Abstract
It is shown that the size effect recently observed by Espinosa, [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, [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.
| Original language | English (US) |
|---|---|
| Article number | 073506 |
| Journal | Journal of Applied Physics |
| Volume | 97 |
| Issue number | 7 |
| DOIs | |
| State | Published - Apr 1 2005 |
Funding
The work of two authors (Z. P. B. and Z. G.) was supported under National Science Foundation Grant No. CMS—0301145 to Northwestern University (directed by Z. P. Bažant). The work of one author (H. D. E.) was sponsored by the National Science Foundation under GOALI Grant No. CMS—0120866 and NSF—NIRT Grant No. CMS—0304472. Part of the work was also supported by the Nanoscale Science and Engineering Initiative of the National Science Foundation under NSF Grant No. EEC—0118025. Three of the authors (H. D. E., Y. Z., and B. P.), are thankful to I. Petrov, J. Mabon, and M. Marshall for insight and assistance in the SEM and TEM work. Microscopy was carried out in the Center for Microanalysis of Materials, University of Illinois, which is partially supported by the U.S. Department of Energy under Grant No. DEFG02—96—ER45439.
ASJC Scopus subject areas
- General Physics and Astronomy