Fractal characteristics and fractal dimension measurement on broken surfaces of aluminum electric porcelain

2005 ◽  
Vol 20 (1) ◽  
pp. 37-41 ◽  
Author(s):  
Yang Zhiyuan ◽  
Zhou Anning
Keyword(s):  
Fractal Dimension ◽  
Electric Porcelain ◽  
Dimension Measurement ◽  
Fractal Characteristics

scholarly journals Development of Back-calculation Model for Aggregate Gradation Determination Using Fractal Theory

2018 ◽  
Vol 159 ◽  
pp. 01006
Author(s):  
Bagus Hario Setiadji ◽  
Supriyono ◽  
Djoko Purwanto
Keyword(s):  
Fractal Dimension ◽  
Fractal Theory ◽  
Asphalt Mixture ◽  
Fractal Dimensions ◽  
Calculation Model ◽  
Careful Consideration ◽  
Upper And Lower Bounds ◽  
Aggregate Gradation ◽  
Fractal Characteristic ◽  
Fractal Characteristics

Several studies have shown that fractal theory can be used to analyze the morphology of aggregate materials in designing the gradation. However, the question arises whether a fractal dimension can actually represent a single aggregate gradation. This study, which is a part of a grand research to determine aggregate gradation based on known asphalt mixture specifications, is performed to clarify the aforementioned question. To do so, two steps of methodology were proposed in this study, that is, step 1 is to determine the fractal characteristics using 3 aggregate gradations (i.e. gradations near upper and lower bounds, and middle gradation); and step 2 is to back-calculate aggregate gradation based on fractal characteristics obtained using 2 scenarios, one-and multi-fractal dimension scenarios. The results of this study indicate that the multi-fractal dimension scenario provides a better prediction of aggregate gradation due to the ability of this scenario to better represent the shape of the original aggregate gradation. However, careful consideration must be observed when using more than two fractal dimensions in predicting aggregate gradation as it will increase the difficulty in developing the fractal characteristic equations.

scholarly journals Effect of Grain Size on Microscopic Pore Structure and Fractal Characteristics of Carbonate-Based Sand and Silicate-Based Sand

2021 ◽  
Vol 5 (4) ◽  
pp. 152
Author(s):  
Shao-Heng He ◽  
Zhi Ding ◽  
Hai-Bo Hu ◽  
Min Gao
Keyword(s):  
Grain Size ◽  
Fractal Dimension ◽  
Pore Structure ◽  
Pore Size ◽  
Quartz Sand ◽  
Glass Bead ◽  
Fractal Theory ◽  
Calcareous Sand ◽  
Wide Range ◽  
Fractal Characteristics

In this study, a series of nuclear magnetic resonance (NMR) tests was conducted on calcareous sand, quartz sand, and glass bead with a wide range of grain sizes, to understand the effect of grain size on the micro-pore structure and fractal characteristics of the carbonate-based sand and silicate-based sand. The pore size distribution (PSD) of the tested materials were obtained from the NMR T2 spectra, and fractal theory was introduced to describe the fractal properties of PSD. Results demonstrate that grain size has a significant effect on the PSD of carbonate-based sand and silicate-based sand. As grain size increases, the PSD of sands evolves from a binary structure with two peaks to a ternary structure with three peaks. The increase in the grain size can cause a remarkable increase in the maximum pore size. It is also found that the more irregular the particle shape, the better the continuity between the large and medium pores. In addition, grain size has a considerable effect on the fractal dimension of the micro-pore structure. The increase of grain size can lead to a significant increase in the heterogeneity and fractal dimension in PSD for calcareous sand, quartz sand and glass bead.

Application of Fractal Theory in Aggregate Gradation Research

2012 ◽  
Vol 204-208 ◽  
pp. 1923-1928
Author(s):  
Bo Tan ◽  
Rui Hua Yang ◽  
Yan Ting Lai
Keyword(s):  
Fractal Dimension ◽  
Fractal Theory ◽  
Asphalt Mixture ◽  
Fractal Dimensions ◽  
Aggregate Gradation ◽  
Structure Characteristics ◽  
Aggregate Distribution ◽  
Dimension Formula ◽  
Mass Fractal ◽  
Fractal Characteristics

