RELIABILITY TEST OF POPULAR FRACTAL TECHNIQUES APPLIED TO SMALL 2-DIMENSIONAL SELF-AFFINE DATA SETS

The fractal dimensions of five fractional Brownian motion (fBm) surfac es of 257X257 pixel size, with Hurst exponent H ranging from 0.1 to 0. 9, were computed by profile, contour, and surface area analyses. A tec hnique was deemed reliable if it demonstrated accuracy, consistency an d sensitivity. Of all the techniques examined, surface area analysis m ethods, namely, two-dimensional pyramid and Peleg methods, were found to be most reliable and efficient for the data size studied. Hence, th ese were employed in a preliminary fractal analysis of poly(methyl met hacrylate) and poly(styrene) fracture surfaces. The surfaces were imag ed at scan sizes ranging from 1-6.5 mu m by atomic force microscopy (A FM). The images indicated the existence of fractal structure and a hig h degree of roughness at microstructural scales for both the surfaces. These observations were supported by the results of the two surface a rea analysis techniques. A more conclusive study was prevented by seve re scoring of the surfaces by the AFM tip at smaller scan sizes and th e availability of only a narrow range of scan sizes.