Self-Affine Fractal Scaling in Fracture Surfaces Generated in Ethylene and Propylene Polymers and Copolymers Fabrice Lapique, 1 Paul Meakin, Jens Feder, Torstein Jøssang Department of Physics, University of Oslo, Box 1048, Oslo 0316, Norway Received 31 August 2000; accepted 8 February 2002 Published online 15 August 2002 in Wiley InterScience (www.interscience.wiley.com). DOI 10.1002/app.11081 ABSTRACT: The fracturing of four different polyolefin ma- terials was studied with the objective of developing a better understanding of the relationships between the morphology of the semicrystalline polymers, the morphology of their fracture surfaces and their mechanical properties. This article is fo- cussed on the quantitative description of the fractures surfaces. The surface structure can be described in terms of self-affine fractal models, and the Hurst exponent(s) and roughness mea- surements can be used to describe quantitatively the fracture surface topography. Fracture surfaces generated in homopoly- mers can be described by a single Hurst exponent, which differs for PE and PP. For copolymers with PE and PP matrices, the Hurst exponent measured on small-length scales was the same as that obtained for the matrix material, but a crossover to a second regime, with a higher Hurst exponent, was found at longer length scales. The crossover was related to the average distance between rubber particles for the PP/PE rubber phase specimen (PP-copo). The introduction of a second component seems to modify the crack propagation at long-length scales, but the propagation at shorter length scales remains un- changed. Environmental stress cracking experiments indicate that each regime can be related to brittle or ductile fracturing processes. © 2002 Wiley Periodicals, Inc. J Appl Polym Sci 86: 973–983, 2002 Key words: fracture; crack propagation; polymers; rough- ness; fractal geometry INTRODUCTION The main objective of the work described in this article was to study the relationships between the morphol- ogy of polymeric materials and the mechanical prop- erties of products manufactured from them through the quantitative characterization of the fracture sur- face. The relationships between morphology and me- chanical properties have been studied in a previous article. 1 The main focus of the present article is on the quantitative description of fracture surfaces. The frac- ture surface can be characterized by measuring the roughness and by studying its self-affine fractal geom- etry. Exploration of the relationships between the su- permolecular structure, the fracture surface topogra- phy, and the fracture performance presents very ex- citing challenges, from both a basic research and an industrial point of view. If a link between the molec- ular structure and mechanical properties can be estab- lished, new concepts could be elaborated to design polymers with superior properties. The materials that were studied are commercially important polyolefins (polyethylenes and polypro- pylenes). International standardized procedures (ISO standard) for industrial test procedures were followed in fracture experiments. The idea that the rough sur- faces produced by the fracture of brittle materials have a self-affine fractal geometry 2,3 is now well estab- lished. The pioneering experimental work was carried out by Mandelbrot et al. 4 using steel. This work has been extended to a wide range of materials including other metals, 5–7 semiconductors, 5 cement-based mate- rials, 8 ceramics and rocks, 5,9 –13 polymers, 14 and natu- ral anisotropic materials such as wood 15 and rocks. 10,12 In addition, the rough surfaces generated by a variety of simple computer models for material fail- ure also appear to be self-affine fractals. 16 Some re- searchers have suggested that the Hurst exponent has a universal (independent of material and processing conditions) value, 17 but others have tried to relate the material dependent Hurst exponent to material prop- erties such as the fracture energy. 9,18 Self-affinity and some mathematical tools to describe the statistically self-affine geometry of fracture surfaces are described later. Scanning electron microscopy (SEM) and optical microscopy, based on vertical scanning interferome- try, were used to qualitatively and quantitatively char- acterize the fracture surfaces. SAMPLES Our study was focused on polyethylene- and polypro- pylene-based materials. Four different materials (see Table I), supplied by Borealis a/s (Rønningen, Nor- way) were chosen because of their relatively simple composition and their industrial interests: 2 polypro- Correspondence to: Fabrice Lapique, SINTEF, P.B. 124 Blindern, N-0314 Oslo, Norway (Fabrice.Lapique@matek. sintef.no). Journal of Applied Polymer Science, Vol. 86, 973–983 (2002) © 2002 Wiley Periodicals, Inc.