The paper presents the fractal dimension formula of distribution of asphalt mixture aggregate diameter by the deducing mass fractal characteristics function. Taking AC-20 and SMA-20 as examples, selected 6 groups of representative grading curves within the grading envelope proposed by the present specification, and calculated their fractal dimensions. The asphalt mixture gradation has fractal dimension D (D∈(1,3)), and the fractal of continuous gradation is single while the fractal of gap-gradation shows multi-fractal with 4.75 as the dividing point. Fractal dimension of aggregate gradation of asphalt mixture reflect the structure characteristics of aggregate distribution, that is, finer is aggregate, bigger is the fractal dimension.

scholarly journals A Study of the Spatial Form of Maling Village, Henan, China

2020 ◽  
Vol 12 (18) ◽  
pp. 7350
Author(s):  
Qindong Fan ◽  
Fengtian Du ◽  
Hu Li
Keyword(s):  
Land Use ◽  
Fractal Dimension ◽  
Fractal Theory ◽  
Stability Index ◽  
Spatial Form ◽  
Land Use Types ◽  
Fractal Characteristics ◽  
Spatial Shape ◽  
The Stability ◽  
The Village

In order to improve the study of the spatial form of villages, fractal theory is used to analyze the plane and facade of Maling Village, Changdai Town, Mengjin County, Luoyang City, Henan Province, China. The results show that the village facade and plane spatial shape of Maling Village have obvious fractal characteristics and the fractal dimension can be used as an important index to evaluate the plane and facade shape of the village. The fractal dimension of each land use type is between 1.2415 and 1.7443. The stability index of land use types in the village follows the order of village construction land > cultivated land > road > garden land > woodland > grassland. The research results can provide decision-making information for the rational use and planning of village land.

scholarly journals Evolution Rules of Fractures for Mudstone under Compression Shear Load and the Fractal Characteristics of Broken Blocks

2019 ◽  
Vol 2019 ◽  
pp. 1-7 ◽  
Author(s):  
Zhaoyun Chai ◽  
Jinbo Bai ◽  
Haiyang Zhang ◽  
Pan Yang
Keyword(s):  
Fractal Dimension ◽  
Compression Test ◽  
Shear Fracture ◽  
Fractal Theory ◽  
Friction Angle ◽  
Shear Loading ◽  
Shear Load ◽  
Deformation And Failure ◽  
Fractal Characteristics ◽  
Logarithmic Relationship

Failure of rocks is commonly induced by compressive and shear coupling loading. Knowledge of the mechanism and process of deformation and failure of rocks under compressive shear loading condition is an important basis for the study of stability in rock engineering. Based on the nonlinear fractal theory, it is possible to examine the evolution rules of fractures in mudstone under compression shear load and the fractal characteristics of broken blocks using the shear compression test with variable angles of mudstone specimens in natural conditions. This research shows that the cohesion and friction angle parameters of rock samples are achieved by draw Mohr’s strength envelope according to the test date of variable-angle shear compression test. It also shows that the shape of load-displacement curves of rocks can be divided into four stages: compaction, elastic, plastic, and fracture, and the curve can accurately represent the transformation and breakage characteristics of rock during shear fracture. And the distribution of broken blocks shows a strong statistical resemblance to the fractal distribution, and the fractal dimension is able to reflect the distribution characteristics of broken blocks. With increasing the shear angle, the fractal dimension of broken blocks decreases in a logarithmic relationship.

scholarly journals The Impacts of Matrix Compositions on Nanopore Structure and Fractal Characteristics of Lacustrine Shales from the Changling Fault Depression, Songliao Basin, China

Minerals ◽  
2019 ◽  
Vol 9 (2) ◽  
pp. 127 ◽  
Author(s):  
Zhuo Li ◽  
Zhikai Liang ◽  
Zhenxue Jiang ◽  
Fenglin Gao ◽  
Yinghan Zhang ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Fractal Dimensions ◽  
Organic Medium ◽  
Songliao Basin ◽  
Sem Images ◽  
Fractal Characteristics ◽  
Inorganic Mineral ◽  
Nanopore Structure ◽  
High Fractal Dimension

