First-Order Size Effects in the Mechanics of Miniaturized Components
This work analyses those size effects that are encountered first upon downscaling, including grain boundary effects, free surface effects, grain statistics effects. The separate influence of first-order effects was carefully investigated from uniaxial tensile tests on high-purity aluminum specimens with a well-defined microstructure of through-thickness grains, whereby the total number of grains in the cross-section was reduced towards a single grain in a cross-section by, first, decreasing the film thickness and, second, for specimens with through-thickness grains decreasing the specimen width. In addition, 3D dislocation-field strain gradient plasticity simulations were employed to analyze the intrinsic size effects, using the grain size and texture as measured experimentally. The work shows that for miniaturized structures with a limited number of columnar grains a unique Hall-Petch relation does not exist, even though a grain boundary effect, i.e. a decrease in stress level (at a given strain) for decreasing grain boundary area per unit volume, is clearly present. When the microstructure is kept constant upon miniaturization, the free surface per unit area increases causing the stress level of the structure to decrease, the effect of which increases towards a single grain in the cross-section. In addition, the work shows that grain statistics effects also contribute to observed weakening, due to insufficient compensation of local (weaker) material properties by the surrounding material (i.e. grains). Finally, grain statistics also significantly increase the statistical variation in mechanical properties for small-sized structures, an effect that is especially important for the reliability of miniature components. The separate influence of these first-order effects as well as their interplay are explained in terms of the movement of the dislocations upon plastic flow.
J.M. Dulieu-Barton, J.D. Lord and R.J. Greene
J.P.M. Hoefnagels et al., "First-Order Size Effects in the Mechanics of Miniaturized Components", Applied Mechanics and Materials, Vols. 13-14, pp. 183-192, 2008