SELF-AFFINE CRACK PROPAGATION PATHS ON TWO TYPES OF PAPER

Abstract

It is established in the literature that the fracture surfaces of three-dimensional materials are self-affine objects characterized by persistent or universal Hurst exponents with values centered around 0,5 and 0,8. Fracture of two-dimensional materials has been less studied and the studies have been concentrated on cellulose paper. Theoretical models in general predict values of the order of 2/3 for the Hurst exponent in two dimensions, however the reported experimental results show dispersion and deviations from that value. Being paper an anisotropic material as a result of its manufacturing process, the effect of this feature has not yet been thoroughly studied, nor has been the effect of thickness sufficiently explored. In this study we analyze two types of paper of different thickness: BPL21 of 30 μm and couché paper of 270 μm; the Hurst exponent of the propagation cracks paths in mode I was determined for the machine, transverse and 45° directions. We confirmed that the Hurst exponent tends to be distributed around the value of 2/3 for both papers in both the machine and transverse directions. However, in the case of couché paper in the direction at 45°, the Hurst exponent is around 0,8, suggesting a transition to tridimensional conditions leading to the universal value of 0,8. Our results support the conjecture that the roughness exponents show three statistical distributions centered on the values 0,5, 2/3 and 0,8.