• Journal of the Korean Society of Safety
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• v.13 no.4
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• pp.71-78
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• 1998

Real crack and fracture surfaces have irregularities producing zigzag contours. These irregularities are analysed by a fractal geometry which has been by a Mandelbrot. We obtained a fractal dimension which is one of the fractal characteristics. It is also estimated by an vertical section method that fractal characteristics in the fractured surfaces can be obtained as the crack grows. Moreover fractal fracture energy that corresponds to an energy release rate is shown to find relationships between fractal dimensions and crack behaviors. From these results, we concluded that a fractal characteristics analysis for a crack can be applied to a fracture mechanics.

• Journal of Advanced Marine Engineering and Technology
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• v.22 no.4
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• pp.522-528
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• 1998

This paper presents a fundamental fractal characteristics of the growing crack that has an irregularity producing a zigzag crack contour. This irregularity is analysed by a fractal geometry in a box counting method that is a very simple technique. First the fractal dimensions and actual fractal extensive crack length are obtained. Also a fractal fracture energy relation with a fractal dimension is found so as to get fractal crack behaviors. Thus it can be shown that the fractal dimension has a possibility as a fracture parameter in a real crack growth length meaning.

• Transactions of the Korean Society of Mechanical Engineers B
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• v.26 no.1
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• pp.18-26
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• 2002

With the introduction of Fractal notation, various fields of engineering adopted fractal notation to express characteristics of geometry involved and one of the most frequently applied areas was turbulence. With research on turbulence regarding the surface as fractal geometry, attempts to analyze turbulent premised flame as fractal geometry also attracted attention as a tool for modeling, for the flame surface can be viewed as fractal geometry. Experiments focused on disclosure of flame characteristics by measuring fractal parameters were done by researchers. But robust principle or theory can't be extracted. Only reported modeling efforts using fractal dimension is flame speed model by Gouldin. This model gives good predictions of flame speed in unstrained case but not in highly strained flame condition. In this research, approaches regarding fractal dimension of flame as one representative value is pointed out as a reason for the absence of robust model. And as an extort to establish robust modeling, Presents methods treating fractal dimension as statistical variable. From this approach flame characteristics reported by experiments such as Da effect on flame structure can be seen quantitatively and shows possibility of flame modeling using fractal parameters with statistical method. From this result more quantitative model can be derived.

• Tribology and Lubricants
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• v.22 no.5
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• pp.276-281
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• 2006

The fractal dimension is quantitatively to define the irregular characteristic of the shape in natural. It can be useful in describing morphological characteristics of various wear particles. This paper was undertaken to diagnose failure condition for sliding members in lubrication by fractal dimension. It will be possible to diagnose wear mechanism, friction and damage state of machines through analysis of shape characteristics for wear particle on driving condition by fractal parameters. In this study, the calculating and analyzing methods of fractal dimensions were constructed for the condition monitoring and wear particle analysis in lubricant condition. So, we carried out the Friction and wear test with the ball on disk type tester, and the fractal parameters of wear particle in lubricated conditions were calculated. Fractal parameters were defined as texture fractal dimension ($D_{t}$), structure fractal dimension ($D_{s}$) and total fractal dimension (D).

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.12 no.5
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• pp.157-162
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• 2013

To analyze the dynamic acceleration characteristics, it is necessary to identify the acceleration model using some methods that can represent the dynamic properties well. In this sense, fractal methods were used for the verification of characteristics of an acceleration signal. To estimate and analyze the geometry of acceleration signal, a fractal interpolation and its analysis was introduced in this paper. The chaotic nature of acceleration signal was considered in fractal modeling. In this study the fractal signal modeling has brought a focus within the scope of the fractal interpolation and fractal dimension. And a new idea of fractal dimension has been introduced and discussed considering the damping ratio and amplitude for its dynamic properties of the signal. The fractal dimension of acceleration with respect to the scaling factor using fixed data points of 1000 points was calculated and discussed. The acceleration behaviors of this results show some different characteristics. And this fractal analysis can be applied to other signal analysis of several machining such as pendulum type grinding and milling which has many dynamic properties in the signal.