The Lower Cretaceous Shahezi shales are the targets for lacustrine shale gas exploration in Changling Fault Depression (CFD), Southern Songliao Basin. In this study, the Shahezi shales were investigated to further understand the impacts of rock compositions, including organic matters and minerals on pore structure and fractal characteristics. An integrated experiment procedure, including total organic carbon (TOC) content, X-ray diffraction (XRD), field emission-scanning electron microscope (FE-SEM), low pressure nitrogen physisorption (LPNP), and mercury intrusion capillary pressure (MICP), was conducted. Seven lithofacies can be identified according to on a mineralogy-based classification scheme for shales. Inorganic mineral hosted pores are the most abundant pore type, while relatively few organic matter (OM) pores are observed in FE-SEM images of the Shahezi shales. Multimodal pore size distribution characteristics were shown in pore width ranges of 0.5–0.9 nm, 3–6 nm, and 10–40 nm. The primary controlling factors for pore structure in Shahezi shales are clay minerals rather than OM. Organic-medium mixed shale (OMMS) has the highest total pore volumes (0.0353 mL/g), followed by organic-rich mixed shale (ORMS) (0.02369 mL/g), while the organic-poor shale (OPS) has the lowest pore volumes of 0.0122 mL/g. Fractal dimensions D1 and D2 (at relative pressures of 0–0.5 and 0.5–1 of LPNP isotherms) were obtained using the Frenkel–Halsey–Hill (FHH) method, with D1 ranging from 2.0336 to 2.5957, and D2 between 2.5779 and 2.8821. Fractal dimensions are associated with specific lithofacies, because each lithofacies has a distinctive composition. Organic-medium argillaceous shale (OMAS), rich in clay, have comparatively high fractal dimension D1. In addition, organic-medium argillaceous shale (ORAS), rich in TOC, have comparatively high fractal dimension D2. OPS shale contains more siliceous and less TOC, with the lowest D1 and D2. Factor analysis indicates that clay contents is the most significant factor controlling the fractal dimensions of the lacustrine Shahezi shale.

scholarly journals Fractal Characteristics of Chip Morphology and Tool Wear in High-Speed Turning of Iron-Based Super Alloy

Materials ◽  
2020 ◽  
Vol 13 (4) ◽  
pp. 1020
Author(s):  
Xu Zhang ◽  
Guangming Zheng ◽  
Xiang Cheng ◽  
Rufeng Xu ◽  
Guoyong Zhao ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Tool Wear ◽  
High Speed ◽  
Cutting Speed ◽  
Fractal Dimensions ◽  
Chip Morphology ◽  
Color Changes ◽  
Fractal Characteristics ◽  
Iron Based ◽  
Super Alloy

Considering that iron-based super alloy is a kind of difficult-to-cut material, it is easy to produce work hardening and serious tool wear during machining. Therefore, this work aims to explore the chip change characteristics and tool wear mechanism during the processing of iron-based super alloy, calculate the fractal dimensions of chip morphology and tool wear morphology, and use fractals to analyze their change trend. Meanwhile, a new cutting tool with a super ZX coating is used for a high-speed dry turning experiment. The results indicate that the morphology of the chip is saw-tooth, and its color changes gradually, due to the oxidation reaction. The main wear mechanisms of the tool involve abrasive wear, adhesive wear, oxidation wear, coating spalling, microcracking and chipping. The fractal dimension of the tool wear surface and chip is increased with the improvement of cutting speed. This work investigates the fractal characteristics of chip morphology and tool wear morphology. The fractal dimension changes regularly with the change of tool wear, which plays an important role in predicting this tool wear. It is also provides some guidance for the efficient processing of an iron-based super alloy.

INVESTIGATION OF DYNAMIC TEXTURE AND FLOW CHARACTERISTICS OF FOAM TRANSPORT IN POROUS MEDIA BASED ON FRACTAL THEORY

Fractals ◽  
2019 ◽  
Vol 27 (01) ◽  
pp. 1940013 ◽  
Author(s):  
FEI WANG ◽  
HAIFENG LI ◽  
DONGXING DU ◽  
XU DONG
Keyword(s):  
Porous Media ◽  
Fractal Dimension ◽  
Fractal Theory ◽  
Dynamic Change ◽  
Quantitative Description ◽  
Flow Characteristics ◽  
Transport In Porous Media ◽  
Steady Stage ◽  
Profile Control ◽  
Fractal Characteristics

