We present here a ‘multiscale’ model of nanoindentation of nanocrystalline copper operating on the micro-macro scale in the sense that the volume subjected to large forces (i.e. that directly under the nanoindenter) is represented by classical microscopic theory, whereas the more distant volume subjected  to smaller residual forces is represented by a classical macroscopic theory [4]. In particular, by allowing the volume directly subjected to external forces to be governed by an interatomic potential the rearrangement of atomic bonds with the onset of plastic deformation may be observed. To complement this, the physical properties of the continuous region surrounding the atomic part are governed by elasticity theory in order to study the long-range effect of the nanoindentation process. The interaction between atoms is based on the empirical tight binding second moment approximation [1] suitable for systems involving dislocated sharing of free electrons, vis-à-vis copper. Since the behaviour of materials under compression and extension is known to be anharmonic, the surrounding continuum is governed by a nonlinear theory of elasticity. In our case the Hencky strain measure [2] is utilised (although alternative measures, namely Green and Biot, are also considered) [3]. Our multiscale model is therefore a quasistatic approach where contributions from kinetic energy terms have been ignored. This approximation is valid in the adiabatic limit where the process of indentation itself occurs within a short  time.  

Acknowledgements: This research was funded by the European Commission PARSEM project MRTN-CT-2004-005583.

REFERENCES

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