scholarly journals Numerical Simulation and Accuracy Verification of Surface Morphology of Metal Materials Based on Fractal Theory

Materials ◽  
2020 ◽  
Vol 13 (18) ◽  
pp. 4158
Author(s):  
Xiaokai Mu ◽  
Wei Sun ◽  
Chong Liu ◽  
Bo Yuan ◽  
Yunlong Wang ◽  
...  
Keyword(s):  
Numerical Simulation ◽  
Fractal Dimension ◽  
Surface Morphology ◽  
Fractal Theory ◽  
Surface Profile ◽  
Reference Value ◽  
Fractal Dimensions ◽  
Current Method ◽  
Simulation Method ◽  
Surface Morphologies

This paper presents a numerical simulation method to determine the surface morphology characteristics of metallic materials. First, a surface profiler (NV5000 5022s) was used to measure the surface, and the morphology data thereof were characterized. Second, fractal theory was used to simulate the surface profile for different fractal dimensions D and scale coefficients G, and statistical analyses of different surface morphologies were carried out. Finally, the fractal dimension D of the simulated morphology and the actual morphology were compared. The analysis showed that the error of fractal dimension D between the two morphologies was less than 10%; meanwhile, the comparison values of the characterization parameters of the simulated morphology and the actual morphology were approximately equal, and the errors were below 6%. Therefore, the current method used to evaluate the surface morphologies of parts processed by the grinding/milling method can be replaced by the simulated method using the corresponding parameters. This method makes it possible to theorize about the surface morphologies of machined parts, and provides a theoretical basis and reference value for the surface morphology design of materials, with the potential to improve the assembly quality of products.

Quantitative Analysis for Micro Geometrical Characteristic of Rough Surface Profile Based on Fractal Theory

2010 ◽  
Vol 154-155 ◽  
pp. 19-22
Author(s):  
Xiu Juan Yang ◽  
Zhi Qian Xu ◽  
Xiang Zhen Yan
Keyword(s):  
Surface Roughness ◽  
Fractal Dimension ◽  
Quantitative Analysis ◽  
Rough Surface ◽  
Vertical Section ◽  
Fractal Theory ◽  
Surface Profile ◽  
Fractal Dimensions ◽  
Geometrical Characteristic ◽  
Accuracy Requirement

In this paper, a quantitative analysis for the micro geometrical characteristic of rough surface profile is researched with the fractal theory. Firstly, the fractal dimensions of profile curves under different surface roughness are obtained by using the vertical section method, and then the theoretical relationship between the surface roughness and the fractal dimension is built. Secondly, according to the surface profile curve composed of many triangle peaks, the angles and heights of them are calculated to study the micro geometrical size. Through their variation laws changing with the fractal parameters, the calculation formulas of their average values related to fractal dimension are obtained by using mathematics regression tools. Finally, combing three theoretical relationships built above, the geometrical characteristic of the rough surface profile can be calculated with the surface roughness and accuracy requirement known.

scholarly journals Dynamic characteristics and fractal representations of crack propagation of rock with different fissures under multiple impact loadings

2021 ◽  
Vol 11 (1) ◽  
Author(s):  
Bing Sun ◽  
Shun Liu ◽  
Sheng Zeng ◽  
Shanyong Wang ◽  
Shaoping Wang
Keyword(s):  
Fractal Dimension ◽  
Crack Propagation ◽  
Crack Growth ◽  
Impact Test ◽  
Fractal Theory ◽  
Dynamic Change ◽  
Fractal Dimensions ◽  
Peak Stress ◽  
Dynamic Mechanical Properties ◽  
Gravitational Potential Energy

AbstractTo investigate the influence of the fissure morphology on the dynamic mechanical properties of the rock and the crack propagation, a drop hammer impact test device was used to conduct impact failure tests on sandstones with different fissure numbers and fissure dips, simultaneously recorded the crack growth after each impact. The box fractal dimension is used to quantitatively analyze the dynamic change in the sandstone cracks and a fractal model of crack growth over time is established based on fractal theory. The results demonstrate that under impact test conditions of the same mass and different heights, the energy absorbed by sandstone accounts for about 26.7% of the gravitational potential energy. But at the same height and different mass, the energy absorbed by the sandstone accounts for about 68.6% of the total energy. As the fissure dip increases and the number of fissures increases, the dynamic peak stress and dynamic elastic modulus of the fractured sandstone gradually decrease. The fractal dimensions of crack evolution tend to increase with time as a whole and assume as a parabolic. Except for one fissure, 60° and 90° specimens, with the extension of time, the increase rate of fractal dimension is decreasing correspondingly.

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.

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.

