Measurement of the mean grain size in a metal by using fractal dimensions

Zhuravel, I. M.; Svirs’ka, L. M.

doi:10.1007/s11003-010-9306-0

Cited by 9 publications

(3 citation statements)

References 1 publication

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“…The more irregular the signal is, the greater the fractal box dimension is. Hence, it can judge the signal's complexity by way of dimensions [5][6][7].…”

Section: + ∈ Z Kmentioning

confidence: 99%

Study on Fractal Box Dimension and Its Application to Fault Diagnosis of Hydraulic Pump

Liu

Chen

2012

AMR

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Fractal box dimension is a new method to represent self-similarity and complexity of non-stationary mechanical fault signal. In this paper, we first present the basic conception of fractal and box dimension. Then we propose the algorithm to calculate the box dimension of discrete signal. On the basis of wavelet packet decomposition, we quantitatively analyze the vibration signal under different conditions with fault characteristic by way of box dimension. Experimental results show that the box dimensions are different in evidence because of the difference of fault mechanism. As a successful application, fractal box dimension can be used to recognize the fault pattern of hydraulic pump effectively.

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“…The more irregular the signal is, the greater the fractal box dimension is. Hence, it can judge the signal's complexity by way of dimensions [5][6][7].…”

Section: + ∈ Z Kmentioning

confidence: 99%

Study on Fractal Box Dimension and Its Application to Fault Diagnosis of Hydraulic Pump

Liu

Chen

2012

AMR

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“…Practical implementation of this formalism allows one to regularize conditionally incorrect problems of metal science [9]. The use of fractal (fractional) dimensions in materials science has made it possible to determine average grain size in metals [10], predict mechanical properties of low-carbon steel after heat treatment [11], estimate residual life of aircraft structures [12], develop a fractal accelerator based on a corrugated plasma waveguide [13], etc. Application of the fractal theory confirms a more accurate estimation of quality characteristics of various materials (cast iron rolls of cold rolling mills [14], metals [15], concretes [16]) due to their ranking which contributes to stabilization of the multi-parameter technology of their production.…”

Section: Introductionmentioning

confidence: 99%

Fractal Model of Estimating Quality of Cold Worked Fuel Cladding Tubes

Vakhrusheva¹,

Volchuk²,

Hruzin³

et al. 2021

Problems of Atomic Science and Technology

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A possibility was considered concerning estimation of grain anisomery in the structure of fuel cladding tubes of corrosion-resistant 026Cr16Ni15Mo3Nb steel of austenitic class rolled according to two flow charts: regular and intensive technologies using fractal formalism. Role of grain boundary hardening during cold plastic deformation was analyzed by studying the effect of the fractal dimension of grains D and their boundaries Dg on 0.2, w, and 5. The best correlation among those that were considered was observed between relative elongation and fractal dimensions of the grain structure (R2 = 0.90). The smallest correlation was observed with the yield stress (R2 = 0.64). It is because of variation of plastic flow processes towards a decrease in the degree of hardening in the material rolled according to the intensive technology. Cold deformation results in refining of the average grain size from 15.50 to 15.42 µm. In this case, extent of the grain boundary length L increased by 17.62% at an iteration step  commensurate with the average grain size which is indicated by a change in the fractal dimension according to L ~ δ1-D. Degree of the grain structure inhomogeneity was estimated using ratios of self-similarity of regions of fractal dimensions of the structure. The obtained results on the level of mechanical properties of fuel cladding tubes made of austenitic steel indicate advantage of the intensive technology over regular one that was confirmed by results of fractal modeling.

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“…At present, the fractal dimension method has been new applications in some processes, such as the characterization of surface profile curves in grinding [5] and milling [6]. For the surface microstructure of materials, such as steel, there is a closely mathematical relationship between fractal dimension and roughness [7], as well as 3rd International Conference on Mechatronics and Information Technology (ICMIT 2016) grain size [8]. At present, the calculation methods for fractal dimension of surface profile include the yard stick method, the power spectrum method, the covariance method, and the structure function method [9].…”

Section: Introductionmentioning

confidence: 99%

Fractal dimension characterization for surface microtopography of copper cut by single point diamond tool

Yang¹,

Wang²,

Zhou³

et al. 2016

Proceedings of the 2016 3rd International Conference on Mechatronics and Information Technology

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Usually roughness reflects the machining quality of the machined surface, but when the roughness of different surfaces is the same or similar, it is not sufficient to accurately distinguish the tool marks and grain concavity and convexity relying only on roughness. Therefore, the yard stick method is a better way to calculate the fractal dimension of the surface. In addition, in order to accurately reflect the grain concavity and convexity, the method of filtering can be used to weaken the influence of tool marks. The results show that the fractal dimension after filtering can reflect the features of grain concavity and convexity quantitatively.

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Measurement of the mean grain size in a metal by using fractal dimensions

Cited by 9 publications

References 1 publication

Study on Fractal Box Dimension and Its Application to Fault Diagnosis of Hydraulic Pump

Study on Fractal Box Dimension and Its Application to Fault Diagnosis of Hydraulic Pump

Fractal Model of Estimating Quality of Cold Worked Fuel Cladding Tubes

Fractal dimension characterization for surface microtopography of copper cut by single point diamond tool

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