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 (PP/PE) 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 ( α ) are obtained numerically through Legendre transform. The shape of the multifractal spectrum of singularities can be well captured by the width of spectrum Δ α and the difference of dimension Δ f . With the increase of the PE content, the fracture surface becomes more irregular and complex, as is manifested by the facts that Δ α increases and Δ f decreases from positive to negative. A qualitative interpretation is provided based on the foaming process.