• Nuclear Engineering and Technology
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• v.54 no.4
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• pp.1175-1184
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• 2022

The pore structure of uranium-bearing sandstone is one of the critical factors that affect the uranium leaching performance. In this article, uranium-bearing sandstone from the Yili Basin, Xinjiang, China, was taken as the research object. The fractal characteristics of the pore structure of the uranium-bearing sandstone were studied using mercury intrusion experiments and fractal theory, and the fractal dimension of the uranium-bearing sandstone was calculated. In addition, the effect of the fractal characteristics of the pore structure of the uranium-bearing sandstone on the uranium leaching kinetics was studied. Then, the kinetics was analyzed using a shrinking nuclear model, and it was determined that the rate of uranium leaching is mainly controlled by the diffusion reaction, and the dissolution rate constant (K) is linearly related to the pore specific surface fractal dimension (D_S) and the pore volume fractal dimension (D_V). Eventually, fractal kinetic models for predicting the in-situ leaching kinetics were established using the unreacted shrinking core model, and the linear relationship between the fractal dimension of the sample's pore structure and the dissolution rate during the leaching was fitted.

• Journal of the Korean Society of Safety
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• v.17 no.4
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• pp.38-44
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• 2002

The application of fractal concept provides an useful method in the study for the quantitative analysis of irregular variations like the fracture surfaces and crack profiles. Fractal curves have characteristics that represents a self-similarity based on the fractal dimension. The fractal dimensions were obtained by the box counting method. In this report, we obtained the nearly stable fractal dimensions of fracture crack profiles for STS316 with CT specimen as the crack advances and the relationships between crack length and fractal dimension. Moreover fractal fracture parameter that corresponds to J-R curve is shown by the relationships between fractal dimension and crack extension. From the results, we concluded that crack extension of high toughness material also shows the fractal characteristics, which can be used in order to evaluate the crack life precisely.

• The Research Journal of the Costume Culture
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• v.29 no.4
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• pp.522-537
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• 2021

The purpose of this study is to develop a knitwear design with the potential for practical use through a combination of science and design by examining the concept and formative characteristics of fractal geometry and applying them to the development of 3D virtual clothing knitwear design. This study produced five main conclusions. First, the sub-concepts of "Repeatability," "Scale variability," and "complexity," which are based on self-similarity, appear together with simple regularity in the fractal formative characteristics shown in fashion design. Second, fashion fields apply fractal geometry in three-dimensional surface textures and optical textile patterns as a method of expression. Third, it was confirmed that various expressions can be created with fractal patterns by using the SDS-ONE APEX 3-4 design system; moreover, fractal patterns are a suitable design source for the development of Jacquard knitwear patterns. Fourth, in the development of knitted jacquard fractal patterns, by arranging the patterns in perspective, the effect of emphasizing or reducing the human body by optical illusion was shown. Fifth, a knit Jacquard structure with a pattern that exhibits fractal modeling characteristics and applying it to a 3D virtual clothing sample design reduces the time required for sample production while expanding the knit design's expression area and reducing costs. Thus, the clothing sample confirmed the effectiveness of practical knitwear design development.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.7 no.4
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• pp.109-114
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• 2008

The fractal dimension aims to quantitatively define the irregular characteristics of the shape in nature. It can be useful in describing morphological characteristics of various wear particles. This paper was undertaken to diagnose failure condition for sliding members in lubrication using fractal dimension. The experiments were undertaken to analyze the shape of wear particles and to diagnose failure condition for sliding members in lubrication using the image processing and the fractal parameters. It was possible to diagnose wear mechanism, friction, and damage state of machines through analysis of shape characteristics for wear particle in driven condition using fractal parameters.

• Structural Engineering and Mechanics
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• v.23 no.2
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• pp.147-161
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• 2006

Recent developments in fractal theory suggest that fractal may provide a more realistic representation of characteristics of cementitious materials. In this paper, the roughness of fracture surfaces in cementitious material has been characterized by fractal theory. A systematic experimental investigation was carried out to examine the dependency of fracture parameters on the aggregate sizes as well as the loading rates. Three maximum aggregate sizes (4.76 mm, 12.7 mm, and 19.1 mm) and two loading rates (slow and fast loading rate) were used. A total of 25 compression tests and 25 tension tests were performed. All fracture parameters exhibited an increase, to varying degrees, when aggregates were added to the mortar matrix. The fracture surfaces of the specimens were digitized and analyzed. Results of the fractal analysis suggested that concrete fracture surfaces exhibit fractal characteristics, and the fractal geometry provide a useful tool for characterizing nonlinear fracture behavior of concrete. Fractal dimension D was monotonically increased as maximum aggregate sizes increase. A new fractal fracture model was developed which considers the size and shape of aggregate, and the crack paths in the constituent phases. Detailed analyses were given for four different types of fracture paths. The fractal fracture model can estimate fractal dimension for multiphase composites.