Determination of nanoindentation size effects and variable material intrinsic length scale for body-centered cubic metals

It is well-known by now that the micro and nanoindentation hardness of metallic materials displays a strong size effect. The objective of this work is to formulate a micromechanical-based model for Temperature and Rate Indentation Size Effects (TRISE) for body centered cubic (BCC) metals encountered in nanoindentation experiments. In this regard, two physically based models are proposed here in order to capture the TRISE in single and polycrystalline materials by considering different expressions of the geometrical necessary dislocations (GNDs) density. The gradient plasticity theory formulates a constitutive framework on the continuum level that bridges the gap between the micromechanical plasticity and the classical continuum plasticity by incorporating the material length scale. A micromechanical-based model of variable material intrinsic length scale is also developed in the present work. The proposed length scale allows for variations in temperature and strain rate and its dependence on the grain size and accumulated plastic strain. The results of indentation experiments performed on niobium, tungsten, and single- and polycrystalline commercially pure iron (very similar to iron alloys) are used here to implement the aforementioned framework in order to predict simultaneously the TRISE and variable length scale at different temperatures, strain rates and various distances from the grain boundary. Numerical analysis is performed using the ABAQUS/VUMAT software with a physically based viscoplastic constitutive model.