The indentation size effect of single-crystalline tungsten revisited

In this study, we have investigated the indentation size effect (ISE) of single crystalline tungsten with low defect density. As expected, the hardness shows a pronounced increase with decreasing indentation depth as well as a strong strain rate dependence. For penetration depths greater than about 300 nm, the ISE is well captured by the Nix–Gao model in the context of geometrically necessary dislocations. However, clear deviations from the model are observed in the low depth regime resulting in a bilinear effect. The hardness behavior in the low depth regime can be modeled assuming a non-uniform spacing of the geometrically necessary dislocations. We propose that the bilinear indentation size effect observed reflects the evolution of the geometrically necessary dislocation density. With increasing strain rate, the bilinear effect becomes less pronounced. This observation can be rationalized by the activation of different slip systems. Graphic abstract