Fractal Dimension Map Research Articles

A Análise de Lineamentos Estruturais, Sob a Óptica da Geometria Fractal, no Maciço Alcalino de Poços de Caldas (MG)

This work presents the evolution of geological history of the Alkalic Mass of Poços de Caldas, based on a lineament study. The lineaments are correlated to ruptil fractures on the ground. For this purpose, the fractal geometry of lineaments was used to explain the results.The lineaments were obtained from Landsat-TM and Radar images. Graphics were generated such as the cumulative frequency of direction, histograms of structural lineaments direction per cumulative length and a plot of direction by lineament length. A map of fractal dimension of these lineaments was generated too.The correspondence between the plans of processed data, the structural context and the location of mineralizations allowed to conclude: (1) the uranium mineralizations are associated to fractures oriented preferentially NW and NE and (2) the zirconium mineralizations are oriented preferentially NS and EW.

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

The fractal dimension and the surface roughness of the fracture surface was estimated using the height data generated by the stereo matching method on Charpy V-notch specimens of the SS400 steel impact-fractured in the temperature range from 194 K (−79°C) to 273 K (0°C). The representative fracture surfaces were quasi-cleavage fracture surface with river patterns and steps between facets at 194 K and ductile fracture surface with dimples and shear steps at 273 K. On the region close to the notch root (fracture initiation site), a definite correlation was not found between the absorbed energy and the fractal dimension of the fracture surface, but both absorbed energy and surface roughness increased with temperature because of increased proportion of ductile fracture surface with the larger surface roughness. There was essentially no difference in the fractal dimension between quasi-cleavage fracture surface and ductile fracture surface. Fracture process including fracture initiation, local crack growth or finally fractured part could be examined by the detection of characteristic fracture patterns using the fractal dimension map (FDM) and the surface roughness map (SRM). Detected steps of various sizes were associated with river patterns or fracture at ferrite grain boundaries on the quasi-cleavage fracture surface, and were associated with dimple walls or shear steps on the ductile fracture surface. Steps on both fracture surfaces were formed by common mechanism, namely, by plastic deformation (shear deformation). The density of steps was larger on the quasi-cleavage fracture surface than on the ductile fracture surface. These steps led to a large fractal dimension of the quasi-cleavage fracture surface comparable with the ductile fracture surface with dimples.

Geometrical analysis and pattern recognition using mapping technologies of three-dimensional fracture surfaces in materials

Geometrical analysis of fracture surfaces in materials was made using newly developed computer programs on the three-dimensional images reconstructed by the stereo matching method. The global value of the fractal dimension of the fracture surface was estimated by the box-counting method on a fatigue fracture surface of a Cu-Be alloy and impact fracture surfaces of a SiC and an alumina. The results of the present analysis were well correlated with those of the two-dimensional fractal analysis. The fractal dimension map (FDM) by the box-counting method and the surface roughness map (SRM) proposed in this study can give important information about the local fracture mechanisms, the crack growth direction or the fracture origin in materials. FDM and SRM have interesting characteristics by which one can discriminate the flat regions, the regions of complex geometry or the steeply inclined areas on a given fracture surface. Pattern recognition using mapping technologies of FDM and SRM is also applicable to the extraction of “hidden patterns” on fracture surfaces, which cannot be observed only by microscopes.