The indentation size effect (ISE) can be summarized as ‘smaller is stronger’ and has been linked to the generation of geometrically necessary dislocations (GNDs). One common model applied to describe the ISE is that of Nix and Gao (Nix, et al., 1998). It is based on strain gradient plasticity and has become the basis for more refined models of the ISE (Durst, et al., 2005) (Durst, et al., 2006). By modifying the material length scale h*, the refined models have reduced the overestimation of Nix-Gao model at the smaller indentation depth, which is known as a shortcoming of this classic model (Pharr, et al., 2010). In order to understand the deformation at small length scale, it is important to study the GND distribution beneath the indenter, which has not yet been comprehensively illustrated.
In this work, we aim at understanding the deformation behavior of tungsten at the microscale and in particular the influence of the strain gradients and the GND distribution. We quantitatively characterized the indentation size effect in tungsten single-crystals of different crystal orientations and compared the results to other metals covering a wide range of modulus-to-hardness ratios. The analysis of dynamic and quasi-static indentation tests showed a bi-linear ISE in tungsten. In addition, in the sub-micrometer regime, significant deviations from the Nix-Gao behavior were observed. By assuming non-uniform dislocation spacings, the characteristic material length scale h* is modified, which should affect the GND distribution, and results in excellent agreement of the modified model at smaller depths for the different materials. The lattice rotation angles and GND densities underneath the indents into single-crystalline tungsten were studied by electron backscatter diffraction. The experimental findings will be compared to the results obtained from crystal plasticity finite element simulations.