Effective modulus of polycrystalline aggregates in different geometrical configurations

In the present study, a finite element scheme with random distribution strategy is employed to systematically investigate the modulus difference of polycrystalline copper aggregates in different geometrical configurations (three-dimensional bulk and thin film configurations). Firstly, the finite element simulation is performed to estimate the effective elastic constants in three-dimensional bulk configuration. The numerical estimations are in good agreement with the existing analytical solutions and experimental measurements. Secondly, the proven finite element scheme is extended to the prediction of the effective moduli of the free-standing and substrate-attached thin films. For the free-standing thin film, the effective Youngʹs modulus decreases with reducing the film thickness. For the substrate-attached thin film, its effective modulus is affected by the relative stiffness between the substrate and the film. The spread of the effective moduli in different configurations could be as large as 20%.