Analysis of local grain boundary strengthening utilizing the extrinsic indentation size effect
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FOCUS ISSUE
INTRINSIC AND EXTRINSIC SIZE EFFECTS IN MATERIALS
Analysis of local grain boundary strengthening utilizing the extrinsic indentation size effect Prasad Pramod Soman1, Erik G. Herbert1,c), Katerina E. Aifantis2,a), Stephen A. Hackney1,b) 1
Department of Materials Science and Engineering, Michigan Technological University, Houghton, Michigan 49931, USA Mechanical and Aerospace Engineering, University of Florida, Gainesville, Florida 32612, USA a) Address all correspondence to these authors. e-mail: kaifantis@ufl.edu b) e-mail: [email protected] c) This author was an editor of this journal during the review and decision stage. For the JMR policy on review and publication of manuscripts authored by editors, please refer to http://www.mrs.org/editor-manuscripts/. 2
Received: 2 January 2019; accepted: 21 February 2019
The extrinsic indentation size effect (ISE) is utilized to analyze the depth-dependent hardness for Berkovich indentation of non-uniform dislocation distributions with one and two dimensional deformation gradients and is then extended to indentation results at grain boundaries. The role of the Berkovich pyramid orientation and placement relative to the grain boundary on extrinsic ISE is considered in terms of slip transmission at yield and plastic incompatibility during post-yield deformation. The results are interpreted using a local dislocation hardening mechanism originally proposed by Ashby, combined with the Hall–Petch equation. The Hall–Petch coefficient determined from the extrinsic ISE of the grain boundary is found to be consistent with the published values for pure Fe and mild steel. A simple, linear continuum strain gradient plasticity model is used to further analyze the results to include contributions from a non-uniform distribution in plastic strain and dislocation density.
Introduction The indentation size effect (ISE) has been studied for two decades, with the most accepted model of the physical origin presented by Nix and Gao [1]. In the context of examining the ISE in thin films, the terms “intrinsic” and “extrinsic” size effect were introduced by Ngan and Ng [2] to distinguish between the indentation response of the film itself versus the combined response of the film/substrate system. Following a slightly modified form of that nomenclature, here we compare and contrast the intrinsic and extrinsic ISE in high-purity and carbon-doped iron. In this context, we use the terms intrinsic and extrinsic to distinguish between the effect of the indenter geometry–induced plastic strain gradient [1], as observed in well-annealed, single crystal surfaces, and the effect(s) of preexisting defect structures in the same material, respectively. Based on that distinction, the depth-dependent hardness, H, as measured by Berkovich nanoindentation experiments, is used to interrogate the structure–property relationship of specific defect structures that show extrinsic size effects. The four cases analyzed are (i) three different well-annealed, single-crystal Fe
ª Materials Research Society 2019
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