Fractal Analysis of Fracture Surfaces of Steel Charpy Specimens

2008 ◽  
Vol 399 ◽  
pp. 43-49
Author(s):  
Claudia Secrieru ◽  
Ion Dumitru

The article focuses on the technical measurements which could be applied to the fracture surfaces of the steel Charpy specimens in order to apply the Fractal Analysis. One could calculate the fractal dimension not directly for a fracture, but for a profile of the fracture. Most common methods for generation of fracture profile are cross-cut techniques and profile measurements techniques [1-2]. We apply three principal methods: Profilometer, Interferometer Light Microscope and the Vertical Section for a specimen made of XC65 after the Charpy test. We compare the advantages and the limits for each technique. We use the Box Counting algorithm applied in the Image J program for determining the fractal dimension of the fracture surface in all three experimental techniques. Then we could characterize the roughness of the fracture profile at different magnifying power by the estimated fractal dimension.

2004 ◽  
Vol 261-263 ◽  
pp. 1593-1598
Author(s):  
M. Tanaka ◽  
Y. Kimura ◽  
A. Kayama ◽  
L. Chouanine ◽  
Reiko Kato ◽  
...  

A computer program of the fractal analysis by the box-counting method was developed for the estimation of the fractal dimension of the three-dimensional fracture surface reconstructed by the stereo matching method. The image reconstruction and fractal analysis were then made on the fracture surfaces of materials created by different mechanisms. There was a correlation between the fractal dimension of the three-dimensional fracture surface and the fractal dimensions evaluated by other methods on ceramics and metals. The effects of microstructures on the fractal dimension were also experimentally discussed.


Author(s):  
Eva Přemyslovská ◽  
Petr Koňas

The aim of this work is description of geometry of fracture surfaces of wood composite materials (cement-bonded particleboard, gypsum-bonded fibreboard and wood particleboard) using fractal analysis and exploration relation between fractal dimension and impact work. Fractal dimension determinated by filtration, volumetric and robust Box-Counting methods and Richardson method is different considering type of material and method. Proportional relationship between fractal dimension (computed by robust BC method) and impact work of mentioned materials was found in other cases non-proportional relationships were founded.


2020 ◽  
pp. 1-8
Author(s):  
Haruhiko Yoshioka ◽  
Kouki Minami ◽  
Hirokazu Odashima ◽  
Keita Miyakawa ◽  
Kayo Horie ◽  
...  

<b><i>Objective:</i></b> The complexity of chromatin (i.e., irregular geometry and distribution) is one of the important factors considered in the cytological diagnosis of cancer. Fractal analysis with Kirsch edge detection is a known technique to detect irregular geometry and distribution in an image. We examined the outer cutoff value for the box-counting (BC) method for fractal analysis of the complexity of chromatin using Kirsch edge detection. <b><i>Materials:</i></b> The following images were used for the analysis: (1) image of the nucleus for Kirsch edge detection measuring 97 × 122 pix (10.7 × 13.4 μm) with a Feret diameter of chromatin mesh (<i>n</i> = 50) measuring 17.3 ± 1.8 pix (1.9 ± 0.5 μm) and chromatin network distance (<i>n</i> = 50) measuring 4.4 ± 1.6 pix (0.49 ± 0.18 μm), and (2) sample images for Kirsch edge detection with varying diameters (10.4, 15.9, and 18.1 μm) and network width of 0.4 μm. <b><i>Methods:</i></b> Three types of bias that can affect the outcomes of fractal analysis in cytological diagnosis were defined. (1) Nuclear position bias: images of 9 different positions generated by shifting the original position of the nucleus in the middle of a 256 × 256 pix (28.1 μm) square frame in 8 compass directions. (2) Nuclear rotation bias: images of 8 different rotations obtained by rotating the original position of the nucleus in 45° increments (0°, 45°, 90°, 135°, 180°, 225°, 270°, and 315°). (3) Nuclear size bias: images of varying size (diameter: 190 pix [10.4 μm], 290 pix [15.9 μm], and 330 pix [18.1 μm]) with the same mesh pattern (network width: 8 pix [0.4 μm]) within a 512 × 512 pix square. Different outer cutoff values for the BC method (256, 128, 64, 32, 16, and 8 pix) were applied for each bias to assess the fractal dimension and to compare the coefficient of variation (CV). <b><i>Results:</i></b> The BC method with the outer cutoff value of 32 pix resulted in the least variation of fractal dimension. Specifically, with the cutoff value of 32 pix, the CV of nuclear position bias, nuclear rotation bias, and nuclear size bias were &#x3c;1% (0.1, 0.4, and 0.3%, respectively), with no significant difference between the position and rotation bias (<i>p</i> = 0.19). Our study suggests that the BC method with the outer cutoff value of 32 pix is suitable for the analysis of the complexity of chromatin with chromatin mesh.


