Sierpinski fractal description of the martensitic transformation

Long, Q.Y.; Yu, Weiping; Zhu, Zhengwu; Zhang, X. M.; Mu, Zaigen; Lung, C.W.

doi:10.1080/01418619308219373

Cited by 9 publications

(4 citation statements)

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“…It was heated at 1250 • C for one hour and then quenched in water. Because the heating temperature was much higher than that used in our previous work [4], we obtained a much larger grain size. The average grain observe the variation of the microstructure during cooling, we selected some fields of vision to be monitored by the metallographical technique of polarization contrast at different temperatures.…”

Section: Experimental Observations and Fractal Modelmentioning

confidence: 86%

“…Unfortunately the model is not a fractal. Long et al [4] suggested a MT model, the fractal dimension of which can be calculated by using different parameters, but the morphology has not yet been observed in a practical situation. In this paper, an uneven fractal model of the MT in a Fe-29%Ni-0.16%C alloy is proposed on the basis of experimental observations.…”

Section: Introductionmentioning

confidence: 99%

See 1 more Smart Citation

Fractal characteristics of the martensitic transformation in a Fe - 29% Ni - 0.16% C alloy

Long

Jiang

et al. 1996

J. Phys. D: Appl. Phys.

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A fractal model of the martensitic transformation (MT) in a Fe - 29% Ni - 0.16% C alloy is proposed on the basis of metallographic observations. It is an uneven fractal that can better describe the microstructure observed in the experiments. The uneven fractal can be produced by an iterated function system (IFS). The IFS code, consisting of two affine maps, is given to calculate the fractal dimension. Finally, we also propose a partition process to simulate the dynamic process of the MT.

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Section: Experimental Observations and Fractal Modelmentioning

confidence: 86%

Section: Introductionmentioning

confidence: 99%

Fractal characteristics of the martensitic transformation in a Fe - 29% Ni - 0.16% C alloy

Long

Jiang

et al. 1996

J. Phys. D: Appl. Phys.

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“…Fractal structures are quite common for two‐phase systems, particularly if they are rapidly quenched into the metastable state, far from equilibrium (Skrotzki, 1991; Long et al , 1993; Schuszter et al , 2003). Hence, we have attempted to make an analysis of the scanning electron microscopy (SEM) images in order to look upon fractal dimension versus scale and sample annealing, i.e.…”

Section: Introductionmentioning

confidence: 99%

Fractal‐like behaviour of the BCC/FCC phase separation in the iron‐gold alloys

Błachowski

Ruebenbauer

Rakowska

et al. 2010

Journal of Microscopy

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Summary Iron‐gold alloys with compositions Fe70Au30 and Fe50Au50 were prepared by arc melting. The alloys were investigated by means of the high‐resolution scanning electron microscopy (SEM‐FEG) in the as‐cast state and upon annealing in two steps, i.e. at 250°C for 24 h and subsequently at 500°C for 48 h. The alloys were composed of two phases, i.e. a BCC phase rich in iron and a FCC phase rich in gold. The single‐phase regions have equivalent diameter of about 50 nm. SEM images show self‐similar structure for the spatial distribution of the above phases on scales ranging from about 1 mm till about 100 nm. The roughness of the images has been used to estimate a fractal dimension of the phase mixture. For larger scales of the as‐cast samples one finds fractal dimension of about 1.7 for Fe70Au30 composition, i.e. very close to the dimension of typical diffusion limited aggregation (DLA) fractals. For annealed samples, dimension 1.1 was found.

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“…The stationary probability distribution at the L-fixed point was shown numerically to fit to a power-law form P͑l͒ ϳ l 2a . This choice was guided, in part, by empirical studies on the microstructure of acicular martensites [2]. In their Comment [3] to our Letter [1], Ben-Naim and Krapivsky have obtained the exact asymptotic form of P͑l͒ for this model at the L-fixed point where it reduces to a multifragmentation problem.…”

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confidence: 99%