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Finite element models of polycrystalline thin films were constructed based on the Monte Carlo method. The models consisted of columnar aggregates of cubic crystals with fiber texture whose axis was <001> direction perpendicular to the film surface. In the Monte Carlo method, the nucleus of a crystal was distributed at positions generated by the random number, and the crystal boundary was formed from the coordinates of the nucleus of crystals by using Voronoi tessellation.The number of grains in a sample volume was changed and fifty models with different orientations were produced for each case.A constant uniaxial displacement was applied to the models to obtain the scatter of elastic properties of thin films under the conditions of plane strain and plane stress. The scatter and mean values of Young's modulus and Poisson' ratio were obtained as functions of the number of the grains within a sample volume. A method is proposed to determine the number of grains for thin films to have macroscopic properties for the cases of various thin films with different degrees of elastic anisotropy.

Finite Element Analysis of Elastic Deformation of Cubic Polycrystalline Thin Films with (001) Fiber Texture