Fractal character of scanning tunneling microscopic images of brittle fracture surfaces on chromium.

Quantitative Evaluation of the Impact Fracture Surfaces of SS400 Steel by the Three-dimensional Geometrical Analysis

“…The fractal dimension of the brittle fracture surface may change largely with spatial distribution of steps, which are associated with shear steps between facets and river patterns. 12,13) As a result, a definite correlation was not found between the absorbed energy and the fractal dimension of the fracture surface in the SS400 steel in this study, while the absorbed energy may increase [1][2][3] or may decrease [4][5][6] with increasing fractal dimension of the fracture surface, depending on materials.…”

“…The fractal dimension dependence of absorbed energy seems to coincide with the result obtained by Mandelbrot et al 1) However, this negative relationship is dubious, because the range of variation in the fractal dimension with temperature is only about 0.05 and is too small to identify any functional dependence of the absorbed energy on the fractal dimension of the fracture surface in this study. According to Matsuoka et al, 12,13) the cleavage fracture surfaces of Cr and Mo has much smaller fractal dimension (about 2.05 in three-dimensional space) than the part of crack linkage in Cr (about 2.16 in three-dimensional space) and a quasi-cleavage fracture surface (about 2.17 to 2.22) in the SS400 steel. Li et al 28) also reported that in pure iron and Cr-Ni steel the fractal dimension of the quasi-cleavage fracture surface is a little larger than that of the transgranular cleavage fracture surface.…”

“…3(b)). 12,13,28) Figure 9 shows the central part of quasi-cleavage fracture surface of SS400 steel (194 K). As known from river patterns, the crack has grown in the direction indicated by an arrow in Fig.…”

“…The scanning probe microscopes (SPM) such as the scanning tunneling microscope (STM) and the atomic force microscope (AFM) have recently been introduced to the fractal analysis of three-dimensional surface morphology. 6,9,12,13) However, these microscopes are not always applicable to complex fracture surfaces of metals and alloys. Computer-aided stereo matching method has been successfully applied to the reconstruction and analysis of three-dimensional images of fracture surfaces in materials.…”

Quantitative Analysis for Shape Irregularity of Ceramic Particles Based on Richardson Effect

“…, the medical science [7], the physical science [8,9], the engineering [10][11][12][13][14], the sociology [15], the economics [16] and so on. Fig.…”