Decoupling indentation size and strain rate effects during nanoindentation: A case study in tungsten
Materials indented at small scales may simultaneously exhibit indentation size and strain rate effects which complicate the identification of the mechanisms that control deformation and strength. Here, in this work, we explore the possibility that indentation size and rate effects in some materials can be decoupled in a simple way. Nanoindentation tests with various load-time histories were carried out to measure the hardness of a tungsten single crystal over a wide range of indentation depths (~500–3600 nm) and indentation strain rates (~5 ×10 –5 –2 ×10 –1 s –1 ). Under these conditions, this material exhibits significant indentation size and rate effects, but the size effect is, to a good approximation, independent of strain rate. It is shown that this behavior can be understood by the Nix-Gao model for the indentation size effect modified to include the effects of a strain rate dependent friction stress. As a consequence, the size and rate dependencies of the hardness can be expressed as the sum of two independent terms: H($\dot{ε}$ i , h c )=H f ($\dot{ε}$ i ) + (H 0 – H f ) $\sqrt{1+ \frac{h^*}{h_c}}$, where H($\dot{ε}$ i , h c ) is the hardness at given indentation strain rate ($\dot{ε}$ i ) and contact depth (h c ), H f ($\dot{ε}$ i ) is the hardness contributed by the rate dependent friction stress, and (H 0 – H f ) and h* are size and rate independent constants that follow from the Nix-Gao analysis. This formula, together with an expression for the rate dependence of H f , was successfully applied to decouple the indentation size and rate effects observed in tungsten. In addition, the physics underlying the rate independence of indentation size effect is discussed, which provides guidance for application of the proposed approach to other materials.