Increasing Initial Yield Stress at Small Length Scales

Plasticity size effects are well known in a wide variety of situations where either the material microstructure or a strain gradient exist at small length scales. Several theories have been developed to describe changes in the work hardening behaviour under these conditions but none that predict a change in the initial yield stress. Careful studies by Chaudhri et al and Pharr et al have unambiguously demonstrated plasticity size effects in ductile metals. In those experiments indentation stress-strain curves were generated using spherical indenters with radii ranging from a few micrometres to several hundred micrometres and these were compared to data from conventional compression tests. Large radius indenters produced a single indentation stress-strain curve independent of indenter radius with a power law hardening coefficient equivalent to that in the compression tests. However, the indentation stress-strain curves appeared at progressively higher pressures for smaller radius indenters. In this paper we model those experiments using finite element analysis methods. By inputting the uniaxial stress-strain data to the model (effectively, using von Mises criterion) the indentation stress-strain curves for the macro size indenters are reproduced. However, the model shows no length scale dependence for any size of indenter. We show that by off-setting the compression stress-strain curve by increasing the initial yield stress and inputting this data to the model, the indentation behaviour of the smaller radius indenters can be modelled. The increase in yield stress with decreasing indenter radius is demonstrated for Cu, Wand Ir and is shown to be consistent with the initiation of yielding over a finite volume.