Complexity-Based Analysis of the Relation between Human Muscle Reaction and Walking Path

2020 ◽  
Vol 19 (03) ◽  
pp. 2050025 ◽  
Author(s):  
Shahul Mujib Kamal ◽  
Sue Sim ◽  
Rui Tee ◽  
Visvamba Nathan ◽  
Hamidreza Namazi
Keyword(s):  
Fractal Dimension ◽  
Statistical Analysis ◽  
Fractal Theory ◽  
Contact Point ◽  
Fractal Dimensions ◽  
Human Muscle ◽  
Physiological Signals ◽  
Eeg Signal ◽  
Leg Muscles ◽  
Emg Signal

Legs are the contact point of humans during walking. In fact, leg muscles react when we walk in different conditions (such as different speeds and paths). In this research, we analyze how walking path affects leg muscles’ reaction. In fact, we investigate how the complexity of muscle reaction is related to the complexity of path of movement. For this purpose, we employ fractal theory. In the experiment, subjects walk on different paths that have different fractal dimensions and then we calculate the fractal dimension of Electromyography (EMG) signals obtained from both legs. The result of our analysis showed that the complexity of EMG signal increases with the increment of complexity of path of movement. The conducted statistical analysis also supported the result of analysis. The method of analysis used in this research can be further applied to find the relation between complexity of path of movement and other physiological signals of humans such as respiration and Electroencephalography (EEG) signal.

scholarly journals Research On the Fractal Dimensions of the Organic-Rich Shale Pores Via Different Models

2022 ◽  
Vol 2152 (1) ◽  
pp. 012020
Author(s):  
Fangyao Dai
Keyword(s):  
Fractal Dimension ◽  
Gas Adsorption ◽  
Fractal Theory ◽  
Fractal Dimensions ◽  
Fractal Model ◽  
Relative Pressure ◽  
Longmaxi Formation ◽  
High Relative Pressure ◽  
Adsorption Data ◽  
Different Dimensions

Abstract Fractal dimension can be used to the pore surface characterize. For pore structures in different sizes, the calculation models of fractal theory should be distinguished due to the different principles of the gas adsorption experiments. To further study the adaptability of the fractal model for gas adsorption experimental data, the author collected shale samples of Longmaxi formation from Well JY1, then CO2 and N2 adsorption provided the PSD curves. In addition, the fractal dimensions of micropore and mesopore were calculated by the Jaroniec fractal model and Frenkel–Halsey–Hill (FHH) fractal model respectively. The research shows that the Jaroniec model may be suitable to calculate CO2 adsorption data and could characterize the fractal dimension of micropore, while the FHH model may be suitable to calculate N2 adsorption data in the high relative pressure region. It suggests that the micropore and mesopore could have different dimensions and the evaluation of the structure in shale pores should consider both of them.

scholarly journals Quantitative Characterization of Heterogeneity in Different Reservoir Spaces of Low-Permeability Sandstone Reservoirs and Its Influence on Physical Properties

2021 ◽  
Vol 2021 ◽  
pp. 1-8
Author(s):  
Fengjuan Dong ◽  
Na Liu ◽  
Zhen Sun ◽  
Xiaolong Wei ◽  
Haonan Wang ◽  
...  
Keyword(s):  
Fractal Dimension ◽  
Pore Structure ◽  
Fractal Theory ◽  
Fractal Dimensions ◽  
Low Permeability ◽  
Quantitative Characterization ◽  
Average Value ◽  
Porosity And Permeability ◽  
Sandstone Reservoirs

The complex pore structure of low-permeability sandstone reservoir makes it difficult to characterize the heterogeneity of pore throat. Taking the reservoir of Sanjianfang formation in QL oilfield as an example, the fractal dimension of different storage spaces is calculated by using fractal theory based on casting thin section, scanning electron microscope, and high-pressure mercury injection, and the correlation between porosity, permeability, and contribution of different storage space permeabilities is analyzed. The results show that the reservoir of Sanjianfang formation in QL oilfield mainly develops small pores, fine pores, and micropores, and the fractal dimension of micropore structure is between 2.6044 and 2.9982, with an average value of 2.8316. The more complex the pore structure is, the stronger the microheterogeneity is. The higher the fractal dimension, the more complex the pore structure and the smaller the porosity and permeability. The fractal dimensions of small pores, fine pores, and micropores increase successively with the decrease in pore radius, and the microstructure heterogeneity of large pores is weaker than that of small pores. It provides a theoretical basis for the exploration and development of low-permeability sandstone reservoirs.

scholarly journals Wavelet Analysis-Based Texture Analysis of Ceramic Surface Images

2021 ◽  
Vol 2021 ◽  
pp. 1-11
Author(s):  
Yanbing Liu ◽  
Bei Zhou ◽  
Xinghua Yang
Keyword(s):  
Fractal Dimension ◽  
Wavelet Analysis ◽  
Light Source ◽  
Detection System ◽  
Fractal Theory ◽  
Three Dimensional ◽  
Surface Profile ◽  
Ceramic Surface ◽  
Fractal Method ◽  
Main Research

