Fractal Description of the Structure of Fresh and Eroded Aluminum shot fineparticles

Abstract

AbstractFractal dimensions are numbers between the classical whole number dimensions which can be used to describe the ruggedness of a fineparticle boundary. This communication explores the utility of fractal dimensions between 1 and 2 for characterizing the ruggedness of fineparticle profiles. This type of fractal boundary is evaluated by estimating the perimeter of a profile of a fineparticle at various levels of scrutiny and then plotting a graph of the logarithm of the perimeter estimates against the logarithm of a unit representing the scale of scrutiny. Such a graph is known as a Richardson plot. Boundaries describable by fractal dimensions exhibit characteristic datalines on this type of graph.Aluminum shot fineparticles produced by the break up of turbulent jet of molten metal have irregular shapes because of the fluid turbulence in the regions where they solidify, but a smooth texture because of the effect of surface tension forces as the fineparticle solidifies. It is shown in this communication that the dataline on a Richardson plot of the estimated perimeter of an aluminum shot fineparticle consists of two regions. The first portion, at coarse levels of scrutiny, permits the calculation of a fractal dimension descriptor of the ruggedness of the profile. A second dataline at high resolution is parallel to the scrutiny axis indicating that at such levels of inspection the profile is effectively smooth and euclidean. Studies are reported of the changes in the ruggedness of an eroding aluminum shot fineparticle suspended in acid. It is shown that fractals can be used to describe the progress of corrosion and that, as corrosion proceeds, the euclidean portion of the Richardson plot of perimeter estimate recedes and disappears within the levels of scrutiny employed in these experiments.