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Toy nanoindentation model and incipient plasticity

Author

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  • Plans, I.
  • Carpio, A.
  • Bonilla, L.L.

Abstract

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.

Suggested Citation

  • Plans, I. & Carpio, A. & Bonilla, L.L., 2009. "Toy nanoindentation model and incipient plasticity," Chaos, Solitons & Fractals, Elsevier, vol. 42(3), pages 1623-1630.
    • Handle: RePEc:eee:chsofr:v:42:y:2009:i:3:p:1623-1630
    DOI: 10.1016/j.chaos.2009.03.031
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    References listed on IDEAS

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    1. Eric Gerde & M. Marder, 2001. "Friction and fracture," Nature, Nature, vol. 413(6853), pages 285-288, September.
    2. Shmuel M. Rubinstein & Gil Cohen & Jay Fineberg, 2004. "Detachment fronts and the onset of dynamic friction," Nature, Nature, vol. 430(7003), pages 1005-1009, August.
    3. David A. Kessler, 2001. "A new crack at friction," Nature, Nature, vol. 413(6853), pages 260-261, September.
    4. Peter Schall & Itai Cohen & David A. Weitz & Frans Spaepen, 2006. "Visualizing dislocation nucleation by indenting colloidal crystals," Nature, Nature, vol. 440(7082), pages 319-323, March.
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