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

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 image and the scale s is observed for different orders q and the scaling exponent image is found to be a nonlinear function of q, confirming the presence of multifractality in the fracture surfaces. The multifractal spectra image are obtained numerically through Legendre transform. The shape of the multifractal spectrum of singularities can be well captured by the width of spectrum image and the difference of dimension image. With the increase of the PE content, the fracture surface becomes more irregular and complex, as is manifested by the facts that image increases and image decreases from positive to negative. A qualitative interpretation is provided based on the foaming process.