Transient multiscale thermoelastic analysis of functionally graded materials

This study is concerned with the transient multiscale analysis of two-phase functionally graded materials within the framework of linearized thermoelasticity. The two-phase material microstructures, which are created using a morphology description function, have material morphologies that depend on the volume fractions of the constituent phases. The functionally graded materials considered here have a smooth spatial variation of microstructure and homogenized material properties. The multiscale problem, which involves both macroscopic and microscopic length scales, is analyzed using asymptotic expansion homogenization coupled with the finite element method. The accuracy of the implemented multiscale analysis is verified by comparing the results against two validation problems. Subsequently, two model problems are studied to illustrate the versatility of the multiscale analysis procedure. In the first model problem, a functionally graded tungsten/copper specimen with spatially varying microstructural morphology and time-varying applied heat flux on its boundary is investigated. The second model problem concerns a functionally graded titanium/zirconia turbine blade geometry with random microstructure. For each of the model problems, the microscale stresses are utilized to perform a direct micromechanical failure analysis.