Multiscale modeling of rate dependence and size effects on nanocrystalline metallic thin films

The high yield strength of nanocrystalline metals is an attractive feature for new technological applications. However, nanocrystallinity also leads to undesired effects, such as increased strain-rate sensitivity and creep rates. The key characteristic responsible for the unique properties of nanocrystalline materials is the relatively large fraction of atoms that lie on the grain boundaries. The grain-boundary structure differs from the crystal lattice by presenting a less ordered arrangement, which promotes diffusion-based deformation mechanisms. The small grain size also affects dislocation-based mechanisms that occur in the grain interior. These competing mechanisms often result in an increased rate sensitivity. This work presents a multiscale finite element solver aimed at capturing the effects of grain-level deformation mechanisms and the material microstructure on the macroscopic elastic and plastic behavior of nanocrystalline thin films. The traditional multiscale method is modified to impose any state of strain or stress on the representative volume element (RVE). This allows us to simulate displacement-controlled tensile tests and load-controlled creep tests. The multiscale method is also adapted to simulate cases in which the separation of scales is valid in only two of the three spatial dimensions. Numerical implementations of the multiscale finite element solver are developed in two (2-D) and three dimensions (3-D). The virtual microstructures used as RVEs in the multiscale analyses are based on Voronoi tesselations specifically adapted to capture the columnar microstructures of the metallic films. The finite element discretization combines triangular or tetrahedral elements to model the volumetric response of individual grains, with interfacial cohesive elements used to capture the response of the grain boundaries. The two grain-level deformation mechanisms incorporated in the multiscale method are the single-crystal plasticity model, aimed to capture the plastic behavior at higher strain rates, and a diffusion-based grain-boundary sliding model, aimed to capture the macroscopic creep behavior. The single-crystal plasticity model is calibrated with the tensile tests at the right strain rates, whereas the grain-boundary sliding model is calibrated with the creep tests. Both the 2-D and 3-D models are validated by predicting the rate sensitivity of a nanocrystalline gold thin film for strain rates ranging from 6.0E-6 to 12.8E-1 1/s, using grain-level deformation models calibrated with the aid of one creep experiment and higher strain-rate tensile tests. The multiscale model also provides a quantitative evaluation of the influence of creep strain during tensile testing of the gold thin films. We demonstrate, that for tensile tests with strain rates below 1E-4 1/s, plasticity caused by grain-boundary sliding may be the deformation mechanism that defines the onset of plasticity. The effect of film thickness on the elastic and plastic properties, as measured by tensile tests, is quantified. The numerical predictions show a decrease in the measured elastic modulus and yield stress with a reduction in the film thickness. Such reductions are a direct consequence of the grain size and film thickness having the same order of magnitude. Experimental observations that corroborate the thickness dependence are presented. We also study the influence of the grain-boundary angle with respect to the film plane on the macroscopic behavior resulting from grain-boundary sliding. Creep test simulations are performed with two sets of RVEs, one with grain boundaries perpendicular to the film plane and one with grain boundaries tilted. The results show a strong influence of the grain-boundary angle on the magnitudes of the three components of tensile strain