Inhomogeneity of the grain size of aircraft engine turbine polycrystalline blades

The determination of the behaviour of inhomogeneous materials with a complex microstructure requires taking into account the inhomogeneity of the grain size, as it is the basis for the process of designing and modelling effective behaviours. Therefore, the functional description of the inhomogeneity is becoming an important issue. The paper presents an analytical approach to the grain size inhomogeneity, based on the derivative of a logarithmic-logistic function. The solution applied enabled an effective evaluation of the inhomogeneity of two macrostructures of aircraft engine turbine blades, characterized by a high degree of diversity in the grain size. For the investigated single-modal and bimodal grain size distributions on a perpendicular projection and for grains with a non-planar surface, we identified the parameters that describe the degree of inhomogeneity of the constituents of weight distributions and we also derived a formula describing the overall degree of inhomogeneity of bimodal distributions. The solution presented in the paper is of a general nature and it can be used to describe the degree of inhomogeneity of multi-modal distributions. All the calculations were performed using the MathematicaŽ package.