2014 ◽  
Vol 1017 ◽  
pp. 187-192
Author(s):  
Qiu Yan Wang ◽  
Zhi Qiang Liang ◽  
Xi Bin Wang ◽  
Wen Xiang Zhao ◽  
Yong Bo Wu ◽  
...  

Conventional characterization methods of grinding surface using surface roughness parameters, e.g., Ra, depend on either the resolution of the measuring instrument or the length of the sample. But fractal dimension (FD) as a scale-independent fractal parameter is effective to evaluate the ground surface at any length scale and represent lots of surface phenomenon at its relevant length scales. In this paper, a three-dimensional (3D) box-counting fractal analysis method is used to investigate ground surface morphology of monocrystal sapphire by calculating 3D fractal dimension of the ground surface. The results obtained show that fractal dimension decreases with the increasing surface roughness. For the ground surface with higher fractal dimension, its microtopography is more exquisite with minor defects. Once the fractal dimension become smaller, deep cracks and pronounced defects are exhibited in ground surface. Moreover, the ground surface obtained in ductile mode has much higher fractal dimension than that in brittle mode. Therefore, the fractal analysis method has the potential to reveal the ground surface characteristics of monocrystal sapphire.


2011 ◽  
Vol 19 (1) ◽  
pp. 45 ◽  
Author(s):  
Ian Parkinson ◽  
Nick Fazzalari

A standardised methodology for the fractal analysis of histological sections of trabecular bone has been established. A modified box counting method has been developed for use on a PC based image analyser (Quantimet 500MC, Leica Cambridge). The effect of image analyser settings, magnification, image orientation and threshold levels, was determined. Also, the range of scale over which trabecular bone is effectively fractal was determined and a method formulated to objectively calculate more than one fractal dimension from the modified Richardson plot. The results show that magnification, image orientation and threshold settings have little effect on the estimate of fractal dimension. Trabecular bone has a lower limit below which it is not fractal (λ<25 μm) and the upper limit is 4250 μm. There are three distinct fractal dimensions for trabecular bone (sectional fractals), with magnitudes greater than 1.0 and less than 2.0. It has been shown that trabecular bone is effectively fractal over a defined range of scale. Also, within this range, there is more than 1 fractal dimension, describing spatial structural entities. Fractal analysis is a model independent method for describing a complex multifaceted structure, which can be adapted for the study of other biological systems. This may be at the cell, tissue or organ level and compliments conventional histomorphometric and stereological techniques.


2020 ◽  
pp. 30-42
Author(s):  
Anna Zhurba ◽  
Michail Gasik

An essential element of fractal analysis of functional coatings is the fractal dimension, which is an important quantitative characteristic. Typically, coating images are represented as colored or halftone, and most fractal dimension algorithms are for binary images. Therefore, an important step in fractal analysis is binarization, which is a threshold separation operation and the result of which is a binary image.The purpose of the study is to study and program the methods of image binarization and to study the influence of these methods on the value of fractal dimension of functional coatings.As a result of the binarization threshold, the image is split into two regions, one containing all pixels with values below a certain threshold and the other containing all pixels with values above that threshold. Of great importance is the determination of the binarization threshold.The study analyzed a number of functional coating images, determined the fractal dimension of the image by the Box Counting method at different binarization thresholds and when applying different binarization methods (binarization with lower and upper threshold, with double restriction, and the average method for determining the optimal binarization threshold) images. The Box Counting method is used to depict any structure on a plane. This method allows us to determine the fractal dimension of not strictly self-similar objects. Each image binarization method is used for different types of images and for solving different problems.As a result, the methods of image binarization were developed and implemented, the fractal dimension of binary images was calculated, and the influence of these methods on the value of fractal dimension of functional coatings was investigated.The surfaces of composite steel structure, metallic porous materials, and natural cave structures are analyzed.


