Determination of Plastic Properties of Polycrystalline Metallic Materials by Nanoindentation - Experiments and Finite El
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Determination of Plastic Properties of Polycrystalline Metallic Materials by Nanoindentation – Experiments and Finite Element Simulations Karsten Durst, Björn Backes, Mathias Göken Materials Science and Engineering, University Erlangen - Nürnberg D-91058 Erlangen, Germany
ABSTRACT The determination of plastic properties of metallic materials by nanoindentation requires the analysis of the indentation process and the evaluation methods. Particular effects on the nanoscale, like the indentation size effect or piling up of the material around the indentation, need to be considered. Nanoindentation experiments were performed on conventional grain sized (CG) as well as on ultrafine-grained (UFG) copper and brass. The indentation experiments were complemented with finite element simulations using the monotonic stress-strain curve as input data. All indentation tests were carried out using cube-corner and Berkovich geometry and thus different amount of plastic strain was applied to the material, according to Tabors theory. We find an excellent agreement between simulations and experiments for the UFG materials from which a representative strain of εB ≈ 0.1 and εcc ≈ 0.2 is determined. With these data, the slope of the stress-strain curve is predicted for all materials down to an indentation depth of 800 nm.
INTRODUCTION The determination of monotonic stress-strain curves from indentation data has been the focus of many studies. Most work is based on Tabors concept on representative strain, which states, that hardness has a simple linear relation (H = Cσy) with the flow stress σy at a representative strain [1]. For metals, which deform fully plastically during conical indentation a constraint factor of C ≈ 3 is found. The constraint factor is approximately constant for materials with a ratio of modulus to flow stress given by E/σy > 100 [2]. In the early work of Tabor and Atkins, values of the representative strain were obtained for indentation with conical indenter with different opening angles [3]. According to Tabors theory a representative strain εB ≈ 8 % is found for the Berkovich pyramid and εCC ≈ 22 % for the cube-corner pyramid. By using the two indenter geometries, the stress-strain characteristic of a material is tested at two different applied strains (figure 1(a)). For applying Tabors approach on experimental nanoindentation data, the local length scale of the indentation problem needs to be considered. At small indentation depth, below ~10 µm, an increasing hardness with decreasing indentation depth is found, which is referred to as the indentation size effect [4]. Another important point in the analysis is the influence of the pile-up of material around the impression, which leads to a wrong hardness determination by the evaluation of the load-displacement curve with the Oliver/Pharr method [5, 6]. To address these problems, we performed nanoindentations with a Berkovich and a cube-corner indenter in brass and copper samples. The monotonic stress-strain behaviour of the materials was determined by
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