Multifractal analysis of the fracture surfaces of foamed polypropylene/polyethylene blends

Abstract

The two-dimensional multifractal detrended fluctuation analysis is applied to reveal the multifractal properties of the fracture surfaces of foamed polypropylene/polyethylene blends at different temperatures. Nice power-law scaling relationship between the detrended fluctuation function $F_q$ and the scale $s$ is observed for different orders $q$ and the scaling exponent $h(q)$ is found to be a nonlinear function of $q$, confirming the presence of multifractality in the fracture surfaces. The multifractal spectra $f(\alpha )$ are obtained numerically through Legendre transform. The shape of the multifractal spectrum of singularities can be well captured by the width of spectrum $\Delta \alpha$ and the difference of dimension $\Delta f$. With the increase of the PE content, the fracture surface becomes more irregular and complex, as is manifested by the facts that $\Delta \alpha$ increases and $\Delta f$ decreases from positive to negative. A qualitative interpretation is provided based on the foaming process.

8 pages

References in corpus (4)

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• Multifractal detrended fluctuation analysis of combustion flames in four-burner impinging entrained-flow gasifier
• Scaling properties of pyrex and silicon surfaces blasted with sharp particles
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