2020 ◽  
Vol 60 (1) ◽  
pp. 184 ◽  
Author(s):  
Abbas Movassagh ◽  
Xi Zhang ◽  
Elaheh Arjomand ◽  
Manouchehr Haghighi

Surface roughness is a crucial parameter in the hydraulic fracturing process, affecting rock toughness, fluid flow and proppant transport; however, the scale-dependent nature of hydraulic fracture surfaces is not well studied. In this paper, we examined four fractal methods, compass, box-counting, variation and roughness-length, to evaluate and compare the fractal dimension of the surface roughness profiles created by laboratory hydraulic fracturing. Synthetic surface profiles were generated by the Weierstrass-Mandelbrot function, which was initially used to test the accuracy of the four methods. Each profile had a predefined fractal dimension that was revisited by these methods. Then, the fractal analysis was performed for experimental fracture surfaces, which were created by a hydraulic fracturing experiment in a true triaxial situation. By comparing fractal analysis results, we found that for both synthetic and laboratory fracture height profiles, the roughness-length method provides a relatively more reliable estimation of the fractal dimension. This method predicts the dimension for synthetic surface within an error of less than 1%, considering a wide range of surface heights from centimetres down to micrometres. By increasing the fractal dimension of surface profiles, the error of fractal estimation increased for all four methods. Among them, the variation method provided the closest results to the roughness-length method when considering both experimental and synthetic surfaces. The evaluated fractal dimension may provide a guideline for either field- or laboratory-scale hydraulic fracturing treatments to evaluate the effects of surface roughness on fracture growth.


Fractals ◽  
2007 ◽  
Vol 15 (01) ◽  
pp. 1-7 ◽  
Author(s):  
NEBOJŠA T. MILOŠEVIĆ ◽  
DUŠAN RISTANOVIĆ ◽  
JOVAN B. STANKOVIĆ ◽  
RADMILA GUDOVIĆ

Through analysis of the morphology of dendritic arborisation of neurons from the substantia gelatinosa of dorsal horns from four different species, we have established that two types of cells (stalked and islet) are always present. The aim of the study was to perform the intra- and/or inter-species comparison of these two neuronal populations by fractal analysis, as well as to clarify the importance of the fractal dimension as an objective and usable morphological parameter. Fractal analysis was carried out adopting the box-counting method. We have shown that the mean fractal dimensions for the stalked cells are significantly different between species. The same is true for the mean fractal dimensions of the islet cells. Still, no significant differences were found for the fractal dimensions of the stalked and islet cells within a particular species. The human species has shown as the only exception where fractal dimensions of these two types of cells differ significantly. This study shows once more that the fractal dimension is a useful and sensitive morphological descriptor of neuronal structures and differences between them.


2015 ◽  
Vol 2015 ◽  
pp. 1-6 ◽  
Author(s):  
Z. Z. Zhang

Experiments on granite specimens after different high temperature under uniaxial compression were conducted and the fracture surfaces were observed by scanning electron microscope (SEM). The fractal dimensions of the fracture surfaces with increasing temperature were calculated, respectively. The fractal dimension of fracture surface is between 1.44 and 1.63. Its value approximately goes up exponentially with the increase of temperature. There is a quadratic polynomial relationship between the rockburst tendency and fractal dimension of fracture surface; namely, a fractal dimension threshold can be obtained. Below the threshold value, a positive correlativity shows between rockburst tendency and fractal dimension; when the fractal dimension is greater than the threshold value, it shows an inverse correlativity.


2011 ◽  
Vol 411 ◽  
pp. 548-551
Author(s):  
Tao Qiang ◽  
De Mei Yu

Polylactide (PLA)-based wood plastic composites (WPCs) were manufactured by extrusion blending followed by injection molding. The fracture surfaces created from the impact test were recorded with SEM. Fractal analysis has been used to calculate the fractal dimension of the fracture surfaces with four different fractal analysis techniques. Then, the correlation between the fractal dimension of the fracture surfaces and its impact strength of the PLA-based WPCs was investigated by the linear regression. The results showed that there is a positive correlation between the impact strength and the fractal dimension.


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