The indentation size effect (ISE) and the bilinear behavior for pure face centered cubic (FCC) metals including aluminum, nickel, silver, and 70/30 copper–zinc (α-brass) alloy using a single Berkovich indenter tip in a single test machine were investigated. The results confirmed that this behavior is mechanistic in nature and were consistent with those reported by A.A. Elmustafa and D.S. Stone [J. Mech. Phys. Solids51, 357–381 (2003)] of the ISE and the bilinear behavior using two separate indenter tips (Berkovich and Vickers) from two separate machines. Therefore, the bilinear behavior is present regardless of tip geometry or machine used. We also investigated the cause for a deviation in the continuous stiffness measurement (CSM) data from discrete data points obtained using the load control protocol at shallow depth. We conducted experiments near grain boundaries to determine if the CSM deviation at shallow depths were caused by a hardening effect due to dislocation interaction with the interface.

Using the tool of two-scale convergence, we provide a rigorous mathematical setting for the homogenization result obtained by Fleck and Willis [J. Mech. Phys. Solids 52 (2004) 1855–1888] concerning the effective plastic behaviour of a strain gradient composite material. Moreover, moving from deformation theory to flow theory, we prove a convergence result for the homogenization of quasistatic evolutions in the presence of isotropic linear hardening.