This paper is conducted to explore a new characterization method as a supplement to the traditional roughness characterization. The main research includes the extraction and evaluation of damage features of ceramic surface morphology by applying wavelet methods, the extraction of damage features in surface contours by using wavelet analysis, and the quantitative evaluation of damage degree by using damage rate and damage mean spacing. By comparing various fractal dimension calculation methods, a fractal dimension method suitable for calculating the ceramic surface was selected, and the fractal method was used to describe the ceramic surface topography as a whole. By comparing different methods of calculating the fractal dimension and further verifying them with the measured three-dimensional morphology, it is found that the vibrational method is more suitable for calculating the fractal dimension of ceramic surface, and its calculation accuracy is investigated, and the results show that the method is a reliable one. Based on the fractal theory, a mathematical model of surface wear and surface sealing was established. Further study of the model shows that the surface with a large fractal dimension has a good sealing effect; the surface corresponding to the best fractal dimension is the most resistant to wear. The fractal method can characterize the complexity of the surface profile as a whole. The wavelet method can describe the ceramic surface profile from a local perspective, and the combination of the two methods can characterize the ceramic surface well. Finally, the experimental device of the ceramic surface defect detection system is constructed, and the joint debugging of hardware and software is completed. Under different light source intensities, ceramic image samples are collected, and the accuracy detection experiments of sample defective edges are conducted, and the results show that the light source has a small impact on the accuracy of ceramic defective edge detection. The results show that the light source has more influence on the accuracy of scratch detection. The results show that the system constructed in this thesis has good applicability for different ceramic sample detection.

scholarly journals The Impact of Nano-Al2O3 on the Physical and Strength Properties as Well as on the Morphology of Cement Composite Crack Surfaces in the Early and Later Maturation Age

Materials ◽  
2021 ◽  
Vol 14 (16) ◽  
pp. 4441
Author(s):  
Wioleta Iskra-Kozak ◽  
Janusz Konkol
Keyword(s):  
Fractal Dimension ◽  
Surface Profile ◽  
Fractal Dimensions ◽  
Cement Composite ◽  
Fracture Morphology ◽  
Strength Properties ◽  
Hardened Cement ◽  
Physical Strength ◽  
Binder Ratio ◽  
The Impact

This article presents the effect of aluminum nanoxide on the physical, strength and structural properties of cement mortars. The mortars were made with a water to binder ratio of 0.5 and a binder to sand ratio of 1:3; and 1%, 2%, 3% and 4% of aluminum nanoxide, respectively, were used by cement weight. First, the consistency of nano-Al2O3 mortars was tested. Next, after 7 days of sample maturation, compressive and flexural strength tests were carried out and continued after 28 and 90 days of the maturing of the mortars. The best test results were obtained for mortars with the addition of 1% aluminum nanoxide, the compressive strength of which increased by about 20% compared to the reference mortars. The water absorption and rising capillary tests as well as SEM observations were also performed. Another aim of the article is the analysis of the fracture morphology of nano-Al2O3 modified mortars. It is assumed that a change of the microstructure of the hardened cement paste affects not only the properties of the modified mortars but also the roughness of the fractures formed as a result of the destruction of the surface. Roughness analysis was performed with methods and tools relevant to fractal geometry. The fractographic analysis showed a significant influence of the modifier in the form of nano-Al2O3 on the values of fractal dimensions. The lowest values of the fractal dimension D and the fractal dimension of the DRP roughness profile of the fracture surface profile lines were obtained for nano-Al2O3 modified mortars. The conducted research proved the fractal dimension to be a parameter extremely sensitive to modifications of mortar composition as well as changes related to the maturation time.

Erosion Characteristics Based on GIS and Fractal Dimensions

2011 ◽  
Vol 271-273 ◽  
pp. 1142-1145
Author(s):  
Chun Xia Yang ◽  
Bin Zhen ◽  
Li Li ◽  
Jing Huang ◽  
Peng Jiao
Keyword(s):  
Fractal Dimension ◽  
Soil Erosion ◽  
Rainfall Intensity ◽  
Fractal Theory ◽  
Three Dimensional ◽  
Laser Scanner ◽  
Fractal Dimensions ◽  
Rill Erosion ◽  
Pattern Complexity ◽  
Erosion Processes

Soil erosion processes and erosion distribution was research focus to establish distributed mathematical equation in the soil erosion areas, GIS techniques and fractal theory provide a means to advance these studies.Slope erosion patterns of bare slope was studied under rainfall intensities of 45、90 and 130mm/h with 20°slope gradient using simulated rainfall experiment. The results showed that the time of rill appeared of lower rainfall intensity was later than that of high rainfall intensity；Within the rainfall time，the rill scale expanded increased with the increasing of rainfall intensity; The erosion distribution was studied by the three-dimensional laser scanner，The trend of rill erosion deep kept roughly consistent with that of sediment; The characteristics was analyzed of slope erosion by GIS, the fractal dimension and sediment were both increased with rainfall intensity, The fractal dimension was increasing with erosion pattern complexity. So the fractal dimension is the representative of erosion complexity.

Sign in / Sign up

Export Citation Format

Share Document