基于CT图像的再生混凝土细观破坏裂纹分形特征

为深入研究再生混凝土的破坏形态和内部裂纹扩展情况与普通混凝土之间的差异,以不同再生粗骨料(RCA)取代率的再生混凝土为研究对象,利用Phoenix v | tome | x s240微焦点工业CT获取再生混凝土加载到90%预估破坏荷载的二维扫描图像,借助Photoshop CS6图像处理软件,对材料内部破坏裂纹进行提取,进而基于分形几何理论,以分形维数及多重分形谱表征裂纹的分形扩展规律,建立分形维数和多重分形谱特征参数与RCA取代率和再生混凝土抗压强度的关系。结果表明:再生混凝土的细观受力破坏模式与普通混凝土不同,其受力破坏形态不仅取决于粗骨料与水泥浆体的界面黏结强度,还取决于RCA自身性能,当裂纹发展至天然粗骨料或强度较高的RCA时会绕过骨料表面继续发展,发展至强度较低的RCA时会贯穿骨料;分形维数可定量描述混凝土材料内部细观裂纹的整体扩展情况,即裂纹越丰富,分形维数越大;多重分形谱可反映从局部到整体不同层次的细观裂纹特征,裂纹分形维数和多重分形谱特征参数均与RCA取代率呈线性下降关系,与抗压强度呈线性增长关系;本研究可为再生混凝土在大型结构工程中的广泛应用奠定理论和实验基础。      

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.     

凹凸棒增强聚丙烯复合材料断裂韧性和断面分维的相关性

本文应用Wiliams新近提出的方法,研究了凹凸棒增强聚丙烯复合材料的冲击断裂韧性(G_c).通过测试断面的轮廓线,采用一种改变粗视化程度的方法,确定出断面的分维.结果表明,断裂韧性和断面分维存在一定的相关性,并就此进行简要讨论.      

Correlation between crack tortuosity and fracture toughness in cementitious material

This paper proposes a new technique for the evaluation of fractal dimension (D) of fracture surface and a quantitative correlation between D and fracture toughness of cementitious materials. The experimental program has been performed on compact tension (CT) specimens (600 × 525 × 125 mm) with three different aggregate sizes (d _max=4.7 mm, 18.8 mm and 37.5 mm). The fractal geometry concept is utilized in the evaluation of fracture surface roughness. To avoid indirect or destructive experimental procedures that are prohibitively laborious and time consuming, a new non-destructive technique is presented. Results of the analysis indicate that the concept of fractal geometry provides a useful tool in the fracture surface characterization. The results also suggest that the fracture toughness can be correlated with the fractal dimension of fracture surface.     

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.     

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.     

混凝土断裂面多重分形谱的二次拟合研究

基于混凝土断裂面的分形特性,采用Weierstrass-Mandelbrot (W-M)分形曲面法构造了具有不同分形特征参数的混凝土分形断裂面;对比研究了混凝土分形断裂曲面的多重分形特性,得到了混凝土分形断裂面的多重分形谱曲线。针对混凝土多重分形谱曲线的几何特性,利用最小二乘法对混凝土分形断裂面的多重分形谱进行了二次拟合;对拟合结果进行了定量分析,并对拟合函数进行改进,从而实现了对混凝土断裂面多重分形谱曲线的简化计算。试验结果与拟合结果的对比研究显示,该文所提出的多重分形谱拟合方法能够较好地实现对混凝土断裂面的多重分形谱曲线的模拟,并对多重分形谱的变化规律和趋势进行较为精确的表达。研究成果对研究混凝土断裂面的形成规律乃至混凝土结构或构件的优化设计提供了一种新的思路和方法。     

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.     

Influence of interface properties on fracture behaviour of concrete

Hardened concrete is a three-phase composite consisting of cement paste, aggregate and interface between cement paste and aggregate. The interface in concrete plays a key role on the overall performance of concrete. The interface properties such as deformation, strength, fracture energy, stress intensity and its influence on stiffness and ductility of concrete have been investigated. The effect of composition of cement, surface characteristics of aggregate and type of loading have been studied. The load-deflection response is linear showing that the linear elastic fracture mechanics (LEFM) is applicable to characterize interface. The crack deformation increases with large rough aggregate surfaces. The strength of interface increases with the richness of concrete mix. The interface fracture energy increases as the roughness of the aggregate surface increases. The interface energy under mode II loading increases with the orientation of aggregate surface with the direction of loading. The chemical reaction between smooth aggregate surface and the cement paste seems to improve the interface energy. The ductility of concrete decreases as the surface area of the strong interface increases. The fracture toughness (stress intensity factor) of the interface seems to be very low, compared with hardened cement paste, mortar and concrete.     

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.     

