-ruptured specimens of the cobalt-nickel- and iron-based heat-resistant alloys. Grain-boundary microcracks linked to the fracture surface were also taken into account in the present analysis by the box-counting method. In the specimens containing many grain-boundary microcracks linked to the fracture surface, the fractal dimension of the grain-boundary fracture was larger in the scale range of more than about one grain-boundary length than in the scale range less than this length. Thus, there was a cross-over in the fractal dimension of the grain-boundary fracture at about one grain-boundary length in these specimens. In the specimens containing much fewer microcracks, there was no clear cross-over in the fractal dimension of the grain-boundary fracture with regard to the scale of the analysis, irrespective of creep-ductility and grain-boundary configuration of the specimens. The fractal dimension of the grain-boundary fracture was generally larger in specimens with serrated grain boundaries than in specimens with straight grain boundaries in these heat-resistant alloys, because the fractal dimension of the grain boundary and the number of the grain-boundary microcracks were larger in the former specimen. The fractal dimension of the grain-boundary fracture did not tend to converge to unity when the scale of the analysis approached the specimen size. The inclusion of near-specimen size data with regard to the scale of the analysis did not affect the fractal dimension of the grain-boundary fracture in these alloys. Thus, the grain-boundary fracture in the creep-ruptured specimens exhibited a fractal nature, at least in the scale range below specimen size, although there was a cross-over in the fractal dimension of the grain-boundary fracture in specimens containing a large number of grain-boundary microcracks.     

SiCw/Al-Al3Ni复合材料断口的分维特征

本文所研究的复合材料,其基体Al-Al₃Ni合金具有很好的组织热稳定性,因而可以通过改变拉伸温度并在组织结构基本不发生变化的情况下,使材料的分维和断裂功发生变化.分维的测量采用断口轮廓法(FPM).研究结果指出,SiCw/Al-Al₃Ni复合材料的分维可分为三部分,每部分分维存在的尺寸范围与组织结构有一定的对应关系.文中还讨论了断裂功与分维之间的关系.