Indentation Size Effect (ISE) in Copper Subjected to Severe Plastic Deformation (SPD)
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INDENTATION hardness of metals has been found to decrease significantly with indentation depth when indentation depths are small, gradually converging to the macroscopic value as the depth increases. As pointed out by Dub et al.,[1] several theories have been proposed to explain this phenomenon labeled as indentation size effect (ISE), with theories based on strain gradient plasticity (SGP) and geometrically necessary dislocations (GNDs) receiving wider acceptance. The resulting analytical model, commonly referred to as the Nix–Gao model,[2] predicts a linear relationship between hardness and the reciprocal of the square root of the indentation depth. Some experimental results on both single crystal and polycrystals have shown a reasonable agreement with the above relationship (as shown by Nix and Gao using experimental results from Ma and Clark, McElhaney et al.),[2–4] while the other results such as the studies by Lim and Chaudhri[5] did not show any such agreement with these theories. Introducing an arbitrary
JOSHUA D. GALE, Graduate Student, AJIT ACHUTHAN, Assistant Professor, and DAVID J. MORRISON, Associate Professor, are with the Department of Mechanical and Aeronautical Engineering, Clarkson University, Potsdam, NY 13699. Contact e-mail: aachutha@ clarkson.edu Manuscript submitted July 4, 2013. METALLURGICAL AND MATERIALS TRANSACTIONS A
numerical factor as a correction factor to the estimated deformation volume has shown better agreement with the Nix and Gao model in some studies.[6,7] Other approaches to obtain a better fit with experimental data include theories based on a bilinear relationship.[8–12] Since ISE is attributed to GNDs, the factors that could affect dislocation nucleation and motion are in turn expected to influence ISE. These factors include the characteristic length scale of microstructural features, the deformation history in terms of the pre-existing plastic strains (work hardening), and possibly the residual stress state. Yang and Vehoff[13] studied the effect of grain size and indentation size on coarse grain and nanocrystalline nickel and found a significant effect of grain size on hardness values. By selectively indenting in a single grain and studying the influence of the grain boundary as indentation depth increased, the authors classified the ISE into three different regions based on indentation depth. When the indentation depth is small with respect to the grain size and the deformation volume is well within the single crystal, hardness decreases with an increase in depth due to GNDs/strain gradient effect. As the indentation depth increases and the deformation volume begins to interact with the grain boundaries, hardness increases with an increase in indentation depth. As the indentation depth increases even more and the deformation volume spreads out to the neighboring crystals, hardness was found to decrease further.
Work hardening has a large impact on the mechanical properties of metal, depending on the severity of the deformation. McElhaney et al.[4] found significant differences in
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