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。     

Geometrical analysis and pattern recognition using mapping technologies of three-dimensional fracture surfaces in materials

Geometrical analysis of fracture surfaces in materials was made using newly developed computer programs on the three-dimensional images reconstructed by the stereo matching method. The global value of the fractal dimension of the fracture surface was estimated by the box-counting method on a fatigue fracture surface of a Cu-Be alloy and impact fracture surfaces of a SiC and an alumina. The results of the present analysis were well correlated with those of the two-dimensional fractal analysis. The fractal dimension map (FDM) by the box-counting method and the surface roughness map (SRM) proposed in this study can give important information about the local fracture mechanisms, the crack growth direction or the fracture origin in materials. FDM and SRM have interesting characteristics by which one can discriminate the flat regions, the regions of complex geometry or the steeply inclined areas on a given fracture surface. Pattern recognition using mapping technologies of FDM and SRM is also applicable to the extraction of “hidden patterns” on fracture surfaces, which cannot be observed only by microscopes.     

Fracture surface topography and fracture mechanism in austenitic SUS316 steel plates fatigued by repeated bending

Fatigue experiments were carried out using the austenitic SUS316 steel plates (the average grain diameter is about 1.3 × 10⁻⁵ m) by repeated bending. The three-dimensional fatigue fracture surfaces were then reconstructed using stereo pairs of scanning electron micrographs by the stereo matching method. Striations were observed on the stage II fatigue fracture surface, while fine slip steps were found on the stage I fatigue fracture surface. The averaged value of the fractal dimension of stage I fracture surface was about 2.2 and was almost the same as that of stage II fracture surface when the fractal dimension was measured in the length scale range smaller than about one grain-boundary length (about 8 × 10⁻⁶ m). This may be attributed to the fact that both fracture surfaces were formed by the same mechanism, namely, slipping-off. According to the two-dimensional fractal analysis, both stage I and stage II fatigue fracture surfaces did not exhibit anisotropy in the length scale range of the fractal analysis smaller than about one grain-boundary length in the SUS316 steel. The fractal dimension of the fatigue fracture surface increased with decreasing the magnification of images when the maximum length scale of the fractal analysis was extended to the size of analyzed area. Magnification dependence of the fractal dimension was associated with large steps and ledges, which were not “typical” fractals.     

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.     

Fractal aspects of ductile and cleavage fracture surfaces

The aim of this paper is to evaluate and interpret the three-dimensional variational fractal dimension of a ductile and a cleavage fracture surface. The fracture surface is acquired by fracturing Charpy impact and static loaded specimens of a low alloy steel in ductile-to-brittle transition temperature range, and reconstructed by a stereoscopic technique. The three-dimensional variational method for measuring fractal dimension is improved by shifting algorithm and tested on the Takagi surface using the local fractal dimension. We find very good fractal behaviour in the ductile area, however, fractal characteristics in the cleavage area are less noticeable. The results are discussed in thermodynamical terms and promote the idea that fractal behaviour reflects the quasi-static process and that the fracture mechanisms in the ductile fracture are independent of strain rate (at least up to 10³ s⁻¹).     

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.     

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.     

基于分形理论分析裂缝形态对纤维/混凝土渗透性的影响

分形维数可以表征裂缝形态,能够用来分析混凝土裂缝断面的粗糙程度。裂缝形态对开裂混凝土的渗透性有重要影响,为研究这种影响,利用劈裂试验获得不同宽度的裂缝,使用不同的纤维种类,并设置多种纤维掺量,得到粗糙程度不同的裂缝断面,通过水渗透试验测量不同裂缝宽度时混凝土的渗透系数。采用激光扫描仪扫描裂缝断面并重构3D断面几何形态,采用立方体覆盖法计算断面分形维数。采用分形维数将实测裂缝宽度和有效裂缝宽度联系起来,联立达西定律和泊肃叶定律建立开裂混凝土渗透系数和分形维数的函数关系。结果表明:使用相同的网格划分法,分形维数随着纤维掺量的增加而增大;渗透系数随着纤维掺量的增加而减小;函数关系式中分形维数的指数绝对值和修正系数都随裂缝宽度增加而减小。      

基于分形理论的CFRP布增强混凝土梁抗弯性能研究

在实验室模拟酸雨腐蚀环境,完成了普通混凝土梁与CFRP布增强混凝土梁的抗弯试验,得到了各级荷载作用下构件表面裂缝的分布与演化过程,验证了受腐蚀CFRP布增强混凝土梁表面裂缝分布的分形特征。基于分形理论分析了受腐蚀混凝土梁在弯曲荷载作用下的开裂及破坏过程,详细讨论了梁表面裂缝的分形维数与其抗弯性能参数(损伤深度、混凝土强度、一阶频率、极限承载力、跨中挠度、位移延性系数)之间的关系。研究表明裂缝分形维数随着损伤深度的增加而减小,CFRP布增强混凝土梁的分形维数大于普通混凝土梁,其分形维数变化率与构件承载力变化率之间存在线性关系;因此梁表面裂缝分布的分形特征可作为CFRP布增强混凝土受弯构件损伤程度的衡量指标的观点,可为今后对“在役混凝土结构承载力和寿命预测的研究”提供参考。