Size and rate dependent dependent necking in thin metallic films

The control of the ductility of thin metallic films is a major issue in a variety of technologies involving flexible electronics, MEMS and deformable coatings. An enhanced closed form 1D imperfection based localization analysis is developed in order to investigate the mechanics of diffuse necking in metallic films. The model relies on a description of the localization process in a finite length specimen using either a 2- or 3- zone model, under plane stress or plane strain tension conditions. A strain gradient plasticity contribution to the stabilization of the localization process is taken into account in the hardening response through a simple estimate of the deformation gradient inside the necking zone. The model, with gradient plasticity effects, is validated towards 2D finite element simulations. The response of the material involves both strain-hardening and rate sensitivity, as well as possible creep relaxation. The plastic flow parameters are related to the grain size and film thickness. The model shows, in agreement with experiments, that the ductility can either drop to small values for very small grain sizes and/or film thickness due to the high strength and to the presence of imperfections, or can remain constant or even increase owing to an increased rate sensitivity resulting from thermally activated mechanisms. This last stabilization effect can be reinforced by gradient plasticity effects if allowed by the dominant deformation mechanism