Epitaxially influenced boundary layer model for size effect in thin metallic films

It is shown that the size effect recently observed by Espinosa et al., [J. Mech. Phys. Solids51, 47 (2003)] in pure tension tests on free thin metallic films can be explained by the existence of a boundary layer of fixed thickness, located at the surface of the film that was attached onto the substrate during deposition. The boundary layer is influenced by the epitaxial effects of crystal growth on the dislocation density and texture (manifested by prevalent crystal plane orientations). This influence is assumed to cause significantly elevated yield strength. Furthermore, the observed gradual postpeak softening, along with its size independence, which is observed in short film strips subjected to pure tension, is explained by slip localization, originating at notch-like defects, and by damage, which can propagate in a stable manner when the film strip under pure tension is sufficiently thin and short. For general applications, the present epitaxially influenced boundary layer model may be combined with the classical strain-gradient plasticity proposed by Gao et al., [J. Mech. Phys. Solids 47, 1239 (1999)], and it is shown that this combination is necessary to fit the test data on both pure tension and bending of thin films by one and the same theory. To deal with films having different crystal grain sizes, the Hall-Petch relation for the yield strength dependence on the grain size needs to be incorporated into the combined theory. For very thin films, in which a flattened grain fills the whole film thickness, the Hall-Petch relation needs a cutoff, and the asymptotic increase of yield strength with diminishing film thickness is then described by the extension of Nix's model of misfit dislocations by Zhang and Zhou [J. Adv. Mater. 38, 51 (2002)]. The final result is a proposal of a general theory for strength, size effect, hardening, and softening of thin metallic films