Space function recovery of the distribution of coating inhomogeneities according to the distribution function on the polished specimen

Abstract

In the experimental studies of the structure of the special coating layer overlaid on metal applying gas-thermal spraying technique, one of the main methods is the study of polished specimen micrography. According to the computer analysis of microphotographs, it is possible to obtain the distribution function of inhomogeneities in the sample. However, since micrography is a flat image, the resulting function will be two-dimensional, whereas in a real sample, the distribution of defects is described by a three-dimensional function. In this paper, the problem of the space function recovery for the distribution of defects in a gas-thermal coating is viewed on the basis of the analysis of polished specimen micrography. The actual inclusion of an irregular shape is replaced by an effective three-axis ellipsoid. The problem is solved in the general form of reduction of the space function f of inhomogeneities distribution according to their distribution function f P on the cross - sectional plane P, which includes some integral transformation I. It is shown that in the special case of spherical particles, the inversion I^(-1) exists and is an integral transformation of the same type as I. The space distribution of spherical particles is also viewed, which does not depend on the longitudinal coordinate z, where particle sizes are limited at each point by a function R(x,y), depending on the coordinates. This distribution is suitable in its essense to the stationary spraying technology, when in deep layers near the substrate, the coating material melts completely and forms a single melt, while closer to the surface and edges, the parts that are not completely melted form inclusions of noticeable sizes. The reduction of the Fuller distribution law, used to optimize the granulometric composition of powder materials, is viewed as a second example. It is found that the reduction of the density of the ellipsoid distribution function to the section of a flat strip transfers the density of the distribution of centers as original, and the product of Fuller distributions times independent parameters is transformed into the product of distributions times the opposite degree parameters and also the previous values of the parameters of the ellipsoid