A fractal study of the fracture surfaces of cement pastes and mortars using a stereoscopic SEM method
TL;DR: In this article, a stereoscopic scanning electron microscopic (SEM) method based on surface areas tallied over a much wider range of measurement scales was used to evaluate the fractal characteristics of fracture surfaces of cement pastes and mortars.
About: This article is published in Cement and Concrete Research.The article was published on 2001-10-01. It has received 81 citations till now. The article focuses on the topics: Fractal dimension & Fractal.
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Journal Article•
TL;DR: In this paper, a modified Richardson fractal equation for profiles and fracture surfaces was proposed to obtain constant slopes from the reversed sigmoidal curve (RSC) for both profiles and surfaces respectively, where slopes from RSCs are related to the new constant fractal dimensions D β and D γ in the modified fractal equations for profiles.
Abstract: The fractal characteristics of a series of fractured AISI 4340 steel specimens were studied experimentally by means of vertical sections through the fracture surface. Extensive fractal data have been generated for both the fracture surfaces and their profiles. Fractal plots for the irregular profile curves differ significantly from those of the infinitely subdivisible curves with “self-similarity” as postulated by Mandelbrot. Instead of a linear fractal curve and constant fractal dimension D , we find a reversed sigmoidal curve (RSC) and variable D . Because of the inadequacies of the linear Richardson fractal equation, we have developed an alternative procedure whereby constant slopes β and γ are obtained from the RSCs for both profiles and surfaces respectively. Since a fractal equation for surfaces apparently does not exist, we propose one that parallels the Richardson equation for profiles. Slopes from the RSCs are related to the new constant fractal dimensions D β and D γ in the modified fractal equations for profiles and fracture surfaces. Some insight into the physical nature of the fractal dimension is afforded by its close similarity to fracture roughness parameters that have simple physical meanings. It is believed that the results of the extensive study may have general validity for the irregular complex curves and surfaces of nature.
187 citations
TL;DR: In this article, the pore structure and mechanical properties of lime-cement mortars are evaluated in order to analyze their potential use, because this kind of mortar could reduce the disadvantages presented by both lime-based and cement-based mortars.
162 citations
Cites background from "A fractal study of the fracture sur..."
...Surface fractal dimension In a previous paper [24], pore fractal objects were defined as dense objects within which there exists a distribution of pores with a fractal structure....
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TL;DR: In this article, the surface fractal dimensions (SFDs) of pore structure of cement pastes and mortars with/without ground granulated blast-furnace slag (GGBS) incorporated into binder were investigated.
152 citations
TL;DR: In this article, the surface fractal dimensions of high-volume fly-ash cement pastes are evaluated for their hardening processes on the basis of mercury intrusion porosimetry (MIP) data.
149 citations
TL;DR: In this paper, the fractal dimension of pore surface and the capillary pore volume were respectively selected as representative parameters for pore size distribution and pore volumes to enhance the reliability of the strength model.
146 citations
References
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Book•
01 Jan 1982
TL;DR: This book is a blend of erudition, popularization, and exposition, and the illustrations include many superb examples of computer graphics that are works of art in their own right.
Abstract: "...a blend of erudition (fascinating and sometimes obscure historical minutiae abound), popularization (mathematical rigor is relegated to appendices) and exposition (the reader need have little knowledge of the fields involved) ...and the illustrations include many superb examples of computer graphics that are works of art in their own right." Nature
24,199 citations
TL;DR: In this article, it was shown that at the molecular-size range, the surfaces of most materials are fractals, that is, at this range, surface geometric irregularities and defects are characteristically self-similar upon variations of resolution.
Abstract: In this letter we report that, at the molecular-size range, the surfaces of most materials are fractals, that is, at this range, surface geometric irregularities and defects are characteristically self-similar upon variations of resolution. The whole range of fractal dimension1, 2⩽D<3, is found in the many examples presented. Two representative examples, namely adsorption of polystyrene on alumina and adsorption of krypton on dolomite are discussed in some detail. Our findings suggest a simple solution to the problem of quantifying the degree of surface irregularity2,3 at a resolution which is of relevance to many aspects of surface science. The results provide a general explanation for phenomenological links between various surface parameters, and we derive a set of equations of use in predicting surface variables.
622 citations
TL;DR: In this article, a modified Richardson fractal equation for profiles and fracture surfaces was proposed to obtain constant slopes from the reversed sigmoidal curve (RSC) for both profiles and surfaces respectively, where slopes from RSCs are related to the new constant fractal dimensions D β and D γ in the modified fractal equations for profiles.
189 citations
Journal Article•
TL;DR: In this paper, a modified Richardson fractal equation for profiles and fracture surfaces was proposed to obtain constant slopes from the reversed sigmoidal curve (RSC) for both profiles and surfaces respectively, where slopes from RSCs are related to the new constant fractal dimensions D β and D γ in the modified fractal equations for profiles.
Abstract: The fractal characteristics of a series of fractured AISI 4340 steel specimens were studied experimentally by means of vertical sections through the fracture surface. Extensive fractal data have been generated for both the fracture surfaces and their profiles. Fractal plots for the irregular profile curves differ significantly from those of the infinitely subdivisible curves with “self-similarity” as postulated by Mandelbrot. Instead of a linear fractal curve and constant fractal dimension D , we find a reversed sigmoidal curve (RSC) and variable D . Because of the inadequacies of the linear Richardson fractal equation, we have developed an alternative procedure whereby constant slopes β and γ are obtained from the RSCs for both profiles and surfaces respectively. Since a fractal equation for surfaces apparently does not exist, we propose one that parallels the Richardson equation for profiles. Slopes from the RSCs are related to the new constant fractal dimensions D β and D γ in the modified fractal equations for profiles and fracture surfaces. Some insight into the physical nature of the fractal dimension is afforded by its close similarity to fracture roughness parameters that have simple physical meanings. It is believed that the results of the extensive study may have general validity for the irregular complex curves and surfaces of nature.
187 citations
TL;DR: In this paper, the fractal dimensions of two titanium alloys were measured and correlated with dynamic tear energy, and an approximate correlation between fractal dimension and dynamic energy was obtained.
175 citations