On the indentation size effect in spherical indentation

Size effects in plasticity at small length scales have been widely reported in a variety of loading situations. The hardness size effect has often been cited as an archetypal example. The indentation size effect was clearly demonstrated by Lim and Chaudhri [Phil. Mag. A 79 2979 (1999)] in spherical indentation experiments on copper and, subsequently, in experiments on iridium by Swadener et al. [J. Mech. Phys. Solids 50 681 (2002)]. They showed that large radius indenters produced an indentation stress - strain curve independent of indenter radius with a hardening coefficient equivalent to that in uniaxial tests on the same materials. For smaller indenters, the indentation stress - strain curves appeared at progressively higher pressures for smaller radius indenters. Here, we present similar experimental data for nickel. We simulate these experiments by inputting the uniaxial stress - strain data into a finite element model, which has no intrinsic length scale dependence (essentially using the von Mises criterion for yield). We show that a simple increase in the initial yield stress of the uniaxial stress - strain curve input to the model, allows the indentation behaviour of the smaller radius indenters to be simulated. The increase in yield stress with decreasing indenter radius is shown to follow a single relation for all the metals studied - Al, Cu, Ni and Ir. We show that the indentation size effect is a geometrical effect - consistent with critical thickness theory for the initiation of yielding over a finite volume. The magnitude of the size effect depends only on indenter radius, providing a predictive method for the yield strength in spherical nanoindentation of bulk materials.