A self-affine geometrical model of dynamic RT-PMMA fractures: implications for fracture energy measurements

Profilometric imaging of fracture surfaces of rubber toughened polymer has been performed at two different resolutions (a) at large scales [10 μ\upmu m–25 mm] using an opto-mechanical profilometer and (b) at small scales [0.195 μ\upmu m–0.48 mm] using an interferometric optical microscope. We introduced a self-affine geometrical model using two parameters: the Hurst exponent and the topothesy. We showed that for rubber toughened materials the approximation of the created surface by a mean flat plane leads to a poor estimation of the dynamic fracture energy GIdcG_Idc. The description of the created rough fracture surface by a self-affine model is shown to provide a significantly better approximation. A new and original geometrical method is introduced to estimate self-affine parameters: the 3D surface scaling method. Hurst exponents are shown to be unique, χ=0.6±0.1\chi =0.6\pm 0.1 for the different fracture zones and measurement scales. Topothesy ratios indicate a significant difference of fracture surface roughness amplitude depending on the observation resolution when the detrending technique is not correctly introduced.