A combined inverse finite element – elastoplastic modelling method to simulate the size-effect in nanoindentation and characterise materials from the nano to micro-scale

Material properties such as hardness can be dependent on the size of the indentation load when that load is small, a phenomenon known as the indentation size effect (ISE). In this work an inverse finite element method (IFEM) is used to investigate the ISE, with reference to experiments with a Berkovich indenter and an aluminium test material. It was found that the yield stress is highly dependent on indentation depth and in order to simulate this, an elastoplastic constitutive relation in which yielding varies with indentation depth/load was developed. It is shown that whereas Young's modulus and Poisson's ratio are not influenced by the length scale over the range tested, the amplitude portion of yield stress, which is independent of hardening and corresponds to the initial stress for a bulk material, changes radically at small indentation depths. Using the proposed material model and material parameters extracted using IFEM, the indentation depth-time and load-depth plots can be predicted at different loads with excellent agreement to experiment; the relative residual achieved between FE modelling displacement and experiment being less than 0.32%. An improved method of determining hardness from nanoindentation test data is also presented, which shows goof agreement with that determined using the IFEM