Effect of Processing on Nix-Gao Bilinear Indentation Results Obtained for High Purity Iron
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MRS Advances © 2018 Materials Research Society. This is an Open Access article,distributed under the terms of the Creative Commons Attribution licence (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, and reproduction in any medium, provided the original work is properly cited. DOI: 10.1557/adv.2018.135
Effect of Processing on Nix-Gao Bilinear Indentation Results Obtained for High Purity Iron Prasad Pramod Soman1 Erik Gregory Herbert1 Katerina E Aifantis2 and Stephen A Hackney1 1
Michigan Technological University, Houghton, MI, United States.
2
Mechanical and Aerospace Engineering, University of Florida, Gainesville, FL, United States.
ABSTRACT
Instrumented indentation of a high purity Fe surface with unresolved surface deformation due to mechanical polishing is compared to the same grain surface annealed at increasing time and temperature. The differences in indentation size effect behavior with annealing are correlated with hardness and electron backscatter diffraction measurements as independent measures of surface layer deformation. It is found that the Nix Gao plot evolves from nonlinear (bilinear) towards the predicted linear relationship as the surface deformation is removed. The experimental observations are rationalized by inclusion of a depth dependent, polishing induced forest dislocation density within the Nix-Gao model.
INTRODUCTION The indentation size effect has been studied for variety of materials reporting significant variation in hardness as a function of depth [1-3]. To explain mechanism responsible for the indentation size effect, various strain gradient plasticity [4-5] and mechanistic models [6-8] have been proposed. Nix and Gao [6] proposed, arguably the most widely accepted mechanistic model, based on geometrically necessary dislocations (GND) required for the indentation plastic shape change and statistically stored dislocations (SSD) due to the indentation characteristic strain [6]. To explain decreasing hardness with increasing depth, this model proposes that GND have an increase in spacing as the indentation depth increases.
The Nix Gao model for indentation of 477
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initially defect free material relates the hardness to the indentation induced dislocation density as
ܪൌ ܪ ටͳ ܪ ൌ ͵ξ͵ߙܾܩඥߩௌௌ , ݄ כൌ
ଷ௧మ ఏ , ଶఘೞ
כ
ߩீே ൌ
ଷ௧మ ఏ ଶ
(1) , where
ߙ- constant=0.5, G- Shear modulus, b- Burger’s vector, ߩீே - GND density, ߩௌௌ - SSD density, ߠ- angle between indenter and un-deformed surface,݄ כCharacteristic depth, ݂ - material dependent factor for volume correction [9]. According to the simplest interpretation of the Nix-Gao indentation size effect theory, the slope of hardness squared (H2) plotted against inverse depth 1/h should be determined by the geometr
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