Bilinear Behavior in the Indentation Size Effect: A Consequence of Strain Gradient Plasticity
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Bilinear Behavior in the Indentation Size Effect: A Consequence of Strain Gradient Plasticity A.A. Elmustafa#, J. Lou*, O. Adewoye*, W.O. Soboyejo* and D.S. Stone+ # NASA Langley Research Center-ConITS, Hampton, VA, U.S.A * Department of Mechanical and Aerospace Engineering and Princeton Materials Institute, Princeton, NJ, U.S.A + Materials Science & Engineering, University of Wisconsin-Madison, WI, U.S.A Abstract This paper examines the effects of stacking fault energy on the micro- and nano-indentation behavior of face-centered-cubic thin films. These include: LIGA nickel MEMS structures, alpha brass, copper and high purity aluminum. The measured hardness are then fitted to a strain gradient plasticity model based on the Taylor dislocation hardening model. Hardness is shown to exhibit a size dependence with different characteristic slopes in the micron and nano-scale regimes. Deep indents are shown to exhibit classical linear behavior. However, shallow indents exhibit an abrupt decrease in slope (almost by a factor of 10), giving rise to a bi-linear behavior. Furthermore, as the gradients become less sharp, the trends in the nano-hardness data become similar to those of the microhardness data predicted by the strain gradient plasticity model. Finally, the effects of stacking fault energy are then discussed within the context of cross-slip and hardening associated with Shockly partials. Introduction In recent years, a number of researchers [1-7] have shown that indentation hardness values at the micron ( 10 nm) exhibit strong dependence on indentation size. This has been attributed largely to the effects of geometrically necessary dislocations (GNDs), which are associated with strain gradients under indenter [1, 7-8]. The indentation size effect has also been modeled in recent work by Nix and Gao [1]. By incorporating the density of geometrically necessary dislocations into the Taylor model [1,3], they were able to derive an expression for a material length scale parameter, l , which is associated largely with stretch gradients [1, 7]. However, in subsequent studies of the indentation size effect, it has become clear that the material length scale parameter, l , may be different in the micron- and nano-scale regimes [6]. The differences are particularly apparent in linearized plots of normalized hardness versus inverse of indentation size. These exhibit two characteristic slopes, one associated with the micron and sub-micron regimes, and the other associated with the nano-scale regime [6]. These two characteristic slopes suggest differences in the underlying dislocation substructures that give rise to the indentation size effect in the micron and nano-scale regimes. They give rise to the so called bi-linear behavior in the indentation size effect [6]. This paper examines the effects of stacking fault energy (SFE) on the indentation size effect in selected face centered cubic materials. These include: a LIGA Ni MEMS structure, alpha brass, copper and high purity aluminum. We have chosen to study the effects
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