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

TL;DR

This study applies multifractal detrended fluctuation analysis to fracture surfaces of foamed polypropylene/polyethylene blends, revealing temperature-dependent multifractal properties and increased surface irregularity with higher PE content.

Contribution

It introduces a two-dimensional multifractal analysis method to characterize fracture surface complexity in polymer blends, linking surface irregularity to composition and processing conditions.

Findings

Multifractal spectra confirm multifractality in fracture surfaces.

Surface irregularity increases with higher PE content.

Temperature influences the multifractal properties of the fracture surfaces.

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.