Effects of finite probe size on self-affine roughness measurements

Abstract

The roughness of fracture surfaces has been shown to exhibit self-affne scale invariance for a wide variety of materials and loading conditions. The range of scales over which this regime extends remains a matter of debate, together with the universality of the associated exponents. The topography of these surfaces is however often investigated with a contact probe that is larger than the micro-structure. In this case, we show that the correlation function of the roughness and the corresponding Hurst exponent $\zeta$ can only be measured down to a length scale $\Delta xc$ which depends on the probe size $R$, on $\zeta$ and on the surface topothesy $l$, and exhibit spurious behavior at smaller scales. First, we derive the dependence of $\Delta xc$ on these parameters from a simple scaling argument. Then we study this dependence numerically and verify our theoretical prediction. Finally, we establish the relevance of this analysis from AFM measurements on an experimental glass fracture surface and provide a metrological procedure for roughness measurements.

4 pages, 4 figures, submitted to PRL

References in corpus (4)

• Scaling exponents for fracture surfaces in homogenous glass and glassy ceramics
• Gaussian Statistics of Fracture Surfaces
• Crack propagation through phase separated glasses: effect of the characteristic size of disorder
• Cleaved surface of i-AlPdMn quasicrystals: Influence of the local temperature elevation at the crack tip on the fracture surface roughness

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