Strain gradient plasticity analysis of the strength and ductility of thin metallic films using an enriched interface model

Abstract

The mechanical response of thin metallic films is simulated using a two-dimensional strain gradient plasticity finite-element model involving grain boundaries in order to investigate the effect of the thickness, grain shape and surface constraint on the strength, ductility and back-stress. The grain boundaries and surface layers are modeled as initially impenetrable to dislocations while allowing for relaxation at a critical stress level. The model captures the variation of the strength with grain size, film thickness, and with the presence or not of constraining surface layers, in agreement with experimental results on Al and Cu films. A decrease in the uniform elongation is predicted with decreasing film thickness due to a loss of strain-hardening capacity and the possible presence of imperfections. These two effects dominate over the stabilizing contribution of the plastic strain gradients. Accounting for the relaxation of the interface constraint affects the magnitude of the back-stress as well as the drop in ductility.

Failure of metals III: Fracture and fatigue of nanostructured metallic materials

“…A similar approach has been followed by Brugger et al [145] specifically focusing on the necking in thin columnar metallic films. The loss of resistance to necking induced by the increasing strength when reducing film thickness can be compensated by the strain gradient effect [145]. A much more simple approach based on a 1D imperfection analysis, accounting for strain gradient effects, has been recently proposed by Pardoen [171] and validated towards the FE calculations of Niordson [380].…”

“…This phenomenon has been studied by Niordson and coworkers [379,380] using 2D FE simulations based on the strain gradient constitutive model of Fleck and Hutchinson [70]. A similar approach has been followed by Brugger et al [145] specifically focusing on the necking in thin columnar metallic films. The loss of resistance to necking induced by the increasing strength when reducing film thickness can be compensated by the strain gradient effect [145].…”

“…Indeed, a small surface roughness amplitude or the presence of surface etch pits, of lithography undulations or of grain boundary grooves on the order of a few nm lead to what can be considered as a significant imperfection in a 100 nm thick film. Also, the presence of an oxide at the surface can lead to an evolution of the constraint imposed to the plastic flow if it breaks during deformation [145] inducing a sudden local softening that favours plastic localization. The importance of imperfections and the statistical effects that result from the distribution of these imperfections as a [333,351,352]; (e) MEMS tensile testing stage by Espinosa and coworkers [354,355]; (f) on chip nanomechanical testing laboratory with internal stress based actuated elementary structures [358,359]; (g) tensile loading through deflection [308,366]; (h) bulge test configuration.…”

“…Factors such as the grain shape, the presence of oxide at the surface and the resistance of this oxide will also play a role in the dislocation starvation capacity, see e.g. [145,146]. (3) When the structure is columnar for thin films and bamboo-types for nanowires with a single grain in the small dimension, the lack of constraint in one or two of the dimensions facilitates the operation of GB sliding and migration mechanisms.…”

Dislocation and back stress dominated viscoplasticity in freestanding sub-micron Pd films

“…Ref. [71]). The only length scale that enters the present model is the grain size in the mechanical threshold expression (6).…”