Ableitung physikalischer Werkstoffkenngrößen aus Indentierungsexperimenten in polykristallinen/ultrafeinkörnigen und einkristallinen Materialien - Simulation und Experiment -
Final Report Abstract
Nanoindentation is a technique, which allows probing the local mechanical properties of materials on a microstructural level. This allows measuring strengthening mechanisms like solid solution strengthening on a local scale. However, indentation results in an inhomogeneous deformation of the material, which leads to the so called indentation size effect (ISE). Up to now it was not clear how to interpret the local hardness results with respect to the macroscopic material behavior. In this project, size effects occurring during indentation testing have been experimentally studied and a model description of these effects has been developed. The experimental investigation was accompanied by finite element simulations of indentations using von Mises as well as strain gradient plasticity simulations of the scale dependency of the mechanical properties. For studying the physical mechanism of the indentation size effect (ISE), fundamental experiments have been conducted on various single crystalline, coarse grained as well as ultrafine-grained (UFG) materials and solid solutions. An experimental methodology for testing the size dependence of hardness has been developed, avoiding measurement artifacts stemming from surface preparation or loading conditions. It is found that the hardness as a function of depth for a given material follows a simple relationship, which yields a linear behavior in the so called Nix-Gao plot, where the hardness squared is plotted as a function of the inverse of the contact depth. This linear behavior as characterized by the characteristic indentation length scale h*, seems to hold true from first dislocation nucleation at depths of ~20 nm up to the macroscopic regime with indentation depths larger than 5 µm. The depth dependence of hardness together with the load-displacement data and pop-in behaviour was modelled from macroscopic stress-strain curves. Using Tabor’s concept of the representative strain together with a Taylor-type dislocation hardening, the statistically stored dislocation (SSD) density is calculated for different indenter geometries. The depth dependent geometrically necessary dislocation density is derived following a Nix-Gao type of analysis. A factor f is introduced in the analysis for considering and correcting the storage volume of the geometrically necessary dislocations (GND). The deformation resistance is then governed by the total dislocation density. With this approach, the hardness depth relation is modelled over the whole indentation length scale from macroscopic hardness down to the pop-in behaviour. For a strain gradient plasticity finite element simulation of the indentation process, a new equation for the experimental determination of the internal material length scale l was derived, using the uniaxial flow stress and the macroscopic hardness of the material in conjunction with the characteristic indentation length scale h*. The internal material length scale used in these models depends strongly on the dislocation density, were a prestraining of the material results in a strong reduction in l. For recrystallised materials with a low dislocation density, strain gradient effects need to be considered and using the experimentally derived values, a good description of load-displacement data and hardness-depth relations is possible.
Publications
- Determination of plastic properties of polycrystalline metallic materials by nanoindentation – experiments and finite element simulations. Mater. Res. Soc. Symp. Proc. Vol. 841, MRS Warrendale, (2005) R11.4.1-R11.4.6
K. Durst, B. Backes, M. Göken
- Indentation size effect in metallic materials: Correcting for the size of the plastic zone. Scripta Mat., 52, (2005), 1093-1097
K. Durst, B. Backes, M. Göken
- Determination of plastic properties of polycrystalline metallic materials by nanoindentation: experiments and finite element simulations. Phil. Mag., 86, (2006), 5541-5551
B. Backes, K. Durst, M. Göken
- Indentation size effect in metallic materials: Modeling strength from pop-in to macroscopic hardness using geometrically necessary dislocations. Acta Materialia, 54, (2006) 2547–2555
K. Durst, B. Backes, O. Franke, M. Göken
- Indentation size effect in NiFe solid solutions. Acta Materialia 55 (2007) 6825 – 6833
K. Durst, O. Franke, A. Böhner, M. Göken
- Ableitung von physikalischen Werkstoffkenngrößen aus Indentierungsexperimenten-Simulation und Experiment. Dissertation Universität Erlangen-Nürnberg, 2009
Björn Eckert
- Revealing Deformation Mechanisms with Nanoindentation. JOM 61 (3) 2009 14-23
D. Kiener, K. Durst, M. Rester, A. Minor
- The correlation between the internal material length scale and the microstructure in nanoindentation experiments and simulations using the conventional mechanism strain gradient plasticity theory. J. Mater. Res. 24 (3) (2009) 1197 - 1207 (2009)
B. Backes, Y.Y. Huang, M. Göken, K. Durst
- Indentation size effect in crystalline materials. Habilitationsschrift, Universität Erlangen Nürnberg, 2010
Karsten Durst
