Análise Multifractal da Dinâmica da Ruptura Mecânica e Fragmentação por Impacto em Cerâmica

Abstract

Many phenomena of mass transport, percolation, fracture and fragmentation existing in nature cannot be explained using only Euclidean geometry, so there is a need to use other geometries, such as Fractal or Multifractal Geometry. Thus, different objects with irregular structures formed through these phenomena, such as ice crystals, fragments, mountain ranges, aggregates of particles, need to be studied and described using fractals. In this work, mechanical rupture through ballistic impact and fragmentation into siliceous porcelain, aluminous porcelain, alumina by means of fractal and multifractal geometry were studied, comparing with the values of glass and acrylic. Ceramics are fragile materials in relation to mechanical breakage and, due to this behavior, the energy dissipation pattern formed by cracks follows an irregular geometry, which can be characterized as a fractal geometry. The samples for the study were shape in the form of discs to perform the ballistic impact test and bars for the three-point flexion test. The glass and acrylic sample were purchased commercially with predetermined diameters and thicknesses. With the data obtained from the ballistic impact tests, statistical and graphical analyzes of the mass fraction of the fragments were performed as a function of the failure probability given by the fraction of smaller fragments F (≤m) for the same impact energy. This fragmentation graph also obtained the toughness of the material. The thermodynamic and multifractal entropy of material fragmentation was calculated using the definitions of Shannon, Reny and Tsallis and comparing the results obtained between them and the relationship with the studied materials. The multifractal analysis was performed by calculating the fractal dimension and the multifractal spectrum. The developed method is economical, since, in order to obtain the Weibull module, it is not necessary to destructively test a large number of specimens. The methodology demonstrated here may also increase the reliability in the production of ceramic materials given the multifract characteristics of these materials.