• KCI Concrete Journal
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• v.14 no.1
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• pp.30-35
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• 2002

The fractal geometry is a non-Euclidean geometry which describes the naturally irregular or fragmented shapes, so that it can be applied to fracture behavior of materials to investigate the fracture process. Fractal curves have a characteristic that represents a self-similarity as an invariant based on the fractal dimension. This fractal geometry was applied to the crack growth of cementitious composites in order to correlate the fracture behavior to microstructures of cementitious composites. The purpose of this study was to find relationships between fractal dimensions and fracture energy. Fracture test was carried out in order to investigate the fracture behavior of plain and fiber reinforced cement composites. The load-CMOD curve and fracture energy of the beams were observed under the three point loading system. The crack profiles were obtained by the image processing system. Box counting method was used to determine the fractal dimension, D$_{f}$. It was known that the linear correlation exists between fractal dimension and fracture energy of the cement composites. The implications of the fractal nature for the crack growth behavior on the fracture energy, G$_{f}$ is apparent.ent.

• Tribology and Lubricants
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• v.33 no.6
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• pp.303-308
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• 2017

Most automobile tire companies have not yet considered the geometric information of a road at the design stage of a tire because the topographical characterization of a road surface is very difficult owing to its vastness and randomness. A road surface shows variable surface roughness values according to magnification, and thus, the contact force between the road and tire significantly fluctuates with respect to the scale. In this study, we make an attempt to define a representative value for surface topographical information at multi-scale levels. To represent surface topography, we use a statistical method called power spectral density (PSD). We use the fast Fourier transform (FFT) and PSD to analyze the height profiles of a random surface. The FFT and PSD of a surface help in obtaining a fractal dimension, which is a representative value of surface topography at all length scales. We develop three surfaces with different fractal dimensions. We use finite element analysis (FEA) to observe the contact forces between a tire and the road surfaces with three different fractal dimensions. The results from FEA reveal that an increase in the fractal dimension decreases the contact length between the tire and road surfaces. On the contrary, the average contact force increases. This result indicates that designing and manufacturing a tire considering the fractal dimension of a road makes safe driving possible, owing to the improvement in service life and braking performance of the tire.

• The Journal of Engineering Geology
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• v.12 no.3
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• pp.333-344
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• 2002

To clarify the relationship between groundwater flow tate and statistical distribution of fractures in Youngchun waterway tunnel, the fracture characteristics and fractal dimensions of groundwater flow section were evaluated. The flow rate of 84,465m$^3$/day was identified in fault, accounting for about 70 percent of the total How rate. The flow rate of 36,525m$^3$/day was identified in joint, accounting for about 30 percent of the total flow rate. The flow late in the NATM section of sedimentary rocks increased with the fractal dimensions. The fractal dimensions determined in fault or fracture zones show more positive relation with the flow rate than those in joint developed zones.

• Journal of the Korean Society of Manufacturing Process Engineers
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• v.5 no.1
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• pp.7-12
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• 2006

Recently, the fractal interpolation methods have been widely introduced and used to estimate and analyze various theoretical and experimental data. Because of the chaotic behaviors of dynamic cutting force data, some method for end-milling force analysis must be used. The fractal analysis used in this paper is fractal linear interpolation and fractal dimension. Also, several methods for computing fractal dimensions have been used in which the fractal dimension of the typical dynamic end-milling force was calculated according to number of data points that are generally lower than 200 data points sampled. This fractal analysis shows a possible prediction of end-milling force that has some dynamic chatter property or stationary property in endmilling operation.

• Communications of the Korean Mathematical Society
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• v.13 no.2
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• pp.281-287
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• 1998

We define a new form of fractals, called the braked subsimilar set from a self similar set and find the relation between their fractal dimensions.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2001.05a
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• pp.47-51
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• 2001

The structural properties of varistors surface studied by fractal phenomenon were investigated to verify the relations of electrical characteristics. The SEM photograph of varistors surface were changed by binary code and the grain shape of that were analyzed by fractal dimension. The void of varistors surface was found by fractal program. The relation between grain density and electrical properties depend on fractal dimension. The grain size in varistors surface was decreased by increasing of oxide antimony addition. The grain size of devices by oxide antimony addition were from 5 to $10[{\mu}m]$. The fractal dimension and electrical properties of varistors surface was related to between grain boundary and grain density. The grain size was decreased by increasing of fractal dimensions.

• KSBB Journal
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• v.10 no.2
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• pp.119-125
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• 1995

The morphology of fungal growth, which is an important variable for separability and rheological property of fermented medium, was quantified with fractal geometry Fractal dimensions were determined for submerged growth of two industrially important fungi, Aspergillus niger and Aspergillus oruzae. The tendency of pellet formation was related to the fractal dimension of fungi.

• Proceedings of the Korean Society of Tribologists and Lubrication Engineers Conference
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• 1998.10a
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• pp.115-123
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• 1998

The morphological analysis of wear particle is a very effective means for machine condition monitoring and fault diagnosis. In order to describe morphology of various wear particle, the wear test was carried out under different experimental conditions. And fractal descriptors was applied to boundary and surface of wear particle with image processing system. These descriptors to analyze shape and surface wear particle are shape fractal dimension and surface fractal dimension. The shape fractal dimension can be derived from the boundary profile and surface fractal dimension can be determined by sum of intensity difference of surface pixel. The morphology of wear particles can be effectively obtained by two fractal dimensions.

• KSBB Journal
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• v.9 no.5
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• pp.512-517
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• 1994

The morphology of fungal growth, which is an important variable for separability and rheological property of fermented medium, was quantified with fractal geometry. Fractal dimensions were determined for submerged growth of two industrially important fungi, Aspergillus niger and Aspergillus oryzae. The tendency of pellet formation was related to the fractal dimension of fungi.

• Proceedings of the Korean Institute of Electrical and Electronic Material Engineers Conference
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• 2006.05a
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• pp.149-151
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• 2006

The surface properties of electrical devices studied by fractal phenomenon were investigated. The SEM photographs of devices surface were changed by binary code and it were analyzed by fractal dimension. The void of devices surface was found by fractal program. The relation between grain density and electrical properties are able to expect to fractal dimension. The grain size in varistors surface was decreased by increasing of oxide antimony addition. The fractal dimension and electrical properties of devices surface was related to between grain boundary and grain density. The grain size was decreased by increasing of fractal dimensions.