Foam fluid has found wide applications in oilfield development, such as profile control, water plugging, gas channeling control, fracturing, and so on. As a non-Newtonian fluid, the successful application of foam is significantly influenced by its structure. The foam texture, however, is complex and irregular, and becomes even more complicated in porous media by the boundary effects. Therefore, the description of dynamic foam structure is crucial and a quantitative description method for foam fluid is worth exploring. In this paper, the fractal characteristics of foam in porous media are verified and combined with foam microdisplacement experiment, and the fractal rule of foam is found. The relationship between fractal dimension and pressure is also discussed. The results show that foam has dynamic fractal characteristics during transport in porous media and the box-counting fractal dimension ranges from 1 to 2. Furthermore, the dynamic change of foam fractal dimension during transport in porous media could be divided into three stages. In the first stage when no foam forms, the fractal dimension is about 2; in the second unsteady foam stage, the fractal dimension is reduced from 1.9 to 1.6; the last one is the steady stage and the fractal dimension is almost constant (about 1.6). Besides, the fractal dimension of foam fluid is closely related to displacement pressure. Low pressure corresponds to higher fractal dimension, and high pressure corresponds to lower fractal dimension. Pressure is negatively linearly correlated with fractal dimension. These results are expected to enrich the understanding of the foam dynamic characteristics in their advanced applications.

Researches on Fractal Features of Graphite Porous Materials

2012 ◽  
Vol 507 ◽  
pp. 25-29 ◽  
Author(s):  
Qi Liu ◽  
Ya Fei Hu ◽  
Qi Li Wang
Keyword(s):  
Fractal Dimension ◽  
Pore Formation ◽  
Inflection Point ◽  
Pore Diameter ◽  
Mercury Porosimetry ◽  
Microscopic Structure ◽  
Fractal Characteristics ◽  
The One ◽  
Main Factor

The mercury porosimetry experiment has tested three different kinds of porosity graphite and the microscopic structure of impregnation antimony materials, and has calculated the corresponding fractal dimension by using the Menger model. The results show that: the main pore diameter of the graphite materials is in the interval of , most of which can be filled by impregnation antimony, and graphite and impregnation antimony materials both have the fractal characteristics. Graphite materials also have the dual fractal characteristics. Its fractal inflection point aperture is about 1μm, and the fractal dimension (3.05 ~ 3.25) of the small pores (φ≤1μm) is less than the one (3.71 ~ 3.95) of the large pores (φ>1μm). The reason why existing the dual fractal characteristics is that the size of the pore formation mechanism is different. Impregnation occurs mainly in the range of large pores, characteristics of which is an important factor to influence the quality of impregnation materials. The material formula is the main factor to influence the large pores and an important guarantee to improve the quality of impregnation products.

scholarly journals Fracture Surface Fractal Characteristics of Alkali-Slag Concrete under Freeze-Thaw Cycles

2017 ◽  
Vol 2017 ◽  
pp. 1-9 ◽  
Author(s):  
Wantong Cai ◽  
Guoping Cen ◽  
Haifu Wang
Keyword(s):  
Fracture Toughness ◽  
Fractal Dimension ◽  
Fracture Surface ◽  
Fractal Theory ◽  
Damage Zone ◽  
Freezing And Thawing ◽  
Freeze Thaw ◽  
Force Direction ◽  
Fractal Characteristics ◽  
Slag Content

Fractal theory is introduced in fracture surface research of alkali-slag concrete (ASC) under freeze-thaw cycles; crack distribution of ASC fracture surface and freeze-thaw damage zone were calculated. Through fractal analysis of ASC sample fracture surfaces, relevance between section fractal dimension and fracture toughness and relationship between material composition and section fractal dimension are clarified. Results show that the specimen’s cracks before freeze-thaw extend along force direction gently, and there are more twists and turns after freezing and thawing; the fractal dimension D also grows from 1.10 to 1.33. SEM internal microcracks’ D of ASC internal microstructure after freezing and thawing is 1.37; 0 to 300 times ASC fractal dimension under freezing and thawing is between 2.10 and 2.23; with freeze-thaw times increasing, ASC fracture toughness decreases and fractal dimension increases, the fractal dimension and fracture toughness have a good linear relationship, and the fractal dimension can reflect the toughening effect of ASC. It is very feasible to evaluate ASC fracture behaviour under freezing and thawing with the fractal theory. Fractal dimension generally increases with activator solution-slag (A/S for short) or slag content. The greater the amount of A/S or slag content, the lower the dimension.

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