Microstructural optimization of a functionally graded transversely isotropic layer

Motivated by current problems in coating technology, this paper addresses the microstructural optimization of a layer which is free of tractions, transversely isotropic, infinite and subjected to a prescribed thermal gradient. The layer's microstructure is characterized as a bi-constituent composite in the form of a continuous matrix perfectly bonded to embedded spheroidal short fibers. Both constituents are assumed to be isotropic in both mechanical and thermal properties. The microstructural parameters are taken to be the volume fraction, aspect ratio, and orientation distribution of the fibers. The composite layer is made functionally graded by assuming that the microstructural parameters vary through the thickness of the layer. The effective properties of the bi-constituent composite are given by the Mori-Tanaka, Hatta-Taya and Rosen-Hashin homogenization theories. The compositional and microstructural properties are determined such that an objective function defined in terms of strain energy and curvature is minimized. Specific results are presented for an aluminum (Al) layer reinforced with silicon carbide (SiC). Comparisons are made to conventional coating technology.