Variable (intrinsic) material length scale for face-centred cubic metals using nano-indentation

The objective of this work is to formulate a micromechanics-based model with a variable (intrinsic) material length scale for face-centred cubic (f.c.c.) metals. The length scale allows for variations in the temperature and the rate indentation size effects (TRISEs) encountered in nano-indentation experiments. In addition, its dependence on the grain size effect and accumulated plastic strain is also incorporated into this model. Two models are proposed here in order to capture the TRISEs in single-crystal and polycrystalline materials through considering different expressions for the density of the geometrically necessary dislocations. Material length scales used in conjunction with gradient theories are also obtained in this work from experimental observations of f.c.c. metals. The results of indentation experiments performed on nickel, gold, copper, and single-crystal platinum and aluminium are used here in order to check the validity of the proposed model as well as the concept assumed with reference to local hardening in nano-indentation. Numerical analysis is performed using ABAQUS/VUMAT software and a physics-based viscoplastic constitutive model.