Nanoindentation investigations to study solid solution hardening in Ni-based diffusion couples
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In this work the hardening effect of Ta and Mo in Ni-base alloys was investigated using a combinatorial approach with diffusion couples. Furthermore, the Ni-Fe system was used as a reference system taking advantage of the full miscibility at high temperatures. Ta was chosen, as aside from having a technical relevance in the Ni-base superalloys, it also has a high miscibility in Ni. The main focus of this paper will be solid solution hardening. It will be shown that even though the determination of hardness is subject to varying indentation size effects (ISE) [K. Durst et al., Acta Mater. 55(20), 6825 (2007)], only a few modifications are necessary to describe solid solution strengthening measured by nanoindentations using the Labusch theory [R. Labusch, Acta Metall. 20(7), 917 (1972)]. Moreover, after a careful evaluation of the results, the data can be used to investigate solid solution hardening effects quickly and efficiently with small amounts of material. I. INTRODUCTION
Modern fourth generation nickel base superalloys consist of a high quantity of different elements (up to 15).1 Many of those are solid solution hardeners for the gphase increasing the creep resistance of the material. Solid solution hardening (SSH) is important for the mechanical behavior, as most of the plastic deformation in the superalloy takes place in the softer g-phase. The diffusion couple technique, which is already widely used for the determination of thermodynamic properties such as diffusion coefficients and phase formation (see e.g., Kodentsov et al.2), is potentially a very valuable tool for creating material property libraries.3–8 Local chemical analysis of diffusion couples with high resolution energy or wavelength dispersive x-ray analysis (EDX/WDX) and nanoindentation allows the correlation of the local chemical composition to the local mechanical properties. Even though chemical analysis has a higher resolution than nanoindentation, this approach offers a unique chance to determine the Young’s modulus as well as the hardness of the material as a function of the chemical composition, for example, Franke et al.9 Early works by Rosbaud,10 Sachs and Weerts,11 Goehler and Sachs,12 Osswald13 as well as Nabarro14 have investigated solid solution hardening effects. The results obtained by these investigators led to a basic understanding of relations between hardness and solid solution strengthening. The early work by Nabarro gives a)
Address all correspondence to this author. e-mail: [email protected] DOI: 10.1557/JMR.2009.0135 J. Mater. Res., Vol. 24, No. 3, Mar 2009
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also a relation between hardness and solid solution strengthening for spherical indentation. This first approach was proposed by Mott and Nabarro, who focused on the influence of the lattice distortion and thus the change in Young’s modulus causing an increase in strength of the materials for both solid solutions and precipitates.14,15 For solid solutions they basically correlate the yield stress sy
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