Physics – Condensed Matter – Materials Science
Scientific paper
2009-03-08
Chaos, Solitons and Fractals 42, 1623-1630 (2009)
Physics
Condensed Matter
Materials Science
22 pages, 5 figures, to appear in Chaos, Solitons and Fractals
Scientific paper
10.1016/j.chaos.2009.03.031
A toy model of two dimensional nanoindentation in finite crystals is proposed. The crystal is described by periodized discrete elasticity whereas the indenter is a rigid strain field of triangular shape representing a hard knife-like indenter. Analysis of the model shows that there are a number of discontinuities in the load vs penetration depth plot which correspond to the creation of dislocation loops. The stress vs depth bifurcation diagram of the model reveals multistable stationary solutions that appear as the dislocation-free branch of solutions develops turning points for increasing stress. Dynamical simulations show that an increment of the applied load leads to nucleation of dislocation loops below the nanoindenter tip. Such dislocations travel inside the bulk of the crystal and accommodate at a certain depth in the sample. In agreement with experiments, hysteresis is observed if the stress is decreased after the first dislocation loop is created. Critical stress values for loop creation and their final location at equilibrium are calculated.
Bonilla Luis L.
Carpio Ana
Plans I.
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